From 2cab28c9053b97b94bb0fdb5e12eb903b059b46e Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Sun, 16 Jan 2022 16:05:19 +0000
Subject: [PATCH] Documentation for 53a6c16730337321e78304b70203667793693bff

---
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-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>                C.<a class="code hl_variable" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> = 0.5 * ((P[i].x * (P[j].x * P[j].x + P[j].y * P[j].y -</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>                                        P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].x * P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].x - P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].y * P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].y) +</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>                              P[j].x * (P[k].x * P[k].x + P[k].y * P[k].y -</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>                                        P[i].x * P[i].x - P[i].y * P[i].y) +</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>                              P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].x * (P[i].x * P[i].x + P[i].y * P[i].y -</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>                                        P[j].x * P[j].x - P[j].y * P[j].y)) /</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>                             (P[i].x * (P[j].y - P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].y) +</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>                              P[j].x * (P[k].y - P[i].y) +</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>                              P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].x * (P[i].y - P[j].y)));</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>                R = (<a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a>(P[i], P[j]) * <a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a>(P[j], P[k]) *</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>                     <a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a>(P[k], P[i])) /</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>                    (4 * <a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#a94682a4a70d5906857ca09de5b9fb2cc">TriangleArea</a>(P[i], P[j], P[k]));</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>                <span class="keywordflow">if</span> (!<a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#aee6d48762c1dfb9f14627927f0c16fad">PointInCircle</a>(P, C, R)) {</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>                    <span class="keywordflow">continue</span>;</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>                }</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>                <span class="keywordflow">if</span> (R &lt;= minR) {</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>                    minR = R;</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>                    minC = C;</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>                }</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>            }</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span> </div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    <span class="comment">// for each point in the list</span></div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; P.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() - 1; i++)</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>        <span class="comment">// for every subsequent point in the list</span></div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = i + 1; j &lt; P.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) {</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>            <span class="comment">// check for diameterically opposite points</span></div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>            C.x = (P[i].x + P[j].x) / 2;</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>            C.<a class="code hl_variable" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> = (P[i].y + P[j].y) / 2;</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>            R = <a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a>(C, P[i]);</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>            <span class="keywordflow">if</span> (!<a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#aee6d48762c1dfb9f14627927f0c16fad">PointInCircle</a>(P, C, R)) {</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>                <span class="keywordflow">continue</span>;</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>            }</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>            <span class="keywordflow">if</span> (R &lt;= minR) {</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>                minR = R;</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>                minC = C;</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>            }</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>        }</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minC.x &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; minC.<a class="code hl_variable" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    <span class="keywordflow">return</span> minR;</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   87</span>                                         {</div>
+<div class="line"><span class="lineno">   88</span>    <span class="keywordtype">double</span> minR = INFINITY;</div>
+<div class="line"><span class="lineno">   89</span>    <span class="keywordtype">double</span> R;</div>
+<div class="line"><span class="lineno">   90</span>    <a class="code hl_struct" href="../../d8/dc8/struct_point.html">Point</a> C;</div>
+<div class="line"><span class="lineno">   91</span>    <a class="code hl_struct" href="../../d8/dc8/struct_point.html">Point</a> minC;</div>
+<div class="line"><span class="lineno">   92</span> </div>
+<div class="line"><span class="lineno">   93</span>    <span class="comment">/* This code is invalid and does not give correct result for TEST 3 */</span></div>
+<div class="line"><span class="lineno">   94</span>    <span class="comment">// for each point in the list</span></div>
+<div class="line"><span class="lineno">   95</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; P.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() - 2; i++)</div>
+<div class="line"><span class="lineno">   96</span>        <span class="comment">// for every subsequent point in the list</span></div>
+<div class="line"><span class="lineno">   97</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = i + 1; j &lt; P.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++)</div>
+<div class="line"><span class="lineno">   98</span>            <span class="comment">// for every subsequent point in the list</span></div>
+<div class="line"><span class="lineno">   99</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> k = j + 1; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt; P.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
+<div class="line"><span class="lineno">  100</span>                <span class="comment">// here, we now have picked three points from the given set of</span></div>
+<div class="line"><span class="lineno">  101</span>                <span class="comment">// points that we can use</span></div>
+<div class="line"><span class="lineno">  102</span>                <span class="comment">// viz., P[i], P[j] and P[k]</span></div>
+<div class="line"><span class="lineno">  103</span>                C.x = -0.5 * ((P[i].y * (P[j].x * P[j].x + P[j].y * P[j].y -</div>
+<div class="line"><span class="lineno">  104</span>                                         P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].x * P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].x - P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].y * P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].y) +</div>
+<div class="line"><span class="lineno">  105</span>                               P[j].y * (P[k].x * P[k].x + P[k].y * P[k].y -</div>
+<div class="line"><span class="lineno">  106</span>                                         P[i].x * P[i].x - P[i].y * P[i].y) +</div>
+<div class="line"><span class="lineno">  107</span>                               P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].y * (P[i].x * P[i].x + P[i].y * P[i].y -</div>
+<div class="line"><span class="lineno">  108</span>                                         P[j].x * P[j].x - P[j].y * P[j].y)) /</div>
+<div class="line"><span class="lineno">  109</span>                              (P[i].x * (P[j].y - P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].y) +</div>
+<div class="line"><span class="lineno">  110</span>                               P[j].x * (P[k].y - P[i].y) +</div>
+<div class="line"><span class="lineno">  111</span>                               P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].x * (P[i].y - P[j].y)));</div>
+<div class="line"><span class="lineno">  112</span>                C.<a class="code hl_variable" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> = 0.5 * ((P[i].x * (P[j].x * P[j].x + P[j].y * P[j].y -</div>
+<div class="line"><span class="lineno">  113</span>                                        P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].x * P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].x - P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].y * P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].y) +</div>
+<div class="line"><span class="lineno">  114</span>                              P[j].x * (P[k].x * P[k].x + P[k].y * P[k].y -</div>
+<div class="line"><span class="lineno">  115</span>                                        P[i].x * P[i].x - P[i].y * P[i].y) +</div>
+<div class="line"><span class="lineno">  116</span>                              P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].x * (P[i].x * P[i].x + P[i].y * P[i].y -</div>
+<div class="line"><span class="lineno">  117</span>                                        P[j].x * P[j].x - P[j].y * P[j].y)) /</div>
+<div class="line"><span class="lineno">  118</span>                             (P[i].x * (P[j].y - P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].y) +</div>
+<div class="line"><span class="lineno">  119</span>                              P[j].x * (P[k].y - P[i].y) +</div>
+<div class="line"><span class="lineno">  120</span>                              P[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>].x * (P[i].y - P[j].y)));</div>
+<div class="line"><span class="lineno">  121</span>                R = (<a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a>(P[i], P[j]) * <a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a>(P[j], P[k]) *</div>
+<div class="line"><span class="lineno">  122</span>                     <a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a>(P[k], P[i])) /</div>
+<div class="line"><span class="lineno">  123</span>                    (4 * <a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#a94682a4a70d5906857ca09de5b9fb2cc">TriangleArea</a>(P[i], P[j], P[k]));</div>
+<div class="line"><span class="lineno">  124</span>                <span class="keywordflow">if</span> (!<a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#aee6d48762c1dfb9f14627927f0c16fad">PointInCircle</a>(P, C, R)) {</div>
+<div class="line"><span class="lineno">  125</span>                    <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno">  126</span>                }</div>
+<div class="line"><span class="lineno">  127</span>                <span class="keywordflow">if</span> (R &lt;= minR) {</div>
+<div class="line"><span class="lineno">  128</span>                    minR = R;</div>
+<div class="line"><span class="lineno">  129</span>                    minC = C;</div>
+<div class="line"><span class="lineno">  130</span>                }</div>
+<div class="line"><span class="lineno">  131</span>            }</div>
+<div class="line"><span class="lineno">  132</span> </div>
+<div class="line"><span class="lineno">  133</span>    <span class="comment">// for each point in the list</span></div>
+<div class="line"><span class="lineno">  134</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; P.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() - 1; i++)</div>
+<div class="line"><span class="lineno">  135</span>        <span class="comment">// for every subsequent point in the list</span></div>
+<div class="line"><span class="lineno">  136</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = i + 1; j &lt; P.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) {</div>
+<div class="line"><span class="lineno">  137</span>            <span class="comment">// check for diameterically opposite points</span></div>
+<div class="line"><span class="lineno">  138</span>            C.x = (P[i].x + P[j].x) / 2;</div>
+<div class="line"><span class="lineno">  139</span>            C.<a class="code hl_variable" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> = (P[i].y + P[j].y) / 2;</div>
+<div class="line"><span class="lineno">  140</span>            R = <a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a>(C, P[i]);</div>
+<div class="line"><span class="lineno">  141</span>            <span class="keywordflow">if</span> (!<a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#aee6d48762c1dfb9f14627927f0c16fad">PointInCircle</a>(P, C, R)) {</div>
+<div class="line"><span class="lineno">  142</span>                <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno">  143</span>            }</div>
+<div class="line"><span class="lineno">  144</span>            <span class="keywordflow">if</span> (R &lt;= minR) {</div>
+<div class="line"><span class="lineno">  145</span>                minR = R;</div>
+<div class="line"><span class="lineno">  146</span>                minC = C;</div>
+<div class="line"><span class="lineno">  147</span>            }</div>
+<div class="line"><span class="lineno">  148</span>        }</div>
+<div class="line"><span class="lineno">  149</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minC.x &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; minC.<a class="code hl_variable" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  150</span>    <span class="keywordflow">return</span> minR;</div>
+<div class="line"><span class="lineno">  151</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
@@ -279,11 +279,11 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>ditance </dd></dl>
-<div class="fragment"><div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>                                                  {</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    <span class="keywordtype">double</span> dx = B.x - A.x;</div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>    <span class="keywordtype">double</span> dy = B.<a class="code hl_variable" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> - A.<a class="code hl_variable" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a>;</div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>((dx * dx) + (dy * dy));</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   37</span>                                                  {</div>
+<div class="line"><span class="lineno">   38</span>    <span class="keywordtype">double</span> dx = B.x - A.x;</div>
+<div class="line"><span class="lineno">   39</span>    <span class="keywordtype">double</span> dy = B.<a class="code hl_variable" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> - A.<a class="code hl_variable" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a>;</div>
+<div class="line"><span class="lineno">   40</span>    <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>((dx * dx) + (dy * dy));</div>
+<div class="line"><span class="lineno">   41</span>}</div>
 <div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -310,14 +310,14 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Main program </p>
-<div class="fragment"><div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>           {</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>    <a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>();</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>    <a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>    <a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>();</div>
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-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  198</span>           {</div>
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+<div class="line"><span class="lineno">  200</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  201</span>    <a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
+<div class="line"><span class="lineno">  202</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  203</span>    <a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>();</div>
+<div class="line"><span class="lineno">  204</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  205</span>}</div>
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 <div class="ttc" id="asmallest__circle_8cpp_html_a6d0455dd5c30adda100e95f0423c786e"><div class="ttname"><a href="../../d0/d01/smallest__circle_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a></div><div class="ttdeci">void test3()</div><div class="ttdef"><b>Definition:</b> smallest_circle.cpp:188</div></div>
 <div class="ttc" id="asmallest__circle_8cpp_html_ae1a3968e7947464bee7714f6d43b7002"><div class="ttname"><a href="../../d0/d01/smallest__circle_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a></div><div class="ttdeci">void test()</div><div class="ttdef"><b>Definition:</b> smallest_circle.cpp:158</div></div>
@@ -372,13 +372,13 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd>True if P lies on or within the circle </dd>
 <dd>
 False if P lies outside the circle </dd></dl>
-<div class="fragment"><div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>                                                                             {</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; P.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a>(P[i], Center) &gt; R)</div>
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-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   72</span>                                                                             {</div>
+<div class="line"><span class="lineno">   73</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; P.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
+<div class="line"><span class="lineno">   74</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a>(P[i], Center) &gt; R)</div>
+<div class="line"><span class="lineno">   75</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   76</span>    }</div>
+<div class="line"><span class="lineno">   77</span>    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   78</span>}</div>
 </div><!-- fragment --><div class="dynheader">
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@@ -406,15 +406,15 @@ Here is the call graph for this function:</div>
  Circle with <br  />
  radius 3.318493136080724 <br  />
  centre at (3.0454545454545454, 1.3181818181818181) </p>
-<div class="fragment"><div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>            {</div>
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-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>    Pv.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(<a class="code hl_typedef" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#af0a6e3521629c25c2b5d620f26429830">Point</a>(4, 1));</div>
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-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#a0b0676df8e4da7a08c7ccaecea344903">circle</a>(Pv) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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 <div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
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@@ -446,14 +446,14 @@ Here is the call graph for this function:</div>
  Circle with <br  />
  radius 1.4142135623730951 <br  />
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  Circle with <br  />
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  centre at (2.142857142857143, 1.7857142857142856) </p><dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000010">Todo:</a></b></dt><dd>This test fails </dd></dl>
-<div class="fragment"><div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>             {</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Point&gt;</a> Pv;</div>
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@@ -160,42 +160,42 @@ Functions</h2></td></tr>
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-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>    <span class="keyword">const</span> <span class="keywordtype">float</span> test_data1[] = {3, 4, 5, -1.4, -3.6, 1.9, 1.};</div>
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-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>        &lt;&lt; <span class="stringliteral">&quot;Enter data. Any non-numeric data will terminate the data input.&quot;</span></div>
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-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>    <a class="code hl_class" href="../../d8/dab/classstatistics_1_1stats__computer2.html">stats_computer2&lt;float&gt;</a> stats2;</div>
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-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; val;</div>
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-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>        <span class="comment">// check for failure to read input. Happens for</span></div>
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-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>            <span class="keywordflow">break</span>;</div>
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-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>        stats1.<a class="code hl_function" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#aa13bf7c38de112f71921a5525d71a2f2">new_val</a>(val);</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>        stats2.<a class="code hl_function" href="../../d8/dab/classstatistics_1_1stats__computer2.html#ade6de704deea24fdc88077b3d9a0d534">new_val</a>(val);</div>
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-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>                  &lt;&lt; <span class="stringliteral">&quot;\tMean: &quot;</span> &lt;&lt; stats1.<a class="code hl_function" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#a390697dcee210b91823ceff04b25081b">mean</a>()</div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>                  &lt;&lt; <span class="stringliteral">&quot;\t Variance: &quot;</span> &lt;&lt; stats1.<a class="code hl_function" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#a27f0a03e2fd2254f1c81fe668226bd92">variance</a>()</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>                  &lt;&lt; <span class="stringliteral">&quot;\t Std: &quot;</span> &lt;&lt; stats1.<a class="code hl_function" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#af57e942d49f4fd70f059f224b4ac07e1">std</a>() &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tMethod 2:&quot;</span></div>
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-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>                  &lt;&lt; <span class="stringliteral">&quot;\t Variance: &quot;</span> &lt;&lt; stats2.<a class="code hl_function" href="../../d8/dab/classstatistics_1_1stats__computer2.html#af6198817084276113b3c064e87ce0555">variance</a>()</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>                  &lt;&lt; <span class="stringliteral">&quot;\t Std: &quot;</span> &lt;&lt; stats2.<a class="code hl_function" href="../../d8/dab/classstatistics_1_1stats__computer2.html#acf2e84df4fc386bb3295016ef8fd156e">std</a>() &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>    }</div>
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+<div class="line"><span class="lineno">  162</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
+<div class="line"><span class="lineno">  163</span>        &lt;&lt; <span class="stringliteral">&quot;Enter data. Any non-numeric data will terminate the data input.&quot;</span></div>
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+<div class="line"><span class="lineno">  166</span>    <a class="code hl_class" href="../../d7/d7c/classstatistics_1_1stats__computer1.html">stats_computer1&lt;float&gt;</a> stats1;</div>
+<div class="line"><span class="lineno">  167</span>    <a class="code hl_class" href="../../d8/dab/classstatistics_1_1stats__computer2.html">stats_computer2&lt;float&gt;</a> stats2;</div>
+<div class="line"><span class="lineno">  168</span> </div>
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+<div class="line"><span class="lineno">  171</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter number: &quot;</span>;</div>
+<div class="line"><span class="lineno">  172</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; val;</div>
+<div class="line"><span class="lineno">  173</span> </div>
+<div class="line"><span class="lineno">  174</span>        <span class="comment">// check for failure to read input. Happens for</span></div>
+<div class="line"><span class="lineno">  175</span>        <span class="comment">// non-numeric data</span></div>
+<div class="line"><span class="lineno">  176</span>        <span class="keywordflow">if</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>.fail())</div>
+<div class="line"><span class="lineno">  177</span>            <span class="keywordflow">break</span>;</div>
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+<div class="line"><span class="lineno">  180</span>        stats2.<a class="code hl_function" href="../../d8/dab/classstatistics_1_1stats__computer2.html#ade6de704deea24fdc88077b3d9a0d534">new_val</a>(val);</div>
+<div class="line"><span class="lineno">  181</span> </div>
+<div class="line"><span class="lineno">  182</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tMethod 1:&quot;</span></div>
+<div class="line"><span class="lineno">  183</span>                  &lt;&lt; <span class="stringliteral">&quot;\tMean: &quot;</span> &lt;&lt; stats1.<a class="code hl_function" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#a390697dcee210b91823ceff04b25081b">mean</a>()</div>
+<div class="line"><span class="lineno">  184</span>                  &lt;&lt; <span class="stringliteral">&quot;\t Variance: &quot;</span> &lt;&lt; stats1.<a class="code hl_function" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#a27f0a03e2fd2254f1c81fe668226bd92">variance</a>()</div>
+<div class="line"><span class="lineno">  185</span>                  &lt;&lt; <span class="stringliteral">&quot;\t Std: &quot;</span> &lt;&lt; stats1.<a class="code hl_function" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#af57e942d49f4fd70f059f224b4ac07e1">std</a>() &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  186</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tMethod 2:&quot;</span></div>
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+<div class="line"><span class="lineno">  188</span>                  &lt;&lt; <span class="stringliteral">&quot;\t Variance: &quot;</span> &lt;&lt; stats2.<a class="code hl_function" href="../../d8/dab/classstatistics_1_1stats__computer2.html#af6198817084276113b3c064e87ce0555">variance</a>()</div>
+<div class="line"><span class="lineno">  189</span>                  &lt;&lt; <span class="stringliteral">&quot;\t Std: &quot;</span> &lt;&lt; stats2.<a class="code hl_function" href="../../d8/dab/classstatistics_1_1stats__computer2.html#acf2e84df4fc386bb3295016ef8fd156e">std</a>() &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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 <div class="ttc" id="aclassstatistics_1_1stats__computer1_html"><div class="ttname"><a href="../../d7/d7c/classstatistics_1_1stats__computer1.html">statistics::stats_computer1</a></div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:27</div></div>
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-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>              &lt;&lt; <span class="stringliteral">&quot;Expected: Mean: &quot;</span> &lt;&lt; mean &lt;&lt; <span class="stringliteral">&quot;\t Variance: &quot;</span> &lt;&lt; variance</div>
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-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tMethod 1:&quot;</span></div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>              &lt;&lt; <span class="stringliteral">&quot;\tMean: &quot;</span> &lt;&lt; stats01.<a class="code hl_function" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#a390697dcee210b91823ceff04b25081b">mean</a>()</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>              &lt;&lt; <span class="stringliteral">&quot;\t Variance: &quot;</span> &lt;&lt; stats01.<a class="code hl_function" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#a27f0a03e2fd2254f1c81fe668226bd92">variance</a>()</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>              &lt;&lt; <span class="stringliteral">&quot;\t Std: &quot;</span> &lt;&lt; stats01.<a class="code hl_function" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#af57e942d49f4fd70f059f224b4ac07e1">std</a>() &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tMethod 2:&quot;</span></div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>              &lt;&lt; <span class="stringliteral">&quot;\tMean: &quot;</span> &lt;&lt; stats02.<a class="code hl_function" href="../../d8/dab/classstatistics_1_1stats__computer2.html#a8290966ad468f2a8c266d008bc60720e">mean</a>()</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>              &lt;&lt; <span class="stringliteral">&quot;\t Variance: &quot;</span> &lt;&lt; stats02.<a class="code hl_function" href="../../d8/dab/classstatistics_1_1stats__computer2.html#af6198817084276113b3c064e87ce0555">variance</a>()</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>              &lt;&lt; <span class="stringliteral">&quot;\t Std: &quot;</span> &lt;&lt; stats02.<a class="code hl_function" href="../../d8/dab/classstatistics_1_1stats__computer2.html#acf2e84df4fc386bb3295016ef8fd156e">std</a>() &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span> </div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    assert(std::abs(stats01.<a class="code hl_function" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#a390697dcee210b91823ceff04b25081b">mean</a>() - mean) &lt; 0.01);</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    assert(std::abs(stats02.<a class="code hl_function" href="../../d8/dab/classstatistics_1_1stats__computer2.html#a8290966ad468f2a8c266d008bc60720e">mean</a>() - mean) &lt; 0.01);</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>    assert(std::abs(stats02.<a class="code hl_function" href="../../d8/dab/classstatistics_1_1stats__computer2.html#af6198817084276113b3c064e87ce0555">variance</a>() - variance) &lt; 0.01);</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span> </div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;(Tests passed)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  118</span>                                                                        {</div>
+<div class="line"><span class="lineno">  119</span>    <span class="keywordtype">float</span> mean = 0.f, variance = 0.f;</div>
+<div class="line"><span class="lineno">  120</span> </div>
+<div class="line"><span class="lineno">  121</span>    <a class="code hl_class" href="../../d7/d7c/classstatistics_1_1stats__computer1.html">stats_computer1&lt;float&gt;</a> stats01;</div>
+<div class="line"><span class="lineno">  122</span>    <a class="code hl_class" href="../../d8/dab/classstatistics_1_1stats__computer2.html">stats_computer2&lt;float&gt;</a> stats02;</div>
+<div class="line"><span class="lineno">  123</span> </div>
+<div class="line"><span class="lineno">  124</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; number_of_samples; i++) {</div>
+<div class="line"><span class="lineno">  125</span>        stats01.<a class="code hl_function" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#aa13bf7c38de112f71921a5525d71a2f2">new_val</a>(test_data[i]);</div>
+<div class="line"><span class="lineno">  126</span>        stats02.<a class="code hl_function" href="../../d8/dab/classstatistics_1_1stats__computer2.html#ade6de704deea24fdc88077b3d9a0d534">new_val</a>(test_data[i]);</div>
+<div class="line"><span class="lineno">  127</span>        mean += test_data[i];</div>
+<div class="line"><span class="lineno">  128</span>    }</div>
+<div class="line"><span class="lineno">  129</span> </div>
+<div class="line"><span class="lineno">  130</span>    mean /= number_of_samples;</div>
+<div class="line"><span class="lineno">  131</span> </div>
+<div class="line"><span class="lineno">  132</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; number_of_samples; i++) {</div>
+<div class="line"><span class="lineno">  133</span>        <span class="keywordtype">float</span> temp = test_data[i] - mean;</div>
+<div class="line"><span class="lineno">  134</span>        variance += temp * temp;</div>
+<div class="line"><span class="lineno">  135</span>    }</div>
+<div class="line"><span class="lineno">  136</span>    variance /= number_of_samples;</div>
+<div class="line"><span class="lineno">  137</span> </div>
+<div class="line"><span class="lineno">  138</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;&lt;&lt;&lt;&lt;&lt;&lt;&lt;&lt; Test Function &gt;&gt;&gt;&gt;&gt;&gt;&gt;&gt;&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
+<div class="line"><span class="lineno">  139</span>              &lt;&lt; <span class="stringliteral">&quot;Expected: Mean: &quot;</span> &lt;&lt; mean &lt;&lt; <span class="stringliteral">&quot;\t Variance: &quot;</span> &lt;&lt; variance</div>
+<div class="line"><span class="lineno">  140</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  141</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tMethod 1:&quot;</span></div>
+<div class="line"><span class="lineno">  142</span>              &lt;&lt; <span class="stringliteral">&quot;\tMean: &quot;</span> &lt;&lt; stats01.<a class="code hl_function" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#a390697dcee210b91823ceff04b25081b">mean</a>()</div>
+<div class="line"><span class="lineno">  143</span>              &lt;&lt; <span class="stringliteral">&quot;\t Variance: &quot;</span> &lt;&lt; stats01.<a class="code hl_function" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#a27f0a03e2fd2254f1c81fe668226bd92">variance</a>()</div>
+<div class="line"><span class="lineno">  144</span>              &lt;&lt; <span class="stringliteral">&quot;\t Std: &quot;</span> &lt;&lt; stats01.<a class="code hl_function" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#af57e942d49f4fd70f059f224b4ac07e1">std</a>() &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tMethod 2:&quot;</span></div>
+<div class="line"><span class="lineno">  146</span>              &lt;&lt; <span class="stringliteral">&quot;\tMean: &quot;</span> &lt;&lt; stats02.<a class="code hl_function" href="../../d8/dab/classstatistics_1_1stats__computer2.html#a8290966ad468f2a8c266d008bc60720e">mean</a>()</div>
+<div class="line"><span class="lineno">  147</span>              &lt;&lt; <span class="stringliteral">&quot;\t Variance: &quot;</span> &lt;&lt; stats02.<a class="code hl_function" href="../../d8/dab/classstatistics_1_1stats__computer2.html#af6198817084276113b3c064e87ce0555">variance</a>()</div>
+<div class="line"><span class="lineno">  148</span>              &lt;&lt; <span class="stringliteral">&quot;\t Std: &quot;</span> &lt;&lt; stats02.<a class="code hl_function" href="../../d8/dab/classstatistics_1_1stats__computer2.html#acf2e84df4fc386bb3295016ef8fd156e">std</a>() &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  149</span> </div>
+<div class="line"><span class="lineno">  150</span>    assert(std::abs(stats01.<a class="code hl_function" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#a390697dcee210b91823ceff04b25081b">mean</a>() - mean) &lt; 0.01);</div>
+<div class="line"><span class="lineno">  151</span>    assert(std::abs(stats02.<a class="code hl_function" href="../../d8/dab/classstatistics_1_1stats__computer2.html#a8290966ad468f2a8c266d008bc60720e">mean</a>() - mean) &lt; 0.01);</div>
+<div class="line"><span class="lineno">  152</span>    assert(std::abs(stats02.<a class="code hl_function" href="../../d8/dab/classstatistics_1_1stats__computer2.html#af6198817084276113b3c064e87ce0555">variance</a>() - variance) &lt; 0.01);</div>
+<div class="line"><span class="lineno">  153</span> </div>
+<div class="line"><span class="lineno">  154</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;(Tests passed)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><span class="lineno">   40</span>            <span class="keywordflow">return</span> ch - <span class="charliteral">&#39;A&#39;</span>;</div>
+<div class="line"><span class="lineno">   41</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (ch &gt;= <span class="charliteral">&#39;a&#39;</span> &amp;&amp; ch &lt;= <span class="charliteral">&#39;z&#39;</span>) {</div>
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 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if successful </dd>
 <dd>
 <code>false</code> if unsuccessful </dd></dl>
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-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>        <span class="keywordflow">if</span> (index == str.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>()) {</div>
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-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>            <span class="comment">//     if (!arr[i])</span></div>
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-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>        <span class="keywordflow">if</span> (var) {</div>
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-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d0/d3e/classdata__structures_1_1trie.html#a4cb0f775b5a4bc14a6d39b5c93883eb6">isEndofWord</a>) {</div>
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-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>        }</div>
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-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  134</span>                                                       {</div>
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+<div class="line"><span class="lineno">  136</span>            <span class="keywordflow">if</span> (!<a class="code hl_variable" href="../../d0/d3e/classdata__structures_1_1trie.html#a4cb0f775b5a4bc14a6d39b5c93883eb6">isEndofWord</a>) {</div>
+<div class="line"><span class="lineno">  137</span>                <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  138</span>            }</div>
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+<div class="line"><span class="lineno">  143</span>            <span class="comment">//         return false;</span></div>
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+<div class="line"><span class="lineno">  145</span>        }</div>
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+<div class="line"><span class="lineno">  149</span>        }</div>
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+<div class="line"><span class="lineno">  154</span>                <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  155</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  156</span>                <span class="keywordtype">int</span> i = 0;</div>
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+<div class="line"><span class="lineno">  159</span>                        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  160</span>                    }</div>
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+<div class="line"><span class="lineno">  162</span>                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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+<div class="line"><span class="lineno">  164</span>        }</div>
+<div class="line"><span class="lineno">  165</span> </div>
+<div class="line"><span class="lineno">  166</span>        <span class="comment">/* should not return here */</span></div>
+<div class="line"><span class="lineno">  167</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;:&quot;</span> &lt;&lt; __LINE__</div>
+<div class="line"><span class="lineno">  168</span>                  &lt;&lt; <span class="stringliteral">&quot;Should not reach this line\n&quot;</span>;</div>
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+<div class="line"><span class="lineno">  170</span>    }</div>
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 <div class="ttc" id="aclassdata__structures_1_1trie_html_aab373beb3f618b90922528c68797d988"><div class="ttname"><a href="../../d0/d3e/classdata__structures_1_1trie.html#aab373beb3f618b90922528c68797d988">data_structures::trie::char_to_int</a></div><div class="ttdeci">uint8_t char_to_int(const char &amp;ch) const</div><div class="ttdoc">Convert a character to integer for indexing.</div><div class="ttdef"><b>Definition:</b> trie_tree.cpp:38</div></div>
@@ -325,29 +325,29 @@ Here is the call graph for this function:</div>
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+<div class="line"><span class="lineno">   32</span>    <span class="comment">// increase `count` by 1 in each iteration</span></div>
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@@ -107,7 +107,7 @@ Inheritance diagram for graph::RootedTree:</div>
 <div class="dynheader">
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@@ -198,9 +198,9 @@ Protected Member Functions</h2></td></tr>
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-<div class="fragment"><div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>        : <a class="code hl_class" href="../../da/d9a/class_graph.html">Graph</a>(undirected_edges.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() + 1, undirected_edges), <a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#ab22a97bf6209a085fc2d788c3c0dacbe">root</a>(root_) {</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>        <a class="code hl_function" href="../../d0/d58/classgraph_1_1_rooted_tree.html#ae6928f3ebd491541e9570e746b877c1e">populate_parents</a>();</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   95</span>        : <a class="code hl_class" href="../../da/d9a/class_graph.html">Graph</a>(undirected_edges.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() + 1, undirected_edges), <a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#ab22a97bf6209a085fc2d788c3c0dacbe">root</a>(root_) {</div>
+<div class="line"><span class="lineno">   96</span>        <a class="code hl_function" href="../../d0/d58/classgraph_1_1_rooted_tree.html#ae6928f3ebd491541e9570e746b877c1e">populate_parents</a>();</div>
+<div class="line"><span class="lineno">   97</span>    }</div>
 <div class="ttc" id="aclass_graph_html"><div class="ttname"><a href="../../da/d9a/class_graph.html">Graph</a></div><div class="ttdef"><b>Definition:</b> bellman_ford.cpp:13</div></div>
 <div class="ttc" id="aclassgraph_1_1_rooted_tree_html_ab22a97bf6209a085fc2d788c3c0dacbe"><div class="ttname"><a href="../../d0/d58/classgraph_1_1_rooted_tree.html#ab22a97bf6209a085fc2d788c3c0dacbe">graph::RootedTree::root</a></div><div class="ttdeci">int root</div><div class="ttdoc">Index of the root vertex.</div><div class="ttdef"><b>Definition:</b> lowest_common_ancestor.cpp:108</div></div>
 <div class="ttc" id="aclassgraph_1_1_rooted_tree_html_ae6928f3ebd491541e9570e746b877c1e"><div class="ttname"><a href="../../d0/d58/classgraph_1_1_rooted_tree.html#ae6928f3ebd491541e9570e746b877c1e">graph::RootedTree::populate_parents</a></div><div class="ttdeci">void populate_parents()</div><div class="ttdoc">Calculate the parents for all the vertices in the tree. Implements the breadth first search algorithm...</div><div class="ttdef"><b>Definition:</b> lowest_common_ancestor.cpp:117</div></div>
@@ -234,28 +234,28 @@ Protected Member Functions</h2></td></tr>
 
 <p>Calculate the parents for all the vertices in the tree. Implements the breadth first search algorithm starting from the root vertex searching the entire tree and labeling parents for all vertices. </p>
 <dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
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-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>            <span class="keywordtype">int</span> vertex = queue_of_vertices.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/front.html">front</a>();</div>
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+<div class="fragment"><div class="line"><span class="lineno">  117</span>                            {</div>
+<div class="line"><span class="lineno">  118</span>        <span class="comment">// Initialize the vector with -1 which indicates the vertex</span></div>
+<div class="line"><span class="lineno">  119</span>        <span class="comment">// wasn&#39;t yet visited.</span></div>
+<div class="line"><span class="lineno">  120</span>        <a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a3831583a91914988897a4cc8748fda43">parent</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>(<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a8930d1470d132b19e430d1c71f94c904">number_of_vertices</a>(), -1);</div>
+<div class="line"><span class="lineno">  121</span>        <a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>(<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a8930d1470d132b19e430d1c71f94c904">number_of_vertices</a>());</div>
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+<div class="line"><span class="lineno">  123</span>        <a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#ab22a97bf6209a085fc2d788c3c0dacbe">root</a>] = 0;</div>
+<div class="line"><span class="lineno">  124</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue&lt;int&gt;</a> queue_of_vertices;</div>
+<div class="line"><span class="lineno">  125</span>        queue_of_vertices.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/push.html">push</a>(<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#ab22a97bf6209a085fc2d788c3c0dacbe">root</a>);</div>
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+<div class="line"><span class="lineno">  127</span>            <span class="keywordtype">int</span> vertex = queue_of_vertices.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/front.html">front</a>();</div>
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+<div class="line"><span class="lineno">  134</span>                    queue_of_vertices.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/push.html">push</a>(neighbor);</div>
+<div class="line"><span class="lineno">  135</span>                }</div>
+<div class="line"><span class="lineno">  136</span>            }</div>
+<div class="line"><span class="lineno">  137</span>        }</div>
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 <div class="ttc" id="aclassgraph_1_1_graph_html_a8930d1470d132b19e430d1c71f94c904"><div class="ttname"><a href="../../dc/d61/classgraph_1_1_graph.html#a8930d1470d132b19e430d1c71f94c904">graph::Graph::number_of_vertices</a></div><div class="ttdeci">int number_of_vertices() const</div><div class="ttdef"><b>Definition:</b> lowest_common_ancestor.cpp:74</div></div>
 <div class="ttc" id="aclassgraph_1_1_rooted_tree_html_a2ee3ad1161ac2532da30c3e22c265ad3"><div class="ttname"><a href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">graph::RootedTree::level</a></div><div class="ttdeci">std::vector&lt; int &gt; level</div><div class="ttdoc">Stores the distance from the root.</div><div class="ttdef"><b>Definition:</b> lowest_common_ancestor.cpp:106</div></div>
@@ -265,11 +265,11 @@ Protected Member Functions</h2></td></tr>
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-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int &gt;</a></div></div>
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 Here is the call graph for this function:</div>
 <div class="dyncontent">
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@@ -284,7 +284,7 @@ Here is the call graph for this function:</div>
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-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>    cur_pos = delete_from-&gt;english[letter_index];</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>    <span class="comment">// Sever the connection from the main trie</span></div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>    delete_from-&gt;english[letter_index] = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span> </div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    <span class="comment">// If number of characters in the suffix are more than 1, recursively delete</span></div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>    <span class="comment">// each character starting from cur_pos using the helper function</span></div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>    <span class="keywordflow">if</span> (n &gt; delete_from_index + 2) {</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>        <a class="code hl_function" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#adef6940391f981ab86767775176b7169">DeleteFrom</a>(cur_pos, entry, delete_from_index + 2);</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>    }</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    <span class="comment">// If the suffix is only 1 char in length</span></div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>        <span class="keyword">delete</span> cur_pos;</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    }</div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  150</span>                                  {</div>
+<div class="line"><span class="lineno">  151</span>    Tnode *cur_pos = <span class="keyword">this</span>,</div>
+<div class="line"><span class="lineno">  152</span>          *delete_from = <span class="keyword">this</span>;  <span class="comment">// Current pointer pointing to root</span></div>
+<div class="line"><span class="lineno">  153</span>    <span class="keywordtype">int</span> letter_index = 0, delete_from_index = 0, i = 0, n = entry.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
+<div class="line"><span class="lineno">  154</span> </div>
+<div class="line"><span class="lineno">  155</span>    <span class="keywordflow">for</span> (i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">  156</span>        <span class="comment">// To ignore case</span></div>
+<div class="line"><span class="lineno">  157</span>        letter_index = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/tolower.html">tolower</a>(entry[i]) - 97;</div>
+<div class="line"><span class="lineno">  158</span> </div>
+<div class="line"><span class="lineno">  159</span>        <span class="comment">// Display error message when given entry is not present in the tree</span></div>
+<div class="line"><span class="lineno">  160</span>        <span class="keywordflow">if</span> (cur_pos-&gt;english[letter_index] == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  161</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Entry not Found&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  162</span>            <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  163</span>        }</div>
+<div class="line"><span class="lineno">  164</span>        <span class="comment">// If the current node is end of word for the current prefix or if it</span></div>
+<div class="line"><span class="lineno">  165</span>        <span class="comment">// has 2 or more branches It cannot be deleted while deleting the</span></div>
+<div class="line"><span class="lineno">  166</span>        <span class="comment">// required entry.</span></div>
+<div class="line"><span class="lineno">  167</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#afca808362c13273ca8c8ae7d58e8eee0">numberOfChildren</a>(cur_pos) &gt; 1 || cur_pos-&gt;endOfWord) {</div>
+<div class="line"><span class="lineno">  168</span>            delete_from = cur_pos;      <span class="comment">// denotes the beginning of the shortest</span></div>
+<div class="line"><span class="lineno">  169</span>                                        <span class="comment">// suffix that is allowed to be deleted</span></div>
+<div class="line"><span class="lineno">  170</span>            delete_from_index = i - 1;  <span class="comment">// Beginning index of the suffix</span></div>
+<div class="line"><span class="lineno">  171</span>                                        <span class="comment">// corresponding to the &#39;entry&#39;</span></div>
+<div class="line"><span class="lineno">  172</span>        }</div>
+<div class="line"><span class="lineno">  173</span> </div>
+<div class="line"><span class="lineno">  174</span>        <span class="comment">// Traversing through the entry</span></div>
+<div class="line"><span class="lineno">  175</span>        cur_pos = cur_pos-&gt;english[letter_index];</div>
+<div class="line"><span class="lineno">  176</span>    }</div>
+<div class="line"><span class="lineno">  177</span> </div>
+<div class="line"><span class="lineno">  178</span>    <span class="comment">// cur_pos now points to the last char of entry. Display message if that</span></div>
+<div class="line"><span class="lineno">  179</span>    <span class="comment">// entry does not exist</span></div>
+<div class="line"><span class="lineno">  180</span>    <span class="keywordflow">if</span> (!cur_pos-&gt;endOfWord) {</div>
+<div class="line"><span class="lineno">  181</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Entry not Found&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  182</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  183</span>    }</div>
+<div class="line"><span class="lineno">  184</span> </div>
+<div class="line"><span class="lineno">  185</span>    <span class="comment">// If cur_pos is not a leaf node, unmark end of word and assign 0 to it&#39;s</span></div>
+<div class="line"><span class="lineno">  186</span>    <span class="comment">// frequency for deletion</span></div>
+<div class="line"><span class="lineno">  187</span>    <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#afca808362c13273ca8c8ae7d58e8eee0">numberOfChildren</a>(cur_pos)) {</div>
+<div class="line"><span class="lineno">  188</span>        cur_pos-&gt;endOfWord = <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  189</span>        cur_pos-&gt;frequency = 0;</div>
+<div class="line"><span class="lineno">  190</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  191</span>    }</div>
+<div class="line"><span class="lineno">  192</span> </div>
+<div class="line"><span class="lineno">  193</span>    <span class="comment">// The first character of the suffix to be deleted</span></div>
+<div class="line"><span class="lineno">  194</span>    letter_index = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/tolower.html">tolower</a>(entry[delete_from_index + 1]) - 97;</div>
+<div class="line"><span class="lineno">  195</span>    <span class="comment">// Point cur_pos to the next node</span></div>
+<div class="line"><span class="lineno">  196</span>    cur_pos = delete_from-&gt;english[letter_index];</div>
+<div class="line"><span class="lineno">  197</span>    <span class="comment">// Sever the connection from the main trie</span></div>
+<div class="line"><span class="lineno">  198</span>    delete_from-&gt;english[letter_index] = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  199</span> </div>
+<div class="line"><span class="lineno">  200</span>    <span class="comment">// If number of characters in the suffix are more than 1, recursively delete</span></div>
+<div class="line"><span class="lineno">  201</span>    <span class="comment">// each character starting from cur_pos using the helper function</span></div>
+<div class="line"><span class="lineno">  202</span>    <span class="keywordflow">if</span> (n &gt; delete_from_index + 2) {</div>
+<div class="line"><span class="lineno">  203</span>        <a class="code hl_function" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#adef6940391f981ab86767775176b7169">DeleteFrom</a>(cur_pos, entry, delete_from_index + 2);</div>
+<div class="line"><span class="lineno">  204</span>    }</div>
+<div class="line"><span class="lineno">  205</span>    <span class="comment">// If the suffix is only 1 char in length</span></div>
+<div class="line"><span class="lineno">  206</span>    <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  207</span>        <span class="keyword">delete</span> cur_pos;</div>
+<div class="line"><span class="lineno">  208</span>    }</div>
+<div class="line"><span class="lineno">  209</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aclassoperations__on__datastructures_1_1trie__operations_1_1_tnode_html_adef6940391f981ab86767775176b7169"><div class="ttname"><a href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#adef6940391f981ab86767775176b7169">operations_on_datastructures::trie_operations::Tnode::DeleteFrom</a></div><div class="ttdeci">void DeleteFrom(Tnode *delete_from, std::string delete_string, int remove_index)</div><div class="ttdoc">Function recursively deletes the substring character by character iterating through the string to be ...</div><div class="ttdef"><b>Definition:</b> trie_multiple_search.cpp:134</div></div>
 <div class="ttc" id="aclassoperations__on__datastructures_1_1trie__operations_1_1_tnode_html_afca808362c13273ca8c8ae7d58e8eee0"><div class="ttname"><a href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#afca808362c13273ca8c8ae7d58e8eee0">operations_on_datastructures::trie_operations::Tnode::numberOfChildren</a></div><div class="ttdeci">uint8_t numberOfChildren(Tnode *node)</div><div class="ttdoc">Function to count the number of children a node in the trie has.</div><div class="ttdef"><b>Definition:</b> trie_multiple_search.cpp:69</div></div>
@@ -402,16 +408,16 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>                                         {</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    <span class="keywordflow">if</span> (delete_string.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() == remove_index) {</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        <span class="keywordtype">int</span> letter_index = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/tolower.html">tolower</a>(delete_string[remove_index]) - 97;</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span> </div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        <a class="code hl_function" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#adef6940391f981ab86767775176b7169">DeleteFrom</a>(delete_from-&gt;english[letter_index], delete_string,</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>                   remove_index + 1);</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span> </div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>        <span class="keyword">delete</span> delete_from;</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    }</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  135</span>                                         {</div>
+<div class="line"><span class="lineno">  136</span>    <span class="keywordflow">if</span> (delete_string.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() == remove_index) {</div>
+<div class="line"><span class="lineno">  137</span>        <span class="keywordtype">int</span> letter_index = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/tolower.html">tolower</a>(delete_string[remove_index]) - 97;</div>
+<div class="line"><span class="lineno">  138</span> </div>
+<div class="line"><span class="lineno">  139</span>        <a class="code hl_function" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#adef6940391f981ab86767775176b7169">DeleteFrom</a>(delete_from-&gt;english[letter_index], delete_string,</div>
+<div class="line"><span class="lineno">  140</span>                   remove_index + 1);</div>
+<div class="line"><span class="lineno">  141</span> </div>
+<div class="line"><span class="lineno">  142</span>        <span class="keyword">delete</span> delete_from;</div>
+<div class="line"><span class="lineno">  143</span>    }</div>
+<div class="line"><span class="lineno">  144</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -444,25 +450,25 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>                                         {</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    Tnode *cur_pos = <span class="keyword">this</span>;</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    <span class="keywordtype">int</span> letter_index = 0;</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span> </div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;i : entry) {</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>        <span class="comment">// To ignore case</span></div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        letter_index = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/tolower.html">tolower</a>(i) - 97;</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span> </div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>        <span class="comment">// Allocate a node for each character of entry if not present in the</span></div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        <span class="comment">// trie</span></div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>        <span class="keywordflow">if</span> (cur_pos-&gt;english[letter_index] == <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>            cur_pos-&gt;english[letter_index] = <span class="keyword">new</span> Tnode();</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>        }</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span> </div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>        cur_pos = cur_pos-&gt;english[letter_index];</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    }</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <span class="comment">// cur_pos points to the last char, mark it as end of word</span></div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    cur_pos-&gt;endOfWord = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  104</span>                                         {</div>
+<div class="line"><span class="lineno">  105</span>    Tnode *cur_pos = <span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  106</span>    <span class="keywordtype">int</span> letter_index = 0;</div>
+<div class="line"><span class="lineno">  107</span> </div>
+<div class="line"><span class="lineno">  108</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;i : entry) {</div>
+<div class="line"><span class="lineno">  109</span>        <span class="comment">// To ignore case</span></div>
+<div class="line"><span class="lineno">  110</span>        letter_index = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/tolower.html">tolower</a>(i) - 97;</div>
+<div class="line"><span class="lineno">  111</span> </div>
+<div class="line"><span class="lineno">  112</span>        <span class="comment">// Allocate a node for each character of entry if not present in the</span></div>
+<div class="line"><span class="lineno">  113</span>        <span class="comment">// trie</span></div>
+<div class="line"><span class="lineno">  114</span>        <span class="keywordflow">if</span> (cur_pos-&gt;english[letter_index] == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  115</span>            cur_pos-&gt;english[letter_index] = <span class="keyword">new</span> Tnode();</div>
+<div class="line"><span class="lineno">  116</span>        }</div>
+<div class="line"><span class="lineno">  117</span> </div>
+<div class="line"><span class="lineno">  118</span>        cur_pos = cur_pos-&gt;english[letter_index];</div>
+<div class="line"><span class="lineno">  119</span>    }</div>
+<div class="line"><span class="lineno">  120</span>    <span class="comment">// cur_pos points to the last char, mark it as end of word</span></div>
+<div class="line"><span class="lineno">  121</span>    cur_pos-&gt;endOfWord = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  122</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -498,10 +504,10 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>count of the number of children of the given node (max 26) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>                                                 {</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        <span class="keywordflow">return</span> ENGLISH_ALPHABET_SIZE -</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>               <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/count.html">std::count</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;english.begin(), <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;english.end(), <span class="keyword">nullptr</span>);</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   69</span>                                                 {</div>
+<div class="line"><span class="lineno">   70</span>        <span class="keywordflow">return</span> ENGLISH_ALPHABET_SIZE -</div>
+<div class="line"><span class="lineno">   71</span>               <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/count.html">std::count</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;english.begin(), <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;english.end(), <span class="keyword">nullptr</span>);</div>
+<div class="line"><span class="lineno">   72</span>    }</div>
 <div class="ttc" id="acount_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/count.html">std::count</a></div><div class="ttdeci">T count(T... args)</div></div>
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 Here is the call graph for this function:</div>
@@ -535,56 +541,56 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00365" name="l00365"></a><span class="lineno">  365</span>                                                      {</div>
-<div class="line"><a id="l00366" name="l00366"></a><span class="lineno">  366</span>    Tnode *cur_pos = <span class="keyword">nullptr</span>, *prev_pos = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00367" name="l00367"></a><span class="lineno">  367</span>    cur_pos = prev_pos = <span class="keyword">this</span>;  <span class="comment">// maintaining 2 pointers, initialized to root</span></div>
-<div class="line"><a id="l00368" name="l00368"></a><span class="lineno">  368</span>    <span class="keywordtype">int</span> letter_index = 0;</div>
-<div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> prefix =</div>
-<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span>        <span class="stringliteral">&quot;&quot;</span>;  <span class="comment">// variable storing the updated value of longest common prefix</span></div>
-<div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue.html">std::priority_queue&lt;std::pair&lt;int, std::string&gt;</a> &gt;</div>
-<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span>        suggestions;  <span class="comment">// max heap to store (frequency, word) in descending order</span></div>
-<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>                      <span class="comment">// of freq</span></div>
-<div class="line"><a id="l00374" name="l00374"></a><span class="lineno">  374</span> </div>
-<div class="line"><a id="l00375" name="l00375"></a><span class="lineno">  375</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue.html">std::priority_queue&lt;std::pair&lt;int, std::string&gt;</a> &gt; *Suggestions =</div>
-<div class="line"><a id="l00376" name="l00376"></a><span class="lineno">  376</span>        &amp;suggestions;</div>
-<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span> </div>
-<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;i : key) {</div>
-<div class="line"><a id="l00379" name="l00379"></a><span class="lineno">  379</span>        letter_index = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/tolower.html">tolower</a>(i) - 97;</div>
-<div class="line"><a id="l00380" name="l00380"></a><span class="lineno">  380</span>        prev_pos = cur_pos;  <span class="comment">// Previous pointer updated to point to the last</span></div>
-<div class="line"><a id="l00381" name="l00381"></a><span class="lineno">  381</span>                             <span class="comment">// char of the longest common prefix</span></div>
-<div class="line"><a id="l00382" name="l00382"></a><span class="lineno">  382</span> </div>
-<div class="line"><a id="l00383" name="l00383"></a><span class="lineno">  383</span>        <span class="comment">// When the node for the character does not exist, longest prefix has</span></div>
-<div class="line"><a id="l00384" name="l00384"></a><span class="lineno">  384</span>        <span class="comment">// been determined and SuggestFreqAutocomplete is called</span></div>
-<div class="line"><a id="l00385" name="l00385"></a><span class="lineno">  385</span>        <span class="keywordflow">if</span> (cur_pos-&gt;english[letter_index] == <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00386" name="l00386"></a><span class="lineno">  386</span>            <a class="code hl_function" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a9e556f52c837190ecf4265b1f05cfe9c">SuggestFreqAutocomplete</a>(prev_pos, prefix, Suggestions);</div>
-<div class="line"><a id="l00387" name="l00387"></a><span class="lineno">  387</span>            <span class="comment">// To display the top 3 results</span></div>
-<div class="line"><a id="l00388" name="l00388"></a><span class="lineno">  388</span>            <a class="code hl_function" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#aacafb8c9f3ebac7ac6c01d9645bb67b6">SelectionTop_3</a>(Suggestions);</div>
-<div class="line"><a id="l00389" name="l00389"></a><span class="lineno">  389</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;- - - - - - - - - - - - - - - - - - - - - - - - - - &quot;</span></div>
-<div class="line"><a id="l00390" name="l00390"></a><span class="lineno">  390</span>                      &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00391" name="l00391"></a><span class="lineno">  391</span>            <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00392" name="l00392"></a><span class="lineno">  392</span>        }</div>
-<div class="line"><a id="l00393" name="l00393"></a><span class="lineno">  393</span>        <span class="comment">// Updating the longest common prefix</span></div>
-<div class="line"><a id="l00394" name="l00394"></a><span class="lineno">  394</span>        prefix += char(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/tolower.html">tolower</a>(i));</div>
-<div class="line"><a id="l00395" name="l00395"></a><span class="lineno">  395</span>        cur_pos = cur_pos-&gt;english[letter_index];</div>
-<div class="line"><a id="l00396" name="l00396"></a><span class="lineno">  396</span>    }</div>
-<div class="line"><a id="l00397" name="l00397"></a><span class="lineno">  397</span>    <span class="comment">// If the key is a valid entry of trie, display it @ top of the suggestions</span></div>
-<div class="line"><a id="l00398" name="l00398"></a><span class="lineno">  398</span>    <span class="keywordflow">if</span> (cur_pos-&gt;endOfWord) {</div>
-<div class="line"><a id="l00399" name="l00399"></a><span class="lineno">  399</span>        (cur_pos-&gt;frequency)++;</div>
-<div class="line"><a id="l00400" name="l00400"></a><span class="lineno">  400</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; key &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00401" name="l00401"></a><span class="lineno">  401</span>    }</div>
-<div class="line"><a id="l00402" name="l00402"></a><span class="lineno">  402</span> </div>
-<div class="line"><a id="l00403" name="l00403"></a><span class="lineno">  403</span>    (void)prev_pos;  <span class="comment">// Idiom to ignore previous pointer</span></div>
-<div class="line"><a id="l00404" name="l00404"></a><span class="lineno">  404</span> </div>
-<div class="line"><a id="l00405" name="l00405"></a><span class="lineno">  405</span>    <span class="comment">// Call for Suggestions when the search key is present as an entry/a prefix</span></div>
-<div class="line"><a id="l00406" name="l00406"></a><span class="lineno">  406</span>    <span class="comment">// in the trie</span></div>
-<div class="line"><a id="l00407" name="l00407"></a><span class="lineno">  407</span>    <a class="code hl_function" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a9e556f52c837190ecf4265b1f05cfe9c">SuggestFreqAutocomplete</a>(cur_pos, prefix, Suggestions);</div>
-<div class="line"><a id="l00408" name="l00408"></a><span class="lineno">  408</span>    <span class="comment">// Display the top 3 results</span></div>
-<div class="line"><a id="l00409" name="l00409"></a><span class="lineno">  409</span>    <a class="code hl_function" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#aacafb8c9f3ebac7ac6c01d9645bb67b6">SelectionTop_3</a>(Suggestions);</div>
-<div class="line"><a id="l00410" name="l00410"></a><span class="lineno">  410</span> </div>
-<div class="line"><a id="l00411" name="l00411"></a><span class="lineno">  411</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;- - - - - - - - - - - - - - - - - - - - - - - - - - &quot;</span></div>
-<div class="line"><a id="l00412" name="l00412"></a><span class="lineno">  412</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00413" name="l00413"></a><span class="lineno">  413</span>    <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00414" name="l00414"></a><span class="lineno">  414</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  365</span>                                                      {</div>
+<div class="line"><span class="lineno">  366</span>    Tnode *cur_pos = <span class="keyword">nullptr</span>, *prev_pos = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  367</span>    cur_pos = prev_pos = <span class="keyword">this</span>;  <span class="comment">// maintaining 2 pointers, initialized to root</span></div>
+<div class="line"><span class="lineno">  368</span>    <span class="keywordtype">int</span> letter_index = 0;</div>
+<div class="line"><span class="lineno">  369</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> prefix =</div>
+<div class="line"><span class="lineno">  370</span>        <span class="stringliteral">&quot;&quot;</span>;  <span class="comment">// variable storing the updated value of longest common prefix</span></div>
+<div class="line"><span class="lineno">  371</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue.html">std::priority_queue&lt;std::pair&lt;int, std::string&gt;</a> &gt;</div>
+<div class="line"><span class="lineno">  372</span>        suggestions;  <span class="comment">// max heap to store (frequency, word) in descending order</span></div>
+<div class="line"><span class="lineno">  373</span>                      <span class="comment">// of freq</span></div>
+<div class="line"><span class="lineno">  374</span> </div>
+<div class="line"><span class="lineno">  375</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue.html">std::priority_queue&lt;std::pair&lt;int, std::string&gt;</a> &gt; *Suggestions =</div>
+<div class="line"><span class="lineno">  376</span>        &amp;suggestions;</div>
+<div class="line"><span class="lineno">  377</span> </div>
+<div class="line"><span class="lineno">  378</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;i : key) {</div>
+<div class="line"><span class="lineno">  379</span>        letter_index = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/tolower.html">tolower</a>(i) - 97;</div>
+<div class="line"><span class="lineno">  380</span>        prev_pos = cur_pos;  <span class="comment">// Previous pointer updated to point to the last</span></div>
+<div class="line"><span class="lineno">  381</span>                             <span class="comment">// char of the longest common prefix</span></div>
+<div class="line"><span class="lineno">  382</span> </div>
+<div class="line"><span class="lineno">  383</span>        <span class="comment">// When the node for the character does not exist, longest prefix has</span></div>
+<div class="line"><span class="lineno">  384</span>        <span class="comment">// been determined and SuggestFreqAutocomplete is called</span></div>
+<div class="line"><span class="lineno">  385</span>        <span class="keywordflow">if</span> (cur_pos-&gt;english[letter_index] == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  386</span>            <a class="code hl_function" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a9e556f52c837190ecf4265b1f05cfe9c">SuggestFreqAutocomplete</a>(prev_pos, prefix, Suggestions);</div>
+<div class="line"><span class="lineno">  387</span>            <span class="comment">// To display the top 3 results</span></div>
+<div class="line"><span class="lineno">  388</span>            <a class="code hl_function" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#aacafb8c9f3ebac7ac6c01d9645bb67b6">SelectionTop_3</a>(Suggestions);</div>
+<div class="line"><span class="lineno">  389</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;- - - - - - - - - - - - - - - - - - - - - - - - - - &quot;</span></div>
+<div class="line"><span class="lineno">  390</span>                      &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  391</span>            <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  392</span>        }</div>
+<div class="line"><span class="lineno">  393</span>        <span class="comment">// Updating the longest common prefix</span></div>
+<div class="line"><span class="lineno">  394</span>        prefix += char(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/tolower.html">tolower</a>(i));</div>
+<div class="line"><span class="lineno">  395</span>        cur_pos = cur_pos-&gt;english[letter_index];</div>
+<div class="line"><span class="lineno">  396</span>    }</div>
+<div class="line"><span class="lineno">  397</span>    <span class="comment">// If the key is a valid entry of trie, display it @ top of the suggestions</span></div>
+<div class="line"><span class="lineno">  398</span>    <span class="keywordflow">if</span> (cur_pos-&gt;endOfWord) {</div>
+<div class="line"><span class="lineno">  399</span>        (cur_pos-&gt;frequency)++;</div>
+<div class="line"><span class="lineno">  400</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; key &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  401</span>    }</div>
+<div class="line"><span class="lineno">  402</span> </div>
+<div class="line"><span class="lineno">  403</span>    (void)prev_pos;  <span class="comment">// Idiom to ignore previous pointer</span></div>
+<div class="line"><span class="lineno">  404</span> </div>
+<div class="line"><span class="lineno">  405</span>    <span class="comment">// Call for Suggestions when the search key is present as an entry/a prefix</span></div>
+<div class="line"><span class="lineno">  406</span>    <span class="comment">// in the trie</span></div>
+<div class="line"><span class="lineno">  407</span>    <a class="code hl_function" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a9e556f52c837190ecf4265b1f05cfe9c">SuggestFreqAutocomplete</a>(cur_pos, prefix, Suggestions);</div>
+<div class="line"><span class="lineno">  408</span>    <span class="comment">// Display the top 3 results</span></div>
+<div class="line"><span class="lineno">  409</span>    <a class="code hl_function" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#aacafb8c9f3ebac7ac6c01d9645bb67b6">SelectionTop_3</a>(Suggestions);</div>
+<div class="line"><span class="lineno">  410</span> </div>
+<div class="line"><span class="lineno">  411</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;- - - - - - - - - - - - - - - - - - - - - - - - - - &quot;</span></div>
+<div class="line"><span class="lineno">  412</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  413</span>    <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  414</span>}</div>
 <div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
 <div class="ttc" id="aclassoperations__on__datastructures_1_1trie__operations_1_1_tnode_html_a9e556f52c837190ecf4265b1f05cfe9c"><div class="ttname"><a href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a9e556f52c837190ecf4265b1f05cfe9c">operations_on_datastructures::trie_operations::Tnode::SuggestFreqAutocomplete</a></div><div class="ttdeci">void SuggestFreqAutocomplete(Tnode *new_root, const std::string &amp;prefix, std::priority_queue&lt; std::pair&lt; int, std::string &gt; &gt; *suggestions)</div><div class="ttdoc">Recursive function to suggest most frequently searched entries of trie which have a given common pref...</div><div class="ttdef"><b>Definition:</b> trie_multiple_search.cpp:337</div></div>
 <div class="ttc" id="aclassoperations__on__datastructures_1_1trie__operations_1_1_tnode_html_aacafb8c9f3ebac7ac6c01d9645bb67b6"><div class="ttname"><a href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#aacafb8c9f3ebac7ac6c01d9645bb67b6">operations_on_datastructures::trie_operations::Tnode::SelectionTop_3</a></div><div class="ttdeci">void SelectionTop_3(std::priority_queue&lt; std::pair&lt; int, std::string &gt; &gt; *suggestions)</div><div class="ttdoc">Function to display the 3 suggestions with highest frequency of search hits.</div><div class="ttdef"><b>Definition:</b> trie_multiple_search.cpp:317</div></div>
@@ -624,27 +630,27 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd>true if the key is found </dd>
 <dd>
 false if the key is not found </dd></dl>
-<div class="fragment"><div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>                                               {</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>    Tnode *cur_pos = <span class="keyword">this</span>;</div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>    <span class="keywordtype">int</span> letter_index = 0;</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span> </div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;i : key) {</div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>        letter_index = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/tolower.html">tolower</a>(i) - 97;</div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>        <span class="comment">// If any character in the order of the key is absent, word not found!</span></div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>        <span class="keywordflow">if</span> (cur_pos-&gt;english[letter_index] == <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>        }</div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>        cur_pos = cur_pos-&gt;english[letter_index];</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    }</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>    <span class="comment">// Word is only present in the trie if the key is a valid complete entry and</span></div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>    <span class="comment">// not just a prefix.</span></div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>    <span class="keywordflow">if</span> (cur_pos-&gt;endOfWord) {</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>        (cur_pos-&gt;frequency)++;</div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>    }</div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  217</span>                                               {</div>
+<div class="line"><span class="lineno">  218</span>    Tnode *cur_pos = <span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  219</span>    <span class="keywordtype">int</span> letter_index = 0;</div>
+<div class="line"><span class="lineno">  220</span> </div>
+<div class="line"><span class="lineno">  221</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;i : key) {</div>
+<div class="line"><span class="lineno">  222</span>        letter_index = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/tolower.html">tolower</a>(i) - 97;</div>
+<div class="line"><span class="lineno">  223</span>        <span class="comment">// If any character in the order of the key is absent, word not found!</span></div>
+<div class="line"><span class="lineno">  224</span>        <span class="keywordflow">if</span> (cur_pos-&gt;english[letter_index] == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  225</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  226</span>        }</div>
+<div class="line"><span class="lineno">  227</span>        cur_pos = cur_pos-&gt;english[letter_index];</div>
+<div class="line"><span class="lineno">  228</span>    }</div>
+<div class="line"><span class="lineno">  229</span>    <span class="comment">// Word is only present in the trie if the key is a valid complete entry and</span></div>
+<div class="line"><span class="lineno">  230</span>    <span class="comment">// not just a prefix.</span></div>
+<div class="line"><span class="lineno">  231</span>    <span class="keywordflow">if</span> (cur_pos-&gt;endOfWord) {</div>
+<div class="line"><span class="lineno">  232</span>        (cur_pos-&gt;frequency)++;</div>
+<div class="line"><span class="lineno">  233</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  234</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  235</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  236</span>    }</div>
+<div class="line"><span class="lineno">  237</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -671,45 +677,45 @@ false if the key is not found </dd></dl>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>                                                  {</div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>    Tnode *cur_pos = <span class="keyword">nullptr</span>, *prev_pos = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>    cur_pos = prev_pos = <span class="keyword">this</span>;  <span class="comment">// maintaining 2 pointers, initialized to root</span></div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>    <span class="keywordtype">int</span> letter_index = 0;</div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> prefix =</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>        <span class="stringliteral">&quot;&quot;</span>;  <span class="comment">// variable storing the updated value of longest common prefix</span></div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span> </div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;i : key) {</div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>        letter_index = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/tolower.html">tolower</a>(i) - 97;</div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>        prev_pos = cur_pos;  <span class="comment">// Previous pointer updated to point to the last</span></div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>                             <span class="comment">// char of the longest common prefix</span></div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span> </div>
-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>        <span class="comment">// When the node for the character does not exist, longest prefix has</span></div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>        <span class="comment">// been determined and SuggestAutocomplete is called</span></div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>        <span class="keywordflow">if</span> (cur_pos-&gt;english[letter_index] == <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>            <a class="code hl_function" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a097913c4badec2b60d50a171ecc299fe">SuggestAutocomplete</a>(prev_pos, prefix);</div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;- - - - - - - - - - - - - - - - - - - - - - - - - - &quot;</span></div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>                      &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>            <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>        }</div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>        <span class="comment">// Updating the longest common prefix</span></div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>        prefix += char(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/tolower.html">tolower</a>(i));</div>
-<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>        cur_pos = cur_pos-&gt;english[letter_index];</div>
-<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>    }</div>
-<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span>    <span class="comment">// If the key is a valid entry of trie, display it @ top of the suggestions</span></div>
-<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>    <span class="keywordflow">if</span> (cur_pos-&gt;endOfWord) {</div>
-<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; key &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>        (cur_pos-&gt;frequency)++;</div>
-<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>    }</div>
-<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span> </div>
-<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span>    (void)prev_pos;  <span class="comment">// Idiom to ignore previous pointer</span></div>
-<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span> </div>
-<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span>    <span class="comment">// Call for suggestions when the search key is present as an entry/a prefix</span></div>
-<div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span>    <span class="comment">// in the trie</span></div>
-<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span>    <a class="code hl_function" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a097913c4badec2b60d50a171ecc299fe">SuggestAutocomplete</a>(cur_pos, prefix);</div>
-<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;- - - - - - - - - - - - - - - - - - - - - - - - - - &quot;</span></div>
-<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>    <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  271</span>                                                  {</div>
+<div class="line"><span class="lineno">  272</span>    Tnode *cur_pos = <span class="keyword">nullptr</span>, *prev_pos = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  273</span>    cur_pos = prev_pos = <span class="keyword">this</span>;  <span class="comment">// maintaining 2 pointers, initialized to root</span></div>
+<div class="line"><span class="lineno">  274</span>    <span class="keywordtype">int</span> letter_index = 0;</div>
+<div class="line"><span class="lineno">  275</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> prefix =</div>
+<div class="line"><span class="lineno">  276</span>        <span class="stringliteral">&quot;&quot;</span>;  <span class="comment">// variable storing the updated value of longest common prefix</span></div>
+<div class="line"><span class="lineno">  277</span> </div>
+<div class="line"><span class="lineno">  278</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;i : key) {</div>
+<div class="line"><span class="lineno">  279</span>        letter_index = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/tolower.html">tolower</a>(i) - 97;</div>
+<div class="line"><span class="lineno">  280</span>        prev_pos = cur_pos;  <span class="comment">// Previous pointer updated to point to the last</span></div>
+<div class="line"><span class="lineno">  281</span>                             <span class="comment">// char of the longest common prefix</span></div>
+<div class="line"><span class="lineno">  282</span> </div>
+<div class="line"><span class="lineno">  283</span>        <span class="comment">// When the node for the character does not exist, longest prefix has</span></div>
+<div class="line"><span class="lineno">  284</span>        <span class="comment">// been determined and SuggestAutocomplete is called</span></div>
+<div class="line"><span class="lineno">  285</span>        <span class="keywordflow">if</span> (cur_pos-&gt;english[letter_index] == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  286</span>            <a class="code hl_function" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a097913c4badec2b60d50a171ecc299fe">SuggestAutocomplete</a>(prev_pos, prefix);</div>
+<div class="line"><span class="lineno">  287</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;- - - - - - - - - - - - - - - - - - - - - - - - - - &quot;</span></div>
+<div class="line"><span class="lineno">  288</span>                      &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  289</span>            <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  290</span>        }</div>
+<div class="line"><span class="lineno">  291</span>        <span class="comment">// Updating the longest common prefix</span></div>
+<div class="line"><span class="lineno">  292</span>        prefix += char(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/tolower.html">tolower</a>(i));</div>
+<div class="line"><span class="lineno">  293</span>        cur_pos = cur_pos-&gt;english[letter_index];</div>
+<div class="line"><span class="lineno">  294</span>    }</div>
+<div class="line"><span class="lineno">  295</span>    <span class="comment">// If the key is a valid entry of trie, display it @ top of the suggestions</span></div>
+<div class="line"><span class="lineno">  296</span>    <span class="keywordflow">if</span> (cur_pos-&gt;endOfWord) {</div>
+<div class="line"><span class="lineno">  297</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; key &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  298</span>        (cur_pos-&gt;frequency)++;</div>
+<div class="line"><span class="lineno">  299</span>    }</div>
+<div class="line"><span class="lineno">  300</span> </div>
+<div class="line"><span class="lineno">  301</span>    (void)prev_pos;  <span class="comment">// Idiom to ignore previous pointer</span></div>
+<div class="line"><span class="lineno">  302</span> </div>
+<div class="line"><span class="lineno">  303</span>    <span class="comment">// Call for suggestions when the search key is present as an entry/a prefix</span></div>
+<div class="line"><span class="lineno">  304</span>    <span class="comment">// in the trie</span></div>
+<div class="line"><span class="lineno">  305</span>    <a class="code hl_function" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a097913c4badec2b60d50a171ecc299fe">SuggestAutocomplete</a>(cur_pos, prefix);</div>
+<div class="line"><span class="lineno">  306</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;- - - - - - - - - - - - - - - - - - - - - - - - - - &quot;</span></div>
+<div class="line"><span class="lineno">  307</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  308</span>    <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  309</span>}</div>
 <div class="ttc" id="aclassoperations__on__datastructures_1_1trie__operations_1_1_tnode_html_a097913c4badec2b60d50a171ecc299fe"><div class="ttname"><a href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a097913c4badec2b60d50a171ecc299fe">operations_on_datastructures::trie_operations::Tnode::SuggestAutocomplete</a></div><div class="ttdeci">void SuggestAutocomplete(Tnode *new_root, const std::string &amp;prefix)</div><div class="ttdoc">Recursive function to suggest all the entries of trie which have a given common prefix.</div><div class="ttdef"><b>Definition:</b> trie_multiple_search.cpp:246</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -743,15 +749,15 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span>                                                              {</div>
-<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>    <span class="comment">// Display Either top 3 or total number of suggestions, whichever is smaller</span></div>
-<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>    <span class="keywordtype">int</span> n = suggestions-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/size.html">size</a>(), Top = 0;</div>
-<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>    Top = n &lt; 3 ? n : 3;</div>
-<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>    <span class="keywordflow">while</span> (Top--) {</div>
-<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; suggestions-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/top.html">top</a>().second &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>        suggestions-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/pop.html">pop</a>();</div>
-<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span>    }</div>
-<div class="line"><a id="l00326" name="l00326"></a><span class="lineno">  326</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  318</span>                                                              {</div>
+<div class="line"><span class="lineno">  319</span>    <span class="comment">// Display Either top 3 or total number of suggestions, whichever is smaller</span></div>
+<div class="line"><span class="lineno">  320</span>    <span class="keywordtype">int</span> n = suggestions-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/size.html">size</a>(), Top = 0;</div>
+<div class="line"><span class="lineno">  321</span>    Top = n &lt; 3 ? n : 3;</div>
+<div class="line"><span class="lineno">  322</span>    <span class="keywordflow">while</span> (Top--) {</div>
+<div class="line"><span class="lineno">  323</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; suggestions-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/top.html">top</a>().second &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  324</span>        suggestions-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/pop.html">pop</a>();</div>
+<div class="line"><span class="lineno">  325</span>    }</div>
+<div class="line"><span class="lineno">  326</span>}</div>
 <div class="ttc" id="apop_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/priority_queue/pop.html">std::priority_queue::pop</a></div><div class="ttdeci">T pop(T... args)</div></div>
 <div class="ttc" id="atop_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/priority_queue/top.html">std::priority_queue::top</a></div><div class="ttdeci">T top(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -797,22 +803,22 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>                                                                        {</div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>    <span class="comment">// Iterate through all 26 nodes as we have to print all strings with the</span></div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>    <span class="comment">// given prefix</span></div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>    <span class="keywordtype">int</span> i = 0;</div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>    <span class="keywordflow">for</span> (i = 0; i &lt; ENGLISH_ALPHABET_SIZE; i++) {</div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>        <span class="keywordflow">if</span> (new_root-&gt;english[i] != <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>            <span class="comment">// Print the sugestion only if it&#39;s a valid complete entry and not</span></div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>            <span class="comment">// just a prefix</span></div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>            <span class="keywordflow">if</span> (new_root-&gt;english[i]-&gt;endOfWord) {</div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; prefix + char(i + 97) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>            }</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span> </div>
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+<div class="line"><span class="lineno">  351</span>                                    suggestions);</div>
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diff --git a/d0/d65/namespacedouble__hashing.html b/d0/d65/namespacedouble__hashing.html
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    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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@@ -186,16 +186,16 @@ bool&#160;</td><td class="memItemRight" valign="bottom"><b>rehashing</b></td></t
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-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>    <span class="comment">// auto* entry = new Entry();</span></div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>    <span class="comment">// entry-&gt;key = key;</span></div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>    <span class="keywordtype">int</span> index = <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a8f8ff4fb018e1bb32d67d8a1885d3200">doubleHash</a>(key, <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>    table[index].key = key;</div>
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-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>    <span class="keywordflow">if</span> (++size / <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(totalSize) &gt;= 0.5) {</div>
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+<div class="fragment"><div class="line"><span class="lineno">  185</span>                  {</div>
+<div class="line"><span class="lineno">  186</span>    <span class="comment">// auto* entry = new Entry();</span></div>
+<div class="line"><span class="lineno">  187</span>    <span class="comment">// entry-&gt;key = key;</span></div>
+<div class="line"><span class="lineno">  188</span>    <span class="keywordtype">int</span> index = <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a8f8ff4fb018e1bb32d67d8a1885d3200">doubleHash</a>(key, <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  189</span>    table[index].key = key;</div>
+<div class="line"><span class="lineno">  190</span>    <span class="comment">// Load factor greater than 0.5 causes resizing</span></div>
+<div class="line"><span class="lineno">  191</span>    <span class="keywordflow">if</span> (++size / <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(totalSize) &gt;= 0.5) {</div>
+<div class="line"><span class="lineno">  192</span>        <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#af4981819aae8bc7e7beeaef02615e30d">rehash</a>();</div>
+<div class="line"><span class="lineno">  193</span>    }</div>
+<div class="line"><span class="lineno">  194</span>}</div>
 <div class="ttc" id="anamespacedouble__hashing_html_a8f8ff4fb018e1bb32d67d8a1885d3200"><div class="ttname"><a href="../../d0/d65/namespacedouble__hashing.html#a8f8ff4fb018e1bb32d67d8a1885d3200">double_hashing::doubleHash</a></div><div class="ttdeci">int doubleHash(int key, bool searching)</div><div class="ttdoc">Performs double hashing to resolve collisions.</div><div class="ttdef"><b>Definition:</b> double_hash_hash_table.cpp:71</div></div>
 <div class="ttc" id="anamespacedouble__hashing_html_af4981819aae8bc7e7beeaef02615e30d"><div class="ttname"><a href="../../d0/d65/namespacedouble__hashing.html#af4981819aae8bc7e7beeaef02615e30d">double_hashing::rehash</a></div><div class="ttdeci">void rehash()</div><div class="ttdef"><b>Definition:</b> double_hash_hash_table.cpp:161</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -228,17 +228,17 @@ Here is the call graph for this function:</div>
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   </dd>
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-<div class="fragment"><div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>                      {</div>
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-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>              &lt;&lt; totalSize &lt;&lt; <span class="stringliteral">&quot; == &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a0d90726ed1de7b3d2ae261baed048003">hashFxn</a>(key) % totalSize;</div>
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-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  212</span>                      {</div>
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+<div class="line"><span class="lineno">  214</span>    <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a1e901418c759627557eff359b8db38cd">display</a>();</div>
+<div class="line"><span class="lineno">  215</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  216</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;hash of &quot;</span> &lt;&lt; key &lt;&lt; <span class="stringliteral">&quot; is &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a0d90726ed1de7b3d2ae261baed048003">hashFxn</a>(key) &lt;&lt; <span class="stringliteral">&quot; % &quot;</span></div>
+<div class="line"><span class="lineno">  217</span>              &lt;&lt; totalSize &lt;&lt; <span class="stringliteral">&quot; == &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a0d90726ed1de7b3d2ae261baed048003">hashFxn</a>(key) % totalSize;</div>
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 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
 <div class="ttc" id="anamespacedouble__hashing_html_a0d90726ed1de7b3d2ae261baed048003"><div class="ttname"><a href="../../d0/d65/namespacedouble__hashing.html#a0d90726ed1de7b3d2ae261baed048003">double_hashing::hashFxn</a></div><div class="ttdeci">size_t hashFxn(int key)</div><div class="ttdoc">Hash a key. Uses the STL library's std::hash() function.</div><div class="ttdef"><b>Definition:</b> double_hash_hash_table.cpp:47</div></div>
@@ -268,20 +268,20 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Displays the table </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
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 <dl class="section return"><dt>Returns</dt><dd>Index of key when found </dd>
 <dd>
 new hash if no conflicts present </dd></dl>
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-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>            }</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>            <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a29f543e2626bad58907661e1e45028a6">searchingProber</a>(entry, key)) {</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Found key!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>                <span class="keywordflow">return</span> index;</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>            }</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Found tombstone or equal hash, checking next&quot;</span></div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>                      &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>            i++;</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>            <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#ac2adfce49ac57f6dbd1778d2c1ce0d2b">putProber</a>(entry, key)) {</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>                <span class="keywordflow">if</span> (!rehashing) {</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Spot found!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>                }</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>                <span class="keywordflow">return</span> index;</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>            }</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>            <span class="keywordflow">if</span> (!rehashing) {</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Spot taken, looking at next (next index:&quot;</span></div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>                          &lt;&lt; <span class="stringliteral">&quot; &quot;</span></div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>                          &lt;&lt; <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(<a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hash</a> + (i * <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a33968a1178289ab61445dd4000df7082">otherHashFxn</a>(key))) %</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>                                 totalSize</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>                          &lt;&lt; <span class="stringliteral">&quot;)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>            }</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>            i++;</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>        }</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>        <span class="keywordflow">if</span> (i == totalSize * 100) {</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;DoubleHash probe failed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>            <span class="keywordflow">return</span> notPresent;</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>        }</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    } <span class="keywordflow">while</span> (entry.<a class="code hl_variable" href="../../d9/dde/structdouble__hashing_1_1_entry.html#ae114967c89dbba3b754dc4976bba3248">key</a> != notPresent);</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <span class="keywordflow">return</span> notPresent;</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   71</span>                                        {</div>
+<div class="line"><span class="lineno">   72</span>    <span class="keywordtype">int</span> hash = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(<a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a0d90726ed1de7b3d2ae261baed048003">hashFxn</a>(key));</div>
+<div class="line"><span class="lineno">   73</span>    <span class="keywordtype">int</span> i = 0;</div>
+<div class="line"><span class="lineno">   74</span>    <a class="code hl_struct" href="../../d9/dde/structdouble__hashing_1_1_entry.html">Entry</a> entry;</div>
+<div class="line"><span class="lineno">   75</span>    <span class="keywordflow">do</span> {</div>
+<div class="line"><span class="lineno">   76</span>        <span class="keywordtype">int</span> index =</div>
+<div class="line"><span class="lineno">   77</span>            <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(hash + (i * <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a33968a1178289ab61445dd4000df7082">otherHashFxn</a>(key))) % totalSize;</div>
+<div class="line"><span class="lineno">   78</span>        entry = table[index];</div>
+<div class="line"><span class="lineno">   79</span>        <span class="keywordflow">if</span> (searching) {</div>
+<div class="line"><span class="lineno">   80</span>            <span class="keywordflow">if</span> (entry.<a class="code hl_variable" href="../../d9/dde/structdouble__hashing_1_1_entry.html#ae114967c89dbba3b754dc4976bba3248">key</a> == notPresent) {</div>
+<div class="line"><span class="lineno">   81</span>                <span class="keywordflow">return</span> notPresent;</div>
+<div class="line"><span class="lineno">   82</span>            }</div>
+<div class="line"><span class="lineno">   83</span>            <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a29f543e2626bad58907661e1e45028a6">searchingProber</a>(entry, key)) {</div>
+<div class="line"><span class="lineno">   84</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Found key!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   85</span>                <span class="keywordflow">return</span> index;</div>
+<div class="line"><span class="lineno">   86</span>            }</div>
+<div class="line"><span class="lineno">   87</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Found tombstone or equal hash, checking next&quot;</span></div>
+<div class="line"><span class="lineno">   88</span>                      &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   89</span>            i++;</div>
+<div class="line"><span class="lineno">   90</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   91</span>            <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#ac2adfce49ac57f6dbd1778d2c1ce0d2b">putProber</a>(entry, key)) {</div>
+<div class="line"><span class="lineno">   92</span>                <span class="keywordflow">if</span> (!rehashing) {</div>
+<div class="line"><span class="lineno">   93</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Spot found!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   94</span>                }</div>
+<div class="line"><span class="lineno">   95</span>                <span class="keywordflow">return</span> index;</div>
+<div class="line"><span class="lineno">   96</span>            }</div>
+<div class="line"><span class="lineno">   97</span>            <span class="keywordflow">if</span> (!rehashing) {</div>
+<div class="line"><span class="lineno">   98</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Spot taken, looking at next (next index:&quot;</span></div>
+<div class="line"><span class="lineno">   99</span>                          &lt;&lt; <span class="stringliteral">&quot; &quot;</span></div>
+<div class="line"><span class="lineno">  100</span>                          &lt;&lt; <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(<a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hash</a> + (i * <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a33968a1178289ab61445dd4000df7082">otherHashFxn</a>(key))) %</div>
+<div class="line"><span class="lineno">  101</span>                                 totalSize</div>
+<div class="line"><span class="lineno">  102</span>                          &lt;&lt; <span class="stringliteral">&quot;)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  103</span>            }</div>
+<div class="line"><span class="lineno">  104</span>            i++;</div>
+<div class="line"><span class="lineno">  105</span>        }</div>
+<div class="line"><span class="lineno">  106</span>        <span class="keywordflow">if</span> (i == totalSize * 100) {</div>
+<div class="line"><span class="lineno">  107</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;DoubleHash probe failed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  108</span>            <span class="keywordflow">return</span> notPresent;</div>
+<div class="line"><span class="lineno">  109</span>        }</div>
+<div class="line"><span class="lineno">  110</span>    } <span class="keywordflow">while</span> (entry.<a class="code hl_variable" href="../../d9/dde/structdouble__hashing_1_1_entry.html#ae114967c89dbba3b754dc4976bba3248">key</a> != notPresent);</div>
+<div class="line"><span class="lineno">  111</span>    <span class="keywordflow">return</span> notPresent;</div>
+<div class="line"><span class="lineno">  112</span>}</div>
 <div class="ttc" id="amd5_8cpp_html_a88705fab5f92adf3427b4cf76ff33edb"><div class="ttname"><a href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hashing::md5::hash</a></div><div class="ttdeci">void * hash(const std::string &amp;message)</div><div class="ttdoc">Converts the string to bytestring and calls the main algorithm.</div><div class="ttdef"><b>Definition:</b> md5.cpp:287</div></div>
 <div class="ttc" id="anamespacedouble__hashing_html_a29f543e2626bad58907661e1e45028a6"><div class="ttname"><a href="../../d0/d65/namespacedouble__hashing.html#a29f543e2626bad58907661e1e45028a6">double_hashing::searchingProber</a></div><div class="ttdeci">bool searchingProber(const Entry &amp;entry, int key)</div><div class="ttdef"><b>Definition:</b> double_hash_hash_table.cpp:133</div></div>
 <div class="ttc" id="anamespacedouble__hashing_html_a33968a1178289ab61445dd4000df7082"><div class="ttname"><a href="../../d0/d65/namespacedouble__hashing.html#a33968a1178289ab61445dd4000df7082">double_hashing::otherHashFxn</a></div><div class="ttdeci">size_t otherHashFxn(int key)</div><div class="ttdoc">Used for second hash function.</div><div class="ttdef"><b>Definition:</b> double_hash_hash_table.cpp:58</div></div>
@@ -409,10 +409,10 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>hash value of the key </dd></dl>
-<div class="fragment"><div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>                        {</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/hash.html">std::hash&lt;int&gt;</a> hash;</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    <span class="keywordflow">return</span> hash(key);</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   47</span>                        {</div>
+<div class="line"><span class="lineno">   48</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/hash.html">std::hash&lt;int&gt;</a> hash;</div>
+<div class="line"><span class="lineno">   49</span>    <span class="keywordflow">return</span> hash(key);</div>
+<div class="line"><span class="lineno">   50</span>}</div>
 <div class="ttc" id="ahash_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/hash.html">std::hash</a></div></div>
 </div><!-- fragment -->
 </div>
@@ -441,10 +441,10 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>hash value of the key </dd></dl>
-<div class="fragment"><div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>                             {</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/hash.html">std::hash&lt;int&gt;</a> hash;</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <span class="keywordflow">return</span> 1 + (7 - (hash(key) % 7));</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   58</span>                             {</div>
+<div class="line"><span class="lineno">   59</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/hash.html">std::hash&lt;int&gt;</a> hash;</div>
+<div class="line"><span class="lineno">   60</span>    <span class="keywordflow">return</span> 1 + (7 - (hash(key) % 7));</div>
+<div class="line"><span class="lineno">   61</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -483,12 +483,12 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if key is not present or is a <code>toumb</code> </dd>
 <dd>
 <code>false</code> is already occupied </dd></dl>
-<div class="fragment"><div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>                                            {</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    <span class="keywordflow">if</span> (entry.<a class="code hl_variable" href="../../d9/dde/structdouble__hashing_1_1_entry.html#ae114967c89dbba3b754dc4976bba3248">key</a> == notPresent || entry.<a class="code hl_variable" href="../../d9/dde/structdouble__hashing_1_1_entry.html#ae114967c89dbba3b754dc4976bba3248">key</a> == tomb) {</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    }</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  120</span>                                            {</div>
+<div class="line"><span class="lineno">  121</span>    <span class="keywordflow">if</span> (entry.<a class="code hl_variable" href="../../d9/dde/structdouble__hashing_1_1_entry.html#ae114967c89dbba3b754dc4976bba3248">key</a> == notPresent || entry.<a class="code hl_variable" href="../../d9/dde/structdouble__hashing_1_1_entry.html#ae114967c89dbba3b754dc4976bba3248">key</a> == tomb) {</div>
+<div class="line"><span class="lineno">  122</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  123</span>    }</div>
+<div class="line"><span class="lineno">  124</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  125</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -507,26 +507,26 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Rehashes the table into a bigger table </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
-<div class="fragment"><div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>              {</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>    <span class="comment">// Necessary so wall of add info isn&#39;t printed all at once</span></div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>    rehashing = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>    <span class="keywordtype">int</span> oldSize = totalSize;</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Entry&gt;</a> oldTable(table);</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    <span class="comment">// Really this should use the next prime number greater than totalSize * 2</span></div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>    table = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Entry&gt;</a>(totalSize * 2);</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    totalSize *= 2;</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; oldSize; i++) {</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>        <span class="keywordflow">if</span> (oldTable[i].key != -1 &amp;&amp; oldTable[i].key != notPresent) {</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>            size--;  <span class="comment">// Size stays the same (add increments size)</span></div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>            <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a79a9c914a6c68275b3640303d7faad8a">add</a>(oldTable[i].key);</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>        }</div>
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-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>    <span class="comment">// delete[] oldTable;</span></div>
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-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  161</span>              {</div>
+<div class="line"><span class="lineno">  162</span>    <span class="comment">// Necessary so wall of add info isn&#39;t printed all at once</span></div>
+<div class="line"><span class="lineno">  163</span>    rehashing = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  164</span>    <span class="keywordtype">int</span> oldSize = totalSize;</div>
+<div class="line"><span class="lineno">  165</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Entry&gt;</a> oldTable(table);</div>
+<div class="line"><span class="lineno">  166</span>    <span class="comment">// Really this should use the next prime number greater than totalSize * 2</span></div>
+<div class="line"><span class="lineno">  167</span>    table = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Entry&gt;</a>(totalSize * 2);</div>
+<div class="line"><span class="lineno">  168</span>    totalSize *= 2;</div>
+<div class="line"><span class="lineno">  169</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; oldSize; i++) {</div>
+<div class="line"><span class="lineno">  170</span>        <span class="keywordflow">if</span> (oldTable[i].key != -1 &amp;&amp; oldTable[i].key != notPresent) {</div>
+<div class="line"><span class="lineno">  171</span>            size--;  <span class="comment">// Size stays the same (add increments size)</span></div>
+<div class="line"><span class="lineno">  172</span>            <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a79a9c914a6c68275b3640303d7faad8a">add</a>(oldTable[i].key);</div>
+<div class="line"><span class="lineno">  173</span>        }</div>
+<div class="line"><span class="lineno">  174</span>    }</div>
+<div class="line"><span class="lineno">  175</span>    <span class="comment">// delete[] oldTable;</span></div>
+<div class="line"><span class="lineno">  176</span>    <span class="comment">// oldTable.reset();</span></div>
+<div class="line"><span class="lineno">  177</span> </div>
+<div class="line"><span class="lineno">  178</span>    rehashing = <span class="keyword">false</span>;</div>
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-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;hash of &quot;</span> &lt;&lt; key &lt;&lt; <span class="stringliteral">&quot; is &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a0d90726ed1de7b3d2ae261baed048003">hashFxn</a>(key) &lt;&lt; <span class="stringliteral">&quot; % &quot;</span></div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>              &lt;&lt; totalSize &lt;&lt; <span class="stringliteral">&quot; == &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a0d90726ed1de7b3d2ae261baed048003">hashFxn</a>(key) % totalSize;</div>
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-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  227</span>                          {</div>
+<div class="line"><span class="lineno">  228</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initial table: &quot;</span>;</div>
+<div class="line"><span class="lineno">  229</span>    <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a1e901418c759627557eff359b8db38cd">display</a>();</div>
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+<div class="line"><span class="lineno">  231</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;hash of &quot;</span> &lt;&lt; key &lt;&lt; <span class="stringliteral">&quot; is &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a0d90726ed1de7b3d2ae261baed048003">hashFxn</a>(key) &lt;&lt; <span class="stringliteral">&quot; % &quot;</span></div>
+<div class="line"><span class="lineno">  232</span>              &lt;&lt; totalSize &lt;&lt; <span class="stringliteral">&quot; == &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a0d90726ed1de7b3d2ae261baed048003">hashFxn</a>(key) % totalSize;</div>
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+<div class="line"><span class="lineno">  234</span>    <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a28083ecac6eb94b643281875c8665931">remove</a>(key);</div>
+<div class="line"><span class="lineno">  235</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;New table: &quot;</span>;</div>
+<div class="line"><span class="lineno">  236</span>    <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a1e901418c759627557eff359b8db38cd">display</a>();</div>
+<div class="line"><span class="lineno">  237</span>}</div>
 <div class="ttc" id="anamespacedouble__hashing_html_a28083ecac6eb94b643281875c8665931"><div class="ttname"><a href="../../d0/d65/namespacedouble__hashing.html#a28083ecac6eb94b643281875c8665931">double_hashing::remove</a></div><div class="ttdeci">void remove(int key)</div><div class="ttdef"><b>Definition:</b> double_hash_hash_table.cpp:199</div></div>
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 Here is the call graph for this function:</div>
@@ -600,15 +600,15 @@ Here is the call graph for this function:</div>
   </table>
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-<div class="fragment"><div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>                     {</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    <span class="keywordtype">int</span> index = <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a8f8ff4fb018e1bb32d67d8a1885d3200">doubleHash</a>(key, <span class="keyword">true</span>);</div>
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-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;key not found&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>    table[index].key = tomb;</div>
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-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  199</span>                     {</div>
+<div class="line"><span class="lineno">  200</span>    <span class="keywordtype">int</span> index = <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a8f8ff4fb018e1bb32d67d8a1885d3200">doubleHash</a>(key, <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  201</span>    <span class="keywordflow">if</span> (index == notPresent) {</div>
+<div class="line"><span class="lineno">  202</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;key not found&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  203</span>    }</div>
+<div class="line"><span class="lineno">  204</span>    table[index].key = tomb;</div>
+<div class="line"><span class="lineno">  205</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Removal successful, leaving tombstone&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  206</span>    size--;</div>
+<div class="line"><span class="lineno">  207</span>}</div>
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 Here is the call graph for this function:</div>
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 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if found </dd>
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-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  133</span>                                                  {</div>
+<div class="line"><span class="lineno">  134</span>    <span class="keywordflow">if</span> (entry.<a class="code hl_variable" href="../../d9/dde/structdouble__hashing_1_1_entry.html#ae114967c89dbba3b754dc4976bba3248">key</a> == key) {</div>
+<div class="line"><span class="lineno">  135</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  136</span>    }</div>
+<div class="line"><span class="lineno">  137</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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 <p >Function that returns the longest palindromic subsequence of a string </p>
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-<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> b = a;</div>
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-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>    <span class="comment">// Finding the length of the longest</span></div>
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-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    assert(<a class="code hl_function" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#a6f73ddd8cd83d784036f131dfc6540c4">lps</a>(<span class="stringliteral">&quot;radar&quot;</span>) == <span class="stringliteral">&quot;radar&quot;</span>);</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    <span class="comment">// lps(&quot;abbcbaa&quot;) return &quot;abcba&quot;</span></div>
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-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    <span class="comment">// lps(&quot;bbbab&quot;) return &quot;bbbb&quot;</span></div>
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-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   75</span>            {</div>
+<div class="line"><span class="lineno">   76</span>    <span class="comment">// lps(&quot;radar&quot;) return &quot;radar&quot;</span></div>
+<div class="line"><span class="lineno">   77</span>    assert(<a class="code hl_function" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#a6f73ddd8cd83d784036f131dfc6540c4">lps</a>(<span class="stringliteral">&quot;radar&quot;</span>) == <span class="stringliteral">&quot;radar&quot;</span>);</div>
+<div class="line"><span class="lineno">   78</span>    <span class="comment">// lps(&quot;abbcbaa&quot;) return &quot;abcba&quot;</span></div>
+<div class="line"><span class="lineno">   79</span>    assert(<a class="code hl_function" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#a6f73ddd8cd83d784036f131dfc6540c4">lps</a>(<span class="stringliteral">&quot;abbcbaa&quot;</span>) == <span class="stringliteral">&quot;abcba&quot;</span>);</div>
+<div class="line"><span class="lineno">   80</span>    <span class="comment">// lps(&quot;bbbab&quot;) return &quot;bbbb&quot;</span></div>
+<div class="line"><span class="lineno">   81</span>    assert(<a class="code hl_function" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#a6f73ddd8cd83d784036f131dfc6540c4">lps</a>(<span class="stringliteral">&quot;bbbab&quot;</span>) == <span class="stringliteral">&quot;bbbb&quot;</span>);</div>
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@@ -144,18 +144,18 @@ list of positive divisors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.</p>
       </table>
 </div><div class="memdoc">
 <p >Main function </p>
-<div class="fragment"><div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>           {</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    <span class="keywordtype">int</span> n;</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    <span class="keywordflow">if</span> (n == 0) {</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All non-zero numbers are divisors of 0 !&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Number of positive divisors is : &quot;</span>;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(n) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    }</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   81</span>           {</div>
+<div class="line"><span class="lineno">   82</span>    <a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
+<div class="line"><span class="lineno">   83</span>    <span class="keywordtype">int</span> n;</div>
+<div class="line"><span class="lineno">   84</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
+<div class="line"><span class="lineno">   85</span>    <span class="keywordflow">if</span> (n == 0) {</div>
+<div class="line"><span class="lineno">   86</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All non-zero numbers are divisors of 0 !&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   87</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   88</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Number of positive divisors is : &quot;</span>;</div>
+<div class="line"><span class="lineno">   89</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(n) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   90</span>    }</div>
+<div class="line"><span class="lineno">   91</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">   92</span>}</div>
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@@ -192,39 +192,39 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>number of positive divisors of n (or 1 if n = 0) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>                                       {</div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>    <span class="keywordflow">if</span> (n &lt; 0) {</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>        n = -n; <span class="comment">// take the absolute value of n</span></div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>    }</div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span> </div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    <span class="keywordtype">int</span> number_of_divisors = 1;</div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span> </div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 2; i * i &lt;= n; i++) {</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>        <span class="comment">// This part is doing the prime factorization.</span></div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>        <span class="comment">// Note that we cannot find a composite divisor of n unless we would</span></div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>        <span class="comment">// already previously find the corresponding prime divisor and dvided</span></div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>        <span class="comment">// n by that prime. Therefore, all the divisors found here will</span></div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>        <span class="comment">// actually be primes.</span></div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>        <span class="comment">// The loop terminates early when it is left with a number n which</span></div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>        <span class="comment">// does not have a divisor smaller or equal to sqrt(n) - that means</span></div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>        <span class="comment">// the remaining number is a prime itself.</span></div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        <span class="keywordtype">int</span> prime_exponent = 0;</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>        <span class="keywordflow">while</span> (n % i == 0) {</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>            <span class="comment">// Repeatedly divide n by the prime divisor n to compute</span></div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>            <span class="comment">// the exponent (e_i in the algorithm description).</span></div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>            prime_exponent++;</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>            n /= i;</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>        }</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>        number_of_divisors *= prime_exponent + 1;</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    }</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <span class="keywordflow">if</span> (n &gt; 1) {</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>        <span class="comment">// In case the remaining number n is a prime number itself</span></div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        <span class="comment">// (essentially p_k^1) the final answer is also multiplied by (e_k+1).</span></div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        number_of_divisors *= 2;</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>    }</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span> </div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    <span class="keywordflow">return</span> number_of_divisors;</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   33</span>                                       {</div>
+<div class="line"><span class="lineno">   34</span>    <span class="keywordflow">if</span> (n &lt; 0) {</div>
+<div class="line"><span class="lineno">   35</span>        n = -n; <span class="comment">// take the absolute value of n</span></div>
+<div class="line"><span class="lineno">   36</span>    }</div>
+<div class="line"><span class="lineno">   37</span> </div>
+<div class="line"><span class="lineno">   38</span>    <span class="keywordtype">int</span> number_of_divisors = 1;</div>
+<div class="line"><span class="lineno">   39</span> </div>
+<div class="line"><span class="lineno">   40</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 2; i * i &lt;= n; i++) {</div>
+<div class="line"><span class="lineno">   41</span>        <span class="comment">// This part is doing the prime factorization.</span></div>
+<div class="line"><span class="lineno">   42</span>        <span class="comment">// Note that we cannot find a composite divisor of n unless we would</span></div>
+<div class="line"><span class="lineno">   43</span>        <span class="comment">// already previously find the corresponding prime divisor and dvided</span></div>
+<div class="line"><span class="lineno">   44</span>        <span class="comment">// n by that prime. Therefore, all the divisors found here will</span></div>
+<div class="line"><span class="lineno">   45</span>        <span class="comment">// actually be primes.</span></div>
+<div class="line"><span class="lineno">   46</span>        <span class="comment">// The loop terminates early when it is left with a number n which</span></div>
+<div class="line"><span class="lineno">   47</span>        <span class="comment">// does not have a divisor smaller or equal to sqrt(n) - that means</span></div>
+<div class="line"><span class="lineno">   48</span>        <span class="comment">// the remaining number is a prime itself.</span></div>
+<div class="line"><span class="lineno">   49</span>        <span class="keywordtype">int</span> prime_exponent = 0;</div>
+<div class="line"><span class="lineno">   50</span>        <span class="keywordflow">while</span> (n % i == 0) {</div>
+<div class="line"><span class="lineno">   51</span>            <span class="comment">// Repeatedly divide n by the prime divisor n to compute</span></div>
+<div class="line"><span class="lineno">   52</span>            <span class="comment">// the exponent (e_i in the algorithm description).</span></div>
+<div class="line"><span class="lineno">   53</span>            prime_exponent++;</div>
+<div class="line"><span class="lineno">   54</span>            n /= i;</div>
+<div class="line"><span class="lineno">   55</span>        }</div>
+<div class="line"><span class="lineno">   56</span>        number_of_divisors *= prime_exponent + 1;</div>
+<div class="line"><span class="lineno">   57</span>    }</div>
+<div class="line"><span class="lineno">   58</span>    <span class="keywordflow">if</span> (n &gt; 1) {</div>
+<div class="line"><span class="lineno">   59</span>        <span class="comment">// In case the remaining number n is a prime number itself</span></div>
+<div class="line"><span class="lineno">   60</span>        <span class="comment">// (essentially p_k^1) the final answer is also multiplied by (e_k+1).</span></div>
+<div class="line"><span class="lineno">   61</span>        number_of_divisors *= 2;</div>
+<div class="line"><span class="lineno">   62</span>    }</div>
+<div class="line"><span class="lineno">   63</span> </div>
+<div class="line"><span class="lineno">   64</span>    <span class="keywordflow">return</span> number_of_divisors;</div>
+<div class="line"><span class="lineno">   65</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -243,13 +243,13 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Test implementations </p>
-<div class="fragment"><div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>             {</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(36) == 9);</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(-36) == 9);</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(1) == 1);</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(2011) == 2); <span class="comment">// 2011 is a prime</span></div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(756) == 24); <span class="comment">// 756 = 2^2 * 3^3 * 7</span></div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   70</span>             {</div>
+<div class="line"><span class="lineno">   71</span>    assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(36) == 9);</div>
+<div class="line"><span class="lineno">   72</span>    assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(-36) == 9);</div>
+<div class="line"><span class="lineno">   73</span>    assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(1) == 1);</div>
+<div class="line"><span class="lineno">   74</span>    assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(2011) == 2); <span class="comment">// 2011 is a prime</span></div>
+<div class="line"><span class="lineno">   75</span>    assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(756) == 24); <span class="comment">// 756 = 2^2 * 3^3 * 7</span></div>
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@@ -130,74 +130,74 @@ Functions</h2></td></tr>
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 <p >Main function </p>
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-<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span> </div>
-<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Matrix size: &quot;</span>;</div>
-<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>;</div>
-<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span> </div>
-<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span>    <span class="comment">// create a 2D matrix by dynamic memory allocation</span></div>
-<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span>    <span class="keywordtype">double</span> **mat = <span class="keyword">new</span> <span class="keywordtype">double</span> *[<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1], **x = <span class="keyword">new</span> <span class="keywordtype">double</span> *[<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>];</div>
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-<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span>            x[i] = <span class="keyword">new</span> <span class="keywordtype">double</span>[<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1];</div>
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-<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span> </div>
-<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>    <span class="comment">// get the matrix elements from user</span></div>
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-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; sol[i][j] &lt;&lt; <span class="stringliteral">&quot;  &quot;</span>;</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>            }</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        }</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    }</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   88</span>           {</div>
+<div class="line"><span class="lineno">   89</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> n = 8;</div>
+<div class="line"><span class="lineno">   90</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;int, n&gt;</a>, n&gt; sol = {0};</div>
+<div class="line"><span class="lineno">   91</span> </div>
+<div class="line"><span class="lineno">   92</span>    <span class="keywordtype">int</span> i = 0, j = 0;</div>
+<div class="line"><span class="lineno">   93</span>    <span class="keywordflow">for</span> (i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">   94</span>        <span class="keywordflow">for</span> (j = 0; j &lt; n; j++) {</div>
+<div class="line"><span class="lineno">   95</span>            sol[i][j] = -1;</div>
+<div class="line"><span class="lineno">   96</span>        }</div>
+<div class="line"><span class="lineno">   97</span>    }</div>
+<div class="line"><span class="lineno">   98</span> </div>
+<div class="line"><span class="lineno">   99</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n&gt;</a> xmov = {2, 1, -1, -2, -2, -1, 1, 2};</div>
+<div class="line"><span class="lineno">  100</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n&gt;</a> ymov = {1, 2, 2, 1, -1, -2, -2, -1};</div>
+<div class="line"><span class="lineno">  101</span> </div>
+<div class="line"><span class="lineno">  102</span>    sol[0][0] = 0;</div>
+<div class="line"><span class="lineno">  103</span> </div>
+<div class="line"><span class="lineno">  104</span>    <span class="keywordtype">bool</span> flag = backtracking::knight_tour::solve&lt;n&gt;(0, 0, 1, sol, xmov, ymov);</div>
+<div class="line"><span class="lineno">  105</span>    <span class="keywordflow">if</span> (flag == <span class="keyword">false</span>) {</div>
+<div class="line"><span class="lineno">  106</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Error: Solution does not exist\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  107</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  108</span>        <span class="keywordflow">for</span> (i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">  109</span>            <span class="keywordflow">for</span> (j = 0; j &lt; n; j++) {</div>
+<div class="line"><span class="lineno">  110</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; sol[i][j] &lt;&lt; <span class="stringliteral">&quot;  &quot;</span>;</div>
+<div class="line"><span class="lineno">  111</span>            }</div>
+<div class="line"><span class="lineno">  112</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  113</span>        }</div>
+<div class="line"><span class="lineno">  114</span>    }</div>
+<div class="line"><span class="lineno">  115</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  116</span>}</div>
 <div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 </div><!-- fragment -->
@@ -321,29 +321,29 @@ template&lt;size_t V&gt; </div>
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if solution exists </dd>
 <dd>
 <code>false</code> if solution does not exist </dd></dl>
-<div class="fragment"><div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>                                                                 {</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> = 0, xnext = 0, ynext = 0;</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span> </div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    <span class="keywordflow">if</span> (<a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a> == V * V) {</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    }</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span> </div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <span class="keywordflow">for</span> (k = 0; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt; V; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        xnext = x + xmov[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>];</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        ynext = y + ymov[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>];</div>
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-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        <span class="keywordflow">if</span> (issafe&lt;V&gt;(xnext, ynext, sol)) {</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>            sol[xnext][ynext] = <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a>;</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span> </div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>            <span class="keywordflow">if</span> (solve&lt;V&gt;(xnext, ynext, <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a> + 1, sol, xmov, ymov) == <span class="keyword">true</span>) {</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>                sol[xnext][ynext] = -1;</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>            }</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>        }</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    }</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   58</span>                                                                 {</div>
+<div class="line"><span class="lineno">   59</span>    <span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> = 0, xnext = 0, ynext = 0;</div>
+<div class="line"><span class="lineno">   60</span> </div>
+<div class="line"><span class="lineno">   61</span>    <span class="keywordflow">if</span> (<a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a> == V * V) {</div>
+<div class="line"><span class="lineno">   62</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   63</span>    }</div>
+<div class="line"><span class="lineno">   64</span> </div>
+<div class="line"><span class="lineno">   65</span>    <span class="keywordflow">for</span> (k = 0; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt; V; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
+<div class="line"><span class="lineno">   66</span>        xnext = x + xmov[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>];</div>
+<div class="line"><span class="lineno">   67</span>        ynext = y + ymov[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>];</div>
+<div class="line"><span class="lineno">   68</span> </div>
+<div class="line"><span class="lineno">   69</span>        <span class="keywordflow">if</span> (issafe&lt;V&gt;(xnext, ynext, sol)) {</div>
+<div class="line"><span class="lineno">   70</span>            sol[xnext][ynext] = <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a>;</div>
+<div class="line"><span class="lineno">   71</span> </div>
+<div class="line"><span class="lineno">   72</span>            <span class="keywordflow">if</span> (solve&lt;V&gt;(xnext, ynext, <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a> + 1, sol, xmov, ymov) == <span class="keyword">true</span>) {</div>
+<div class="line"><span class="lineno">   73</span>                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   74</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   75</span>                sol[xnext][ynext] = -1;</div>
+<div class="line"><span class="lineno">   76</span>            }</div>
+<div class="line"><span class="lineno">   77</span>        }</div>
+<div class="line"><span class="lineno">   78</span>    }</div>
+<div class="line"><span class="lineno">   79</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   80</span>}</div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
 <div class="ttc" id="atower__of__hanoi_8cpp_html_af4cfc41e546f1f8d25f01e0804e8b61d"><div class="ttname"><a href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a></div><div class="ttdeci">void mov(tower *From, tower *To)</div><div class="ttdef"><b>Definition:</b> tower_of_hanoi.cpp:39</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -361,7 +361,7 @@ Here is the call graph for this function:</div>
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+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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 <link href="../../tabs.css" rel="stylesheet" type="text/css"/>
@@ -30,8 +30,8 @@ MathJax.Hub.Config({
 <div id="titlearea">
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  <tbody>
- <tr style="height: 56px;">
-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
+  <td id="projectalign">
    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
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    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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-<!-- Generated by Doxygen 1.9.2 -->
+<!-- Generated by Doxygen 1.9.3 -->
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@@ -111,7 +111,7 @@ $(document).ready(function(){initNavTree('df/d34/classprobability_1_1windowed__m
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+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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diff --git a/d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html b/d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html
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@@ -30,8 +30,8 @@ MathJax.Hub.Config({
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- <tr style="height: 56px;">
-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
+  <td id="projectalign">
    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
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@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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+<!-- Generated by Doxygen 1.9.3 -->
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 var searchBox = new SearchBox("searchBox", "../../search",'Search','.html');
@@ -108,6 +108,12 @@ Inheritance diagram for range_queries::heavy_light_decomposition::Tree&lt; X &gt
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 </div>
 <center><span class="legend">[<a target="top" href="../../graph_legend.html">legend</a>]</span></center></div>
+<div class="dynheader">
+Collaboration diagram for range_queries::heavy_light_decomposition::Tree&lt; X &gt;:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/d4c/classrange__queries_1_1heavy__light__decomposition_1_1_tree__coll__graph.svg" width="626" height="248"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+<center><span class="legend">[<a target="top" href="../../graph_legend.html">legend</a>]</span></center></div>
 <table class="memberdecls">
 <tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
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@@ -210,7 +216,7 @@ template&lt;typename X &gt; </div>
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+          <td class="memname"><a class="el" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html">range_queries::heavy_light_decomposition::Tree</a>&lt; X &gt;::Tree </td>
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@@ -231,15 +237,16 @@ template&lt;typename X &gt; </div>
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-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    <span class="comment">/* Initialize and resize all the vectors */</span></div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa6c37e840355b9fb2105181c578694e8">t_root</a> = 0; <span class="comment">/* Default */</span></div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab1aeaefa1bd97b867c652ba916fbdb43">t_adj</a>.resize(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">t_nodes</a>);</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">t_par</a>.assign(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">t_nodes</a>, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab2ab020f798d00be2613ecf63074b7c1">t_maxlift</a>, -1));</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">t_depth</a>.assign(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">t_nodes</a>, 0);</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ada1494fccbc7f1f07b2f9be9f7e07ad5">t_size</a>.assign(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">t_nodes</a>, 1);</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>    <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a135b7952593c9b1aae38fcaf1cc1abf7">t_val</a>.resize(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">t_nodes</a>);</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>  }</div>
+<div class="fragment"><div class="line"><span class="lineno">  141</span>      : <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">t_nodes</a>(nodes), <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab2ab020f798d00be2613ecf63074b7c1">t_maxlift</a>(<span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/floor.html">floor</a>(log2(nodes))) + 1) {</div>
+<div class="line"><span class="lineno">  142</span>    <span class="comment">/* Initialize and resize all the vectors */</span></div>
+<div class="line"><span class="lineno">  143</span>    <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa6c37e840355b9fb2105181c578694e8">t_root</a> = 0; <span class="comment">/* Default */</span></div>
+<div class="line"><span class="lineno">  144</span>    <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab1aeaefa1bd97b867c652ba916fbdb43">t_adj</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/resize.html">resize</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">t_nodes</a>);</div>
+<div class="line"><span class="lineno">  145</span>    <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">t_par</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/assign.html">assign</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">t_nodes</a>, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab2ab020f798d00be2613ecf63074b7c1">t_maxlift</a>, -1));</div>
+<div class="line"><span class="lineno">  146</span>    <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">t_depth</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/assign.html">assign</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">t_nodes</a>, 0);</div>
+<div class="line"><span class="lineno">  147</span>    <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ada1494fccbc7f1f07b2f9be9f7e07ad5">t_size</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/assign.html">assign</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">t_nodes</a>, 1);</div>
+<div class="line"><span class="lineno">  148</span>    <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a135b7952593c9b1aae38fcaf1cc1abf7">t_val</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/resize.html">resize</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">t_nodes</a>);</div>
+<div class="line"><span class="lineno">  149</span>  }</div>
+<div class="ttc" id="aassign_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/assign.html">std::vector::assign</a></div><div class="ttdeci">T assign(T... args)</div></div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_a0efd0b9c564092f443ca97030d866ef1"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">range_queries::heavy_light_decomposition::Tree::t_depth</a></div><div class="ttdeci">std::vector&lt; int &gt; t_depth</div><div class="ttdoc">a vector to store the depth of a node,</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:88</div></div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_a135b7952593c9b1aae38fcaf1cc1abf7"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a135b7952593c9b1aae38fcaf1cc1abf7">range_queries::heavy_light_decomposition::Tree::t_val</a></div><div class="ttdeci">std::vector&lt; X &gt; t_val</div><div class="ttdoc">values of nodes</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:92</div></div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_a350157a5fb79f76fceae33fc84171203"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">range_queries::heavy_light_decomposition::Tree::t_par</a></div><div class="ttdeci">std::vector&lt; std::vector&lt; int &gt; &gt; t_par</div><div class="ttdoc">a matrix to store every node's 2^kth parent</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:87</div></div>
@@ -249,8 +256,15 @@ template&lt;typename X &gt; </div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_ada1494fccbc7f1f07b2f9be9f7e07ad5"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ada1494fccbc7f1f07b2f9be9f7e07ad5">range_queries::heavy_light_decomposition::Tree::t_size</a></div><div class="ttdeci">std::vector&lt; int &gt; t_size</div><div class="ttdoc">a vector to store the subtree size rooted at node</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:89</div></div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_ae4630fa70a80a1dc65a875488a67178a"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">range_queries::heavy_light_decomposition::Tree::t_nodes</a></div><div class="ttdeci">const int t_nodes</div><div class="ttdoc">number of nodes</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:84</div></div>
 <div class="ttc" id="afloor_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/floor.html">std::floor</a></div><div class="ttdeci">T floor(T... args)</div></div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
-</div><!-- fragment -->
+<div class="ttc" id="aresize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/resize.html">std::vector::resize</a></div><div class="ttdeci">T resize(T... args)</div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int &gt;</a></div></div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree_a835fb2bbb27307b8cacad9b287968bc1_cgraph.svg" width="336" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
 </div>
 </div>
 <h2 class="groupheader">Member Function Documentation</h2>
@@ -299,11 +313,18 @@ template&lt;typename X &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>                                          {</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab1aeaefa1bd97b867c652ba916fbdb43">t_adj</a>[u].push_back(v);</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>    <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab1aeaefa1bd97b867c652ba916fbdb43">t_adj</a>[v].push_back(u);</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>  }</div>
-</div><!-- fragment -->
+<div class="fragment"><div class="line"><span class="lineno">  157</span>                                          {</div>
+<div class="line"><span class="lineno">  158</span>    <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab1aeaefa1bd97b867c652ba916fbdb43">t_adj</a>[u].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(v);</div>
+<div class="line"><span class="lineno">  159</span>    <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab1aeaefa1bd97b867c652ba916fbdb43">t_adj</a>[v].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(u);</div>
+<div class="line"><span class="lineno">  160</span>  }</div>
+<div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree_a79ab4601c4a95c0902ac04e779e5f54d_cgraph.svg" width="360" height="67"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
 </div>
 </div>
 <a id="ab916d554afa8ca5230b4310c2c69fae0" name="ab916d554afa8ca5230b4310c2c69fae0"></a>
@@ -340,7 +361,7 @@ template&lt;typename X &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>{ <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa6c37e840355b9fb2105181c578694e8">t_root</a> = new_root; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  167</span>{ <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa6c37e840355b9fb2105181c578694e8">t_root</a> = new_root; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -389,23 +410,23 @@ template&lt;typename X &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>                                  {</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">t_par</a>[u][0] = p;</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    <span class="keywordflow">if</span> (p != -1) {</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>      <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">t_depth</a>[u] = 1 + <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">t_depth</a>[p];</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    }</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 1; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt; <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab2ab020f798d00be2613ecf63074b7c1">t_maxlift</a>; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>      <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">t_par</a>[u][k - 1] != -1) {</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>        <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">t_par</a>[u][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] = <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">t_par</a>[<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">t_par</a>[u][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> - 1]][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> - 1];</div>
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-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span> </div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> &amp;v : <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab1aeaefa1bd97b867c652ba916fbdb43">t_adj</a>[u]) {</div>
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-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    }</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>  }</div>
+<div class="fragment"><div class="line"><span class="lineno">  116</span>                                  {</div>
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+<div class="line"><span class="lineno">  118</span>    <span class="keywordflow">if</span> (p != -1) {</div>
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+<div class="line"><span class="lineno">  120</span>    }</div>
+<div class="line"><span class="lineno">  121</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 1; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt; <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab2ab020f798d00be2613ecf63074b7c1">t_maxlift</a>; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
+<div class="line"><span class="lineno">  122</span>      <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">t_par</a>[u][k - 1] != -1) {</div>
+<div class="line"><span class="lineno">  123</span>        <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">t_par</a>[u][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] = <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">t_par</a>[<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">t_par</a>[u][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> - 1]][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> - 1];</div>
+<div class="line"><span class="lineno">  124</span>      }</div>
+<div class="line"><span class="lineno">  125</span>    }</div>
+<div class="line"><span class="lineno">  126</span> </div>
+<div class="line"><span class="lineno">  127</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> &amp;v : <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab1aeaefa1bd97b867c652ba916fbdb43">t_adj</a>[u]) {</div>
+<div class="line"><span class="lineno">  128</span>      <span class="keywordflow">if</span> (v ^ p) {</div>
+<div class="line"><span class="lineno">  129</span>        <a class="code hl_function" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae8de7aefcb6635d3dacdd174cd4890c4">dfs_lca</a>(v, u);</div>
+<div class="line"><span class="lineno">  130</span>      }</div>
+<div class="line"><span class="lineno">  131</span>    }</div>
+<div class="line"><span class="lineno">  132</span>  }</div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_ae8de7aefcb6635d3dacdd174cd4890c4"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae8de7aefcb6635d3dacdd174cd4890c4">range_queries::heavy_light_decomposition::Tree::dfs_lca</a></div><div class="ttdeci">void dfs_lca(int u, int p=-1)</div><div class="ttdoc">Utility function to populate the t_par vector.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:116</div></div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -463,14 +484,14 @@ template&lt;typename X &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>                                   {</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> &amp;v : <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab1aeaefa1bd97b867c652ba916fbdb43">t_adj</a>[u]) {</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>      <span class="keywordflow">if</span> (v ^ p) {</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>        <a class="code hl_function" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa339c31ec74cd86a4842a8b09653d460">dfs_size</a>(v, u);</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>        <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ada1494fccbc7f1f07b2f9be9f7e07ad5">t_size</a>[u] += <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ada1494fccbc7f1f07b2f9be9f7e07ad5">t_size</a>[v];</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>      }</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    }</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>  }</div>
+<div class="fragment"><div class="line"><span class="lineno">  101</span>                                   {</div>
+<div class="line"><span class="lineno">  102</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> &amp;v : <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab1aeaefa1bd97b867c652ba916fbdb43">t_adj</a>[u]) {</div>
+<div class="line"><span class="lineno">  103</span>      <span class="keywordflow">if</span> (v ^ p) {</div>
+<div class="line"><span class="lineno">  104</span>        <a class="code hl_function" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa339c31ec74cd86a4842a8b09653d460">dfs_size</a>(v, u);</div>
+<div class="line"><span class="lineno">  105</span>        <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ada1494fccbc7f1f07b2f9be9f7e07ad5">t_size</a>[u] += <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ada1494fccbc7f1f07b2f9be9f7e07ad5">t_size</a>[v];</div>
+<div class="line"><span class="lineno">  106</span>      }</div>
+<div class="line"><span class="lineno">  107</span>    }</div>
+<div class="line"><span class="lineno">  108</span>  }</div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_aa339c31ec74cd86a4842a8b09653d460"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa339c31ec74cd86a4842a8b09653d460">range_queries::heavy_light_decomposition::Tree::dfs_size</a></div><div class="ttdeci">void dfs_size(int u, int p=-1)</div><div class="ttdoc">Utility function to compute sub-tree sizes.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:101</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -508,11 +529,11 @@ template&lt;typename X &gt; </div>
 
 <p>This function must be called after the tree adjacency list and node values are populated The function initializes the required parameters, and populates the segment tree. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>              {</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>    assert(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">t_nodes</a> &gt; 0);</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>    <a class="code hl_function" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa339c31ec74cd86a4842a8b09653d460">dfs_size</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa6c37e840355b9fb2105181c578694e8">t_root</a>);</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>    <a class="code hl_function" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae8de7aefcb6635d3dacdd174cd4890c4">dfs_lca</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa6c37e840355b9fb2105181c578694e8">t_root</a>);</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>  }</div>
+<div class="fragment"><div class="line"><span class="lineno">  186</span>              {</div>
+<div class="line"><span class="lineno">  187</span>    assert(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">t_nodes</a> &gt; 0);</div>
+<div class="line"><span class="lineno">  188</span>    <a class="code hl_function" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa339c31ec74cd86a4842a8b09653d460">dfs_size</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa6c37e840355b9fb2105181c578694e8">t_root</a>);</div>
+<div class="line"><span class="lineno">  189</span>    <a class="code hl_function" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae8de7aefcb6635d3dacdd174cd4890c4">dfs_lca</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa6c37e840355b9fb2105181c578694e8">t_root</a>);</div>
+<div class="line"><span class="lineno">  190</span>  }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -567,10 +588,10 @@ template&lt;typename X &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>the kth ancestor of node </dd></dl>
-<div class="fragment"><div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>                                           {</div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>    <a class="code hl_function" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ac7761255f2ba06b398b9aae5e4dce5f3">lift</a>(&amp;p, dist);</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>    <span class="keywordflow">return</span> p;</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>  }</div>
+<div class="fragment"><div class="line"><span class="lineno">  218</span>                                           {</div>
+<div class="line"><span class="lineno">  219</span>    <a class="code hl_function" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ac7761255f2ba06b398b9aae5e4dce5f3">lift</a>(&amp;p, dist);</div>
+<div class="line"><span class="lineno">  220</span>    <span class="keywordflow">return</span> p;</div>
+<div class="line"><span class="lineno">  221</span>  }</div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_ac7761255f2ba06b398b9aae5e4dce5f3"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ac7761255f2ba06b398b9aae5e4dce5f3">range_queries::heavy_light_decomposition::Tree::lift</a></div><div class="ttdeci">void lift(int *const p, int dist)</div><div class="ttdoc">The function lifts a node, k units up the tree. The lifting is done in place, and the result is store...</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:200</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -626,25 +647,25 @@ template&lt;typename X &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>the least common ancestor of node a, and node b </dd></dl>
-<div class="fragment"><div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>                        {</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>    assert(a &gt;= 0 and b &gt;= 0 and a &lt; <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">t_nodes</a> and b &lt; <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">t_nodes</a>);</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">t_depth</a>[a] &gt; <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">t_depth</a>[b]) {</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>      <a class="code hl_function" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ac7761255f2ba06b398b9aae5e4dce5f3">lift</a>(&amp;a, <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">t_depth</a>[a] - <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">t_depth</a>[b]);</div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>    }</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">t_depth</a>[b] &gt; <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">t_depth</a>[a]) {</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>      <a class="code hl_function" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ac7761255f2ba06b398b9aae5e4dce5f3">lift</a>(&amp;b, <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">t_depth</a>[b] - <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">t_depth</a>[a]);</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>    }</div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>    <span class="keywordflow">if</span> (a == b) {</div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>      <span class="keywordflow">return</span> a;</div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>    }</div>
-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab2ab020f798d00be2613ecf63074b7c1">t_maxlift</a> - 1; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &gt;= 0; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>--) {</div>
-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>      <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">t_par</a>[a][k] != <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">t_par</a>[b][k]) {</div>
-<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>        a = <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">t_par</a>[a][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>];</div>
-<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>        b = <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">t_par</a>[b][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>];</div>
-<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>      }</div>
-<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>    }</div>
-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>    <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">t_par</a>[a][0];</div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>  }</div>
+<div class="fragment"><div class="line"><span class="lineno">  229</span>                        {</div>
+<div class="line"><span class="lineno">  230</span>    assert(a &gt;= 0 and b &gt;= 0 and a &lt; <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">t_nodes</a> and b &lt; <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">t_nodes</a>);</div>
+<div class="line"><span class="lineno">  231</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">t_depth</a>[a] &gt; <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">t_depth</a>[b]) {</div>
+<div class="line"><span class="lineno">  232</span>      <a class="code hl_function" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ac7761255f2ba06b398b9aae5e4dce5f3">lift</a>(&amp;a, <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">t_depth</a>[a] - <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">t_depth</a>[b]);</div>
+<div class="line"><span class="lineno">  233</span>    }</div>
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-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        <span class="keywordflow">return</span> 128 + f.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#a7d2285a8a6e20b77f82f1f0351afe76e">_trz</a>();</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  135</span>                           {</div>
+<div class="line"><span class="lineno">  136</span>        <span class="keywordflow">if</span> (s) {</div>
+<div class="line"><span class="lineno">  137</span>            <span class="keywordflow">return</span> s.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#a7d2285a8a6e20b77f82f1f0351afe76e">_trz</a>();</div>
+<div class="line"><span class="lineno">  138</span>        }</div>
+<div class="line"><span class="lineno">  139</span>        <span class="keywordflow">return</span> 128 + f.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#a7d2285a8a6e20b77f82f1f0351afe76e">_trz</a>();</div>
+<div class="line"><span class="lineno">  140</span>    }</div>
 <div class="ttc" id="aclassuint128__t_html_a7d2285a8a6e20b77f82f1f0351afe76e"><div class="ttname"><a href="../../db/d9a/classuint128__t.html#a7d2285a8a6e20b77f82f1f0351afe76e">uint128_t::_trz</a></div><div class="ttdeci">uint32_t _trz()</div><div class="ttdoc">Trailing zeroes in binary.</div><div class="ttdef"><b>Definition:</b> uint128_t.hpp:162</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -836,34 +836,34 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>pair denoting quotient and remainder. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00421" name="l00421"></a><span class="lineno">  421</span>                                                             {</div>
-<div class="line"><a id="l00422" name="l00422"></a><span class="lineno">  422</span>        <span class="keywordflow">if</span> (*<span class="keyword">this</span> &lt; p) {  <span class="comment">// if this is less than divisor</span></div>
-<div class="line"><a id="l00423" name="l00423"></a><span class="lineno">  423</span>            <span class="keywordflow">return</span> {<a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(0), *<span class="keyword">this</span>};</div>
-<div class="line"><a id="l00424" name="l00424"></a><span class="lineno">  424</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (*<span class="keyword">this</span> == p) {  <span class="comment">// if this is equal to divisor</span></div>
-<div class="line"><a id="l00425" name="l00425"></a><span class="lineno">  425</span>            <span class="keywordflow">return</span> {<a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(1), <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(0)};</div>
-<div class="line"><a id="l00426" name="l00426"></a><span class="lineno">  426</span>        }</div>
-<div class="line"><a id="l00427" name="l00427"></a><span class="lineno">  427</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> tmp = p, tmp2 = *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00428" name="l00428"></a><span class="lineno">  428</span>        uint16_t <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> = tmp.<a class="code hl_function" href="../../d1/d83/classuint256__t.html#a033d66c965e8d1fbc5bafb59ad60e163">_lez</a>() - <a class="code hl_function" href="../../d1/d83/classuint256__t.html#a033d66c965e8d1fbc5bafb59ad60e163">_lez</a>();</div>
-<div class="line"><a id="l00429" name="l00429"></a><span class="lineno">  429</span>        tmp &lt;&lt;= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>;</div>
-<div class="line"><a id="l00430" name="l00430"></a><span class="lineno">  430</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> quotient(0);</div>
-<div class="line"><a id="l00431" name="l00431"></a><span class="lineno">  431</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> zero(0);</div>
-<div class="line"><a id="l00432" name="l00432"></a><span class="lineno">  432</span>        <span class="keywordflow">while</span> (tmp2 &gt;= p) {</div>
-<div class="line"><a id="l00433" name="l00433"></a><span class="lineno">  433</span>            uint16_t shf = tmp2._lez() - tmp.<a class="code hl_function" href="../../d1/d83/classuint256__t.html#a033d66c965e8d1fbc5bafb59ad60e163">_lez</a>();</div>
-<div class="line"><a id="l00434" name="l00434"></a><span class="lineno">  434</span>            <span class="keywordflow">if</span> (shf) {</div>
-<div class="line"><a id="l00435" name="l00435"></a><span class="lineno">  435</span>                tmp &gt;&gt;= shf;</div>
-<div class="line"><a id="l00436" name="l00436"></a><span class="lineno">  436</span>                quotient &lt;&lt;= shf;</div>
-<div class="line"><a id="l00437" name="l00437"></a><span class="lineno">  437</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> -= shf;</div>
-<div class="line"><a id="l00438" name="l00438"></a><span class="lineno">  438</span>            }</div>
-<div class="line"><a id="l00439" name="l00439"></a><span class="lineno">  439</span>            <span class="keywordflow">if</span> (tmp2 &lt; tmp) {</div>
-<div class="line"><a id="l00440" name="l00440"></a><span class="lineno">  440</span>                tmp &gt;&gt;= 1;</div>
-<div class="line"><a id="l00441" name="l00441"></a><span class="lineno">  441</span>                quotient &lt;&lt;= 1;</div>
-<div class="line"><a id="l00442" name="l00442"></a><span class="lineno">  442</span>                --<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>;</div>
-<div class="line"><a id="l00443" name="l00443"></a><span class="lineno">  443</span>            }</div>
-<div class="line"><a id="l00444" name="l00444"></a><span class="lineno">  444</span>            tmp2 -= tmp;</div>
-<div class="line"><a id="l00445" name="l00445"></a><span class="lineno">  445</span>            ++quotient;</div>
-<div class="line"><a id="l00446" name="l00446"></a><span class="lineno">  446</span>        }</div>
-<div class="line"><a id="l00447" name="l00447"></a><span class="lineno">  447</span>        <span class="keywordflow">return</span> {quotient &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>, tmp2};</div>
-<div class="line"><a id="l00448" name="l00448"></a><span class="lineno">  448</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  421</span>                                                             {</div>
+<div class="line"><span class="lineno">  422</span>        <span class="keywordflow">if</span> (*<span class="keyword">this</span> &lt; p) {  <span class="comment">// if this is less than divisor</span></div>
+<div class="line"><span class="lineno">  423</span>            <span class="keywordflow">return</span> {<a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(0), *<span class="keyword">this</span>};</div>
+<div class="line"><span class="lineno">  424</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (*<span class="keyword">this</span> == p) {  <span class="comment">// if this is equal to divisor</span></div>
+<div class="line"><span class="lineno">  425</span>            <span class="keywordflow">return</span> {<a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(1), <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(0)};</div>
+<div class="line"><span class="lineno">  426</span>        }</div>
+<div class="line"><span class="lineno">  427</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> tmp = p, tmp2 = *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  428</span>        uint16_t <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> = tmp.<a class="code hl_function" href="../../d1/d83/classuint256__t.html#a033d66c965e8d1fbc5bafb59ad60e163">_lez</a>() - <a class="code hl_function" href="../../d1/d83/classuint256__t.html#a033d66c965e8d1fbc5bafb59ad60e163">_lez</a>();</div>
+<div class="line"><span class="lineno">  429</span>        tmp &lt;&lt;= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>;</div>
+<div class="line"><span class="lineno">  430</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> quotient(0);</div>
+<div class="line"><span class="lineno">  431</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> zero(0);</div>
+<div class="line"><span class="lineno">  432</span>        <span class="keywordflow">while</span> (tmp2 &gt;= p) {</div>
+<div class="line"><span class="lineno">  433</span>            uint16_t shf = tmp2._lez() - tmp.<a class="code hl_function" href="../../d1/d83/classuint256__t.html#a033d66c965e8d1fbc5bafb59ad60e163">_lez</a>();</div>
+<div class="line"><span class="lineno">  434</span>            <span class="keywordflow">if</span> (shf) {</div>
+<div class="line"><span class="lineno">  435</span>                tmp &gt;&gt;= shf;</div>
+<div class="line"><span class="lineno">  436</span>                quotient &lt;&lt;= shf;</div>
+<div class="line"><span class="lineno">  437</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> -= shf;</div>
+<div class="line"><span class="lineno">  438</span>            }</div>
+<div class="line"><span class="lineno">  439</span>            <span class="keywordflow">if</span> (tmp2 &lt; tmp) {</div>
+<div class="line"><span class="lineno">  440</span>                tmp &gt;&gt;= 1;</div>
+<div class="line"><span class="lineno">  441</span>                quotient &lt;&lt;= 1;</div>
+<div class="line"><span class="lineno">  442</span>                --<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>;</div>
+<div class="line"><span class="lineno">  443</span>            }</div>
+<div class="line"><span class="lineno">  444</span>            tmp2 -= tmp;</div>
+<div class="line"><span class="lineno">  445</span>            ++quotient;</div>
+<div class="line"><span class="lineno">  446</span>        }</div>
+<div class="line"><span class="lineno">  447</span>        <span class="keywordflow">return</span> {quotient &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>, tmp2};</div>
+<div class="line"><span class="lineno">  448</span>    }</div>
 <div class="ttc" id="aclassuint256__t_html"><div class="ttname"><a href="../../d1/d83/classuint256__t.html">uint256_t</a></div><div class="ttdoc">class for 256-bit unsigned integer</div><div class="ttdef"><b>Definition:</b> uint256_t.hpp:33</div></div>
 <div class="ttc" id="aclassuint256__t_html_a033d66c965e8d1fbc5bafb59ad60e163"><div class="ttname"><a href="../../d1/d83/classuint256__t.html#a033d66c965e8d1fbc5bafb59ad60e163">uint256_t::_lez</a></div><div class="ttdeci">uint32_t _lez()</div><div class="ttdoc">Leading zeroes in binary.</div><div class="ttdef"><b>Definition:</b> uint256_t.hpp:123</div></div>
 <div class="ttc" id="aleft_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::left</a></div><div class="ttdeci">T left(T... args)</div></div>
@@ -901,7 +901,7 @@ Here is the call graph for this function:</div>
 
 <p>returns lower 128-bit integer part </p>
 <dl class="section return"><dt>Returns</dt><dd>returns lower 128-bit integer part </dd></dl>
-<div class="fragment"><div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>{ <span class="keywordflow">return</span> s; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  169</span>{ <span class="keywordflow">return</span> s; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -930,7 +930,7 @@ Here is the call graph for this function:</div>
 
 <p>casting operator to boolean value </p>
 <dl class="section return"><dt>Returns</dt><dd>true if value of this is non-zero, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>{ <span class="keywordflow">return</span> f || s; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  146</span>{ <span class="keywordflow">return</span> f || s; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -967,9 +967,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>integer value casted to mentioned type </dd></dl>
-<div class="fragment"><div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>                                       {</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>        <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(s);</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  155</span>                                       {</div>
+<div class="line"><span class="lineno">  156</span>        <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(s);</div>
+<div class="line"><span class="lineno">  157</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -998,7 +998,7 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
 
 <p>casting operator to <a class="el" href="../../db/d9a/classuint128__t.html" title="class for 128-bit unsigned integer">uint128_t</a> </p>
 <dl class="section return"><dt>Returns</dt><dd>returns lower 128-bit integer part </dd></dl>
-<div class="fragment"><div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>{ <span class="keywordflow">return</span> s; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  163</span>{ <span class="keywordflow">return</span> s; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1027,7 +1027,7 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
 
 <p>operator ! for <a class="el" href="../../d1/d83/classuint256__t.html" title="class for 256-bit unsigned integer">uint256_t</a> </p>
 <dl class="section return"><dt>Returns</dt><dd>true if this has zero value, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00596" name="l00596"></a><span class="lineno">  596</span>{ <span class="keywordflow">return</span> !f &amp;&amp; !s; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  596</span>{ <span class="keywordflow">return</span> !f &amp;&amp; !s; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1071,9 +1071,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is not equal to other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00690" name="l00690"></a><span class="lineno">  690</span>                                    {</div>
-<div class="line"><a id="l00691" name="l00691"></a><span class="lineno">  691</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> != <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(other);</div>
-<div class="line"><a id="l00692" name="l00692"></a><span class="lineno">  692</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  690</span>                                    {</div>
+<div class="line"><span class="lineno">  691</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> != <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(other);</div>
+<div class="line"><span class="lineno">  692</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1109,9 +1109,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is not equal than other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00588" name="l00588"></a><span class="lineno">  588</span>                                                   {</div>
-<div class="line"><a id="l00589" name="l00589"></a><span class="lineno">  589</span>        <span class="keywordflow">return</span> !((*this) == other);</div>
-<div class="line"><a id="l00590" name="l00590"></a><span class="lineno">  590</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  588</span>                                                   {</div>
+<div class="line"><span class="lineno">  589</span>        <span class="keywordflow">return</span> !((*this) == other);</div>
+<div class="line"><span class="lineno">  590</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1155,11 +1155,11 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>unsigned 256-bit remainder. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00509" name="l00509"></a><span class="lineno">  509</span>                                           {</div>
-<div class="line"><a id="l00510" name="l00510"></a><span class="lineno">  510</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> tmp = *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00511" name="l00511"></a><span class="lineno">  511</span>        tmp %= <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(p);</div>
-<div class="line"><a id="l00512" name="l00512"></a><span class="lineno">  512</span>        <span class="keywordflow">return</span> tmp;</div>
-<div class="line"><a id="l00513" name="l00513"></a><span class="lineno">  513</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  509</span>                                           {</div>
+<div class="line"><span class="lineno">  510</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> tmp = *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  511</span>        tmp %= <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(p);</div>
+<div class="line"><span class="lineno">  512</span>        <span class="keywordflow">return</span> tmp;</div>
+<div class="line"><span class="lineno">  513</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1195,7 +1195,7 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>unsigned 256-bit remainder. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00499" name="l00499"></a><span class="lineno">  499</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../d1/d83/classuint256__t.html#a8161d52d369e525f4e61129376adfcf1">divide</a>(p).second; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  499</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../d1/d83/classuint256__t.html#a8161d52d369e525f4e61129376adfcf1">divide</a>(p).second; }</div>
 <div class="ttc" id="aclassuint256__t_html_a8161d52d369e525f4e61129376adfcf1"><div class="ttname"><a href="../../d1/d83/classuint256__t.html#a8161d52d369e525f4e61129376adfcf1">uint256_t::divide</a></div><div class="ttdeci">std::pair&lt; uint256_t, uint256_t &gt; divide(const uint256_t &amp;p)</div><div class="ttdoc">divide function for uint256_t and other integer types.</div><div class="ttdef"><b>Definition:</b> uint256_t.hpp:421</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -1246,10 +1246,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this set as unsigned 256-bit remainder. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00533" name="l00533"></a><span class="lineno">  533</span>                                             {</div>
-<div class="line"><a id="l00534" name="l00534"></a><span class="lineno">  534</span>        *<span class="keyword">this</span> %= <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(p);</div>
-<div class="line"><a id="l00535" name="l00535"></a><span class="lineno">  535</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00536" name="l00536"></a><span class="lineno">  536</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  533</span>                                             {</div>
+<div class="line"><span class="lineno">  534</span>        *<span class="keyword">this</span> %= <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(p);</div>
+<div class="line"><span class="lineno">  535</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  536</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1285,10 +1285,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this set as unsigned 256-bit remainder. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00520" name="l00520"></a><span class="lineno">  520</span>                                                     {</div>
-<div class="line"><a id="l00521" name="l00521"></a><span class="lineno">  521</span>        *<span class="keyword">this</span> = <a class="code hl_function" href="../../d1/d83/classuint256__t.html#a8161d52d369e525f4e61129376adfcf1">divide</a>(p).second;</div>
-<div class="line"><a id="l00522" name="l00522"></a><span class="lineno">  522</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00523" name="l00523"></a><span class="lineno">  523</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  520</span>                                                     {</div>
+<div class="line"><span class="lineno">  521</span>        *<span class="keyword">this</span> = <a class="code hl_function" href="../../d1/d83/classuint256__t.html#a8161d52d369e525f4e61129376adfcf1">divide</a>(p).second;</div>
+<div class="line"><span class="lineno">  522</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  523</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -1338,9 +1338,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>value of this &amp; p (&amp; is bit-wise operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00811" name="l00811"></a><span class="lineno">  811</span>                                           {</div>
-<div class="line"><a id="l00812" name="l00812"></a><span class="lineno">  812</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> &amp; <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(p);</div>
-<div class="line"><a id="l00813" name="l00813"></a><span class="lineno">  813</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  811</span>                                           {</div>
+<div class="line"><span class="lineno">  812</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> &amp; <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(p);</div>
+<div class="line"><span class="lineno">  813</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1376,9 +1376,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>value of this &amp; p (&amp; is bit-wise operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00820" name="l00820"></a><span class="lineno">  820</span>                                                   {</div>
-<div class="line"><a id="l00821" name="l00821"></a><span class="lineno">  821</span>        <span class="keywordflow">return</span> {f &amp; p.f, s &amp; p.s};</div>
-<div class="line"><a id="l00822" name="l00822"></a><span class="lineno">  822</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  820</span>                                                   {</div>
+<div class="line"><span class="lineno">  821</span>        <span class="keywordflow">return</span> {f &amp; p.f, s &amp; p.s};</div>
+<div class="line"><span class="lineno">  822</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1422,9 +1422,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is both values are non-zero, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00702" name="l00702"></a><span class="lineno">  702</span>                                       {</div>
-<div class="line"><a id="l00703" name="l00703"></a><span class="lineno">  703</span>        <span class="keywordflow">return</span> (s || f) &amp;&amp; (b);</div>
-<div class="line"><a id="l00704" name="l00704"></a><span class="lineno">  704</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  702</span>                                       {</div>
+<div class="line"><span class="lineno">  703</span>        <span class="keywordflow">return</span> (s || f) &amp;&amp; (b);</div>
+<div class="line"><span class="lineno">  704</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1460,9 +1460,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if both of the values are not zero, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00603" name="l00603"></a><span class="lineno">  603</span>                                               {</div>
-<div class="line"><a id="l00604" name="l00604"></a><span class="lineno">  604</span>        <span class="keywordflow">return</span> (s || f) &amp;&amp; (b.s || b.f);</div>
-<div class="line"><a id="l00605" name="l00605"></a><span class="lineno">  605</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  603</span>                                               {</div>
+<div class="line"><span class="lineno">  604</span>        <span class="keywordflow">return</span> (s || f) &amp;&amp; (b.s || b.f);</div>
+<div class="line"><span class="lineno">  605</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1506,10 +1506,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this = this &amp; p (&amp; is bit-wise operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00843" name="l00843"></a><span class="lineno">  843</span>                                            {</div>
-<div class="line"><a id="l00844" name="l00844"></a><span class="lineno">  844</span>        s &amp;= p.s;</div>
-<div class="line"><a id="l00845" name="l00845"></a><span class="lineno">  845</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00846" name="l00846"></a><span class="lineno">  846</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  843</span>                                            {</div>
+<div class="line"><span class="lineno">  844</span>        s &amp;= p.s;</div>
+<div class="line"><span class="lineno">  845</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  846</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1545,11 +1545,11 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this = this &amp; p (&amp; is bit-wise operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00829" name="l00829"></a><span class="lineno">  829</span>                                                     {</div>
-<div class="line"><a id="l00830" name="l00830"></a><span class="lineno">  830</span>        f &amp;= p.f;</div>
-<div class="line"><a id="l00831" name="l00831"></a><span class="lineno">  831</span>        s &amp;= p.s;</div>
-<div class="line"><a id="l00832" name="l00832"></a><span class="lineno">  832</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00833" name="l00833"></a><span class="lineno">  833</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  829</span>                                                     {</div>
+<div class="line"><span class="lineno">  830</span>        f &amp;= p.f;</div>
+<div class="line"><span class="lineno">  831</span>        s &amp;= p.s;</div>
+<div class="line"><span class="lineno">  832</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  833</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1578,7 +1578,7 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
 
 <p>operator () for <a class="el" href="../../d1/d83/classuint256__t.html" title="class for 256-bit unsigned integer">uint256_t</a> </p>
 <dl class="section return"><dt>Returns</dt><dd>true if this value is non-zero, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00620" name="l00620"></a><span class="lineno">  620</span>{ <span class="keywordflow">return</span> s || f; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  620</span>{ <span class="keywordflow">return</span> s || f; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1622,9 +1622,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>multiplication of this and p, returning <a class="el" href="../../d1/d83/classuint256__t.html" title="class for 256-bit unsigned integer">uint256_t</a> integer </dd></dl>
-<div class="fragment"><div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span>                                           {</div>
-<div class="line"><a id="l00363" name="l00363"></a><span class="lineno">  363</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> * <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(p);</div>
-<div class="line"><a id="l00364" name="l00364"></a><span class="lineno">  364</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  362</span>                                           {</div>
+<div class="line"><span class="lineno">  363</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> * <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(p);</div>
+<div class="line"><span class="lineno">  364</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1660,18 +1660,18 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>multiplication of this and p, returning <a class="el" href="../../d1/d83/classuint256__t.html" title="class for 256-bit unsigned integer">uint256_t</a> integer </dd></dl>
-<div class="fragment"><div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span>                                            {</div>
-<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> f_first(s.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#a1ee2f1ffbd9984faad34883eb45e9705">upper</a>()), f_second(s.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#aa69e1064c0b0b1df1c61acd2ea04fabd">lower</a>()), s_first(p.s.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#a1ee2f1ffbd9984faad34883eb45e9705">upper</a>()),</div>
-<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>            s_second(p.s.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#aa69e1064c0b0b1df1c61acd2ea04fabd">lower</a>());</div>
-<div class="line"><a id="l00374" name="l00374"></a><span class="lineno">  374</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> fi = f_first * s_first, se = f_first * s_second,</div>
-<div class="line"><a id="l00375" name="l00375"></a><span class="lineno">  375</span>                  th = s_first * f_second, fo = s_second * f_second;</div>
-<div class="line"><a id="l00376" name="l00376"></a><span class="lineno">  376</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> tmp = se &lt;&lt; 64, tmp2 = th &lt;&lt; 64;</div>
-<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span>        <span class="keywordtype">int</span> cc = (tmp + tmp2 &lt; tmp);</div>
-<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span>        tmp += tmp2;</div>
-<div class="line"><a id="l00379" name="l00379"></a><span class="lineno">  379</span>        cc += (tmp + fo &lt; tmp);</div>
-<div class="line"><a id="l00380" name="l00380"></a><span class="lineno">  380</span>        <span class="keywordflow">return</span> {f * p.s + s * p.f + fi + se.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#a1ee2f1ffbd9984faad34883eb45e9705">upper</a>() + th.upper() + cc,</div>
-<div class="line"><a id="l00381" name="l00381"></a><span class="lineno">  381</span>                tmp + fo};</div>
-<div class="line"><a id="l00382" name="l00382"></a><span class="lineno">  382</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  371</span>                                            {</div>
+<div class="line"><span class="lineno">  372</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> f_first(s.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#a1ee2f1ffbd9984faad34883eb45e9705">upper</a>()), f_second(s.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#aa69e1064c0b0b1df1c61acd2ea04fabd">lower</a>()), s_first(p.s.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#a1ee2f1ffbd9984faad34883eb45e9705">upper</a>()),</div>
+<div class="line"><span class="lineno">  373</span>            s_second(p.s.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#aa69e1064c0b0b1df1c61acd2ea04fabd">lower</a>());</div>
+<div class="line"><span class="lineno">  374</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> fi = f_first * s_first, se = f_first * s_second,</div>
+<div class="line"><span class="lineno">  375</span>                  th = s_first * f_second, fo = s_second * f_second;</div>
+<div class="line"><span class="lineno">  376</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> tmp = se &lt;&lt; 64, tmp2 = th &lt;&lt; 64;</div>
+<div class="line"><span class="lineno">  377</span>        <span class="keywordtype">int</span> cc = (tmp + tmp2 &lt; tmp);</div>
+<div class="line"><span class="lineno">  378</span>        tmp += tmp2;</div>
+<div class="line"><span class="lineno">  379</span>        cc += (tmp + fo &lt; tmp);</div>
+<div class="line"><span class="lineno">  380</span>        <span class="keywordflow">return</span> {f * p.s + s * p.f + fi + se.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#a1ee2f1ffbd9984faad34883eb45e9705">upper</a>() + th.upper() + cc,</div>
+<div class="line"><span class="lineno">  381</span>                tmp + fo};</div>
+<div class="line"><span class="lineno">  382</span>    }</div>
 <div class="ttc" id="aclassuint128__t_html_a1ee2f1ffbd9984faad34883eb45e9705"><div class="ttname"><a href="../../db/d9a/classuint128__t.html#a1ee2f1ffbd9984faad34883eb45e9705">uint128_t::upper</a></div><div class="ttdeci">uint64_t upper() const</div><div class="ttdoc">returns upper 64-bit integer part</div><div class="ttdef"><b>Definition:</b> uint128_t.hpp:207</div></div>
 <div class="ttc" id="aclassuint128__t_html_aa69e1064c0b0b1df1c61acd2ea04fabd"><div class="ttname"><a href="../../db/d9a/classuint128__t.html#aa69e1064c0b0b1df1c61acd2ea04fabd">uint128_t::lower</a></div><div class="ttdeci">uint64_t lower() const</div><div class="ttdoc">returns lower 64-bit integer part</div><div class="ttdef"><b>Definition:</b> uint128_t.hpp:201</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -1723,9 +1723,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>multiplication of this and p, returning this </dd></dl>
-<div class="fragment"><div class="line"><a id="l00392" name="l00392"></a><span class="lineno">  392</span>                                             {</div>
-<div class="line"><a id="l00393" name="l00393"></a><span class="lineno">  393</span>        <span class="keywordflow">return</span> (*<span class="keyword">this</span> *= <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(p));</div>
-<div class="line"><a id="l00394" name="l00394"></a><span class="lineno">  394</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  392</span>                                             {</div>
+<div class="line"><span class="lineno">  393</span>        <span class="keywordflow">return</span> (*<span class="keyword">this</span> *= <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(p));</div>
+<div class="line"><span class="lineno">  394</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1761,19 +1761,19 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>multiplication of this and p, returning this </dd></dl>
-<div class="fragment"><div class="line"><a id="l00401" name="l00401"></a><span class="lineno">  401</span>                                              {</div>
-<div class="line"><a id="l00402" name="l00402"></a><span class="lineno">  402</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> f_first(s.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#a1ee2f1ffbd9984faad34883eb45e9705">upper</a>()), f_second(s.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#aa69e1064c0b0b1df1c61acd2ea04fabd">lower</a>()), s_first(p.s.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#a1ee2f1ffbd9984faad34883eb45e9705">upper</a>()),</div>
-<div class="line"><a id="l00403" name="l00403"></a><span class="lineno">  403</span>            s_second(p.s.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#aa69e1064c0b0b1df1c61acd2ea04fabd">lower</a>());</div>
-<div class="line"><a id="l00404" name="l00404"></a><span class="lineno">  404</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> fi = f_first * s_first, se = f_first * s_second,</div>
-<div class="line"><a id="l00405" name="l00405"></a><span class="lineno">  405</span>                  th = s_first * f_second, fo = s_second * f_second;</div>
-<div class="line"><a id="l00406" name="l00406"></a><span class="lineno">  406</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> tmp = se &lt;&lt; 64, tmp2 = th &lt;&lt; 64;</div>
-<div class="line"><a id="l00407" name="l00407"></a><span class="lineno">  407</span>        <span class="keywordtype">int</span> cc = (tmp + tmp2 &lt; tmp);</div>
-<div class="line"><a id="l00408" name="l00408"></a><span class="lineno">  408</span>        tmp += tmp2;</div>
-<div class="line"><a id="l00409" name="l00409"></a><span class="lineno">  409</span>        cc += (tmp + fo &lt; tmp);</div>
-<div class="line"><a id="l00410" name="l00410"></a><span class="lineno">  410</span>        f = f * p.s + s * p.f + fi + se.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#a1ee2f1ffbd9984faad34883eb45e9705">upper</a>() + th.upper() + cc;</div>
-<div class="line"><a id="l00411" name="l00411"></a><span class="lineno">  411</span>        s = tmp + fo;</div>
-<div class="line"><a id="l00412" name="l00412"></a><span class="lineno">  412</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00413" name="l00413"></a><span class="lineno">  413</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  401</span>                                              {</div>
+<div class="line"><span class="lineno">  402</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> f_first(s.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#a1ee2f1ffbd9984faad34883eb45e9705">upper</a>()), f_second(s.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#aa69e1064c0b0b1df1c61acd2ea04fabd">lower</a>()), s_first(p.s.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#a1ee2f1ffbd9984faad34883eb45e9705">upper</a>()),</div>
+<div class="line"><span class="lineno">  403</span>            s_second(p.s.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#aa69e1064c0b0b1df1c61acd2ea04fabd">lower</a>());</div>
+<div class="line"><span class="lineno">  404</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> fi = f_first * s_first, se = f_first * s_second,</div>
+<div class="line"><span class="lineno">  405</span>                  th = s_first * f_second, fo = s_second * f_second;</div>
+<div class="line"><span class="lineno">  406</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> tmp = se &lt;&lt; 64, tmp2 = th &lt;&lt; 64;</div>
+<div class="line"><span class="lineno">  407</span>        <span class="keywordtype">int</span> cc = (tmp + tmp2 &lt; tmp);</div>
+<div class="line"><span class="lineno">  408</span>        tmp += tmp2;</div>
+<div class="line"><span class="lineno">  409</span>        cc += (tmp + fo &lt; tmp);</div>
+<div class="line"><span class="lineno">  410</span>        f = f * p.s + s * p.f + fi + se.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#a1ee2f1ffbd9984faad34883eb45e9705">upper</a>() + th.upper() + cc;</div>
+<div class="line"><span class="lineno">  411</span>        s = tmp + fo;</div>
+<div class="line"><span class="lineno">  412</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  413</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -1823,10 +1823,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>addition of this and p, returning <a class="el" href="../../d1/d83/classuint256__t.html" title="class for 256-bit unsigned integer">uint256_t</a> integer </dd></dl>
-<div class="fragment"><div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>                                           {</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>        <span class="keywordtype">bool</span> app = s + p &lt; s;</div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(f + app, s + p);</div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  220</span>                                           {</div>
+<div class="line"><span class="lineno">  221</span>        <span class="keywordtype">bool</span> app = s + p &lt; s;</div>
+<div class="line"><span class="lineno">  222</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(f + app, s + p);</div>
+<div class="line"><span class="lineno">  223</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1862,10 +1862,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>addition of this and p, returning <a class="el" href="../../d1/d83/classuint256__t.html" title="class for 256-bit unsigned integer">uint256_t</a> integer </dd></dl>
-<div class="fragment"><div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>                                                   {</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>        <span class="keywordtype">bool</span> app = (s + p.s &lt; s);</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>        <span class="keywordflow">return</span> {f + app + p.f, s + p.s};</div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  230</span>                                                   {</div>
+<div class="line"><span class="lineno">  231</span>        <span class="keywordtype">bool</span> app = (s + p.s &lt; s);</div>
+<div class="line"><span class="lineno">  232</span>        <span class="keywordflow">return</span> {f + app + p.f, s + p.s};</div>
+<div class="line"><span class="lineno">  233</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1894,10 +1894,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
 
 <p>pre-increment operator </p>
 <dl class="section return"><dt>Returns</dt><dd>incremented value of this. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>                                   {</div>
-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>        *<span class="keyword">this</span> += 1;</div>
-<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  266</span>                                   {</div>
+<div class="line"><span class="lineno">  267</span>        *<span class="keyword">this</span> += 1;</div>
+<div class="line"><span class="lineno">  268</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  269</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1927,10 +1927,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
 
 <p>post-increment operator </p>
 <dl class="section return"><dt>Returns</dt><dd>incremented value of this. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>                                     {</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>        ++*<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  275</span>                                     {</div>
+<div class="line"><span class="lineno">  276</span>        ++*<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  277</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  278</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1974,12 +1974,12 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>addition of this and p, returning this </dd></dl>
-<div class="fragment"><div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>                                             {</div>
-<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>        <span class="keywordtype">bool</span> app = (p + s &lt; s);</div>
-<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>        this-&gt;f += app;</div>
-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>        this-&gt;s += p;</div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  243</span>                                             {</div>
+<div class="line"><span class="lineno">  244</span>        <span class="keywordtype">bool</span> app = (p + s &lt; s);</div>
+<div class="line"><span class="lineno">  245</span>        this-&gt;f += app;</div>
+<div class="line"><span class="lineno">  246</span>        this-&gt;s += p;</div>
+<div class="line"><span class="lineno">  247</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  248</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2015,12 +2015,12 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>addition of this and p, returning this </dd></dl>
-<div class="fragment"><div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>                                                     {</div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>        <span class="keywordtype">bool</span> app = (s + p.s &lt; s);</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>        f = f + app + p.f;</div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>        s = s + p.s;</div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  255</span>                                                     {</div>
+<div class="line"><span class="lineno">  256</span>        <span class="keywordtype">bool</span> app = (s + p.s &lt; s);</div>
+<div class="line"><span class="lineno">  257</span>        f = f + app + p.f;</div>
+<div class="line"><span class="lineno">  258</span>        s = s + p.s;</div>
+<div class="line"><span class="lineno">  259</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  260</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2049,7 +2049,7 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
 
 <p>operator - using twos complement </p>
 <dl class="section return"><dt>Returns</dt><dd>2's complement of this. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>{ <span class="keywordflow">return</span> ~*<span class="keyword">this</span> + <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(1); }</div>
+<div class="fragment"><div class="line"><span class="lineno">  307</span>{ <span class="keywordflow">return</span> ~*<span class="keyword">this</span> + <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(1); }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2093,10 +2093,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>subtraction of this and p, returning <a class="el" href="../../d1/d83/classuint256__t.html" title="class for 256-bit unsigned integer">uint256_t</a> integer </dd></dl>
-<div class="fragment"><div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>                                           {</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>        <span class="keywordtype">bool</span> app = (p &gt; s);</div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(f - app, s - p);</div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  288</span>                                           {</div>
+<div class="line"><span class="lineno">  289</span>        <span class="keywordtype">bool</span> app = (p &gt; s);</div>
+<div class="line"><span class="lineno">  290</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(f - app, s - p);</div>
+<div class="line"><span class="lineno">  291</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2132,10 +2132,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>subtraction of this and p, returning <a class="el" href="../../d1/d83/classuint256__t.html" title="class for 256-bit unsigned integer">uint256_t</a> integer </dd></dl>
-<div class="fragment"><div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>                                                   {</div>
-<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>        <span class="keywordtype">bool</span> app = s &lt; p.s;</div>
-<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span>        <span class="keywordflow">return</span> {f - p.f - app, s - p.s};</div>
-<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  298</span>                                                   {</div>
+<div class="line"><span class="lineno">  299</span>        <span class="keywordtype">bool</span> app = s &lt; p.s;</div>
+<div class="line"><span class="lineno">  300</span>        <span class="keywordflow">return</span> {f - p.f - app, s - p.s};</div>
+<div class="line"><span class="lineno">  301</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2164,10 +2164,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
 
 <p>operator &ndash; (pre-decrement) </p>
 <dl class="section return"><dt>Returns</dt><dd>decremented value of this </dd></dl>
-<div class="fragment"><div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span>                                   {</div>
-<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span>        *<span class="keyword">this</span> -= 1;</div>
-<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  313</span>                                   {</div>
+<div class="line"><span class="lineno">  314</span>        *<span class="keyword">this</span> -= 1;</div>
+<div class="line"><span class="lineno">  315</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  316</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2197,10 +2197,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
 
 <p>operator &ndash; (post-decrement) </p>
 <dl class="section return"><dt>Returns</dt><dd>decremented value of this </dd></dl>
-<div class="fragment"><div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>                                       {</div>
-<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>        --*<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  322</span>                                       {</div>
+<div class="line"><span class="lineno">  323</span>        --*<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  324</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  325</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2244,12 +2244,12 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>subtraction of this and p, returning this </dd></dl>
-<div class="fragment"><div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span>                                           {</div>
-<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span>        <span class="keywordtype">bool</span> app = (p &gt; s);</div>
-<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span>        f = f - app;</div>
-<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span>        s = s - p;</div>
-<div class="line"><a id="l00339" name="l00339"></a><span class="lineno">  339</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00340" name="l00340"></a><span class="lineno">  340</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  335</span>                                           {</div>
+<div class="line"><span class="lineno">  336</span>        <span class="keywordtype">bool</span> app = (p &gt; s);</div>
+<div class="line"><span class="lineno">  337</span>        f = f - app;</div>
+<div class="line"><span class="lineno">  338</span>        s = s - p;</div>
+<div class="line"><span class="lineno">  339</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  340</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2285,12 +2285,12 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>subtraction of this and p, returning this </dd></dl>
-<div class="fragment"><div class="line"><a id="l00347" name="l00347"></a><span class="lineno">  347</span>                                                     {</div>
-<div class="line"><a id="l00348" name="l00348"></a><span class="lineno">  348</span>        <span class="keywordtype">bool</span> app = s &lt; p.s;</div>
-<div class="line"><a id="l00349" name="l00349"></a><span class="lineno">  349</span>        f = f - app - p.f;</div>
-<div class="line"><a id="l00350" name="l00350"></a><span class="lineno">  350</span>        s = s - p.s;</div>
-<div class="line"><a id="l00351" name="l00351"></a><span class="lineno">  351</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00352" name="l00352"></a><span class="lineno">  352</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  347</span>                                                     {</div>
+<div class="line"><span class="lineno">  348</span>        <span class="keywordtype">bool</span> app = s &lt; p.s;</div>
+<div class="line"><span class="lineno">  349</span>        f = f - app - p.f;</div>
+<div class="line"><span class="lineno">  350</span>        s = s - p.s;</div>
+<div class="line"><span class="lineno">  351</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  352</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2334,11 +2334,11 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>unsigned 256-bit quotient. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00458" name="l00458"></a><span class="lineno">  458</span>                                           {</div>
-<div class="line"><a id="l00459" name="l00459"></a><span class="lineno">  459</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> tmp = *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00460" name="l00460"></a><span class="lineno">  460</span>        tmp /= <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(p);</div>
-<div class="line"><a id="l00461" name="l00461"></a><span class="lineno">  461</span>        <span class="keywordflow">return</span> tmp;</div>
-<div class="line"><a id="l00462" name="l00462"></a><span class="lineno">  462</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  458</span>                                           {</div>
+<div class="line"><span class="lineno">  459</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> tmp = *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  460</span>        tmp /= <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(p);</div>
+<div class="line"><span class="lineno">  461</span>        <span class="keywordflow">return</span> tmp;</div>
+<div class="line"><span class="lineno">  462</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2374,7 +2374,7 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>unsigned 256-bit quotient. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00469" name="l00469"></a><span class="lineno">  469</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../d1/d83/classuint256__t.html#a8161d52d369e525f4e61129376adfcf1">divide</a>(p).first; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  469</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../d1/d83/classuint256__t.html#a8161d52d369e525f4e61129376adfcf1">divide</a>(p).first; }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -2424,10 +2424,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this set as unsigned 256-bit quotient. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00489" name="l00489"></a><span class="lineno">  489</span>                                             {</div>
-<div class="line"><a id="l00490" name="l00490"></a><span class="lineno">  490</span>        *<span class="keyword">this</span> /= <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(p);</div>
-<div class="line"><a id="l00491" name="l00491"></a><span class="lineno">  491</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00492" name="l00492"></a><span class="lineno">  492</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  489</span>                                             {</div>
+<div class="line"><span class="lineno">  490</span>        *<span class="keyword">this</span> /= <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(p);</div>
+<div class="line"><span class="lineno">  491</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  492</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2463,10 +2463,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this set as unsigned 256-bit quotient. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00476" name="l00476"></a><span class="lineno">  476</span>                                                     {</div>
-<div class="line"><a id="l00477" name="l00477"></a><span class="lineno">  477</span>        *<span class="keyword">this</span> = <a class="code hl_function" href="../../d1/d83/classuint256__t.html#a8161d52d369e525f4e61129376adfcf1">divide</a>(p).first;</div>
-<div class="line"><a id="l00478" name="l00478"></a><span class="lineno">  478</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00479" name="l00479"></a><span class="lineno">  479</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  476</span>                                                     {</div>
+<div class="line"><span class="lineno">  477</span>        *<span class="keyword">this</span> = <a class="code hl_function" href="../../d1/d83/classuint256__t.html#a8161d52d369e525f4e61129376adfcf1">divide</a>(p).first;</div>
+<div class="line"><span class="lineno">  478</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  479</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
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 <div class="dyncontent">
@@ -2516,9 +2516,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is less than other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00630" name="l00630"></a><span class="lineno">  630</span>                                   {</div>
-<div class="line"><a id="l00631" name="l00631"></a><span class="lineno">  631</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> &lt; <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(other);</div>
-<div class="line"><a id="l00632" name="l00632"></a><span class="lineno">  632</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  630</span>                                   {</div>
+<div class="line"><span class="lineno">  631</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> &lt; <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(other);</div>
+<div class="line"><span class="lineno">  632</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2554,9 +2554,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is less than other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00543" name="l00543"></a><span class="lineno">  543</span>                                                  {</div>
-<div class="line"><a id="l00544" name="l00544"></a><span class="lineno">  544</span>        <span class="keywordflow">return</span> f &lt; other.f || (f == other.f &amp;&amp; s &lt; other.s);</div>
-<div class="line"><a id="l00545" name="l00545"></a><span class="lineno">  545</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  543</span>                                                  {</div>
+<div class="line"><span class="lineno">  544</span>        <span class="keywordflow">return</span> f &lt; other.f || (f == other.f &amp;&amp; s &lt; other.s);</div>
+<div class="line"><span class="lineno">  545</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2600,15 +2600,15 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>value of this shifted by p to left </dd></dl>
-<div class="fragment"><div class="line"><a id="l00733" name="l00733"></a><span class="lineno">  733</span>                                     {</div>
-<div class="line"><a id="l00734" name="l00734"></a><span class="lineno">  734</span>        <span class="keywordflow">if</span> (!p) {</div>
-<div class="line"><a id="l00735" name="l00735"></a><span class="lineno">  735</span>            <span class="keywordflow">return</span> {this-&gt;f, this-&gt;s};</div>
-<div class="line"><a id="l00736" name="l00736"></a><span class="lineno">  736</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (p &gt;= 128) {</div>
-<div class="line"><a id="l00737" name="l00737"></a><span class="lineno">  737</span>            <span class="keywordflow">return</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>((this-&gt;s &lt;&lt; (p - 128)), <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0));</div>
-<div class="line"><a id="l00738" name="l00738"></a><span class="lineno">  738</span>        }</div>
-<div class="line"><a id="l00739" name="l00739"></a><span class="lineno">  739</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>((this-&gt;f &lt;&lt; p) + (this-&gt;s &gt;&gt; (128 - p)),</div>
-<div class="line"><a id="l00740" name="l00740"></a><span class="lineno">  740</span>                         (this-&gt;s &lt;&lt; p));</div>
-<div class="line"><a id="l00741" name="l00741"></a><span class="lineno">  741</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  733</span>                                     {</div>
+<div class="line"><span class="lineno">  734</span>        <span class="keywordflow">if</span> (!p) {</div>
+<div class="line"><span class="lineno">  735</span>            <span class="keywordflow">return</span> {this-&gt;f, this-&gt;s};</div>
+<div class="line"><span class="lineno">  736</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (p &gt;= 128) {</div>
+<div class="line"><span class="lineno">  737</span>            <span class="keywordflow">return</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>((this-&gt;s &lt;&lt; (p - 128)), <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0));</div>
+<div class="line"><span class="lineno">  738</span>        }</div>
+<div class="line"><span class="lineno">  739</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>((this-&gt;f &lt;&lt; p) + (this-&gt;s &gt;&gt; (128 - p)),</div>
+<div class="line"><span class="lineno">  740</span>                         (this-&gt;s &lt;&lt; p));</div>
+<div class="line"><span class="lineno">  741</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2652,18 +2652,18 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this shifted by p to left </dd></dl>
-<div class="fragment"><div class="line"><a id="l00751" name="l00751"></a><span class="lineno">  751</span>                                       {</div>
-<div class="line"><a id="l00752" name="l00752"></a><span class="lineno">  752</span>        <span class="keywordflow">if</span> (p) {</div>
-<div class="line"><a id="l00753" name="l00753"></a><span class="lineno">  753</span>            <span class="keywordflow">if</span> (p &gt;= 128) {</div>
-<div class="line"><a id="l00754" name="l00754"></a><span class="lineno">  754</span>                this-&gt;f = (this-&gt;s &lt;&lt; (p - 128));</div>
-<div class="line"><a id="l00755" name="l00755"></a><span class="lineno">  755</span>                this-&gt;s = <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0);</div>
-<div class="line"><a id="l00756" name="l00756"></a><span class="lineno">  756</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00757" name="l00757"></a><span class="lineno">  757</span>                f = ((this-&gt;s &gt;&gt; (128 - p)) + (this-&gt;f &lt;&lt; p));</div>
-<div class="line"><a id="l00758" name="l00758"></a><span class="lineno">  758</span>                s = (this-&gt;s &lt;&lt; p);</div>
-<div class="line"><a id="l00759" name="l00759"></a><span class="lineno">  759</span>            }</div>
-<div class="line"><a id="l00760" name="l00760"></a><span class="lineno">  760</span>        }</div>
-<div class="line"><a id="l00761" name="l00761"></a><span class="lineno">  761</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00762" name="l00762"></a><span class="lineno">  762</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  751</span>                                       {</div>
+<div class="line"><span class="lineno">  752</span>        <span class="keywordflow">if</span> (p) {</div>
+<div class="line"><span class="lineno">  753</span>            <span class="keywordflow">if</span> (p &gt;= 128) {</div>
+<div class="line"><span class="lineno">  754</span>                this-&gt;f = (this-&gt;s &lt;&lt; (p - 128));</div>
+<div class="line"><span class="lineno">  755</span>                this-&gt;s = <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0);</div>
+<div class="line"><span class="lineno">  756</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  757</span>                f = ((this-&gt;s &gt;&gt; (128 - p)) + (this-&gt;f &lt;&lt; p));</div>
+<div class="line"><span class="lineno">  758</span>                s = (this-&gt;s &lt;&lt; p);</div>
+<div class="line"><span class="lineno">  759</span>            }</div>
+<div class="line"><span class="lineno">  760</span>        }</div>
+<div class="line"><span class="lineno">  761</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  762</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2707,9 +2707,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is less than or equal to other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00642" name="l00642"></a><span class="lineno">  642</span>                                    {</div>
-<div class="line"><a id="l00643" name="l00643"></a><span class="lineno">  643</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> &lt;= <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(other);</div>
-<div class="line"><a id="l00644" name="l00644"></a><span class="lineno">  644</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  642</span>                                    {</div>
+<div class="line"><span class="lineno">  643</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> &lt;= <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(other);</div>
+<div class="line"><span class="lineno">  644</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2745,9 +2745,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is less than or equal to other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00552" name="l00552"></a><span class="lineno">  552</span>                                                   {</div>
-<div class="line"><a id="l00553" name="l00553"></a><span class="lineno">  553</span>        <span class="keywordflow">return</span> f &lt; other.f || (f == other.f &amp;&amp; s &lt;= other.s);</div>
-<div class="line"><a id="l00554" name="l00554"></a><span class="lineno">  554</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  552</span>                                                   {</div>
+<div class="line"><span class="lineno">  553</span>        <span class="keywordflow">return</span> f &lt; other.f || (f == other.f &amp;&amp; s &lt;= other.s);</div>
+<div class="line"><span class="lineno">  554</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2783,10 +2783,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this pointer with it's value equal to <code>p</code> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>                                                    {</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>        <a class="code hl_function" href="../../d1/d83/classuint256__t.html#afee82fa5052e9d8c946b9205b943cec4">__get_integer_from_string</a>(p);</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  202</span>                                                    {</div>
+<div class="line"><span class="lineno">  203</span>        <a class="code hl_function" href="../../d1/d83/classuint256__t.html#afee82fa5052e9d8c946b9205b943cec4">__get_integer_from_string</a>(p);</div>
+<div class="line"><span class="lineno">  204</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  205</span>    }</div>
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 <div class="dyncontent">
@@ -2836,10 +2836,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this pointer with it's value equal to <code>p</code> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>                                            {</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>        this-&gt;s = p;</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  192</span>                                            {</div>
+<div class="line"><span class="lineno">  193</span>        this-&gt;s = p;</div>
+<div class="line"><span class="lineno">  194</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  195</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2918,9 +2918,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is equal to other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00678" name="l00678"></a><span class="lineno">  678</span>                                    {</div>
-<div class="line"><a id="l00679" name="l00679"></a><span class="lineno">  679</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> == <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(other);</div>
-<div class="line"><a id="l00680" name="l00680"></a><span class="lineno">  680</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  678</span>                                    {</div>
+<div class="line"><span class="lineno">  679</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> == <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(other);</div>
+<div class="line"><span class="lineno">  680</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2956,9 +2956,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is equal than other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00579" name="l00579"></a><span class="lineno">  579</span>                                                   {</div>
-<div class="line"><a id="l00580" name="l00580"></a><span class="lineno">  580</span>        <span class="keywordflow">return</span> f == other.f &amp;&amp; s == other.s;</div>
-<div class="line"><a id="l00581" name="l00581"></a><span class="lineno">  581</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  579</span>                                                   {</div>
+<div class="line"><span class="lineno">  580</span>        <span class="keywordflow">return</span> f == other.f &amp;&amp; s == other.s;</div>
+<div class="line"><span class="lineno">  581</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3002,9 +3002,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is greater than other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00654" name="l00654"></a><span class="lineno">  654</span>                                   {</div>
-<div class="line"><a id="l00655" name="l00655"></a><span class="lineno">  655</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> &gt; <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(other);</div>
-<div class="line"><a id="l00656" name="l00656"></a><span class="lineno">  656</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  654</span>                                   {</div>
+<div class="line"><span class="lineno">  655</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> &gt; <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(other);</div>
+<div class="line"><span class="lineno">  656</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3040,9 +3040,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is greater than other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00561" name="l00561"></a><span class="lineno">  561</span>                                                  {</div>
-<div class="line"><a id="l00562" name="l00562"></a><span class="lineno">  562</span>        <span class="keywordflow">return</span> f &gt; other.f || (f == other.f &amp;&amp; s &gt; other.s);</div>
-<div class="line"><a id="l00563" name="l00563"></a><span class="lineno">  563</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  561</span>                                                  {</div>
+<div class="line"><span class="lineno">  562</span>        <span class="keywordflow">return</span> f &gt; other.f || (f == other.f &amp;&amp; s &gt; other.s);</div>
+<div class="line"><span class="lineno">  563</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3086,9 +3086,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is greater than or equal other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00666" name="l00666"></a><span class="lineno">  666</span>                                    {</div>
-<div class="line"><a id="l00667" name="l00667"></a><span class="lineno">  667</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> &gt;= <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(other);</div>
-<div class="line"><a id="l00668" name="l00668"></a><span class="lineno">  668</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  666</span>                                    {</div>
+<div class="line"><span class="lineno">  667</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> &gt;= <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(other);</div>
+<div class="line"><span class="lineno">  668</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3124,9 +3124,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is greater than or equal than other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00570" name="l00570"></a><span class="lineno">  570</span>                                                   {</div>
-<div class="line"><a id="l00571" name="l00571"></a><span class="lineno">  571</span>        <span class="keywordflow">return</span> (f &gt; other.f) || (f == other.f &amp;&amp; s &gt;= other.s);</div>
-<div class="line"><a id="l00572" name="l00572"></a><span class="lineno">  572</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  570</span>                                                   {</div>
+<div class="line"><span class="lineno">  571</span>        <span class="keywordflow">return</span> (f &gt; other.f) || (f == other.f &amp;&amp; s &gt;= other.s);</div>
+<div class="line"><span class="lineno">  572</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3170,15 +3170,15 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>value of this shifted by p to right </dd></dl>
-<div class="fragment"><div class="line"><a id="l00772" name="l00772"></a><span class="lineno">  772</span>                                     {</div>
-<div class="line"><a id="l00773" name="l00773"></a><span class="lineno">  773</span>        <span class="keywordflow">if</span> (!p) {</div>
-<div class="line"><a id="l00774" name="l00774"></a><span class="lineno">  774</span>            <span class="keywordflow">return</span> {this-&gt;f, this-&gt;s};</div>
-<div class="line"><a id="l00775" name="l00775"></a><span class="lineno">  775</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (p &gt;= 128) {</div>
-<div class="line"><a id="l00776" name="l00776"></a><span class="lineno">  776</span>            <span class="keywordflow">return</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0), (this-&gt;f &gt;&gt; (p - 128)));</div>
-<div class="line"><a id="l00777" name="l00777"></a><span class="lineno">  777</span>        }</div>
-<div class="line"><a id="l00778" name="l00778"></a><span class="lineno">  778</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>((this-&gt;f &gt;&gt; p),</div>
-<div class="line"><a id="l00779" name="l00779"></a><span class="lineno">  779</span>                         (this-&gt;s &gt;&gt; p) + (this-&gt;f &lt;&lt; (128 - p)));</div>
-<div class="line"><a id="l00780" name="l00780"></a><span class="lineno">  780</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  772</span>                                     {</div>
+<div class="line"><span class="lineno">  773</span>        <span class="keywordflow">if</span> (!p) {</div>
+<div class="line"><span class="lineno">  774</span>            <span class="keywordflow">return</span> {this-&gt;f, this-&gt;s};</div>
+<div class="line"><span class="lineno">  775</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (p &gt;= 128) {</div>
+<div class="line"><span class="lineno">  776</span>            <span class="keywordflow">return</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0), (this-&gt;f &gt;&gt; (p - 128)));</div>
+<div class="line"><span class="lineno">  777</span>        }</div>
+<div class="line"><span class="lineno">  778</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>((this-&gt;f &gt;&gt; p),</div>
+<div class="line"><span class="lineno">  779</span>                         (this-&gt;s &gt;&gt; p) + (this-&gt;f &lt;&lt; (128 - p)));</div>
+<div class="line"><span class="lineno">  780</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3222,18 +3222,18 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this shifted by p to right </dd></dl>
-<div class="fragment"><div class="line"><a id="l00790" name="l00790"></a><span class="lineno">  790</span>                                       {</div>
-<div class="line"><a id="l00791" name="l00791"></a><span class="lineno">  791</span>        <span class="keywordflow">if</span> (p) {</div>
-<div class="line"><a id="l00792" name="l00792"></a><span class="lineno">  792</span>            <span class="keywordflow">if</span> (p &gt;= 128) {</div>
-<div class="line"><a id="l00793" name="l00793"></a><span class="lineno">  793</span>                f = <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0);</div>
-<div class="line"><a id="l00794" name="l00794"></a><span class="lineno">  794</span>                s = (this-&gt;f &gt;&gt; (p - 128));</div>
-<div class="line"><a id="l00795" name="l00795"></a><span class="lineno">  795</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00796" name="l00796"></a><span class="lineno">  796</span>                s = (this-&gt;s &gt;&gt; p) + (this-&gt;f &lt;&lt; (128 - p));</div>
-<div class="line"><a id="l00797" name="l00797"></a><span class="lineno">  797</span>                f = (this-&gt;f &gt;&gt; p);</div>
-<div class="line"><a id="l00798" name="l00798"></a><span class="lineno">  798</span>            }</div>
-<div class="line"><a id="l00799" name="l00799"></a><span class="lineno">  799</span>        }</div>
-<div class="line"><a id="l00800" name="l00800"></a><span class="lineno">  800</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00801" name="l00801"></a><span class="lineno">  801</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  790</span>                                       {</div>
+<div class="line"><span class="lineno">  791</span>        <span class="keywordflow">if</span> (p) {</div>
+<div class="line"><span class="lineno">  792</span>            <span class="keywordflow">if</span> (p &gt;= 128) {</div>
+<div class="line"><span class="lineno">  793</span>                f = <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0);</div>
+<div class="line"><span class="lineno">  794</span>                s = (this-&gt;f &gt;&gt; (p - 128));</div>
+<div class="line"><span class="lineno">  795</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  796</span>                s = (this-&gt;s &gt;&gt; p) + (this-&gt;f &lt;&lt; (128 - p));</div>
+<div class="line"><span class="lineno">  797</span>                f = (this-&gt;f &gt;&gt; p);</div>
+<div class="line"><span class="lineno">  798</span>            }</div>
+<div class="line"><span class="lineno">  799</span>        }</div>
+<div class="line"><span class="lineno">  800</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  801</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3277,9 +3277,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>value of this ^ p (^ is bit-wise <a class="el" href="../../d7/d47/namespace_x_o_r.html" title="Functions for XOR cipher algorithm.">XOR</a> operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00901" name="l00901"></a><span class="lineno">  901</span>                                           {</div>
-<div class="line"><a id="l00902" name="l00902"></a><span class="lineno">  902</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(f, s ^ p);</div>
-<div class="line"><a id="l00903" name="l00903"></a><span class="lineno">  903</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  901</span>                                           {</div>
+<div class="line"><span class="lineno">  902</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(f, s ^ p);</div>
+<div class="line"><span class="lineno">  903</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3315,9 +3315,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>value of this ^ p (^ is bit-wise <a class="el" href="../../d7/d47/namespace_x_o_r.html" title="Functions for XOR cipher algorithm.">XOR</a> operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00910" name="l00910"></a><span class="lineno">  910</span>                                                   {</div>
-<div class="line"><a id="l00911" name="l00911"></a><span class="lineno">  911</span>        <span class="keywordflow">return</span> {this-&gt;f ^ p.f, this-&gt;s ^ p.s};</div>
-<div class="line"><a id="l00912" name="l00912"></a><span class="lineno">  912</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  910</span>                                                   {</div>
+<div class="line"><span class="lineno">  911</span>        <span class="keywordflow">return</span> {this-&gt;f ^ p.f, this-&gt;s ^ p.s};</div>
+<div class="line"><span class="lineno">  912</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3361,10 +3361,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this = this ^ p (^ is bit-wise <a class="el" href="../../d7/d47/namespace_x_o_r.html" title="Functions for XOR cipher algorithm.">XOR</a> operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00933" name="l00933"></a><span class="lineno">  933</span>                                             {</div>
-<div class="line"><a id="l00934" name="l00934"></a><span class="lineno">  934</span>        s ^= p;</div>
-<div class="line"><a id="l00935" name="l00935"></a><span class="lineno">  935</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00936" name="l00936"></a><span class="lineno">  936</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  933</span>                                             {</div>
+<div class="line"><span class="lineno">  934</span>        s ^= p;</div>
+<div class="line"><span class="lineno">  935</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  936</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3400,11 +3400,11 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this = this ^ p (^ is bit-wise <a class="el" href="../../d7/d47/namespace_x_o_r.html" title="Functions for XOR cipher algorithm.">XOR</a> operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00919" name="l00919"></a><span class="lineno">  919</span>                                                     {</div>
-<div class="line"><a id="l00920" name="l00920"></a><span class="lineno">  920</span>        f ^= p.f;</div>
-<div class="line"><a id="l00921" name="l00921"></a><span class="lineno">  921</span>        s ^= p.s;</div>
-<div class="line"><a id="l00922" name="l00922"></a><span class="lineno">  922</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00923" name="l00923"></a><span class="lineno">  923</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  919</span>                                                     {</div>
+<div class="line"><span class="lineno">  920</span>        f ^= p.f;</div>
+<div class="line"><span class="lineno">  921</span>        s ^= p.s;</div>
+<div class="line"><span class="lineno">  922</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  923</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3448,9 +3448,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>value of this | p (| is bit-wise operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00856" name="l00856"></a><span class="lineno">  856</span>                                           {</div>
-<div class="line"><a id="l00857" name="l00857"></a><span class="lineno">  857</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> | <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(p);</div>
-<div class="line"><a id="l00858" name="l00858"></a><span class="lineno">  858</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  856</span>                                           {</div>
+<div class="line"><span class="lineno">  857</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> | <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(p);</div>
+<div class="line"><span class="lineno">  858</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3486,9 +3486,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>value of this | p (| is bit-wise OR operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00865" name="l00865"></a><span class="lineno">  865</span>                                                   {</div>
-<div class="line"><a id="l00866" name="l00866"></a><span class="lineno">  866</span>        <span class="keywordflow">return</span> {this-&gt;f | p.f, this-&gt;s | p.s};</div>
-<div class="line"><a id="l00867" name="l00867"></a><span class="lineno">  867</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  865</span>                                                   {</div>
+<div class="line"><span class="lineno">  866</span>        <span class="keywordflow">return</span> {this-&gt;f | p.f, this-&gt;s | p.s};</div>
+<div class="line"><span class="lineno">  867</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3532,10 +3532,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this = this | p (| is bit-wise OR operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00877" name="l00877"></a><span class="lineno">  877</span>                                             {</div>
-<div class="line"><a id="l00878" name="l00878"></a><span class="lineno">  878</span>        s |= p;</div>
-<div class="line"><a id="l00879" name="l00879"></a><span class="lineno">  879</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00880" name="l00880"></a><span class="lineno">  880</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  877</span>                                             {</div>
+<div class="line"><span class="lineno">  878</span>        s |= p;</div>
+<div class="line"><span class="lineno">  879</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  880</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3571,11 +3571,11 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this = this | p (| is bit-wise OR operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00887" name="l00887"></a><span class="lineno">  887</span>                                                     {</div>
-<div class="line"><a id="l00888" name="l00888"></a><span class="lineno">  888</span>        f |= p.f;</div>
-<div class="line"><a id="l00889" name="l00889"></a><span class="lineno">  889</span>        s |= p.s;</div>
-<div class="line"><a id="l00890" name="l00890"></a><span class="lineno">  890</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00891" name="l00891"></a><span class="lineno">  891</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  887</span>                                                     {</div>
+<div class="line"><span class="lineno">  888</span>        f |= p.f;</div>
+<div class="line"><span class="lineno">  889</span>        s |= p.s;</div>
+<div class="line"><span class="lineno">  890</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  891</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3619,9 +3619,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is either one of the values are non-zero, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00715" name="l00715"></a><span class="lineno">  715</span>                                       {</div>
-<div class="line"><a id="l00716" name="l00716"></a><span class="lineno">  716</span>        <span class="keywordflow">return</span> (s || f) || (b);</div>
-<div class="line"><a id="l00717" name="l00717"></a><span class="lineno">  717</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  715</span>                                       {</div>
+<div class="line"><span class="lineno">  716</span>        <span class="keywordflow">return</span> (s || f) || (b);</div>
+<div class="line"><span class="lineno">  717</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3657,9 +3657,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if one of the values are not zero, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00612" name="l00612"></a><span class="lineno">  612</span>                                               {</div>
-<div class="line"><a id="l00613" name="l00613"></a><span class="lineno">  613</span>        <span class="keywordflow">return</span> (s || f) || (b.s || b.f);</div>
-<div class="line"><a id="l00614" name="l00614"></a><span class="lineno">  614</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  612</span>                                               {</div>
+<div class="line"><span class="lineno">  613</span>        <span class="keywordflow">return</span> (s || f) || (b.s || b.f);</div>
+<div class="line"><span class="lineno">  614</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3688,7 +3688,7 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
 
 <p>operator ~ for <a class="el" href="../../d1/d83/classuint256__t.html" title="class for 256-bit unsigned integer">uint256_t</a> </p>
 <dl class="section return"><dt>Returns</dt><dd>1's complement of this number </dd></dl>
-<div class="fragment"><div class="line"><a id="l00723" name="l00723"></a><span class="lineno">  723</span>{ <span class="keywordflow">return</span> {~f, ~s}; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  723</span>{ <span class="keywordflow">return</span> {~f, ~s}; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3717,7 +3717,7 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
 
 <p>returns upper 128-bit integer part </p>
 <dl class="section return"><dt>Returns</dt><dd>returns upper 128-bit integer part </dd></dl>
-<div class="fragment"><div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>{ <span class="keywordflow">return</span> f; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  175</span>{ <span class="keywordflow">return</span> f; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3766,31 +3766,31 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>op, ostream object. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00947" name="l00947"></a><span class="lineno">  947</span>                                                               {</div>
-<div class="line"><a id="l00948" name="l00948"></a><span class="lineno">  948</span>        <span class="keywordflow">if</span> (!p.f) {</div>
-<div class="line"><a id="l00949" name="l00949"></a><span class="lineno">  949</span>            op &lt;&lt; p.s;</div>
-<div class="line"><a id="l00950" name="l00950"></a><span class="lineno">  950</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00951" name="l00951"></a><span class="lineno">  951</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> out = <span class="stringliteral">&quot;0&quot;</span>, p_2 = <span class="stringliteral">&quot;1&quot;</span>;</div>
-<div class="line"><a id="l00952" name="l00952"></a><span class="lineno">  952</span>            <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> L(1);</div>
-<div class="line"><a id="l00953" name="l00953"></a><span class="lineno">  953</span>            <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; 128; ++i) {</div>
-<div class="line"><a id="l00954" name="l00954"></a><span class="lineno">  954</span>                <span class="keywordflow">if</span> ((p.s &amp; L)) {</div>
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-<div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span>    <span class="keywordtype">int</span> u = 0, v = 0;</div>
-<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; e; ++i)</div>
-<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span>    {</div>
-<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; u &gt;&gt; v;</div>
-<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span>        <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>.addEdge(u, v);</div>
-<div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span>    }</div>
-<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>  </div>
-<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>    <span class="keywordtype">int</span> res = <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>.hopcroftKarpAlgorithm();</div>
-<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Maximum matching is &quot;</span> &lt;&lt; res &lt;&lt;<span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span> </div>
-<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span> </div>
-<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  307</span>{</div>
+<div class="line"><span class="lineno">  308</span>    <a class="code hl_function" href="../../d1/d9a/hopcroft__karp_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();  <span class="comment">// perform self-tests</span></div>
+<div class="line"><span class="lineno">  309</span> </div>
+<div class="line"><span class="lineno">  310</span>    <span class="keywordtype">int</span> v1 = 0, v2 = 0, e = 0;</div>
+<div class="line"><span class="lineno">  311</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; v1 &gt;&gt; v2 &gt;&gt; e; <span class="comment">// vertices of left side, right side and edges</span></div>
+<div class="line"><span class="lineno">  312</span>    <a class="code hl_class" href="../../d8/d69/classgraph_1_1_h_k_graph.html">HKGraph</a> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>(v1, v2);  </div>
+<div class="line"><span class="lineno">  313</span>    <span class="keywordtype">int</span> u = 0, v = 0;</div>
+<div class="line"><span class="lineno">  314</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; e; ++i)</div>
+<div class="line"><span class="lineno">  315</span>    {</div>
+<div class="line"><span class="lineno">  316</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; u &gt;&gt; v;</div>
+<div class="line"><span class="lineno">  317</span>        <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>.addEdge(u, v);</div>
+<div class="line"><span class="lineno">  318</span>    }</div>
+<div class="line"><span class="lineno">  319</span>  </div>
+<div class="line"><span class="lineno">  320</span>    <span class="keywordtype">int</span> res = <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>.hopcroftKarpAlgorithm();</div>
+<div class="line"><span class="lineno">  321</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Maximum matching is &quot;</span> &lt;&lt; res &lt;&lt;<span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  322</span> </div>
+<div class="line"><span class="lineno">  323</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  324</span> </div>
+<div class="line"><span class="lineno">  325</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aclassgraph_1_1_h_k_graph_html"><div class="ttname"><a href="../../d8/d69/classgraph_1_1_h_k_graph.html">graph::HKGraph</a></div><div class="ttdoc">Represents Bipartite graph for Hopcroft Karp implementation.</div><div class="ttdef"><b>Definition:</b> hopcroft_karp.cpp:67</div></div>
@@ -202,7 +202,7 @@ Algorithm</h3>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../d1/d9a/hopcroft__karp_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="574" height="134"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d1/d9a/hopcroft__karp_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="100%" height="425"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
 </div>
 </div>
 
@@ -223,56 +223,56 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Self-test implementation </p><dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
-<div class="fragment"><div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>            {</div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>     <span class="comment">// Sample test case 1</span></div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>         <span class="keywordtype">int</span> v1a = 3, v1b = 5, e1 = 2;  <span class="comment">// vertices of left side, right side and edges</span></div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>         <a class="code hl_class" href="../../d8/d69/classgraph_1_1_h_k_graph.html">HKGraph</a> g1(v1a, v1b); <span class="comment">// execute the algorithm </span></div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span> </div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>         g1.addEdge(0,1);</div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>         g1.addEdge(1,4);</div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span> </div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>         <span class="keywordtype">int</span> expected_res1 = 0; <span class="comment">// for the above sample data, this is the expected output</span></div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>         <span class="keywordtype">int</span> res1 = g1.hopcroftKarpAlgorithm();</div>
-<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span> </div>
-<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>         assert(res1 == expected_res1); <span class="comment">// assert check to ensure that the algorithm executed correctly for test 1</span></div>
-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>    </div>
-<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>     <span class="comment">// Sample test case 2</span></div>
-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>             <span class="keywordtype">int</span> v2a = 4, v2b = 4, e2 = 6;  <span class="comment">// vertices of left side, right side and edges</span></div>
-<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>         <a class="code hl_class" href="../../d8/d69/classgraph_1_1_h_k_graph.html">HKGraph</a> g2(v2a, v2b); <span class="comment">// execute the algorithm </span></div>
-<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span> </div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>             g2.addEdge(1,1);</div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>         g2.addEdge(1,3);</div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>         g2.addEdge(2,3);</div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>         g2.addEdge(3,4);</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>         g2.addEdge(4,3);</div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>             g2.addEdge(4,2);</div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>    </div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>         <span class="keywordtype">int</span> expected_res2 = 0; <span class="comment">// for the above sample data, this is the expected output</span></div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>         <span class="keywordtype">int</span> res2 = g2.hopcroftKarpAlgorithm();</div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span> </div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>         assert(res2 == expected_res2); <span class="comment">// assert check to ensure that the algorithm executed correctly for test 2</span></div>
-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>    </div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>      <span class="comment">// Sample test case 3</span></div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>             <span class="keywordtype">int</span> v3a = 6, v3b = 6, e3 = 4;  <span class="comment">// vertices of left side, right side and edges</span></div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>         <a class="code hl_class" href="../../d8/d69/classgraph_1_1_h_k_graph.html">HKGraph</a> g3(v3a, v3b); <span class="comment">// execute the algorithm </span></div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span> </div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>             g3.addEdge(0,1);</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>         g3.addEdge(1,4);</div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>         g3.addEdge(1,5);</div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>         g3.addEdge(5,0);</div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span> </div>
-<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>         <span class="keywordtype">int</span> expected_res3 = 0; <span class="comment">// for the above sample data, this is the expected output</span></div>
-<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>         <span class="keywordtype">int</span> res3 = g3.hopcroftKarpAlgorithm();</div>
-<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span> </div>
-<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>         assert(res3 == expected_res3); <span class="comment">// assert check to ensure that the algorithm executed correctly for test 3</span></div>
-<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>    </div>
-<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>    </div>
-<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>        </div>
-<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  255</span>            {</div>
+<div class="line"><span class="lineno">  256</span>     <span class="comment">// Sample test case 1</span></div>
+<div class="line"><span class="lineno">  257</span>         <span class="keywordtype">int</span> v1a = 3, v1b = 5, e1 = 2;  <span class="comment">// vertices of left side, right side and edges</span></div>
+<div class="line"><span class="lineno">  258</span>         <a class="code hl_class" href="../../d8/d69/classgraph_1_1_h_k_graph.html">HKGraph</a> g1(v1a, v1b); <span class="comment">// execute the algorithm </span></div>
+<div class="line"><span class="lineno">  259</span> </div>
+<div class="line"><span class="lineno">  260</span>         g1.addEdge(0,1);</div>
+<div class="line"><span class="lineno">  261</span>         g1.addEdge(1,4);</div>
+<div class="line"><span class="lineno">  262</span> </div>
+<div class="line"><span class="lineno">  263</span>         <span class="keywordtype">int</span> expected_res1 = 0; <span class="comment">// for the above sample data, this is the expected output</span></div>
+<div class="line"><span class="lineno">  264</span>         <span class="keywordtype">int</span> res1 = g1.hopcroftKarpAlgorithm();</div>
+<div class="line"><span class="lineno">  265</span> </div>
+<div class="line"><span class="lineno">  266</span>         assert(res1 == expected_res1); <span class="comment">// assert check to ensure that the algorithm executed correctly for test 1</span></div>
+<div class="line"><span class="lineno">  267</span>    </div>
+<div class="line"><span class="lineno">  268</span>     <span class="comment">// Sample test case 2</span></div>
+<div class="line"><span class="lineno">  269</span>             <span class="keywordtype">int</span> v2a = 4, v2b = 4, e2 = 6;  <span class="comment">// vertices of left side, right side and edges</span></div>
+<div class="line"><span class="lineno">  270</span>         <a class="code hl_class" href="../../d8/d69/classgraph_1_1_h_k_graph.html">HKGraph</a> g2(v2a, v2b); <span class="comment">// execute the algorithm </span></div>
+<div class="line"><span class="lineno">  271</span> </div>
+<div class="line"><span class="lineno">  272</span>             g2.addEdge(1,1);</div>
+<div class="line"><span class="lineno">  273</span>         g2.addEdge(1,3);</div>
+<div class="line"><span class="lineno">  274</span>         g2.addEdge(2,3);</div>
+<div class="line"><span class="lineno">  275</span>         g2.addEdge(3,4);</div>
+<div class="line"><span class="lineno">  276</span>         g2.addEdge(4,3);</div>
+<div class="line"><span class="lineno">  277</span>             g2.addEdge(4,2);</div>
+<div class="line"><span class="lineno">  278</span>    </div>
+<div class="line"><span class="lineno">  279</span>         <span class="keywordtype">int</span> expected_res2 = 0; <span class="comment">// for the above sample data, this is the expected output</span></div>
+<div class="line"><span class="lineno">  280</span>         <span class="keywordtype">int</span> res2 = g2.hopcroftKarpAlgorithm();</div>
+<div class="line"><span class="lineno">  281</span> </div>
+<div class="line"><span class="lineno">  282</span>         assert(res2 == expected_res2); <span class="comment">// assert check to ensure that the algorithm executed correctly for test 2</span></div>
+<div class="line"><span class="lineno">  283</span>    </div>
+<div class="line"><span class="lineno">  284</span>      <span class="comment">// Sample test case 3</span></div>
+<div class="line"><span class="lineno">  285</span>             <span class="keywordtype">int</span> v3a = 6, v3b = 6, e3 = 4;  <span class="comment">// vertices of left side, right side and edges</span></div>
+<div class="line"><span class="lineno">  286</span>         <a class="code hl_class" href="../../d8/d69/classgraph_1_1_h_k_graph.html">HKGraph</a> g3(v3a, v3b); <span class="comment">// execute the algorithm </span></div>
+<div class="line"><span class="lineno">  287</span> </div>
+<div class="line"><span class="lineno">  288</span>             g3.addEdge(0,1);</div>
+<div class="line"><span class="lineno">  289</span>         g3.addEdge(1,4);</div>
+<div class="line"><span class="lineno">  290</span>         g3.addEdge(1,5);</div>
+<div class="line"><span class="lineno">  291</span>         g3.addEdge(5,0);</div>
+<div class="line"><span class="lineno">  292</span> </div>
+<div class="line"><span class="lineno">  293</span>         <span class="keywordtype">int</span> expected_res3 = 0; <span class="comment">// for the above sample data, this is the expected output</span></div>
+<div class="line"><span class="lineno">  294</span>         <span class="keywordtype">int</span> res3 = g3.hopcroftKarpAlgorithm();</div>
+<div class="line"><span class="lineno">  295</span> </div>
+<div class="line"><span class="lineno">  296</span>         assert(res3 == expected_res3); <span class="comment">// assert check to ensure that the algorithm executed correctly for test 3</span></div>
+<div class="line"><span class="lineno">  297</span>    </div>
+<div class="line"><span class="lineno">  298</span>    </div>
+<div class="line"><span class="lineno">  299</span>        </div>
+<div class="line"><span class="lineno">  300</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../d1/d9a/hopcroft__karp_8cpp_a88ec9ad42717780d6caaff9d3d6977f9_cgraph.svg" width="475" height="134"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d1/d9a/hopcroft__karp_8cpp_a88ec9ad42717780d6caaff9d3d6977f9_cgraph.svg" width="648" height="167"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
 </div>
 </div>
 
@@ -284,7 +284,7 @@ Here is the call graph for this function:</div>
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   <ul>
     <li class="navelem"><a class="el" href="../../dir_12552d7fa429bf94a2e32e5cf39f7e69.html">graph</a></li><li class="navelem"><a class="el" href="../../d1/d9a/hopcroft__karp_8cpp.html">hopcroft_karp.cpp</a></li>
-    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.2 </li>
+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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diff --git a/d1/d9a/hopcroft__karp_8cpp_a88ec9ad42717780d6caaff9d3d6977f9_cgraph.map b/d1/d9a/hopcroft__karp_8cpp_a88ec9ad42717780d6caaff9d3d6977f9_cgraph.map
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-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
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    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
    </div>
    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
 </table>
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 <!-- end header part -->
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+<!-- Generated by Doxygen 1.9.3 -->
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@@ -185,7 +185,7 @@ Functions</h2></td></tr>
 <dl class="section return"><dt>Returns</dt><dd>the computed function value at that call </dd></dl>
 <dl class="section examples"><dt>Examples</dt><dd><a class="el" href="../../dc/dc4/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2numerical_methods_2rungekutta_8cpp-example.html#a0">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp</a>.</dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>{ <span class="keywordflow">return</span> ((x - y) / 2.0); }</div>
+<div class="fragment"><div class="line"><span class="lineno">   33</span>{ <span class="keywordflow">return</span> ((x - y) / 2.0); }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -207,10 +207,10 @@ Functions</h2></td></tr>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>           {</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    <a class="code hl_function" href="../../d1/da6/rungekutta_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// Execute the tests</span></div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  130</span>           {</div>
+<div class="line"><span class="lineno">  131</span>    <a class="code hl_function" href="../../d1/da6/rungekutta_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// Execute the tests</span></div>
+<div class="line"><span class="lineno">  132</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  133</span>}</div>
 <div class="ttc" id="arungekutta_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d1/da6/rungekutta_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Tests to check algorithm implementation.</div><div class="ttdef"><b>Definition:</b> rungekutta.cpp:100</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -272,45 +272,45 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd>the value of y at thr required value of x from the initial conditions </dd></dl>
 <dl class="section examples"><dt>Examples</dt><dd><a class="el" href="../../dc/dc4/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2numerical_methods_2rungekutta_8cpp-example.html#a1">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp</a>.</dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>                                   {</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <span class="comment">// Count number of iterations</span></div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <span class="comment">// using step size or</span></div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    <span class="comment">// step height h</span></div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span> </div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    <span class="comment">// n calucates the number of iterations</span></div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    <span class="comment">// k1, k2, k3, k4 are the Runge Kutta variables</span></div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <span class="comment">// used for calculation of y at each iteration</span></div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span> </div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <span class="keyword">auto</span> n = <span class="keyword">static_cast&lt;</span>uint64_t<span class="keyword">&gt;</span>((x - init_x) / <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>);</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <span class="comment">// used a vector container for the variables</span></div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>(4, 0.0);</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span> </div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    <span class="comment">// Iterate for number of iterations</span></div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span> </div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <span class="keywordtype">double</span> y = init_y;</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt;= n; ++i) {</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>        <span class="comment">// Apply Runge Kutta Formulas</span></div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        <span class="comment">// to find next value of y</span></div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>        <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>[0] = <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> * <a class="code hl_function" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a>(init_x, y);</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>[1] = <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> * <a class="code hl_function" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a>(init_x + 0.5 * <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, y + 0.5 * k[0]);</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>        <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>[2] = <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> * <a class="code hl_function" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a>(init_x + 0.5 * <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, y + 0.5 * k[1]);</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>        <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>[3] = <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> * <a class="code hl_function" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a>(init_x + <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, y + k[2]);</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span> </div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        <span class="comment">// Update next value of y</span></div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span> </div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>        y += (1.0 / 6.0) * (k[0] + 2 * k[1] + 2 * k[2] + k[3]);</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span> </div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>        <span class="comment">// Update next value of x</span></div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span> </div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        init_x += <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    }</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span> </div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    <span class="keywordflow">return</span> y;</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   58</span>                                   {</div>
+<div class="line"><span class="lineno">   59</span>    <span class="comment">// Count number of iterations</span></div>
+<div class="line"><span class="lineno">   60</span>    <span class="comment">// using step size or</span></div>
+<div class="line"><span class="lineno">   61</span>    <span class="comment">// step height h</span></div>
+<div class="line"><span class="lineno">   62</span> </div>
+<div class="line"><span class="lineno">   63</span>    <span class="comment">// n calucates the number of iterations</span></div>
+<div class="line"><span class="lineno">   64</span>    <span class="comment">// k1, k2, k3, k4 are the Runge Kutta variables</span></div>
+<div class="line"><span class="lineno">   65</span>    <span class="comment">// used for calculation of y at each iteration</span></div>
+<div class="line"><span class="lineno">   66</span> </div>
+<div class="line"><span class="lineno">   67</span>    <span class="keyword">auto</span> n = <span class="keyword">static_cast&lt;</span>uint64_t<span class="keyword">&gt;</span>((x - init_x) / <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>);</div>
+<div class="line"><span class="lineno">   68</span>    <span class="comment">// used a vector container for the variables</span></div>
+<div class="line"><span class="lineno">   69</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>(4, 0.0);</div>
+<div class="line"><span class="lineno">   70</span> </div>
+<div class="line"><span class="lineno">   71</span>    <span class="comment">// Iterate for number of iterations</span></div>
+<div class="line"><span class="lineno">   72</span> </div>
+<div class="line"><span class="lineno">   73</span>    <span class="keywordtype">double</span> y = init_y;</div>
+<div class="line"><span class="lineno">   74</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt;= n; ++i) {</div>
+<div class="line"><span class="lineno">   75</span>        <span class="comment">// Apply Runge Kutta Formulas</span></div>
+<div class="line"><span class="lineno">   76</span>        <span class="comment">// to find next value of y</span></div>
+<div class="line"><span class="lineno">   77</span>        <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>[0] = <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> * <a class="code hl_function" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a>(init_x, y);</div>
+<div class="line"><span class="lineno">   78</span>        <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>[1] = <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> * <a class="code hl_function" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a>(init_x + 0.5 * <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, y + 0.5 * k[0]);</div>
+<div class="line"><span class="lineno">   79</span>        <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>[2] = <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> * <a class="code hl_function" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a>(init_x + 0.5 * <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, y + 0.5 * k[1]);</div>
+<div class="line"><span class="lineno">   80</span>        <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>[3] = <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> * <a class="code hl_function" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a>(init_x + <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, y + k[2]);</div>
+<div class="line"><span class="lineno">   81</span> </div>
+<div class="line"><span class="lineno">   82</span>        <span class="comment">// Update next value of y</span></div>
+<div class="line"><span class="lineno">   83</span> </div>
+<div class="line"><span class="lineno">   84</span>        y += (1.0 / 6.0) * (k[0] + 2 * k[1] + 2 * k[2] + k[3]);</div>
+<div class="line"><span class="lineno">   85</span> </div>
+<div class="line"><span class="lineno">   86</span>        <span class="comment">// Update next value of x</span></div>
+<div class="line"><span class="lineno">   87</span> </div>
+<div class="line"><span class="lineno">   88</span>        init_x += <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>;</div>
+<div class="line"><span class="lineno">   89</span>    }</div>
+<div class="line"><span class="lineno">   90</span> </div>
+<div class="line"><span class="lineno">   91</span>    <span class="keywordflow">return</span> y;</div>
+<div class="line"><span class="lineno">   92</span>}</div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
 <div class="ttc" id="ahash__search_8cpp_html_a566eaf0ffafd50bc61e644561fd27001"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a></div><div class="ttdeci">int h(int key)</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:45</div></div>
 <div class="ttc" id="arungekutta_8cpp_html_a450497475f5607333f9aca8f88901579"><div class="ttname"><a href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a></div><div class="ttdeci">static double change(double x, double y)</div><div class="ttdoc">for using the vector container</div><div class="ttdef"><b>Definition:</b> rungekutta.cpp:33</div></div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; double &gt;</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -345,31 +345,31 @@ Here is the call graph for this function:</div>
 
 <p>Tests to check algorithm implementation. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>                   {</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The Runge Kutta function will be tested on the basis of &quot;</span></div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>                 <span class="stringliteral">&quot;precomputed values\n&quot;</span>;</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span> </div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1....&quot;</span></div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>              &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    <span class="keywordtype">double</span> valfirst = <a class="code hl_function" href="../../d1/da6/rungekutta_8cpp.html#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a>(</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>        2, 3, 4, 0.2);  <span class="comment">// Tests the function with pre calculated values</span></div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    assert(valfirst == 3.10363932323749570);</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 1\n&quot;</span>;</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span> </div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2....&quot;</span></div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>              &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    <span class="keywordtype">double</span> valsec = <a class="code hl_function" href="../../d1/da6/rungekutta_8cpp.html#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a>(</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>        1, 2, 5, 0.1);  <span class="comment">// The value of step changed</span></div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    assert(valsec == 3.40600589380261409);</div>
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-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span> </div>
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+<div class="line"><span class="lineno">  101</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The Runge Kutta function will be tested on the basis of &quot;</span></div>
+<div class="line"><span class="lineno">  102</span>                 <span class="stringliteral">&quot;precomputed values\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  103</span> </div>
+<div class="line"><span class="lineno">  104</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1....&quot;</span></div>
+<div class="line"><span class="lineno">  105</span>              &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  106</span>    <span class="keywordtype">double</span> valfirst = <a class="code hl_function" href="../../d1/da6/rungekutta_8cpp.html#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a>(</div>
+<div class="line"><span class="lineno">  107</span>        2, 3, 4, 0.2);  <span class="comment">// Tests the function with pre calculated values</span></div>
+<div class="line"><span class="lineno">  108</span>    assert(valfirst == 3.10363932323749570);</div>
+<div class="line"><span class="lineno">  109</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 1\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  110</span> </div>
+<div class="line"><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2....&quot;</span></div>
+<div class="line"><span class="lineno">  112</span>              &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  113</span>    <span class="keywordtype">double</span> valsec = <a class="code hl_function" href="../../d1/da6/rungekutta_8cpp.html#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a>(</div>
+<div class="line"><span class="lineno">  114</span>        1, 2, 5, 0.1);  <span class="comment">// The value of step changed</span></div>
+<div class="line"><span class="lineno">  115</span>    assert(valsec == 3.40600589380261409);</div>
+<div class="line"><span class="lineno">  116</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 2\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  117</span> </div>
+<div class="line"><span class="lineno">  118</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3....&quot;</span></div>
+<div class="line"><span class="lineno">  119</span>              &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  120</span>    <span class="keywordtype">double</span> valthird = <a class="code hl_function" href="../../d1/da6/rungekutta_8cpp.html#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a>(</div>
+<div class="line"><span class="lineno">  121</span>        -1, 3, 4, 0.1);  <span class="comment">// Tested with negative value</span></div>
+<div class="line"><span class="lineno">  122</span>    assert(valthird == 2.49251005860244268);</div>
+<div class="line"><span class="lineno">  123</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 3\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  124</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int64_t, size&gt;</a> unsortedArray{};</div>
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-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>}</div>
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+<div class="line"><span class="lineno">  161</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">time</a>(<span class="keyword">nullptr</span>));</div>
+<div class="line"><span class="lineno">  162</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int64_t, size&gt;</a> unsortedArray{};</div>
+<div class="line"><span class="lineno">  163</span>    assert(from &lt; to);</div>
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+<div class="line"><span class="lineno">  166</span>        int64_t randomNum = from + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">rand</a>() % (to - from + 1);</div>
+<div class="line"><span class="lineno">  167</span>        <span class="keywordflow">if</span> (randomNum) {</div>
+<div class="line"><span class="lineno">  168</span>            unsortedArray[i] = randomNum;</div>
+<div class="line"><span class="lineno">  169</span>            i++;</div>
+<div class="line"><span class="lineno">  170</span>        }</div>
+<div class="line"><span class="lineno">  171</span>    }</div>
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+<div class="fragment"><div class="line"><span class="lineno">   88</span>                                                   {</div>
+<div class="line"><span class="lineno">   89</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">time</a>(<span class="keyword">nullptr</span>));  <span class="comment">// Initialize random number generator.</span></div>
+<div class="line"><span class="lineno">   90</span>    int64_t randomPivotIndex = start + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">rand</a>() % (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start + 1);</div>
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-<div class="line"><a id="l00326" name="l00326"></a><span class="lineno">  326</span>    <span class="keyword">const</span> int64_t inputSize = 10;</div>
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+<div class="line"><span class="lineno">  326</span>    <span class="keyword">const</span> int64_t inputSize = 10;</div>
+<div class="line"><span class="lineno">  327</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int64_t, inputSize&gt;</a> unsorted_array =</div>
+<div class="line"><span class="lineno">  328</span>        sorting::random_pivot_quick_sort::generateUnsortedArray&lt;inputSize&gt;(</div>
+<div class="line"><span class="lineno">  329</span>            50, 1000);</div>
+<div class="line"><span class="lineno">  330</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Unsorted array is : &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  331</span>    <a class="code hl_function" href="../../d1/daa/random__pivot__quick__sort_8cpp.html#ac3281dc34a9cfd7beb332419b8a0aa10">sorting::random_pivot_quick_sort::showArray</a>(unsorted_array);</div>
+<div class="line"><span class="lineno">  332</span> </div>
+<div class="line"><span class="lineno">  333</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int64_t, inputSize&gt;</a> sorted_array =</div>
+<div class="line"><span class="lineno">  334</span>        <a class="code hl_function" href="../../d1/daa/random__pivot__quick__sort_8cpp.html#a7d2e7465e7b5d54c2de6d5e9db1ea6a5">sorting::random_pivot_quick_sort::quickSortRP</a>(</div>
+<div class="line"><span class="lineno">  335</span>            unsorted_array, 0, unsorted_array.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/size.html">size</a>() - 1);</div>
+<div class="line"><span class="lineno">  336</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Sorted array is : &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  337</span>    <a class="code hl_function" href="../../d1/daa/random__pivot__quick__sort_8cpp.html#ac3281dc34a9cfd7beb332419b8a0aa10">sorting::random_pivot_quick_sort::showArray</a>(sorted_array);</div>
+<div class="line"><span class="lineno">  338</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  339</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
 <div class="ttc" id="arandom__pivot__quick__sort_8cpp_html_a7d2e7465e7b5d54c2de6d5e9db1ea6a5"><div class="ttname"><a href="../../d1/daa/random__pivot__quick__sort_8cpp.html#a7d2e7465e7b5d54c2de6d5e9db1ea6a5">sorting::random_pivot_quick_sort::quickSortRP</a></div><div class="ttdeci">std::array&lt; int64_t, size &gt; quickSortRP(std::array&lt; int64_t, size &gt; arr, int64_t start, int64_t end)</div><div class="ttdoc">Random pivot quick sort function. This function is the starting point of the algorithm.</div><div class="ttdef"><b>Definition:</b> random_pivot_quick_sort.cpp:130</div></div>
@@ -420,22 +420,22 @@ template&lt;size_t size&gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>std::tuple&lt;int64_t , std::array&lt;int64_t , size&gt;&gt; A tuple of pivot index and pivot sorted array. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>                                                             {</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    int64_t pivot = arr[<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a>];  <span class="comment">// Randomly selected element will be here from</span></div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>                               <span class="comment">// caller function (quickSortRP()).</span></div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    int64_t pInd = start;</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span> </div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <span class="keywordflow">for</span> (int64_t i = start; i &lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a>; i++) {</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        <span class="keywordflow">if</span> (arr[i] &lt;= pivot) {</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[i], arr[pInd]);  <span class="comment">// swapping the elements from current</span></div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>                                           <span class="comment">// index to pInd.</span></div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>            pInd++;</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>        }</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    }</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[pInd],</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>              arr[end]);  <span class="comment">// swapping the pivot element to its sorted position</span></div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/tuple/make_tuple.html">std::make_tuple</a>(pInd, arr);</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  104</span>                                                             {</div>
+<div class="line"><span class="lineno">  105</span>    int64_t pivot = arr[<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a>];  <span class="comment">// Randomly selected element will be here from</span></div>
+<div class="line"><span class="lineno">  106</span>                               <span class="comment">// caller function (quickSortRP()).</span></div>
+<div class="line"><span class="lineno">  107</span>    int64_t pInd = start;</div>
+<div class="line"><span class="lineno">  108</span> </div>
+<div class="line"><span class="lineno">  109</span>    <span class="keywordflow">for</span> (int64_t i = start; i &lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a>; i++) {</div>
+<div class="line"><span class="lineno">  110</span>        <span class="keywordflow">if</span> (arr[i] &lt;= pivot) {</div>
+<div class="line"><span class="lineno">  111</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[i], arr[pInd]);  <span class="comment">// swapping the elements from current</span></div>
+<div class="line"><span class="lineno">  112</span>                                           <span class="comment">// index to pInd.</span></div>
+<div class="line"><span class="lineno">  113</span>            pInd++;</div>
+<div class="line"><span class="lineno">  114</span>        }</div>
+<div class="line"><span class="lineno">  115</span>    }</div>
+<div class="line"><span class="lineno">  116</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[pInd],</div>
+<div class="line"><span class="lineno">  117</span>              arr[end]);  <span class="comment">// swapping the pivot element to its sorted position</span></div>
+<div class="line"><span class="lineno">  118</span>    <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/tuple/make_tuple.html">std::make_tuple</a>(pInd, arr);</div>
+<div class="line"><span class="lineno">  119</span>}</div>
 <div class="ttc" id="amake_tuple_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/tuple/make_tuple.html">std::make_tuple</a></div><div class="ttdeci">T make_tuple(T... args)</div></div>
 <div class="ttc" id="aswap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a></div><div class="ttdeci">T swap(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -496,26 +496,26 @@ template&lt;size_t size&gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>std::array&lt;int64_t , size&gt; A fully sorted array in ascending order. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>                                                                  {</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    <span class="keywordflow">if</span> (start &lt; end) {</div>
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-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span> </div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>        <span class="comment">// switching the pivot with right most bound.</span></div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[end], arr[randomIndex]);</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span> </div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>        int64_t pivotIndex = 0;</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        <span class="comment">// getting pivot index and pivot sorted array.</span></div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/tuple/tie.html">std::tie</a>(pivotIndex, arr) = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/partition.html">partition</a>(arr, start, end);</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span> </div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>        <span class="comment">// Recursively calling</span></div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt;int64_t, arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/size.html">size</a>()&gt; rightSortingLeft =</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>            <a class="code hl_function" href="../../d1/daa/random__pivot__quick__sort_8cpp.html#a7d2e7465e7b5d54c2de6d5e9db1ea6a5">quickSortRP</a>(arr, start, pivotIndex - 1);</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt;int64_t, arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/size.html">size</a>()&gt; full_sorted =</div>
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-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  131</span>                                                                  {</div>
+<div class="line"><span class="lineno">  132</span>    <span class="keywordflow">if</span> (start &lt; end) {</div>
+<div class="line"><span class="lineno">  133</span>        int64_t randomIndex = <a class="code hl_function" href="../../d1/daa/random__pivot__quick__sort_8cpp.html#aac5657b4fe2251cd21073f44233f6ea5">getRandomIndex</a>(start, end);</div>
+<div class="line"><span class="lineno">  134</span> </div>
+<div class="line"><span class="lineno">  135</span>        <span class="comment">// switching the pivot with right most bound.</span></div>
+<div class="line"><span class="lineno">  136</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[end], arr[randomIndex]);</div>
+<div class="line"><span class="lineno">  137</span> </div>
+<div class="line"><span class="lineno">  138</span>        int64_t pivotIndex = 0;</div>
+<div class="line"><span class="lineno">  139</span>        <span class="comment">// getting pivot index and pivot sorted array.</span></div>
+<div class="line"><span class="lineno">  140</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/tuple/tie.html">std::tie</a>(pivotIndex, arr) = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/partition.html">partition</a>(arr, start, end);</div>
+<div class="line"><span class="lineno">  141</span> </div>
+<div class="line"><span class="lineno">  142</span>        <span class="comment">// Recursively calling</span></div>
+<div class="line"><span class="lineno">  143</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt;int64_t, arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/size.html">size</a>()&gt; rightSortingLeft =</div>
+<div class="line"><span class="lineno">  144</span>            <a class="code hl_function" href="../../d1/daa/random__pivot__quick__sort_8cpp.html#a7d2e7465e7b5d54c2de6d5e9db1ea6a5">quickSortRP</a>(arr, start, pivotIndex - 1);</div>
+<div class="line"><span class="lineno">  145</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt;int64_t, arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/size.html">size</a>()&gt; full_sorted =</div>
+<div class="line"><span class="lineno">  146</span>            <a class="code hl_function" href="../../d1/daa/random__pivot__quick__sort_8cpp.html#a7d2e7465e7b5d54c2de6d5e9db1ea6a5">quickSortRP</a>(rightSortingLeft, pivotIndex + 1, end);</div>
+<div class="line"><span class="lineno">  147</span>        arr = full_sorted;</div>
+<div class="line"><span class="lineno">  148</span>    }</div>
+<div class="line"><span class="lineno">  149</span>    <span class="keywordflow">return</span> arr;</div>
+<div class="line"><span class="lineno">  150</span>}</div>
 <div class="ttc" id="apartition_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/partition.html">std::partition</a></div><div class="ttdeci">T partition(T... args)</div></div>
 <div class="ttc" id="arandom__pivot__quick__sort_8cpp_html_aac5657b4fe2251cd21073f44233f6ea5"><div class="ttname"><a href="../../d1/daa/random__pivot__quick__sort_8cpp.html#aac5657b4fe2251cd21073f44233f6ea5">sorting::random_pivot_quick_sort::getRandomIndex</a></div><div class="ttdeci">int64_t getRandomIndex(int64_t start, int64_t end)</div><div class="ttdoc">Takes the start and end indices of an array and returns a random int64_teger between the range of tho...</div><div class="ttdef"><b>Definition:</b> random_pivot_quick_sort.cpp:88</div></div>
 <div class="ttc" id="atie_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/tuple/tie.html">std::tie</a></div><div class="ttdeci">T tie(T... args)</div></div>
@@ -560,12 +560,12 @@ template&lt;size_t T&gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   73</span>                                         {</div>
+<div class="line"><span class="lineno">   74</span>    <span class="keywordflow">for</span> (int64_t i = 0; i &lt; arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/size.html">size</a>(); i++) {</div>
+<div class="line"><span class="lineno">   75</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; arr[i] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">   76</span>    }</div>
+<div class="line"><span class="lineno">   77</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   78</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -600,10 +600,10 @@ Here is the call graph for this function:</div>
 
 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>                   {</div>
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+<div class="fragment"><div class="line"><span class="lineno">  312</span>                   {</div>
+<div class="line"><span class="lineno">  313</span>    <a class="code hl_class" href="../../d5/d58/class_test_cases.html">TestCases</a> tc = <a class="code hl_class" href="../../d5/d58/class_test_cases.html">TestCases</a>();</div>
+<div class="line"><span class="lineno">  314</span>    tc.<a class="code hl_function" href="../../d5/d58/class_test_cases.html#aeabea90c02f9159e4a784bbf736e1e23">runTests</a>();</div>
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+<div class="line"><span class="lineno">   67</span>    <span class="comment">// Fourth test on 10 choose 4</span></div>
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+<div class="line"><span class="lineno">  100</span>    }</div>
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+<div class="line"><span class="lineno">  102</span>}</div>
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-<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a></div></div>
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 Here is the call graph for this function:</div>
@@ -256,56 +256,56 @@ template&lt;typename T &gt; </div>
 <dl class="section return"><dt>Returns</dt><dd>0 if no errors </dd>
 <dd>
 negative if error occurred </dd></dl>
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-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>        <span class="keywordflow">for</span> (col = row; col &lt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; col++) {</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>            <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
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-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>            <span class="comment">// Evaluate U[i,k]</span></div>
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-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>        <span class="comment">// Lower triangular matrix</span></div>
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+Collaboration diagram for stack&lt; Type &gt;:</div>
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 <p >Default constructor </p>
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+<div class="line"><span class="lineno">   43</span>        <a class="code hl_variable" href="../../d1/dc2/classstack.html#ac512a3efdc84a5f5c9f53905c8e219b0">size</a> = 0;</div>
+<div class="line"><span class="lineno">   44</span>    }</div>
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 <p >Copy constructor </p>
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 <p >Show stack </p>
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-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>        <a class="code hl_class" href="../../d5/da1/structnode.html">node&lt;Type&gt;</a> *current = <a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>;</div>
-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Top --&gt; &quot;</span>;</div>
-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>        <span class="keywordflow">while</span> (current != <span class="keyword">nullptr</span>) {</div>
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-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Size of stack: &quot;</span> &lt;&lt; <a class="code hl_variable" href="../../d1/dc2/classstack.html#ac512a3efdc84a5f5c9f53905c8e219b0">size</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   29</span>                   {</div>
+<div class="line"><span class="lineno">   30</span>        <a class="code hl_class" href="../../d5/da1/structnode.html">node&lt;Type&gt;</a> *current = <a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>;</div>
+<div class="line"><span class="lineno">   31</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Top --&gt; &quot;</span>;</div>
+<div class="line"><span class="lineno">   32</span>        <span class="keywordflow">while</span> (current != <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">   33</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; current-&gt;data &lt;&lt; <span class="stringliteral">&quot;  &quot;</span>;</div>
+<div class="line"><span class="lineno">   34</span>            current = current-&gt;next;</div>
+<div class="line"><span class="lineno">   35</span>        }</div>
+<div class="line"><span class="lineno">   36</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   37</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Size of stack: &quot;</span> &lt;&lt; <a class="code hl_variable" href="../../d1/dc2/classstack.html#ac512a3efdc84a5f5c9f53905c8e219b0">size</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   38</span>    }</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -363,7 +369,7 @@ template&lt;class Type &gt; </div>
 </table>
 </div><div class="memdoc">
 <p >Determine whether the stack is empty </p>
-<div class="fragment"><div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>{ <span class="keywordflow">return</span> (<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> == <span class="keyword">nullptr</span>); }</div>
+<div class="fragment"><div class="line"><span class="lineno">   80</span>{ <span class="keywordflow">return</span> (<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> == <span class="keyword">nullptr</span>); }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -393,35 +399,35 @@ template&lt;class Type &gt; </div>
 </table>
 </div><div class="memdoc">
 <p >Overload "=" the assignment operator </p>
-<div class="fragment"><div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>                                                          {</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>        <a class="code hl_class" href="../../d5/da1/structnode.html">node&lt;Type&gt;</a> *newNode, *current, *last;</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span> </div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>        <span class="comment">/* If stack is no empty, make it empty */</span></div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> != <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>            <a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> = <span class="keyword">nullptr</span>;</div>
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-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>        <span class="keywordflow">if</span> (otherStack.<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> == <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>            <a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> = <span class="keyword">nullptr</span>;</div>
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-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>            current = otherStack.<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>;</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>            <a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> = <span class="keyword">new</span> <a class="code hl_class" href="../../d5/da1/structnode.html">node&lt;Type&gt;</a>;</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>            <a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>-&gt;data = current-&gt;data;</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>            <a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>-&gt;next = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>            last = <a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>;</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>            current = current-&gt;next;</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>            <span class="comment">/* Copy the remaining stack */</span></div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>            <span class="keywordflow">while</span> (current != <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>                newNode = <span class="keyword">new</span> <a class="code hl_class" href="../../d5/da1/structnode.html">node&lt;Type&gt;</a>;</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>                newNode-&gt;data = current-&gt;data;</div>
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-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>                last = newNode;</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>                current = current-&gt;next;</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>            }</div>
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-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>        <a class="code hl_variable" href="../../d1/dc2/classstack.html#ac512a3efdc84a5f5c9f53905c8e219b0">size</a> = otherStack.<a class="code hl_variable" href="../../d1/dc2/classstack.html#ac512a3efdc84a5f5c9f53905c8e219b0">size</a>;</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  115</span>                                                          {</div>
+<div class="line"><span class="lineno">  116</span>        <a class="code hl_class" href="../../d5/da1/structnode.html">node&lt;Type&gt;</a> *newNode, *current, *last;</div>
+<div class="line"><span class="lineno">  117</span> </div>
+<div class="line"><span class="lineno">  118</span>        <span class="comment">/* If stack is no empty, make it empty */</span></div>
+<div class="line"><span class="lineno">  119</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> != <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  120</span>            <a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  121</span>        }</div>
+<div class="line"><span class="lineno">  122</span>        <span class="keywordflow">if</span> (otherStack.<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  123</span>            <a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  124</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  125</span>            current = otherStack.<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>;</div>
+<div class="line"><span class="lineno">  126</span>            <a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> = <span class="keyword">new</span> <a class="code hl_class" href="../../d5/da1/structnode.html">node&lt;Type&gt;</a>;</div>
+<div class="line"><span class="lineno">  127</span>            <a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>-&gt;data = current-&gt;data;</div>
+<div class="line"><span class="lineno">  128</span>            <a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>-&gt;next = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  129</span>            last = <a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>;</div>
+<div class="line"><span class="lineno">  130</span>            current = current-&gt;next;</div>
+<div class="line"><span class="lineno">  131</span>            <span class="comment">/* Copy the remaining stack */</span></div>
+<div class="line"><span class="lineno">  132</span>            <span class="keywordflow">while</span> (current != <span class="keyword">nullptr</span>) {</div>
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+<div class="line"><span class="lineno">  141</span>        <a class="code hl_variable" href="../../d1/dc2/classstack.html#ac512a3efdc84a5f5c9f53905c8e219b0">size</a> = otherStack.<a class="code hl_variable" href="../../d1/dc2/classstack.html#ac512a3efdc84a5f5c9f53905c8e219b0">size</a>;</div>
+<div class="line"><span class="lineno">  142</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
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 </div><!-- fragment -->
 </div>
 </div>
@@ -450,17 +456,17 @@ template&lt;class Type &gt; </div>
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 <p >Remove the top element of the stack </p>
-<div class="fragment"><div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>               {</div>
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-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>        <span class="keywordflow">if</span> (!<a class="code hl_function" href="../../d1/dc2/classstack.html#a066e4505155b009913c47b2648b1067a">isEmptyStack</a>()) {</div>
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-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>            <span class="keyword">delete</span> temp;</div>
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-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>        }</div>
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+<div class="fragment"><div class="line"><span class="lineno">   99</span>               {</div>
+<div class="line"><span class="lineno">  100</span>        <a class="code hl_class" href="../../d5/da1/structnode.html">node&lt;Type&gt;</a> *temp;</div>
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 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -497,14 +503,14 @@ template&lt;class Type &gt; </div>
 </table>
 </div><div class="memdoc">
 <p >Add new item to the stack </p>
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-<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>            <span class="keywordflow">case</span> 2:</div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to remove = &quot;</span>;</div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>                <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a75854f5aa216e61219154c62167ce8f0">linear_probing::removalInfo</a>(key);</div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>            <span class="keywordflow">case</span> 3: {</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to search = &quot;</span>;</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>                <a class="code hl_struct" href="../../db/d19/structlinear__probing_1_1_entry.html">Entry</a> entry = table[<a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a6322209aaa91b7bbf16f96e1cc52b746">linear_probing::linearProbe</a>(key, <span class="keyword">true</span>)];</div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>                <span class="keywordflow">if</span> (entry.<a class="code hl_variable" href="../../db/d19/structlinear__probing_1_1_entry.html#a4d84e90b73022083761f85f8586c4c2a">key</a> == linear_probing::notPresent) {</div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Key not present&quot;</span>;</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>                }</div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>            }</div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>            <span class="keywordflow">case</span> 4:</div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter element to generate hash = &quot;</span>;</div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hash of &quot;</span> &lt;&lt; key</div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>                          &lt;&lt; <span class="stringliteral">&quot; is = &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a4bde7a47f98dd1ad24c84038e2608527">linear_probing::hashFxn</a>(key);</div>
-<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>            <span class="keywordflow">case</span> 5:</div>
-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>                <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#ad87b71d810901fab69c4ad9d4d0fa635">linear_probing::display</a>();</div>
-<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>            <span class="keywordflow">default</span>:</div>
-<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>                loop = <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>                <span class="comment">// delete[] table;</span></div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>        }</div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>    }</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  224</span>           {</div>
+<div class="line"><span class="lineno">  225</span>    <span class="keywordtype">int</span> cmd = 0, <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hash</a> = 0, key = 0;</div>
+<div class="line"><span class="lineno">  226</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the initial size of Hash Table. = &quot;</span>;</div>
+<div class="line"><span class="lineno">  227</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; totalSize;</div>
+<div class="line"><span class="lineno">  228</span>    table = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Entry&gt;</a>(totalSize);</div>
+<div class="line"><span class="lineno">  229</span>    <span class="keywordtype">bool</span> loop = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  230</span>    <span class="keywordflow">while</span> (loop) {</div>
+<div class="line"><span class="lineno">  231</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  232</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;PLEASE CHOOSE -&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  233</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1. Add key. (Numeric only)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  234</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2. Remove key.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  235</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3. Find key.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  236</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4. Generate Hash. (Numeric only)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  237</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;5. Display Hash table.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  238</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;6. Exit.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  239</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; cmd;</div>
+<div class="line"><span class="lineno">  240</span>        <span class="keywordflow">switch</span> (cmd) {</div>
+<div class="line"><span class="lineno">  241</span>            <span class="keywordflow">case</span> 1:</div>
+<div class="line"><span class="lineno">  242</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to add = &quot;</span>;</div>
+<div class="line"><span class="lineno">  243</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
+<div class="line"><span class="lineno">  244</span>                <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a16680b8a37d442c2f208faa286e33908">linear_probing::addInfo</a>(key);</div>
+<div class="line"><span class="lineno">  245</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  246</span>            <span class="keywordflow">case</span> 2:</div>
+<div class="line"><span class="lineno">  247</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to remove = &quot;</span>;</div>
+<div class="line"><span class="lineno">  248</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
+<div class="line"><span class="lineno">  249</span>                <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a75854f5aa216e61219154c62167ce8f0">linear_probing::removalInfo</a>(key);</div>
+<div class="line"><span class="lineno">  250</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  251</span>            <span class="keywordflow">case</span> 3: {</div>
+<div class="line"><span class="lineno">  252</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to search = &quot;</span>;</div>
+<div class="line"><span class="lineno">  253</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
+<div class="line"><span class="lineno">  254</span>                <a class="code hl_struct" href="../../db/d19/structlinear__probing_1_1_entry.html">Entry</a> entry = table[<a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a6322209aaa91b7bbf16f96e1cc52b746">linear_probing::linearProbe</a>(key, <span class="keyword">true</span>)];</div>
+<div class="line"><span class="lineno">  255</span>                <span class="keywordflow">if</span> (entry.<a class="code hl_variable" href="../../db/d19/structlinear__probing_1_1_entry.html#a4d84e90b73022083761f85f8586c4c2a">key</a> == linear_probing::notPresent) {</div>
+<div class="line"><span class="lineno">  256</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Key not present&quot;</span>;</div>
+<div class="line"><span class="lineno">  257</span>                }</div>
+<div class="line"><span class="lineno">  258</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  259</span>            }</div>
+<div class="line"><span class="lineno">  260</span>            <span class="keywordflow">case</span> 4:</div>
+<div class="line"><span class="lineno">  261</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter element to generate hash = &quot;</span>;</div>
+<div class="line"><span class="lineno">  262</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
+<div class="line"><span class="lineno">  263</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hash of &quot;</span> &lt;&lt; key</div>
+<div class="line"><span class="lineno">  264</span>                          &lt;&lt; <span class="stringliteral">&quot; is = &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a4bde7a47f98dd1ad24c84038e2608527">linear_probing::hashFxn</a>(key);</div>
+<div class="line"><span class="lineno">  265</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  266</span>            <span class="keywordflow">case</span> 5:</div>
+<div class="line"><span class="lineno">  267</span>                <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#ad87b71d810901fab69c4ad9d4d0fa635">linear_probing::display</a>();</div>
+<div class="line"><span class="lineno">  268</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  269</span>            <span class="keywordflow">default</span>:</div>
+<div class="line"><span class="lineno">  270</span>                loop = <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  271</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  272</span>                <span class="comment">// delete[] table;</span></div>
+<div class="line"><span class="lineno">  273</span>        }</div>
+<div class="line"><span class="lineno">  274</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  275</span>    }</div>
+<div class="line"><span class="lineno">  276</span>    <span class="keywordflow">return</span> 0;</div>
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@@ -273,7 +273,7 @@ bool&#160;</td><td class="memItemRight" valign="bottom"><b>linear_probing::rehas
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   <ul>
     <li class="navelem"><a class="el" href="../../dir_ece9b94c107bbaa1dd68197a8c9983b9.html">hashing</a></li><li class="navelem"><a class="el" href="../../d1/dc7/linear__probing__hash__table_8cpp.html">linear_probing_hash_table.cpp</a></li>
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+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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diff --git a/d1/dcc/wiggle__sort_8cpp.html b/d1/dcc/wiggle__sort_8cpp.html
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- <tr style="height: 56px;">
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+<!-- Generated by Doxygen 1.9.3 -->
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 <div class="contents">
 
-<p><a href="https://leetcode.com/problems/wiggle-sort-ii/" target="_blank">Wiggle Sort Algorithm</a> Implementation  
+<p>[Wiggle Sort Algorithm] (<a href="https://leetcode.com/problems/wiggle-sort-ii/">https://leetcode.com/problems/wiggle-sort-ii/</a>) Implementation  
 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
 <code>#include &lt;cassert&gt;</code><br />
@@ -136,7 +136,7 @@ Functions</h2></td></tr>
 <tr class="separator:gae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
 </table>
 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
-<div class="textblock"><p ><a href="https://leetcode.com/problems/wiggle-sort-ii/" target="_blank">Wiggle Sort Algorithm</a> Implementation </p>
+<div class="textblock"><p >[Wiggle Sort Algorithm] (<a href="https://leetcode.com/problems/wiggle-sort-ii/">https://leetcode.com/problems/wiggle-sort-ii/</a>) Implementation </p>
 <dl class="section author"><dt>Author</dt><dd><a href="http://github.com/roshan0708" target="_blank">Roshan Kanwar</a></dd></dl>
 <p>Wiggle Sort sorts the array into a wave like array. An array ‘arr[0..n-1]’ is sorted in wave form, if arr[0] &gt;= arr[1] &lt;= arr[2] &gt;= arr[3] &lt;= arr[4] &gt;= ….. </p>
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@@ -168,25 +168,25 @@ template&lt;typename T &gt; </div>
 </dl>
 <dl class="section examples"><dt>Examples</dt><dd><a class="el" href="../../dd/db0/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2sorting_2wiggle_sort_8cpp-example.html#a1">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/sorting/wiggle_sort.cpp</a>.</dd>
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@@ -160,28 +160,28 @@ Functions</h2></td></tr>
 <p >Temp variable to x0 and x1</p>
 <p >Newly calculated root</p>
 <p >Returning final root</p>
-<div class="fragment"><div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>                                          {</div>
-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>    <span class="keywordtype">int</span> i = 1;  <span class="comment">/// To find initial root or rough approximation</span></div>
-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span> </div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>    <span class="keywordflow">while</span> (i * i &lt;= radicand) {</div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>        i++;</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    }</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span> </div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    i--;  <span class="comment">/// Real Initial value will be i-1 as loop stops on +1 value</span></div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span> </div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>    <span class="keywordtype">double</span> x0 = i;  <span class="comment">/// Storing previous value for comparison</span></div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    <span class="keywordtype">double</span> x1 =</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>        (radicand / x0 + x0) / 2;  <span class="comment">/// Storing calculated value for comparison</span></div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>    <span class="keywordtype">double</span> temp = NAN;             <span class="comment">/// Temp variable to x0 and x1</span></div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span> </div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    <span class="keywordflow">while</span> (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(x0, x1) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(x0, x1) &lt; 0.0001) {</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>        temp = (radicand / x1 + x1) / 2;  <span class="comment">/// Newly calculated root</span></div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>        x0 = x1;</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>        x1 = temp;</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    }</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span> </div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    <span class="keywordflow">return</span> x1;  <span class="comment">/// Returning final root</span></div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   30</span>                                          {</div>
+<div class="line"><span class="lineno">   31</span>    <span class="keywordtype">int</span> i = 1;  <span class="comment">/// To find initial root or rough approximation</span></div>
+<div class="line"><span class="lineno">   32</span> </div>
+<div class="line"><span class="lineno">   33</span>    <span class="keywordflow">while</span> (i * i &lt;= radicand) {</div>
+<div class="line"><span class="lineno">   34</span>        i++;</div>
+<div class="line"><span class="lineno">   35</span>    }</div>
+<div class="line"><span class="lineno">   36</span> </div>
+<div class="line"><span class="lineno">   37</span>    i--;  <span class="comment">/// Real Initial value will be i-1 as loop stops on +1 value</span></div>
+<div class="line"><span class="lineno">   38</span> </div>
+<div class="line"><span class="lineno">   39</span>    <span class="keywordtype">double</span> x0 = i;  <span class="comment">/// Storing previous value for comparison</span></div>
+<div class="line"><span class="lineno">   40</span>    <span class="keywordtype">double</span> x1 =</div>
+<div class="line"><span class="lineno">   41</span>        (radicand / x0 + x0) / 2;  <span class="comment">/// Storing calculated value for comparison</span></div>
+<div class="line"><span class="lineno">   42</span>    <span class="keywordtype">double</span> temp = NAN;             <span class="comment">/// Temp variable to x0 and x1</span></div>
+<div class="line"><span class="lineno">   43</span> </div>
+<div class="line"><span class="lineno">   44</span>    <span class="keywordflow">while</span> (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(x0, x1) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(x0, x1) &lt; 0.0001) {</div>
+<div class="line"><span class="lineno">   45</span>        temp = (radicand / x1 + x1) / 2;  <span class="comment">/// Newly calculated root</span></div>
+<div class="line"><span class="lineno">   46</span>        x0 = x1;</div>
+<div class="line"><span class="lineno">   47</span>        x1 = temp;</div>
+<div class="line"><span class="lineno">   48</span>    }</div>
+<div class="line"><span class="lineno">   49</span> </div>
+<div class="line"><span class="lineno">   50</span>    <span class="keywordflow">return</span> x1;  <span class="comment">/// Returning final root</span></div>
+<div class="line"><span class="lineno">   51</span>}</div>
 <div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
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@@ -244,59 +244,59 @@ y if n!=1 </dd></dl>
 <p >Updating the last n/2 elements</p>
 <p >Deleting dynamic array ye</p>
 <p >Deleting dynamic array yo</p>
-<div class="fragment"><div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>                                                                           {</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>    <span class="keywordflow">if</span> (n == 1) {</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>        <span class="keywordflow">return</span> p;  <span class="comment">/// Base Case To return</span></div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    }</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span> </div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>    <span class="keywordtype">double</span> pi = 2 * asin(1.0);  <span class="comment">/// Declaring value of pi</span></div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span> </div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> om = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        cos(2 * pi / n), sin(2 * pi / n));  <span class="comment">/// Calculating value of omega</span></div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span> </div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    <span class="keyword">auto</span> *pe = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2];  <span class="comment">/// Coefficients of even power</span></div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span> </div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    <span class="keyword">auto</span> *po = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2];  <span class="comment">/// Coefficients of odd power</span></div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span> </div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <span class="keywordtype">int</span> k1 = 0, k2 = 0;</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>        <span class="keywordflow">if</span> (j % 2 == 0) {</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>            pe[k1++] = p[j];  <span class="comment">/// Assigning values of even Coefficients</span></div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span> </div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>            po[k2++] = p[j];  <span class="comment">/// Assigning value of odd Coefficients</span></div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        }</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    }</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span> </div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *ye =</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#a158fd271b9a53e8f3f60b08b18857150">FastFourierTransform</a>(pe, n / 2);  <span class="comment">/// Recursive Call</span></div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span> </div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *yo =</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#a158fd271b9a53e8f3f60b08b18857150">FastFourierTransform</a>(po, n / 2);  <span class="comment">/// Recursive Call</span></div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span> </div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    <span class="keyword">auto</span> *y = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n];  <span class="comment">/// Final value representation list</span></div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span> </div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    k1 = 0, k2 = 0;</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span> </div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n / 2; i++) {</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        y[i] =</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>            ye[k1] + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2];  <span class="comment">/// Updating the first n/2 elements</span></div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        y[i + n / 2] =</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>            ye[k1] - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2];  <span class="comment">/// Updating the last n/2 elements</span></div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span> </div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>        k1++;</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        k2++;</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    }</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span> </div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    <span class="keywordflow">if</span> (n != 2) {</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>        <span class="keyword">delete</span>[] pe;</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>        <span class="keyword">delete</span>[] po;</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    }</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span> </div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    <span class="keyword">delete</span>[] ye;  <span class="comment">/// Deleting dynamic array ye</span></div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    <span class="keyword">delete</span>[] yo;  <span class="comment">/// Deleting dynamic array yo</span></div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    <span class="keywordflow">return</span> y;</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   41</span>                                                                           {</div>
+<div class="line"><span class="lineno">   42</span>    <span class="keywordflow">if</span> (n == 1) {</div>
+<div class="line"><span class="lineno">   43</span>        <span class="keywordflow">return</span> p;  <span class="comment">/// Base Case To return</span></div>
+<div class="line"><span class="lineno">   44</span>    }</div>
+<div class="line"><span class="lineno">   45</span> </div>
+<div class="line"><span class="lineno">   46</span>    <span class="keywordtype">double</span> pi = 2 * asin(1.0);  <span class="comment">/// Declaring value of pi</span></div>
+<div class="line"><span class="lineno">   47</span> </div>
+<div class="line"><span class="lineno">   48</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> om = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(</div>
+<div class="line"><span class="lineno">   49</span>        cos(2 * pi / n), sin(2 * pi / n));  <span class="comment">/// Calculating value of omega</span></div>
+<div class="line"><span class="lineno">   50</span> </div>
+<div class="line"><span class="lineno">   51</span>    <span class="keyword">auto</span> *pe = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2];  <span class="comment">/// Coefficients of even power</span></div>
+<div class="line"><span class="lineno">   52</span> </div>
+<div class="line"><span class="lineno">   53</span>    <span class="keyword">auto</span> *po = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2];  <span class="comment">/// Coefficients of odd power</span></div>
+<div class="line"><span class="lineno">   54</span> </div>
+<div class="line"><span class="lineno">   55</span>    <span class="keywordtype">int</span> k1 = 0, k2 = 0;</div>
+<div class="line"><span class="lineno">   56</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
+<div class="line"><span class="lineno">   57</span>        <span class="keywordflow">if</span> (j % 2 == 0) {</div>
+<div class="line"><span class="lineno">   58</span>            pe[k1++] = p[j];  <span class="comment">/// Assigning values of even Coefficients</span></div>
+<div class="line"><span class="lineno">   59</span> </div>
+<div class="line"><span class="lineno">   60</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   61</span>            po[k2++] = p[j];  <span class="comment">/// Assigning value of odd Coefficients</span></div>
+<div class="line"><span class="lineno">   62</span>        }</div>
+<div class="line"><span class="lineno">   63</span>    }</div>
+<div class="line"><span class="lineno">   64</span> </div>
+<div class="line"><span class="lineno">   65</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *ye =</div>
+<div class="line"><span class="lineno">   66</span>        <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#a158fd271b9a53e8f3f60b08b18857150">FastFourierTransform</a>(pe, n / 2);  <span class="comment">/// Recursive Call</span></div>
+<div class="line"><span class="lineno">   67</span> </div>
+<div class="line"><span class="lineno">   68</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *yo =</div>
+<div class="line"><span class="lineno">   69</span>        <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#a158fd271b9a53e8f3f60b08b18857150">FastFourierTransform</a>(po, n / 2);  <span class="comment">/// Recursive Call</span></div>
+<div class="line"><span class="lineno">   70</span> </div>
+<div class="line"><span class="lineno">   71</span>    <span class="keyword">auto</span> *y = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n];  <span class="comment">/// Final value representation list</span></div>
+<div class="line"><span class="lineno">   72</span> </div>
+<div class="line"><span class="lineno">   73</span>    k1 = 0, k2 = 0;</div>
+<div class="line"><span class="lineno">   74</span> </div>
+<div class="line"><span class="lineno">   75</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n / 2; i++) {</div>
+<div class="line"><span class="lineno">   76</span>        y[i] =</div>
+<div class="line"><span class="lineno">   77</span>            ye[k1] + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2];  <span class="comment">/// Updating the first n/2 elements</span></div>
+<div class="line"><span class="lineno">   78</span>        y[i + n / 2] =</div>
+<div class="line"><span class="lineno">   79</span>            ye[k1] - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2];  <span class="comment">/// Updating the last n/2 elements</span></div>
+<div class="line"><span class="lineno">   80</span> </div>
+<div class="line"><span class="lineno">   81</span>        k1++;</div>
+<div class="line"><span class="lineno">   82</span>        k2++;</div>
+<div class="line"><span class="lineno">   83</span>    }</div>
+<div class="line"><span class="lineno">   84</span> </div>
+<div class="line"><span class="lineno">   85</span>    <span class="keywordflow">if</span> (n != 2) {</div>
+<div class="line"><span class="lineno">   86</span>        <span class="keyword">delete</span>[] pe;</div>
+<div class="line"><span class="lineno">   87</span>        <span class="keyword">delete</span>[] po;</div>
+<div class="line"><span class="lineno">   88</span>    }</div>
+<div class="line"><span class="lineno">   89</span> </div>
+<div class="line"><span class="lineno">   90</span>    <span class="keyword">delete</span>[] ye;  <span class="comment">/// Deleting dynamic array ye</span></div>
+<div class="line"><span class="lineno">   91</span>    <span class="keyword">delete</span>[] yo;  <span class="comment">/// Deleting dynamic array yo</span></div>
+<div class="line"><span class="lineno">   92</span>    <span class="keywordflow">return</span> y;</div>
+<div class="line"><span class="lineno">   93</span>}</div>
 <div class="ttc" id="acomplex_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a></div></div>
 <div class="ttc" id="anamespacenumerical__methods_html_a158fd271b9a53e8f3f60b08b18857150"><div class="ttname"><a href="../../d1/de0/namespacenumerical__methods.html#a158fd271b9a53e8f3f60b08b18857150">numerical_methods::FastFourierTransform</a></div><div class="ttdeci">std::complex&lt; double &gt; * FastFourierTransform(std::complex&lt; double &gt; *p, uint8_t n)</div><div class="ttdoc">FastFourierTransform is a recursive function which returns list of complex numbers.</div><div class="ttdef"><b>Definition:</b> fast_fourier_transform.cpp:41</div></div>
 <div class="ttc" id="apow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a></div><div class="ttdeci">T pow(T... args)</div></div>
@@ -362,62 +362,62 @@ y if n!=1 </dd></dl>
 <p >Updating the last n/2 elements</p>
 <p >Deleting dynamic array ye</p>
 <p >Deleting dynamic array yo</p>
-<div class="fragment"><div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>                                                             {</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    <span class="keywordflow">if</span> (n == 1) {</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>        <span class="keywordflow">return</span> p;  <span class="comment">/// Base Case To return</span></div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    }</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span> </div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>    <span class="keywordtype">double</span> pi = 2 * asin(1.0);  <span class="comment">/// Declaring value of pi</span></div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span> </div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> om = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>        cos(2 * pi / n), sin(2 * pi / n));  <span class="comment">/// Calculating value of omega</span></div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span> </div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>(om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>() / n);  <span class="comment">/// One change in comparison with DFT</span></div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>    om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>(om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>() / n);  <span class="comment">/// One change in comparison with DFT</span></div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span> </div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>    <span class="keyword">auto</span> *pe = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2];  <span class="comment">/// Coefficients of even power</span></div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span> </div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    <span class="keyword">auto</span> *po = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2];  <span class="comment">/// Coefficients of odd power</span></div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span> </div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    <span class="keywordtype">int</span> k1 = 0, k2 = 0;</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>        <span class="keywordflow">if</span> (j % 2 == 0) {</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>            pe[k1++] = p[j];  <span class="comment">/// Assigning values of even Coefficients</span></div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span> </div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>            po[k2++] = p[j];  <span class="comment">/// Assigning value of odd Coefficients</span></div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>        }</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    }</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span> </div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *ye =</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a>(pe, n / 2);  <span class="comment">/// Recursive Call</span></div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span> </div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *yo =</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a>(po, n / 2);  <span class="comment">/// Recursive Call</span></div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span> </div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <span class="keyword">auto</span> *y = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n];  <span class="comment">/// Final value representation list</span></div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span> </div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    k1 = 0, k2 = 0;</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span> </div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n / 2; i++) {</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>        y[i] =</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>            ye[k1] + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2];  <span class="comment">/// Updating the first n/2 elements</span></div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>        y[i + n / 2] =</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>            ye[k1] - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2];  <span class="comment">/// Updating the last n/2 elements</span></div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span> </div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>        k1++;</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        k2++;</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    }</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span> </div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    <span class="keywordflow">if</span> (n != 2) {</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        <span class="keyword">delete</span>[] pe;</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>        <span class="keyword">delete</span>[] po;</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    }</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span> </div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>    <span class="keyword">delete</span>[] ye;  <span class="comment">/// Deleting dynamic array ye</span></div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    <span class="keyword">delete</span>[] yo;  <span class="comment">/// Deleting dynamic array yo</span></div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    <span class="keywordflow">return</span> y;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   34</span>                                                             {</div>
+<div class="line"><span class="lineno">   35</span>    <span class="keywordflow">if</span> (n == 1) {</div>
+<div class="line"><span class="lineno">   36</span>        <span class="keywordflow">return</span> p;  <span class="comment">/// Base Case To return</span></div>
+<div class="line"><span class="lineno">   37</span>    }</div>
+<div class="line"><span class="lineno">   38</span> </div>
+<div class="line"><span class="lineno">   39</span>    <span class="keywordtype">double</span> pi = 2 * asin(1.0);  <span class="comment">/// Declaring value of pi</span></div>
+<div class="line"><span class="lineno">   40</span> </div>
+<div class="line"><span class="lineno">   41</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> om = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(</div>
+<div class="line"><span class="lineno">   42</span>        cos(2 * pi / n), sin(2 * pi / n));  <span class="comment">/// Calculating value of omega</span></div>
+<div class="line"><span class="lineno">   43</span> </div>
+<div class="line"><span class="lineno">   44</span>    om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>(om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>() / n);  <span class="comment">/// One change in comparison with DFT</span></div>
+<div class="line"><span class="lineno">   45</span>    om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>(om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>() / n);  <span class="comment">/// One change in comparison with DFT</span></div>
+<div class="line"><span class="lineno">   46</span> </div>
+<div class="line"><span class="lineno">   47</span>    <span class="keyword">auto</span> *pe = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2];  <span class="comment">/// Coefficients of even power</span></div>
+<div class="line"><span class="lineno">   48</span> </div>
+<div class="line"><span class="lineno">   49</span>    <span class="keyword">auto</span> *po = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2];  <span class="comment">/// Coefficients of odd power</span></div>
+<div class="line"><span class="lineno">   50</span> </div>
+<div class="line"><span class="lineno">   51</span>    <span class="keywordtype">int</span> k1 = 0, k2 = 0;</div>
+<div class="line"><span class="lineno">   52</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
+<div class="line"><span class="lineno">   53</span>        <span class="keywordflow">if</span> (j % 2 == 0) {</div>
+<div class="line"><span class="lineno">   54</span>            pe[k1++] = p[j];  <span class="comment">/// Assigning values of even Coefficients</span></div>
+<div class="line"><span class="lineno">   55</span> </div>
+<div class="line"><span class="lineno">   56</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   57</span>            po[k2++] = p[j];  <span class="comment">/// Assigning value of odd Coefficients</span></div>
+<div class="line"><span class="lineno">   58</span>        }</div>
+<div class="line"><span class="lineno">   59</span>    }</div>
+<div class="line"><span class="lineno">   60</span> </div>
+<div class="line"><span class="lineno">   61</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *ye =</div>
+<div class="line"><span class="lineno">   62</span>        <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a>(pe, n / 2);  <span class="comment">/// Recursive Call</span></div>
+<div class="line"><span class="lineno">   63</span> </div>
+<div class="line"><span class="lineno">   64</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *yo =</div>
+<div class="line"><span class="lineno">   65</span>        <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a>(po, n / 2);  <span class="comment">/// Recursive Call</span></div>
+<div class="line"><span class="lineno">   66</span> </div>
+<div class="line"><span class="lineno">   67</span>    <span class="keyword">auto</span> *y = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n];  <span class="comment">/// Final value representation list</span></div>
+<div class="line"><span class="lineno">   68</span> </div>
+<div class="line"><span class="lineno">   69</span>    k1 = 0, k2 = 0;</div>
+<div class="line"><span class="lineno">   70</span> </div>
+<div class="line"><span class="lineno">   71</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n / 2; i++) {</div>
+<div class="line"><span class="lineno">   72</span>        y[i] =</div>
+<div class="line"><span class="lineno">   73</span>            ye[k1] + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2];  <span class="comment">/// Updating the first n/2 elements</span></div>
+<div class="line"><span class="lineno">   74</span>        y[i + n / 2] =</div>
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-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        <span class="keywordflow">return</span> x * x + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">cos</a>(x) + <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#ac00616a4e40d3cd5cfb4da87d9ff9af0">exp</a>(x) + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(x) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(x);</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    });</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test Case 2&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;function: x^2 + cos(x) + e^x + log^2(x)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;range: [.023, 3.69]&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;value: &quot;</span> &lt;&lt; test_2 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <a class="code hl_function" href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">math::test_eval</a>(test_2, 58.71291345202729, .001);</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;=====================&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span> </div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>    <span class="keywordtype">double</span> test_3 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">math::integral_approx</a>(</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>        10.78, 24.899, [](<span class="keyword">const</span> <span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> x * x * x - x * x + 378; });</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test Case 3&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;function: x^3 - x^2 + 378&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;range: [10.78, 24.899]&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;value: &quot;</span> &lt;&lt; test_3 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    <a class="code hl_function" href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">math::test_eval</a>(test_3, 93320.65915078377, .001);</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;=====================&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span> </div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    <span class="keywordtype">double</span> test_4 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">math::integral_approx</a>(</div>
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-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>        [](<span class="keyword">const</span> <span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">cos</a>(x) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/tan.html">tan</a>(x) * x * x + <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#ac00616a4e40d3cd5cfb4da87d9ff9af0">exp</a>(x); },</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>        .00001);</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test Case 4&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;function: cos(x)*tan(x)*x^2 + e^x&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;range: [.101, .505]&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;value: &quot;</span> &lt;&lt; test_4 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <a class="code hl_function" href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">math::test_eval</a>(test_4, 0.566485986311631, .001);</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 4 Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;=====================&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span> </div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    <span class="keywordtype">double</span> test_5 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">math::integral_approx</a>(</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>        -1, 1, [](<span class="keyword">const</span> <span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#ac00616a4e40d3cd5cfb4da87d9ff9af0">exp</a>(-1 / (x * x)); });</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test Case 5&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;function: e^(-1/x^2)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;range: [-1, 1]&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;value: &quot;</span> &lt;&lt; test_5 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    <a class="code hl_function" href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">math::test_eval</a>(test_5, 0.1781477117815607, .001);</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 5 Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   64</span>                   {</div>
+<div class="line"><span class="lineno">   65</span>    <span class="keywordtype">double</span> test_1 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">math::integral_approx</a>(</div>
+<div class="line"><span class="lineno">   66</span>        3.24, 7.56, [](<span class="keyword">const</span> <span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(x) + <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#ac00616a4e40d3cd5cfb4da87d9ff9af0">exp</a>(x) + x; });</div>
+<div class="line"><span class="lineno">   67</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test Case 1&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   68</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;function: log(x) + e^x + x&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   69</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;range: [3.24, 7.56]&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   70</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;value: &quot;</span> &lt;&lt; test_1 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   71</span>    <a class="code hl_function" href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">math::test_eval</a>(test_1, 1924.80384023549, .001);</div>
+<div class="line"><span class="lineno">   72</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   73</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;=====================&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   74</span> </div>
+<div class="line"><span class="lineno">   75</span>    <span class="keywordtype">double</span> test_2 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">math::integral_approx</a>(0.023, 3.69, [](<span class="keyword">const</span> <span class="keywordtype">double</span> x) {</div>
+<div class="line"><span class="lineno">   76</span>        <span class="keywordflow">return</span> x * x + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">cos</a>(x) + <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#ac00616a4e40d3cd5cfb4da87d9ff9af0">exp</a>(x) + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(x) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(x);</div>
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+<div class="line"><span class="lineno">   79</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;function: x^2 + cos(x) + e^x + log^2(x)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   80</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;range: [.023, 3.69]&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   81</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;value: &quot;</span> &lt;&lt; test_2 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   82</span>    <a class="code hl_function" href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">math::test_eval</a>(test_2, 58.71291345202729, .001);</div>
+<div class="line"><span class="lineno">   83</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   84</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;=====================&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   85</span> </div>
+<div class="line"><span class="lineno">   86</span>    <span class="keywordtype">double</span> test_3 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">math::integral_approx</a>(</div>
+<div class="line"><span class="lineno">   87</span>        10.78, 24.899, [](<span class="keyword">const</span> <span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> x * x * x - x * x + 378; });</div>
+<div class="line"><span class="lineno">   88</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test Case 3&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   89</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;function: x^3 - x^2 + 378&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   90</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;range: [10.78, 24.899]&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   91</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;value: &quot;</span> &lt;&lt; test_3 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><span class="lineno">   93</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><span class="lineno">   95</span> </div>
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+<div class="line"><span class="lineno">   97</span>        .101, .505,</div>
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+<div class="line"><span class="lineno">  100</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test Case 4&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  101</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;function: cos(x)*tan(x)*x^2 + e^x&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  102</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;range: [.101, .505]&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  103</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;value: &quot;</span> &lt;&lt; test_4 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><span class="lineno">  105</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 4 Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><span class="lineno">  110</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test Case 5&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;function: e^(-1/x^2)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  112</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;range: [-1, 1]&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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diff --git a/d1/ded/windowed__median_8cpp.html b/d1/ded/windowed__median_8cpp.html
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@@ -203,52 +203,52 @@ Algorithm</h3>
 <p >Window size in the range [3, 10]</p>
 <p >Random array values (positive/negative)</p>
 <p >Testing randomized test</p>
-<div class="fragment"><div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>                                       {<span class="comment"></span></div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span><span class="comment">    /// A few fixed test cases</span></div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span><span class="comment"></span>    <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({1, 2, 3, 4, 5, 6, 7, 8, 9},</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>         3);  <span class="comment">/// Array of sorted values; odd window size</span></div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>    <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({9, 8, 7, 6, 5, 4, 3, 2, 1},</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>         3);  <span class="comment">/// Array of sorted values - decreasing; odd window size</span></div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>    <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({9, 8, 7, 6, 5, 4, 5, 6}, 4);     <span class="comment">/// Even window size</span></div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({3, 3, 3, 3, 3, 3, 3, 3, 3}, 3);  <span class="comment">/// Array with repeating values</span></div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({3, 3, 3, 3, 7, 3, 3, 3, 3}, 3);  <span class="comment">/// Array with same values except one</span></div>
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-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>            vals.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">rand</a>() - RAND_MAX);  <span class="comment">/// Random array values (positive/negative)</span></div>
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-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>        <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>(vals, windowSize);  <span class="comment">/// Testing randomized test</span></div>
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-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  198</span>                                       {<span class="comment"></span></div>
+<div class="line"><span class="lineno">  199</span><span class="comment">    /// A few fixed test cases</span></div>
+<div class="line"><span class="lineno">  200</span><span class="comment"></span>    <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({1, 2, 3, 4, 5, 6, 7, 8, 9},</div>
+<div class="line"><span class="lineno">  201</span>         3);  <span class="comment">/// Array of sorted values; odd window size</span></div>
+<div class="line"><span class="lineno">  202</span>    <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({9, 8, 7, 6, 5, 4, 3, 2, 1},</div>
+<div class="line"><span class="lineno">  203</span>         3);  <span class="comment">/// Array of sorted values - decreasing; odd window size</span></div>
+<div class="line"><span class="lineno">  204</span>    <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({9, 8, 7, 6, 5, 4, 5, 6}, 4);     <span class="comment">/// Even window size</span></div>
+<div class="line"><span class="lineno">  205</span>    <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({3, 3, 3, 3, 3, 3, 3, 3, 3}, 3);  <span class="comment">/// Array with repeating values</span></div>
+<div class="line"><span class="lineno">  206</span>    <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({3, 3, 3, 3, 7, 3, 3, 3, 3}, 3);  <span class="comment">/// Array with same values except one</span></div>
+<div class="line"><span class="lineno">  207</span>    <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({4, 3, 3, -5, -5, 1, 3, 4, 5},</div>
+<div class="line"><span class="lineno">  208</span>         5);  <span class="comment">/// Array that includes repeating values including negatives</span></div>
+<div class="line"><span class="lineno">  209</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  210</span><span class="comment">    /// Array with large values - sum of few pairs exceeds MAX_INT. Window size</span></div>
+<div class="line"><span class="lineno">  211</span><span class="comment">    /// is even - testing calculation of average median between two middle</span></div>
+<div class="line"><span class="lineno">  212</span><span class="comment">    /// values</span></div>
+<div class="line"><span class="lineno">  213</span><span class="comment"></span>    <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({470211272, 101027544, 1457850878, 1458777923, 2007237709, 823564440,</div>
+<div class="line"><span class="lineno">  214</span>          1115438165, 1784484492, 74243042, 114807987},</div>
+<div class="line"><span class="lineno">  215</span>         6);</div>
+<div class="line"><span class="lineno">  216</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  217</span><span class="comment">    /// Random test cases</span></div>
+<div class="line"><span class="lineno">  218</span><span class="comment"></span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<span class="keyword">static_cast&lt;</span><span class="keywordtype">unsigned</span> <span class="keywordtype">int</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>)));</div>
+<div class="line"><span class="lineno">  219</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> vals;</div>
+<div class="line"><span class="lineno">  220</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 8; i &lt; 100; i++) {</div>
+<div class="line"><span class="lineno">  221</span>        <span class="keyword">const</span> <span class="keyword">auto</span> n =</div>
+<div class="line"><span class="lineno">  222</span>            1 + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() /</div>
+<div class="line"><span class="lineno">  223</span>                    ((RAND_MAX + 5u) / 20);  <span class="comment">/// Array size in the range [5, 20]</span></div>
+<div class="line"><span class="lineno">  224</span>        <span class="keyword">auto</span> windowSize =</div>
+<div class="line"><span class="lineno">  225</span>            1 + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() / ((RAND_MAX + 3u) /</div>
+<div class="line"><span class="lineno">  226</span>                               10);  <span class="comment">/// Window size in the range [3, 10]</span></div>
+<div class="line"><span class="lineno">  227</span>        vals.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/clear.html">clear</a>();</div>
+<div class="line"><span class="lineno">  228</span>        vals.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/reserve.html">reserve</a>(n);</div>
+<div class="line"><span class="lineno">  229</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">  230</span>            vals.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(</div>
+<div class="line"><span class="lineno">  231</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">rand</a>() - RAND_MAX);  <span class="comment">/// Random array values (positive/negative)</span></div>
+<div class="line"><span class="lineno">  232</span>        }</div>
+<div class="line"><span class="lineno">  233</span>        <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>(vals, windowSize);  <span class="comment">/// Testing randomized test</span></div>
+<div class="line"><span class="lineno">  234</span>    }</div>
+<div class="line"><span class="lineno">  235</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  236</span>}</div>
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-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int &gt;</a></div></div>
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 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -302,20 +302,20 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <p >Comparing medians: efficient function vs. Naive one</p>
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-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> val : vals) {</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>        windowedMedian.insert(val);</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span><span class="comment"></span> </div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span><span class="comment">        /// Comparing medians: efficient function vs. Naive one</span></div>
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-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  182</span>                                                             {</div>
+<div class="line"><span class="lineno">  183</span>    <a class="code hl_class" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html">probability::windowed_median::WindowedMedian</a> windowedMedian(windowSize);</div>
+<div class="line"><span class="lineno">  184</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> val : vals) {</div>
+<div class="line"><span class="lineno">  185</span>        windowedMedian.insert(val);</div>
+<div class="line"><span class="lineno">  186</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  187</span><span class="comment">        /// Comparing medians: efficient function vs. Naive one</span></div>
+<div class="line"><span class="lineno">  188</span><span class="comment"></span>        assert(windowedMedian.getMedian() == windowedMedian.getMedianNaive());</div>
+<div class="line"><span class="lineno">  189</span>    }</div>
+<div class="line"><span class="lineno">  190</span>}</div>
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 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
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@@ -327,7 +327,7 @@ Here is the call graph for this function:</div>
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-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>    <span class="keywordflow">while</span> (t-&gt;succ() != <span class="keyword">nullptr</span>) {</div>
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+<div class="line"><span class="lineno">  183</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;List is Empty!&quot;</span>;</div>
+<div class="line"><span class="lineno">  184</span>        <span class="keywordflow">return</span>;</div>
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+<div class="line"><span class="lineno">  187</span>    <span class="keywordflow">while</span> (t-&gt;succ() != <span class="keyword">nullptr</span>) {</div>
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 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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 <div class="ttc" id="ashared_ptr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr</a></div></div>
@@ -287,30 +287,30 @@ Here is the call graph for this function:</div>
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+<div class="line"><span class="lineno">  112</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ab87eecc80068fc5a80e98e83536885f2">last</a> == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  113</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  114</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  115</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  116</span>    }</div>
+<div class="line"><span class="lineno">  117</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -429,15 +429,15 @@ false if the list is not empty </dd></dl>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>                                 {</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ae8424a4fce3d483f7c85d6f6a5c79a1a">isEmpty</a>()) {</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>        <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#aa3801cea564a3b3bb7b03abfffdcf1e1">first</a>-&gt;succ() = std::make_shared&lt;link&gt;(new_elem);</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>        <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ab87eecc80068fc5a80e98e83536885f2">last</a> = <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#aa3801cea564a3b3bb7b03abfffdcf1e1">first</a>-&gt;succ();</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>        <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ab87eecc80068fc5a80e98e83536885f2">last</a>-&gt;succ() = std::make_shared&lt;link&gt;(new_elem);</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>        <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ab87eecc80068fc5a80e98e83536885f2">last</a> = <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ab87eecc80068fc5a80e98e83536885f2">last</a>-&gt;succ();</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    }</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  123</span>                                 {</div>
+<div class="line"><span class="lineno">  124</span>    <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ae8424a4fce3d483f7c85d6f6a5c79a1a">isEmpty</a>()) {</div>
+<div class="line"><span class="lineno">  125</span>        <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#aa3801cea564a3b3bb7b03abfffdcf1e1">first</a>-&gt;succ() = std::make_shared&lt;link&gt;(new_elem);</div>
+<div class="line"><span class="lineno">  126</span>        <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ab87eecc80068fc5a80e98e83536885f2">last</a> = <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#aa3801cea564a3b3bb7b03abfffdcf1e1">first</a>-&gt;succ();</div>
+<div class="line"><span class="lineno">  127</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  128</span>        <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ab87eecc80068fc5a80e98e83536885f2">last</a>-&gt;succ() = std::make_shared&lt;link&gt;(new_elem);</div>
+<div class="line"><span class="lineno">  129</span>        <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ab87eecc80068fc5a80e98e83536885f2">last</a> = <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ab87eecc80068fc5a80e98e83536885f2">last</a>-&gt;succ();</div>
+<div class="line"><span class="lineno">  130</span>    }</div>
+<div class="line"><span class="lineno">  131</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -468,16 +468,16 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>                                  {</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ae8424a4fce3d483f7c85d6f6a5c79a1a">isEmpty</a>()) {</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#aa3801cea564a3b3bb7b03abfffdcf1e1">first</a>-&gt;succ() = std::make_shared&lt;link&gt;(new_elem);</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>        <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ab87eecc80068fc5a80e98e83536885f2">last</a> = <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#aa3801cea564a3b3bb7b03abfffdcf1e1">first</a>-&gt;succ();</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;link&gt;</a> t = std::make_shared&lt;link&gt;(new_elem);</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>        t-&gt;succ() = <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#aa3801cea564a3b3bb7b03abfffdcf1e1">first</a>-&gt;succ();</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>        <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#aa3801cea564a3b3bb7b03abfffdcf1e1">first</a>-&gt;succ() = t;</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    }</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  137</span>                                  {</div>
+<div class="line"><span class="lineno">  138</span>    <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ae8424a4fce3d483f7c85d6f6a5c79a1a">isEmpty</a>()) {</div>
+<div class="line"><span class="lineno">  139</span>        <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#aa3801cea564a3b3bb7b03abfffdcf1e1">first</a>-&gt;succ() = std::make_shared&lt;link&gt;(new_elem);</div>
+<div class="line"><span class="lineno">  140</span>        <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ab87eecc80068fc5a80e98e83536885f2">last</a> = <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#aa3801cea564a3b3bb7b03abfffdcf1e1">first</a>-&gt;succ();</div>
+<div class="line"><span class="lineno">  141</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  142</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;link&gt;</a> t = std::make_shared&lt;link&gt;(new_elem);</div>
+<div class="line"><span class="lineno">  143</span>        t-&gt;succ() = <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#aa3801cea564a3b3bb7b03abfffdcf1e1">first</a>-&gt;succ();</div>
+<div class="line"><span class="lineno">  144</span>        <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#aa3801cea564a3b3bb7b03abfffdcf1e1">first</a>-&gt;succ() = t;</div>
+<div class="line"><span class="lineno">  145</span>    }</div>
+<div class="line"><span class="lineno">  146</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -504,17 +504,17 @@ Here is the call graph for this function:</div>
 
 <p>Utility function for reversing a list. </p>
 <p >Using the current, previous, and next pointer. </p><dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>                       {</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *curr = head;</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/prev.html">prev</a> = <span class="keyword">nullptr</span>, *next_node = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    <span class="keywordflow">while</span> (curr != <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>        next_node = curr-&gt;next;</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>        curr-&gt;next = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/prev.html">prev</a>;</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/prev.html">prev</a> = curr;</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>        curr = next_node;</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    }</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    head = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/prev.html">prev</a>;</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  107</span>                       {</div>
+<div class="line"><span class="lineno">  108</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *curr = head;</div>
+<div class="line"><span class="lineno">  109</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/prev.html">prev</a> = <span class="keyword">nullptr</span>, *next_node = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  110</span>    <span class="keywordflow">while</span> (curr != <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  111</span>        next_node = curr-&gt;next;</div>
+<div class="line"><span class="lineno">  112</span>        curr-&gt;next = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/prev.html">prev</a>;</div>
+<div class="line"><span class="lineno">  113</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/prev.html">prev</a> = curr;</div>
+<div class="line"><span class="lineno">  114</span>        curr = next_node;</div>
+<div class="line"><span class="lineno">  115</span>    }</div>
+<div class="line"><span class="lineno">  116</span>    head = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/prev.html">prev</a>;</div>
+<div class="line"><span class="lineno">  117</span>}</div>
 <div class="ttc" id="aprev_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/prev.html">std::prev</a></div><div class="ttdeci">T prev(T... args)</div></div>
 </div><!-- fragment -->
 </div>
@@ -541,22 +541,22 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>                                              {</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>    <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ae8424a4fce3d483f7c85d6f6a5c79a1a">isEmpty</a>()) {</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;List is Empty!&quot;</span>;</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>        <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>    }</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;link&gt;</a> t = <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#aa3801cea564a3b3bb7b03abfffdcf1e1">first</a>;</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>    <span class="keywordflow">while</span> (t != <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ab87eecc80068fc5a80e98e83536885f2">last</a> &amp;&amp; t-&gt;succ()-&gt;val() != find_elem) {</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>        t = t-&gt;succ();</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    }</div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    <span class="keywordflow">if</span> (t == <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ab87eecc80068fc5a80e98e83536885f2">last</a>) {</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Element not found\n&quot;</span>;</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>        <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>    }</div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Element was found\n&quot;</span>;</div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>    <span class="keywordflow">return</span> t-&gt;succ();</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  197</span>                                              {</div>
+<div class="line"><span class="lineno">  198</span>    <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ae8424a4fce3d483f7c85d6f6a5c79a1a">isEmpty</a>()) {</div>
+<div class="line"><span class="lineno">  199</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;List is Empty!&quot;</span>;</div>
+<div class="line"><span class="lineno">  200</span>        <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  201</span>    }</div>
+<div class="line"><span class="lineno">  202</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;link&gt;</a> t = <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#aa3801cea564a3b3bb7b03abfffdcf1e1">first</a>;</div>
+<div class="line"><span class="lineno">  203</span>    <span class="keywordflow">while</span> (t != <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ab87eecc80068fc5a80e98e83536885f2">last</a> &amp;&amp; t-&gt;succ()-&gt;val() != find_elem) {</div>
+<div class="line"><span class="lineno">  204</span>        t = t-&gt;succ();</div>
+<div class="line"><span class="lineno">  205</span>    }</div>
+<div class="line"><span class="lineno">  206</span>    <span class="keywordflow">if</span> (t == <a class="code hl_variable" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ab87eecc80068fc5a80e98e83536885f2">last</a>) {</div>
+<div class="line"><span class="lineno">  207</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Element not found\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  208</span>        <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  209</span>    }</div>
+<div class="line"><span class="lineno">  210</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Element was found\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  211</span>    <span class="keywordflow">return</span> t-&gt;succ();</div>
+<div class="line"><span class="lineno">  212</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -583,13 +583,13 @@ Here is the call graph for this function:</div>
 
 <p>Utility function to find the top element of the list. </p>
 <dl class="section return"><dt>Returns</dt><dd>the top element of the list </dd></dl>
-<div class="fragment"><div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>                  {</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    <span class="keywordflow">if</span> (!<a class="code hl_function" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ae8424a4fce3d483f7c85d6f6a5c79a1a">isEmpty</a>()) {</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>        <span class="keywordflow">return</span> head-&gt;val;</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    } <span class="keywordflow">else</span> {</div>
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+<div class="line"><span class="lineno">   62</span>    p = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#af413b1740073db54796642b0ab814d6d">hashtab</a>[index].next;</div>
+<div class="line"><span class="lineno">   63</span>    <span class="keywordflow">if</span> (p != NULL) {</div>
+<div class="line"><span class="lineno">   64</span>        n-&gt;next = p;</div>
+<div class="line"><span class="lineno">   65</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#af413b1740073db54796642b0ab814d6d">hashtab</a>[index].next = n;</div>
+<div class="line"><span class="lineno">   66</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   67</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#af413b1740073db54796642b0ab814d6d">hashtab</a>[index].next = n;</div>
+<div class="line"><span class="lineno">   68</span>    }</div>
+<div class="line"><span class="lineno">   69</span>}</div>
 <div class="ttc" id="ahash__search_8cpp_html_a566eaf0ffafd50bc61e644561fd27001"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a></div><div class="ttdeci">int h(int key)</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:45</div></div>
 <div class="ttc" id="ahash__search_8cpp_html_ad6fcd983304f85afa199d97a9b0ca9f6"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#ad6fcd983304f85afa199d97a9b0ca9f6">link</a></div><div class="ttdeci">struct list * link</div><div class="ttdoc">pointer to nodes</div></div>
 <div class="ttc" id="ahash__search_8cpp_html_af413b1740073db54796642b0ab814d6d"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#af413b1740073db54796642b0ab814d6d">hashtab</a></div><div class="ttdeci">node hashtab[HASHMAX]</div><div class="ttdoc">array of nodes</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:35</div></div>
@@ -258,7 +258,7 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd>hash value for <code>key</code> </dd></dl>
 <dl class="section examples"><dt>Examples</dt><dd><a class="el" href="../../dc/dc4/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2numerical_methods_2rungekutta_8cpp-example.html#a2">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp</a>.</dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>{ <span class="keywordflow">return</span> key % <a class="code hl_define" href="../../d1/df3/hash__search_8cpp.html#a77c722016053a1d484aa177ce205b367">HASHMAX</a>; }</div>
+<div class="fragment"><div class="line"><span class="lineno">   45</span>{ <span class="keywordflow">return</span> key % <a class="code hl_define" href="../../d1/df3/hash__search_8cpp.html#a77c722016053a1d484aa177ce205b367">HASHMAX</a>; }</div>
 <div class="ttc" id="ahash__search_8cpp_html_a77c722016053a1d484aa177ce205b367"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a77c722016053a1d484aa177ce205b367">HASHMAX</a></div><div class="ttdeci">#define HASHMAX</div><div class="ttdoc">Determines the length of the hash table.</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:22</div></div>
 </div><!-- fragment -->
 </div>
@@ -291,27 +291,27 @@ Here is the call graph for this function:</div>
 <p >Input the key to be searched, and get the hash header position through the H (int key) function, then one-dimensional linear search. If found </p><dl class="section return"><dt>Returns</dt><dd>element depth and number of searches If not found </dd>
 <dd>
 -1 </dd></dl>
-<div class="fragment"><div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>                                       {  <span class="comment">// Hash lookup function</span></div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">link</a> pointer;</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    <span class="keywordtype">int</span> index;</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span> </div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    *counter = 0;</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    index = <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>(key);</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    pointer = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#af413b1740073db54796642b0ab814d6d">hashtab</a>[index].next;</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span> </div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;data[&quot;</span> &lt;&lt; index &lt;&lt; <span class="stringliteral">&quot;]:&quot;</span>;</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span> </div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>    <span class="keywordflow">while</span> (pointer != NULL) {</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>        counter[0]++;</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;data[&quot;</span> &lt;&lt; pointer-&gt;key &lt;&lt; <span class="stringliteral">&quot;]:&quot;</span>;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        <span class="keywordflow">if</span> (pointer-&gt;key == key)</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>            <span class="keywordflow">return</span> 1;</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>        <span class="keywordflow">else</span></div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>            pointer = pointer-&gt;next;</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    }</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span> </div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   76</span>                                       {  <span class="comment">// Hash lookup function</span></div>
+<div class="line"><span class="lineno">   77</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">link</a> pointer;</div>
+<div class="line"><span class="lineno">   78</span>    <span class="keywordtype">int</span> index;</div>
+<div class="line"><span class="lineno">   79</span> </div>
+<div class="line"><span class="lineno">   80</span>    *counter = 0;</div>
+<div class="line"><span class="lineno">   81</span>    index = <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>(key);</div>
+<div class="line"><span class="lineno">   82</span>    pointer = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#af413b1740073db54796642b0ab814d6d">hashtab</a>[index].next;</div>
+<div class="line"><span class="lineno">   83</span> </div>
+<div class="line"><span class="lineno">   84</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;data[&quot;</span> &lt;&lt; index &lt;&lt; <span class="stringliteral">&quot;]:&quot;</span>;</div>
+<div class="line"><span class="lineno">   85</span> </div>
+<div class="line"><span class="lineno">   86</span>    <span class="keywordflow">while</span> (pointer != NULL) {</div>
+<div class="line"><span class="lineno">   87</span>        counter[0]++;</div>
+<div class="line"><span class="lineno">   88</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;data[&quot;</span> &lt;&lt; pointer-&gt;key &lt;&lt; <span class="stringliteral">&quot;]:&quot;</span>;</div>
+<div class="line"><span class="lineno">   89</span>        <span class="keywordflow">if</span> (pointer-&gt;key == key)</div>
+<div class="line"><span class="lineno">   90</span>            <span class="keywordflow">return</span> 1;</div>
+<div class="line"><span class="lineno">   91</span>        <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">   92</span>            pointer = pointer-&gt;next;</div>
+<div class="line"><span class="lineno">   93</span>    }</div>
+<div class="line"><span class="lineno">   94</span> </div>
+<div class="line"><span class="lineno">   95</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">   96</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -338,47 +338,47 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >main function </p>
-<div class="fragment"><div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>           {</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">link</a> p;</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <span class="keywordtype">int</span> key, index, i, counter;  <span class="comment">// Key is the value to be found</span></div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    index = 0;</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span> </div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <span class="comment">// You can write the input mode here</span></div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <span class="keywordflow">while</span> (index &lt; <a class="code hl_define" href="../../d1/df3/hash__search_8cpp.html#a392fb874e547e582e9c66a08a1f23326">MAX</a>) {  <span class="comment">// Construct hash table</span></div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>        <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#ad0831425f1389166a9518f422d0c6ec5">create_list</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[index]);</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>        index++;</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    }</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span> </div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_define" href="../../d1/df3/hash__search_8cpp.html#a77c722016053a1d484aa177ce205b367">HASHMAX</a>; i++) {  <span class="comment">// Output hash table</span></div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;hashtab [&quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;]\n&quot;</span>;</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span> </div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        p = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#af413b1740073db54796642b0ab814d6d">hashtab</a>[i].next;</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span> </div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>        <span class="keywordflow">while</span> (p != NULL) {</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;please int key:&quot;</span>;</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>            <span class="keywordflow">if</span> (p-&gt;key &gt; 0)</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;[&quot;</span> &lt;&lt; p-&gt;key &lt;&lt; <span class="stringliteral">&quot;]&quot;</span>;</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>            p = p-&gt;next;</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        }</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    }</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span> </div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    <span class="keywordflow">while</span> (key != -1) {</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>        <span class="comment">// You can write the input mode here</span></div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>        <span class="comment">// test key = 10</span></div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>        key = 10;</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a36ea13c16028f18ef2d5ff47f3fda7a2">hash_search</a>(key, &amp;counter))</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;search time = &quot;</span> &lt;&lt; counter &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>        <span class="keywordflow">else</span></div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;no found!\n&quot;</span>;</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>        key = -1;  <span class="comment">// Exit test</span></div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>        <span class="comment">/* The test sample is returned as:</span></div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span><span class="comment">         * data[0]:data[5]:data[15]:data[10]:search time = 3 The search is</span></div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span><span class="comment">         * successful. There are 10 in this set of data */</span></div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    }</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span> </div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   99</span>           {</div>
+<div class="line"><span class="lineno">  100</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">link</a> p;</div>
+<div class="line"><span class="lineno">  101</span>    <span class="keywordtype">int</span> key, index, i, counter;  <span class="comment">// Key is the value to be found</span></div>
+<div class="line"><span class="lineno">  102</span>    index = 0;</div>
+<div class="line"><span class="lineno">  103</span> </div>
+<div class="line"><span class="lineno">  104</span>    <span class="comment">// You can write the input mode here</span></div>
+<div class="line"><span class="lineno">  105</span>    <span class="keywordflow">while</span> (index &lt; <a class="code hl_define" href="../../d1/df3/hash__search_8cpp.html#a392fb874e547e582e9c66a08a1f23326">MAX</a>) {  <span class="comment">// Construct hash table</span></div>
+<div class="line"><span class="lineno">  106</span>        <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#ad0831425f1389166a9518f422d0c6ec5">create_list</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[index]);</div>
+<div class="line"><span class="lineno">  107</span>        index++;</div>
+<div class="line"><span class="lineno">  108</span>    }</div>
+<div class="line"><span class="lineno">  109</span> </div>
+<div class="line"><span class="lineno">  110</span>    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_define" href="../../d1/df3/hash__search_8cpp.html#a77c722016053a1d484aa177ce205b367">HASHMAX</a>; i++) {  <span class="comment">// Output hash table</span></div>
+<div class="line"><span class="lineno">  111</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;hashtab [&quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;]\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  112</span> </div>
+<div class="line"><span class="lineno">  113</span>        p = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#af413b1740073db54796642b0ab814d6d">hashtab</a>[i].next;</div>
+<div class="line"><span class="lineno">  114</span> </div>
+<div class="line"><span class="lineno">  115</span>        <span class="keywordflow">while</span> (p != NULL) {</div>
+<div class="line"><span class="lineno">  116</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;please int key:&quot;</span>;</div>
+<div class="line"><span class="lineno">  117</span>            <span class="keywordflow">if</span> (p-&gt;key &gt; 0)</div>
+<div class="line"><span class="lineno">  118</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;[&quot;</span> &lt;&lt; p-&gt;key &lt;&lt; <span class="stringliteral">&quot;]&quot;</span>;</div>
+<div class="line"><span class="lineno">  119</span>            p = p-&gt;next;</div>
+<div class="line"><span class="lineno">  120</span>        }</div>
+<div class="line"><span class="lineno">  121</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  122</span>    }</div>
+<div class="line"><span class="lineno">  123</span> </div>
+<div class="line"><span class="lineno">  124</span>    <span class="keywordflow">while</span> (key != -1) {</div>
+<div class="line"><span class="lineno">  125</span>        <span class="comment">// You can write the input mode here</span></div>
+<div class="line"><span class="lineno">  126</span>        <span class="comment">// test key = 10</span></div>
+<div class="line"><span class="lineno">  127</span>        key = 10;</div>
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+<div class="line"><span class="lineno">  132</span>        key = -1;  <span class="comment">// Exit test</span></div>
+<div class="line"><span class="lineno">  133</span>        <span class="comment">/* The test sample is returned as:</span></div>
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+<div class="line"><span class="lineno">   34</span>        <a class="code hl_variable" href="../../d1/df6/class_easter_year_month_day.html#a01a068eae0b6fa8f86f5f60c2840bbde">month</a> = newMonth;</div>
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-<div class="fragment"><div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>                                            {</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i] = new_val;</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    <span class="keywordflow">while</span> (i != 0 &amp;&amp; <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[parent(i)] &gt; <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i]) {</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(<a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i], <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[parent(i)]);</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>        i = parent(i);</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    }</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   76</span>                                            {</div>
+<div class="line"><span class="lineno">   77</span>    <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i] = new_val;</div>
+<div class="line"><span class="lineno">   78</span>    <span class="keywordflow">while</span> (i != 0 &amp;&amp; <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[parent(i)] &gt; <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i]) {</div>
+<div class="line"><span class="lineno">   79</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(<a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i], <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[parent(i)]);</div>
+<div class="line"><span class="lineno">   80</span>        i = parent(i);</div>
+<div class="line"><span class="lineno">   81</span>    }</div>
+<div class="line"><span class="lineno">   82</span>}</div>
 <div class="ttc" id="aswap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a></div><div class="ttdeci">T swap(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -267,10 +267,10 @@ Here is the call graph for this function:</div>
 </div><div class="memdoc">
 <p >Deletes a key stored at index i</p>
 <p >This function deletes key at index i. It first reduced value to minus infinite, then calls <a class="el" href="../../d2/d05/class_min_heap.html#a4014f1edaed0bd7db0c0d2ca53228980">extractMin()</a> </p>
-<div class="fragment"><div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>                             {</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    <a class="code hl_function" href="../../d2/d05/class_min_heap.html#aa7f726cc6327955d22871592227432f5">decreaseKey</a>(i, INT_MIN);</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    <a class="code hl_function" href="../../d2/d05/class_min_heap.html#a4014f1edaed0bd7db0c0d2ca53228980">extractMin</a>();</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  105</span>                             {</div>
+<div class="line"><span class="lineno">  106</span>    <a class="code hl_function" href="../../d2/d05/class_min_heap.html#aa7f726cc6327955d22871592227432f5">decreaseKey</a>(i, INT_MIN);</div>
+<div class="line"><span class="lineno">  107</span>    <a class="code hl_function" href="../../d2/d05/class_min_heap.html#a4014f1edaed0bd7db0c0d2ca53228980">extractMin</a>();</div>
+<div class="line"><span class="lineno">  108</span>}</div>
 <div class="ttc" id="aclass_min_heap_html_a4014f1edaed0bd7db0c0d2ca53228980"><div class="ttname"><a href="../../d2/d05/class_min_heap.html#a4014f1edaed0bd7db0c0d2ca53228980">MinHeap::extractMin</a></div><div class="ttdeci">int extractMin()</div><div class="ttdef"><b>Definition:</b> binaryheap.cpp:85</div></div>
 <div class="ttc" id="aclass_min_heap_html_aa7f726cc6327955d22871592227432f5"><div class="ttname"><a href="../../d2/d05/class_min_heap.html#aa7f726cc6327955d22871592227432f5">MinHeap::decreaseKey</a></div><div class="ttdeci">void decreaseKey(int i, int new_val)</div><div class="ttdef"><b>Definition:</b> binaryheap.cpp:76</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -297,22 +297,22 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >to extract the root which is the minimum element </p>
-<div class="fragment"><div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>                        {</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a> &lt;= 0)</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>        <span class="keywordflow">return</span> INT_MAX;</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a> == 1) {</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a>--;</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[0];</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    }</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span> </div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    <span class="comment">// Store the minimum value, and remove it from heap</span></div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>    <span class="keywordtype">int</span> root = <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[0];</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>    <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[0] = <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[<a class="code hl_variable" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a> - 1];</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a>--;</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    <a class="code hl_function" href="../../d2/d05/class_min_heap.html#aaef438c1056492cb62c4a4d9035b5cad">MinHeapify</a>(0);</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span> </div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>    <span class="keywordflow">return</span> root;</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   85</span>                        {</div>
+<div class="line"><span class="lineno">   86</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a> &lt;= 0)</div>
+<div class="line"><span class="lineno">   87</span>        <span class="keywordflow">return</span> INT_MAX;</div>
+<div class="line"><span class="lineno">   88</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a> == 1) {</div>
+<div class="line"><span class="lineno">   89</span>        <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a>--;</div>
+<div class="line"><span class="lineno">   90</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[0];</div>
+<div class="line"><span class="lineno">   91</span>    }</div>
+<div class="line"><span class="lineno">   92</span> </div>
+<div class="line"><span class="lineno">   93</span>    <span class="comment">// Store the minimum value, and remove it from heap</span></div>
+<div class="line"><span class="lineno">   94</span>    <span class="keywordtype">int</span> root = <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[0];</div>
+<div class="line"><span class="lineno">   95</span>    <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[0] = <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[<a class="code hl_variable" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a> - 1];</div>
+<div class="line"><span class="lineno">   96</span>    <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a>--;</div>
+<div class="line"><span class="lineno">   97</span>    <a class="code hl_function" href="../../d2/d05/class_min_heap.html#aaef438c1056492cb62c4a4d9035b5cad">MinHeapify</a>(0);</div>
+<div class="line"><span class="lineno">   98</span> </div>
+<div class="line"><span class="lineno">   99</span>    <span class="keywordflow">return</span> root;</div>
+<div class="line"><span class="lineno">  100</span>}</div>
 <div class="ttc" id="aclass_min_heap_html_aaef438c1056492cb62c4a4d9035b5cad"><div class="ttname"><a href="../../d2/d05/class_min_heap.html#aaef438c1056492cb62c4a4d9035b5cad">MinHeap::MinHeapify</a></div><div class="ttdeci">void MinHeapify(int)</div><div class="ttdef"><b>Definition:</b> binaryheap.cpp:113</div></div>
 </div><!-- fragment -->
 </div>
@@ -340,7 +340,7 @@ Here is the call graph for this function:</div>
 </table>
 </div><div class="memdoc">
 <p >Returns the minimum key (key at root) from min heap </p>
-<div class="fragment"><div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[0]; }</div>
+<div class="fragment"><div class="line"><span class="lineno">   43</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[0]; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -360,23 +360,23 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Inserts a new key 'k' </p>
-<div class="fragment"><div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>                             {</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a> == <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a88b4aa3e66392a3eabbf2517a9a79a02">capacity</a>) {</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nOverflow: Could not insertKey\n&quot;</span>;</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>        <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    }</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span> </div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    <span class="comment">// First insert the new key at the end</span></div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>    <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a>++;</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    <span class="keywordtype">int</span> i = <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a> - 1;</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i] = <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>;</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span> </div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <span class="comment">// Fix the min heap property if it is violated</span></div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <span class="keywordflow">while</span> (i != 0 &amp;&amp; <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[parent(i)] &gt; <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i]) {</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(<a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i], <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[parent(i)]);</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        i = parent(i);</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>    }</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   55</span>                             {</div>
+<div class="line"><span class="lineno">   56</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a> == <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a88b4aa3e66392a3eabbf2517a9a79a02">capacity</a>) {</div>
+<div class="line"><span class="lineno">   57</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nOverflow: Could not insertKey\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   58</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">   59</span>    }</div>
+<div class="line"><span class="lineno">   60</span> </div>
+<div class="line"><span class="lineno">   61</span>    <span class="comment">// First insert the new key at the end</span></div>
+<div class="line"><span class="lineno">   62</span>    <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a>++;</div>
+<div class="line"><span class="lineno">   63</span>    <span class="keywordtype">int</span> i = <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a> - 1;</div>
+<div class="line"><span class="lineno">   64</span>    <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i] = <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>;</div>
+<div class="line"><span class="lineno">   65</span> </div>
+<div class="line"><span class="lineno">   66</span>    <span class="comment">// Fix the min heap property if it is violated</span></div>
+<div class="line"><span class="lineno">   67</span>    <span class="keywordflow">while</span> (i != 0 &amp;&amp; <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[parent(i)] &gt; <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i]) {</div>
+<div class="line"><span class="lineno">   68</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(<a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i], <a class="code hl_variable" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[parent(i)]);</div>
+<div class="line"><span class="lineno">   69</span>        i = parent(i);</div>
+<div class="line"><span class="lineno">   70</span>    }</div>
+<div class="line"><span class="lineno">   71</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
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@@ -412,7 +412,7 @@ Here is the call graph for this function:</div>
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 <p >to get index of left child of node at index i </p>
-<div class="fragment"><div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>{ <span class="keywordflow">return</span> (2 * i + 1); }</div>
+<div class="fragment"><div class="line"><span class="lineno">   31</span>{ <span class="keywordflow">return</span> (2 * i + 1); }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -433,19 +433,19 @@ Here is the call graph for this function:</div>
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 <p >to heapify a subtree with the root at given index</p>
 <p >A recursive method to heapify a subtree with the root at given index This method assumes that the subtrees are already heapified </p>
-<div class="fragment"><div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>                              {</div>
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@@ -158,20 +158,20 @@ template&lt;typename T &gt; </div>
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 <p >Same algorithm with little different formula. It still calculates in \(O(\log N)\) </p>
-<div class="fragment"><div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>                                   {</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    <span class="comment">// negative power. a^b = 1 / (a^-b)</span></div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    <span class="keywordflow">if</span> (b &lt; 0)</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>        <span class="keywordflow">return</span> 1.0 / <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power_linear</a>(a, -b);</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span> </div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <span class="keywordtype">double</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = 1;</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    <span class="keywordflow">while</span> (b) {</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>        <span class="keywordflow">if</span> (b &amp; 1)</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>            <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> * a;</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>        a = a * a;</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        b = b &gt;&gt; 1;</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    }</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   50</span>                                   {</div>
+<div class="line"><span class="lineno">   51</span>    <span class="comment">// negative power. a^b = 1 / (a^-b)</span></div>
+<div class="line"><span class="lineno">   52</span>    <span class="keywordflow">if</span> (b &lt; 0)</div>
+<div class="line"><span class="lineno">   53</span>        <span class="keywordflow">return</span> 1.0 / <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power_linear</a>(a, -b);</div>
+<div class="line"><span class="lineno">   54</span> </div>
+<div class="line"><span class="lineno">   55</span>    <span class="keywordtype">double</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = 1;</div>
+<div class="line"><span class="lineno">   56</span>    <span class="keywordflow">while</span> (b) {</div>
+<div class="line"><span class="lineno">   57</span>        <span class="keywordflow">if</span> (b &amp; 1)</div>
+<div class="line"><span class="lineno">   58</span>            <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> * a;</div>
+<div class="line"><span class="lineno">   59</span>        a = a * a;</div>
+<div class="line"><span class="lineno">   60</span>        b = b &gt;&gt; 1;</div>
+<div class="line"><span class="lineno">   61</span>    }</div>
+<div class="line"><span class="lineno">   62</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">   63</span>}</div>
 <div class="ttc" id="afast__power_8cpp_html_a0d4e3f0099a6975b74a314a35bd0f94d"><div class="ttname"><a href="../../d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power_linear</a></div><div class="ttdeci">double fast_power_linear(T a, T b)</div><div class="ttdef"><b>Definition:</b> fast_power.cpp:50</div></div>
 <div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -211,24 +211,24 @@ template&lt;typename T &gt; </div>
       </table>
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 <p >algorithm implementation for \(a^b\) </p>
-<div class="fragment"><div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>                                      {</div>
-<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>    <span class="comment">// negative power. a^b = 1 / (a^-b)</span></div>
-<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>    <span class="keywordflow">if</span> (b &lt; 0)</div>
-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>        <span class="keywordflow">return</span> 1.0 / <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(a, -b);</div>
-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span> </div>
-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>    <span class="keywordflow">if</span> (b == 0)</div>
-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>        <span class="keywordflow">return</span> 1;</div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>    T bottom = <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(a, b &gt;&gt; 1);</div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>    <span class="comment">// Since it is integer division b/2 = (b-1)/2 where b is odd.</span></div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    <span class="comment">// Therefore, case2 is easily solved by integer division.</span></div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span> </div>
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-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    <span class="keywordflow">if</span> ((b &amp; 1) == 0)  <span class="comment">// case1</span></div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = bottom * bottom;</div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    <span class="keywordflow">else</span>  <span class="comment">// case2</span></div>
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-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   26</span>                                      {</div>
+<div class="line"><span class="lineno">   27</span>    <span class="comment">// negative power. a^b = 1 / (a^-b)</span></div>
+<div class="line"><span class="lineno">   28</span>    <span class="keywordflow">if</span> (b &lt; 0)</div>
+<div class="line"><span class="lineno">   29</span>        <span class="keywordflow">return</span> 1.0 / <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(a, -b);</div>
+<div class="line"><span class="lineno">   30</span> </div>
+<div class="line"><span class="lineno">   31</span>    <span class="keywordflow">if</span> (b == 0)</div>
+<div class="line"><span class="lineno">   32</span>        <span class="keywordflow">return</span> 1;</div>
+<div class="line"><span class="lineno">   33</span>    T bottom = <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(a, b &gt;&gt; 1);</div>
+<div class="line"><span class="lineno">   34</span>    <span class="comment">// Since it is integer division b/2 = (b-1)/2 where b is odd.</span></div>
+<div class="line"><span class="lineno">   35</span>    <span class="comment">// Therefore, case2 is easily solved by integer division.</span></div>
+<div class="line"><span class="lineno">   36</span> </div>
+<div class="line"><span class="lineno">   37</span>    <span class="keywordtype">double</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">   38</span>    <span class="keywordflow">if</span> ((b &amp; 1) == 0)  <span class="comment">// case1</span></div>
+<div class="line"><span class="lineno">   39</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = bottom * bottom;</div>
+<div class="line"><span class="lineno">   40</span>    <span class="keywordflow">else</span>  <span class="comment">// case2</span></div>
+<div class="line"><span class="lineno">   41</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = bottom * bottom * a;</div>
+<div class="line"><span class="lineno">   42</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">   43</span>}</div>
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 Here is the call graph for this function:</div>
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 <p >Main function </p>
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-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/ios_base/sync_with_stdio.html">std::ios_base::sync_with_stdio</a>(<span class="keyword">false</span>);</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span> </div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testing...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 20; i++) {</div>
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+<div class="fragment"><div class="line"><span class="lineno">   68</span>           {</div>
+<div class="line"><span class="lineno">   69</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
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-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>    <span class="comment">// Example 2. Creating array of doubles.</span></div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nTest 2 - as a std::array...&quot;</span>;</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, size&gt;</a> double_arr = {-100.2, 10.2, 20.0, 9.0, 7.5, 7.2};</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, size&gt;</a> sorted_arr = <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a2f8bc626eb57acae24a94636a23af6a1">sorting::gnomeSort</a>(double_arr);</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(sorted_arr), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(sorted_arr)));</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; Passed\n&quot;</span>;</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; size; i++) {</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; double_arr[i] &lt;&lt; <span class="stringliteral">&quot;, &quot;</span>;</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    }</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span> </div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    <span class="comment">// Example 3. Creating random array of float.</span></div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nTest 3 - 200 random numbers as a std::array...&quot;</span>;</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> size2 = 200;</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;float, size2&gt;</a> rand_arr{};</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span> </div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;a : rand_arr) {</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>        <span class="comment">// generate random numbers between -5.0 and 4.99</span></div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>        a = float(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 1000 - 500) / 100.f;</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    }</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span> </div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;float, size2&gt;</a> float_arr = <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a2f8bc626eb57acae24a94636a23af6a1">sorting::gnomeSort</a>(rand_arr);</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(float_arr), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(float_arr)));</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; Passed\n&quot;</span>;</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <span class="comment">// for (int i = 0; i &lt; size; i++) std::cout &lt;&lt; double_arr[i] &lt;&lt; &quot;, &quot;;</span></div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   85</span>                   {</div>
+<div class="line"><span class="lineno">   86</span>    <span class="comment">// Example 1. Creating array of int,</span></div>
+<div class="line"><span class="lineno">   87</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 - as a C-array...&quot;</span>;</div>
+<div class="line"><span class="lineno">   88</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> size = 6;</div>
+<div class="line"><span class="lineno">   89</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, size&gt;</a> arr = {-22, 100, 150, 35, -10, 99};</div>
+<div class="line"><span class="lineno">   90</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a2f8bc626eb57acae24a94636a23af6a1">sorting::gnomeSort</a>(arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/data.html">data</a>(),</div>
+<div class="line"><span class="lineno">   91</span>                       size);  <span class="comment">// pass array data as a C-style array pointer</span></div>
+<div class="line"><span class="lineno">   92</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr)));</div>
+<div class="line"><span class="lineno">   93</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; Passed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   94</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; size; i++) {</div>
+<div class="line"><span class="lineno">   95</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; arr[i] &lt;&lt; <span class="stringliteral">&quot;, &quot;</span>;</div>
+<div class="line"><span class="lineno">   96</span>    }</div>
+<div class="line"><span class="lineno">   97</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   98</span> </div>
+<div class="line"><span class="lineno">   99</span>    <span class="comment">// Example 2. Creating array of doubles.</span></div>
+<div class="line"><span class="lineno">  100</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nTest 2 - as a std::array...&quot;</span>;</div>
+<div class="line"><span class="lineno">  101</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, size&gt;</a> double_arr = {-100.2, 10.2, 20.0, 9.0, 7.5, 7.2};</div>
+<div class="line"><span class="lineno">  102</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, size&gt;</a> sorted_arr = <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a2f8bc626eb57acae24a94636a23af6a1">sorting::gnomeSort</a>(double_arr);</div>
+<div class="line"><span class="lineno">  103</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(sorted_arr), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(sorted_arr)));</div>
+<div class="line"><span class="lineno">  104</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; Passed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  105</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; size; i++) {</div>
+<div class="line"><span class="lineno">  106</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; double_arr[i] &lt;&lt; <span class="stringliteral">&quot;, &quot;</span>;</div>
+<div class="line"><span class="lineno">  107</span>    }</div>
+<div class="line"><span class="lineno">  108</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  109</span> </div>
+<div class="line"><span class="lineno">  110</span>    <span class="comment">// Example 3. Creating random array of float.</span></div>
+<div class="line"><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nTest 3 - 200 random numbers as a std::array...&quot;</span>;</div>
+<div class="line"><span class="lineno">  112</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> size2 = 200;</div>
+<div class="line"><span class="lineno">  113</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;float, size2&gt;</a> rand_arr{};</div>
+<div class="line"><span class="lineno">  114</span> </div>
+<div class="line"><span class="lineno">  115</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;a : rand_arr) {</div>
+<div class="line"><span class="lineno">  116</span>        <span class="comment">// generate random numbers between -5.0 and 4.99</span></div>
+<div class="line"><span class="lineno">  117</span>        a = float(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 1000 - 500) / 100.f;</div>
+<div class="line"><span class="lineno">  118</span>    }</div>
+<div class="line"><span class="lineno">  119</span> </div>
+<div class="line"><span class="lineno">  120</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;float, size2&gt;</a> float_arr = <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a2f8bc626eb57acae24a94636a23af6a1">sorting::gnomeSort</a>(rand_arr);</div>
+<div class="line"><span class="lineno">  121</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(float_arr), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(float_arr)));</div>
+<div class="line"><span class="lineno">  122</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; Passed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  123</span>    <span class="comment">// for (int i = 0; i &lt; size; i++) std::cout &lt;&lt; double_arr[i] &lt;&lt; &quot;, &quot;;</span></div>
+<div class="line"><span class="lineno">  124</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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@@ -150,36 +150,36 @@ Functions</h2></td></tr>
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 <p >jump search implementation </p>
-<div class="fragment"><div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span>                                        {</div>
-<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span>    <span class="comment">// Finding block size to be jumped</span></div>
-<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span>    <span class="keywordtype">int</span> step = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(n);</div>
-<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span> </div>
-<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span>    <span class="comment">// Finding the block where element is</span></div>
-<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span>    <span class="comment">// present (if it is present)</span></div>
-<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span>    <span class="keywordtype">int</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/prev.html">prev</a> = 0;</div>
-<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span>    <span class="keywordflow">while</span> (arr[<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(step, n) - 1] &lt; x) {</div>
-<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/prev.html">prev</a> = step;</div>
-<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>        step += <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(n);</div>
-<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>        <span class="keywordflow">if</span> (prev &gt;= n)</div>
-<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>            <span class="keywordflow">return</span> -1;</div>
-<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span>    }</div>
-<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span> </div>
-<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>    <span class="comment">// Doing a linear search for x in block</span></div>
-<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>    <span class="comment">// beginning with prev.</span></div>
-<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>    <span class="keywordflow">while</span> (arr[prev] &lt; x) {</div>
-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/prev.html">prev</a>++;</div>
-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span> </div>
-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>        <span class="comment">// If we reached next block or end of</span></div>
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+<!-- Generated by Doxygen 1.9.3 -->
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@@ -200,12 +200,12 @@ template&lt;class T &gt; </div>
   </dd>
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 <dl class="section return"><dt>Returns</dt><dd>number of inversions in input array, sorts the array </dd></dl>
-<div class="fragment"><div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>                                                     {</div>
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-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    temp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/reserve.html">reserve</a>(size);</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>    temp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/assign.html">assign</a>(size, 0);</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a>(arr, temp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a>(), 0, size - 1);</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  164</span>                                                     {</div>
+<div class="line"><span class="lineno">  165</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> temp;</div>
+<div class="line"><span class="lineno">  166</span>    temp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/reserve.html">reserve</a>(size);</div>
+<div class="line"><span class="lineno">  167</span>    temp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/assign.html">assign</a>(size, 0);</div>
+<div class="line"><span class="lineno">  168</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a>(arr, temp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a>(), 0, size - 1);</div>
+<div class="line"><span class="lineno">  169</span>}</div>
 <div class="ttc" id="aassign_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/assign.html">std::vector::assign</a></div><div class="ttdeci">T assign(T... args)</div></div>
 <div class="ttc" id="adata_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/data.html">std::vector::data</a></div><div class="ttdeci">T data(T... args)</div></div>
 <div class="ttc" id="agroup__sorting_html_gab6b14fea48d9841e29b9fc26be6e05d7"><div class="ttname"><a href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a></div><div class="ttdeci">void mergeSort(int *arr, int l, int r)</div><div class="ttdef"><b>Definition:</b> merge_sort.cpp:71</div></div>
@@ -238,11 +238,11 @@ Here is the call graph for this function:</div>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>           {</div>
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-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>    <span class="comment">// body(); // test your own array</span></div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  271</span>           {</div>
+<div class="line"><span class="lineno">  272</span>    <a class="code hl_function" href="../../d2/d26/count__inversions_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// Run test implementations</span></div>
+<div class="line"><span class="lineno">  273</span>    <span class="comment">// body(); // test your own array</span></div>
+<div class="line"><span class="lineno">  274</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  275</span>}</div>
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 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -313,35 +313,35 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>number of inversions found in merge step </dd></dl>
-<div class="fragment"><div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>                                                                             {</div>
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-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    uint32_t j = mid + 1;    <span class="comment">/* j --&gt; index for right sub-array */</span></div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    uint32_t <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>;       <span class="comment">/* k --&gt; index for resultant array temp */</span></div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    uint32_t inv_count = 0;  <span class="comment">// inversion count</span></div>
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-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    <span class="keywordflow">while</span> ((i &lt;= mid) &amp;&amp; (j &lt;= right)) {</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>        <span class="keywordflow">if</span> (arr[i] &lt;= arr[j]) {</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>            temp[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++] = arr[i++];</div>
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-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>            inv_count +=</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>                (mid - i +</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>                 1);  <span class="comment">// tricky; may vary depending on selection of sub-array</span></div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>        }</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    }</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <span class="comment">// Add remaining elements from the larger subarray to the end of temp</span></div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <span class="keywordflow">while</span> (i &lt;= mid) {</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        temp[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++] = arr[i++];</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    }</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <span class="keywordflow">while</span> (j &lt;= right) {</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>        temp[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++] = arr[j++];</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    }</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    <span class="comment">// Copy temp[] to arr[]</span></div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <span class="keywordflow">for</span> (k = left; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt;= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        arr[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] = temp[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>];</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    }</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    <span class="keywordflow">return</span> inv_count;</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   85</span>                                                                             {</div>
+<div class="line"><span class="lineno">   86</span>    uint32_t i = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>;       <span class="comment">/* i --&gt; index of left sub-array */</span></div>
+<div class="line"><span class="lineno">   87</span>    uint32_t j = mid + 1;    <span class="comment">/* j --&gt; index for right sub-array */</span></div>
+<div class="line"><span class="lineno">   88</span>    uint32_t <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>;       <span class="comment">/* k --&gt; index for resultant array temp */</span></div>
+<div class="line"><span class="lineno">   89</span>    uint32_t inv_count = 0;  <span class="comment">// inversion count</span></div>
+<div class="line"><span class="lineno">   90</span> </div>
+<div class="line"><span class="lineno">   91</span>    <span class="keywordflow">while</span> ((i &lt;= mid) &amp;&amp; (j &lt;= right)) {</div>
+<div class="line"><span class="lineno">   92</span>        <span class="keywordflow">if</span> (arr[i] &lt;= arr[j]) {</div>
+<div class="line"><span class="lineno">   93</span>            temp[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++] = arr[i++];</div>
+<div class="line"><span class="lineno">   94</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   95</span>            temp[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++] = arr[j++];</div>
+<div class="line"><span class="lineno">   96</span>            inv_count +=</div>
+<div class="line"><span class="lineno">   97</span>                (mid - i +</div>
+<div class="line"><span class="lineno">   98</span>                 1);  <span class="comment">// tricky; may vary depending on selection of sub-array</span></div>
+<div class="line"><span class="lineno">   99</span>        }</div>
+<div class="line"><span class="lineno">  100</span>    }</div>
+<div class="line"><span class="lineno">  101</span>    <span class="comment">// Add remaining elements from the larger subarray to the end of temp</span></div>
+<div class="line"><span class="lineno">  102</span>    <span class="keywordflow">while</span> (i &lt;= mid) {</div>
+<div class="line"><span class="lineno">  103</span>        temp[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++] = arr[i++];</div>
+<div class="line"><span class="lineno">  104</span>    }</div>
+<div class="line"><span class="lineno">  105</span>    <span class="keywordflow">while</span> (j &lt;= right) {</div>
+<div class="line"><span class="lineno">  106</span>        temp[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++] = arr[j++];</div>
+<div class="line"><span class="lineno">  107</span>    }</div>
+<div class="line"><span class="lineno">  108</span>    <span class="comment">// Copy temp[] to arr[]</span></div>
+<div class="line"><span class="lineno">  109</span>    <span class="keywordflow">for</span> (k = left; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt;= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
+<div class="line"><span class="lineno">  110</span>        arr[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] = temp[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>];</div>
+<div class="line"><span class="lineno">  111</span>    }</div>
+<div class="line"><span class="lineno">  112</span>    <span class="keywordflow">return</span> inv_count;</div>
+<div class="line"><span class="lineno">  113</span>}</div>
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 <div class="ttc" id="aleft_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::left</a></div><div class="ttdeci">T left(T... args)</div></div>
 </div><!-- fragment -->
@@ -399,20 +399,20 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>number of inversions in array </dd></dl>
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-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        <span class="comment">// Add inversions in left and right sub-arrays</span></div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>        inv_count += <a class="code hl_function" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a>(arr, temp, left, mid);  <span class="comment">// left sub-array</span></div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        inv_count += <a class="code hl_function" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a>(arr, temp, mid + 1, right);</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span> </div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>        <span class="comment">// inversions in the merge step</span></div>
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-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  132</span>                                                                   {</div>
+<div class="line"><span class="lineno">  133</span>    uint32_t mid = 0, inv_count = 0;</div>
+<div class="line"><span class="lineno">  134</span>    <span class="keywordflow">if</span> (right &gt; left) {</div>
+<div class="line"><span class="lineno">  135</span>        <span class="comment">// midpoint to split the array</span></div>
+<div class="line"><span class="lineno">  136</span>        mid = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>) / 2;</div>
+<div class="line"><span class="lineno">  137</span>        <span class="comment">// Add inversions in left and right sub-arrays</span></div>
+<div class="line"><span class="lineno">  138</span>        inv_count += <a class="code hl_function" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a>(arr, temp, left, mid);  <span class="comment">// left sub-array</span></div>
+<div class="line"><span class="lineno">  139</span>        inv_count += <a class="code hl_function" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a>(arr, temp, mid + 1, right);</div>
+<div class="line"><span class="lineno">  140</span> </div>
+<div class="line"><span class="lineno">  141</span>        <span class="comment">// inversions in the merge step</span></div>
+<div class="line"><span class="lineno">  142</span>        inv_count += <a class="code hl_function" href="../../d5/d4c/group__sorting.html#ga460c61cd948203b4816bef2accb3fc73">merge</a>(arr, temp, left, mid, right);</div>
+<div class="line"><span class="lineno">  143</span>    }</div>
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-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span> </div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>        <span class="comment">/* store the converged eigen value */</span></div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>        eigen_vals[num_eigs] = last_eig;</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>        <span class="comment">// A[0][num_eigs][num_eigs];</span></div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>        <span class="keywordflow">if</span> (print_intermediates) {</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;========================\n&quot;</span>;</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Eigen value: &quot;</span> &lt;&lt; last_eig &lt;&lt; <span class="stringliteral">&quot;,\n&quot;</span>;</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;========================\n&quot;</span>;</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>        }</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span> </div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>        num_eigs--;</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>        rows--;</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>        columns--;</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>    }</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>    eigen_vals[0] = A[0][0][0];</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span> </div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>    <span class="keywordflow">if</span> (print_intermediates) {</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; Q &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; R &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>    }</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span> </div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>    <span class="keywordflow">return</span> eigen_vals;</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   99</span>                                                                     {</div>
+<div class="line"><span class="lineno">  100</span>    <span class="keywordtype">int</span> rows = A-&gt;size();</div>
+<div class="line"><span class="lineno">  101</span>    <span class="keywordtype">int</span> columns = rows;</div>
+<div class="line"><span class="lineno">  102</span>    <span class="keywordtype">int</span> counter = 0, num_eigs = rows - 1;</div>
+<div class="line"><span class="lineno">  103</span>    <span class="keywordtype">double</span> last_eig = 0;</div>
+<div class="line"><span class="lineno">  104</span> </div>
+<div class="line"><span class="lineno">  105</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; Q(rows);</div>
+<div class="line"><span class="lineno">  106</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; R(columns);</div>
+<div class="line"><span class="lineno">  107</span> </div>
+<div class="line"><span class="lineno">  108</span>    <span class="comment">/* number of eigen values = matrix size */</span></div>
+<div class="line"><span class="lineno">  109</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> eigen_vals(rows);</div>
+<div class="line"><span class="lineno">  110</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; rows; i++) {</div>
+<div class="line"><span class="lineno">  111</span>        Q[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(columns);</div>
+<div class="line"><span class="lineno">  112</span>        R[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(columns);</div>
+<div class="line"><span class="lineno">  113</span>    }</div>
+<div class="line"><span class="lineno">  114</span> </div>
+<div class="line"><span class="lineno">  115</span>    <span class="comment">/* continue till all eigen values are found */</span></div>
+<div class="line"><span class="lineno">  116</span>    <span class="keywordflow">while</span> (num_eigs &gt; 0) {</div>
+<div class="line"><span class="lineno">  117</span>        <span class="comment">/* iterate with QR decomposition */</span></div>
+<div class="line"><span class="lineno">  118</span>        <span class="keywordflow">while</span> (std::abs(A[0][num_eigs][num_eigs - 1]) &gt;</div>
+<div class="line"><span class="lineno">  119</span>               <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/numeric_limits.html">std::numeric_limits&lt;double&gt;::epsilon</a>()) {</div>
+<div class="line"><span class="lineno">  120</span>            <span class="comment">// initial approximation = last diagonal element</span></div>
+<div class="line"><span class="lineno">  121</span>            last_eig = A[0][num_eigs][num_eigs];</div>
+<div class="line"><span class="lineno">  122</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; rows; i++) {</div>
+<div class="line"><span class="lineno">  123</span>                A[0][i][i] -= last_eig; <span class="comment">/* A - cI */</span></div>
+<div class="line"><span class="lineno">  124</span>            }</div>
+<div class="line"><span class="lineno">  125</span> </div>
+<div class="line"><span class="lineno">  126</span>            <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a73ce637634fc49e1d10d190eb388ebf1">qr_decompose</a>(*A, &amp;Q, &amp;R);</div>
+<div class="line"><span class="lineno">  127</span> </div>
+<div class="line"><span class="lineno">  128</span>            <span class="keywordflow">if</span> (print_intermediates) {</div>
+<div class="line"><span class="lineno">  129</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; *A &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  130</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; Q &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  131</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; R &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  132</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/fprintf.html">printf</a>(<span class="stringliteral">&quot;-------------------- %d ---------------------\n&quot;</span>,</div>
+<div class="line"><span class="lineno">  133</span>                       ++counter);</div>
+<div class="line"><span class="lineno">  134</span>            }</div>
+<div class="line"><span class="lineno">  135</span> </div>
+<div class="line"><span class="lineno">  136</span>            <span class="comment">// new approximation A&#39; = R * Q</span></div>
+<div class="line"><span class="lineno">  137</span>            <a class="code hl_function" href="../../de/d75/qr__eigen__values_8cpp.html#abb8bf4c55e10685a5eb2ad3797fde1ae">mat_mul</a>(R, Q, A);</div>
+<div class="line"><span class="lineno">  138</span> </div>
+<div class="line"><span class="lineno">  139</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; rows; i++) {</div>
+<div class="line"><span class="lineno">  140</span>                A[0][i][i] += last_eig; <span class="comment">/* A + cI */</span></div>
+<div class="line"><span class="lineno">  141</span>            }</div>
+<div class="line"><span class="lineno">  142</span>        }</div>
+<div class="line"><span class="lineno">  143</span> </div>
+<div class="line"><span class="lineno">  144</span>        <span class="comment">/* store the converged eigen value */</span></div>
+<div class="line"><span class="lineno">  145</span>        eigen_vals[num_eigs] = last_eig;</div>
+<div class="line"><span class="lineno">  146</span>        <span class="comment">// A[0][num_eigs][num_eigs];</span></div>
+<div class="line"><span class="lineno">  147</span>        <span class="keywordflow">if</span> (print_intermediates) {</div>
+<div class="line"><span class="lineno">  148</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;========================\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  149</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Eigen value: &quot;</span> &lt;&lt; last_eig &lt;&lt; <span class="stringliteral">&quot;,\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  150</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;========================\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  151</span>        }</div>
+<div class="line"><span class="lineno">  152</span> </div>
+<div class="line"><span class="lineno">  153</span>        num_eigs--;</div>
+<div class="line"><span class="lineno">  154</span>        rows--;</div>
+<div class="line"><span class="lineno">  155</span>        columns--;</div>
+<div class="line"><span class="lineno">  156</span>    }</div>
+<div class="line"><span class="lineno">  157</span>    eigen_vals[0] = A[0][0][0];</div>
+<div class="line"><span class="lineno">  158</span> </div>
+<div class="line"><span class="lineno">  159</span>    <span class="keywordflow">if</span> (print_intermediates) {</div>
+<div class="line"><span class="lineno">  160</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; Q &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  161</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; R &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  162</span>    }</div>
+<div class="line"><span class="lineno">  163</span> </div>
+<div class="line"><span class="lineno">  164</span>    <span class="keywordflow">return</span> eigen_vals;</div>
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 <p >operator to print a matrix </p>
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+<div class="line"><span class="lineno">   56</span> </div>
+<div class="line"><span class="lineno">   57</span>    out.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/ios_base/precision.html">precision</a>(4);</div>
+<div class="line"><span class="lineno">   58</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; v.size(); row++) {</div>
+<div class="line"><span class="lineno">   59</span>        out &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::right</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(width) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a>(separator)</div>
+<div class="line"><span class="lineno">   60</span>            &lt;&lt; v[row];</div>
+<div class="line"><span class="lineno">   61</span>    }</div>
+<div class="line"><span class="lineno">   62</span> </div>
+<div class="line"><span class="lineno">   63</span>    <span class="keywordflow">return</span> out;</div>
+<div class="line"><span class="lineno">   64</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -408,64 +408,64 @@ template&lt;typename T &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>  {</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> ROWS = A.size();        <span class="comment">// number of rows of A</span></div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> COLUMNS = A[0].size();  <span class="comment">// number of columns of A</span></div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> col_vector(ROWS);</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> col_vector2(ROWS);</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> tmp_vector(ROWS);</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span> </div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; COLUMNS; i++) {</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>        <span class="comment">/* for each column =&gt; R is a square matrix of NxN */</span></div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>        <span class="keywordtype">int</span> j;</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>        R[0][i] = 0.; <span class="comment">/* make R upper triangular */</span></div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span> </div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>        <span class="comment">/* get corresponding Q vector */</span></div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span><span class="comment">// parallelize on threads</span></div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>        <span class="keywordflow">for</span> (j = 0; j &lt; ROWS; j++) {</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>            tmp_vector[j] = A[j][i]; <span class="comment">/* accumulator for uk */</span></div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>            col_vector[j] = A[j][i];</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>        }</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>        <span class="keywordflow">for</span> (j = 0; j &lt; i; j++) {</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; ROWS; k++) {</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>                col_vector2[k] = Q[0][k][j];</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>            }</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>            col_vector2 = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a6d3c7dce1f142141f509d09f6c0e25dc">vector_proj</a>(col_vector, col_vector2);</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>            tmp_vector -= col_vector2;</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>        }</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span> </div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>        <span class="keywordtype">double</span> <a class="code hl_function" href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8">mag</a> = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">vector_mag</a>(tmp_vector);</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span> </div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span><span class="comment">// parallelize on threads</span></div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>        <span class="keywordflow">for</span> (j = 0; j &lt; ROWS; j++) Q[0][j][i] = tmp_vector[j] / mag;</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span> </div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>            <span class="comment">/* compute upper triangular values of R */</span></div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span><span class="comment">// parallelize on threads</span></div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> kk = 0; kk &lt; ROWS; kk++) {</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>            col_vector[kk] = Q[0][kk][i];</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>        }</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span> </div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span><span class="comment">// parallelize on threads</span></div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = i; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt; COLUMNS; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> kk = 0; kk &lt; ROWS; kk++) {</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>                col_vector2[kk] = A[kk][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>];</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>            }</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>            R[0][i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] = (col_vector * col_vector2).<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>();</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>        }</div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    }</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  150</span>  {</div>
+<div class="line"><span class="lineno">  151</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> ROWS = A.size();        <span class="comment">// number of rows of A</span></div>
+<div class="line"><span class="lineno">  152</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> COLUMNS = A[0].size();  <span class="comment">// number of columns of A</span></div>
+<div class="line"><span class="lineno">  153</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> col_vector(ROWS);</div>
+<div class="line"><span class="lineno">  154</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> col_vector2(ROWS);</div>
+<div class="line"><span class="lineno">  155</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> tmp_vector(ROWS);</div>
+<div class="line"><span class="lineno">  156</span> </div>
+<div class="line"><span class="lineno">  157</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; COLUMNS; i++) {</div>
+<div class="line"><span class="lineno">  158</span>        <span class="comment">/* for each column =&gt; R is a square matrix of NxN */</span></div>
+<div class="line"><span class="lineno">  159</span>        <span class="keywordtype">int</span> j;</div>
+<div class="line"><span class="lineno">  160</span>        R[0][i] = 0.; <span class="comment">/* make R upper triangular */</span></div>
+<div class="line"><span class="lineno">  161</span> </div>
+<div class="line"><span class="lineno">  162</span>        <span class="comment">/* get corresponding Q vector */</span></div>
+<div class="line"><span class="lineno">  163</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  164</span><span class="comment">// parallelize on threads</span></div>
+<div class="line"><span class="lineno">  165</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  166</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  167</span>        <span class="keywordflow">for</span> (j = 0; j &lt; ROWS; j++) {</div>
+<div class="line"><span class="lineno">  168</span>            tmp_vector[j] = A[j][i]; <span class="comment">/* accumulator for uk */</span></div>
+<div class="line"><span class="lineno">  169</span>            col_vector[j] = A[j][i];</div>
+<div class="line"><span class="lineno">  170</span>        }</div>
+<div class="line"><span class="lineno">  171</span>        <span class="keywordflow">for</span> (j = 0; j &lt; i; j++) {</div>
+<div class="line"><span class="lineno">  172</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; ROWS; k++) {</div>
+<div class="line"><span class="lineno">  173</span>                col_vector2[k] = Q[0][k][j];</div>
+<div class="line"><span class="lineno">  174</span>            }</div>
+<div class="line"><span class="lineno">  175</span>            col_vector2 = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a6d3c7dce1f142141f509d09f6c0e25dc">vector_proj</a>(col_vector, col_vector2);</div>
+<div class="line"><span class="lineno">  176</span>            tmp_vector -= col_vector2;</div>
+<div class="line"><span class="lineno">  177</span>        }</div>
+<div class="line"><span class="lineno">  178</span> </div>
+<div class="line"><span class="lineno">  179</span>        <span class="keywordtype">double</span> <a class="code hl_function" href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8">mag</a> = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">vector_mag</a>(tmp_vector);</div>
+<div class="line"><span class="lineno">  180</span> </div>
+<div class="line"><span class="lineno">  181</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  182</span><span class="comment">// parallelize on threads</span></div>
+<div class="line"><span class="lineno">  183</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  184</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  185</span>        <span class="keywordflow">for</span> (j = 0; j &lt; ROWS; j++) Q[0][j][i] = tmp_vector[j] / mag;</div>
+<div class="line"><span class="lineno">  186</span> </div>
+<div class="line"><span class="lineno">  187</span>            <span class="comment">/* compute upper triangular values of R */</span></div>
+<div class="line"><span class="lineno">  188</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  189</span><span class="comment">// parallelize on threads</span></div>
+<div class="line"><span class="lineno">  190</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  191</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  192</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> kk = 0; kk &lt; ROWS; kk++) {</div>
+<div class="line"><span class="lineno">  193</span>            col_vector[kk] = Q[0][kk][i];</div>
+<div class="line"><span class="lineno">  194</span>        }</div>
+<div class="line"><span class="lineno">  195</span> </div>
+<div class="line"><span class="lineno">  196</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  197</span><span class="comment">// parallelize on threads</span></div>
+<div class="line"><span class="lineno">  198</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  199</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  200</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = i; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt; COLUMNS; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
+<div class="line"><span class="lineno">  201</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> kk = 0; kk &lt; ROWS; kk++) {</div>
+<div class="line"><span class="lineno">  202</span>                col_vector2[kk] = A[kk][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>];</div>
+<div class="line"><span class="lineno">  203</span>            }</div>
+<div class="line"><span class="lineno">  204</span>            R[0][i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] = (col_vector * col_vector2).<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>();</div>
+<div class="line"><span class="lineno">  205</span>        }</div>
+<div class="line"><span class="lineno">  206</span>    }</div>
+<div class="line"><span class="lineno">  207</span>}</div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
 <div class="ttc" id="anamespacemachine__learning_html_a6f1c98c016ad34ff3d9f39372161bd35"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">machine_learning::sum</a></div><div class="ttdeci">T sum(const std::vector&lt; std::valarray&lt; T &gt; &gt; &amp;A)</div><div class="ttdef"><b>Definition:</b> vector_ops.hpp:232</div></div>
 <div class="ttc" id="anamespaceqr__algorithm_html_a6d3c7dce1f142141f509d09f6c0e25dc"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html#a6d3c7dce1f142141f509d09f6c0e25dc">qr_algorithm::vector_proj</a></div><div class="ttdeci">std::valarray&lt; T &gt; vector_proj(const std::valarray&lt; T &gt; &amp;a, const std::valarray&lt; T &gt; &amp;b)</div><div class="ttdef"><b>Definition:</b> qr_decompose.h:104</div></div>
@@ -519,12 +519,12 @@ template&lt;typename T &gt; </div>
 <p >Compute dot product of two vectors of equal lengths</p>
 <p >If \(\vec{a}=\left[a_0,a_1,a_2,...,a_L\right]\) and \(\vec{b}=\left[b_0,b_1,b_1,...,b_L\right]\) then \(\vec{a}\cdot\vec{b}=\displaystyle\sum_{i=0}^L a_i\times b_i\)</p>
 <dl class="section return"><dt>Returns</dt><dd>\(\vec{a}\cdot\vec{b}\) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>                                                                           {</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <span class="keywordflow">return</span> (a * b).sum();</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    <span class="comment">// could also use following</span></div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <span class="comment">// return std::inner_product(std::begin(a), std::end(a), std::begin(b),</span></div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    <span class="comment">// 0.f);</span></div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   76</span>                                                                           {</div>
+<div class="line"><span class="lineno">   77</span>    <span class="keywordflow">return</span> (a * b).sum();</div>
+<div class="line"><span class="lineno">   78</span>    <span class="comment">// could also use following</span></div>
+<div class="line"><span class="lineno">   79</span>    <span class="comment">// return std::inner_product(std::begin(a), std::end(a), std::begin(b),</span></div>
+<div class="line"><span class="lineno">   80</span>    <span class="comment">// 0.f);</span></div>
+<div class="line"><span class="lineno">   81</span>}</div>
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@@ -556,10 +556,10 @@ template&lt;typename T &gt; </div>
 <p >Compute magnitude of vector.</p>
 <p >If \(\vec{a}=\left[a_0,a_1,a_2,...,a_L\right]\) then \(\left|\vec{a}\right|=\sqrt{\displaystyle\sum_{i=0}^L a_i^2}\)</p>
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@@ -603,20 +603,20 @@ template&lt;typename T &gt; </div>
 </p>
 <dl class="section return"><dt>Returns</dt><dd>NULL if error, otherwise pointer to output </dd></dl>
 <p >check for division by zero using machine epsilon</p>
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+<div class="fragment"><div class="line"><span class="lineno">  105</span>                                                      {</div>
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+<div class="line"><span class="lineno">  108</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  109</span><span class="comment">    /*! check for division by zero using machine epsilon */</span></div>
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+<div class="line"><span class="lineno">  111</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;[&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;] Possible division by zero\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  112</span>        <span class="keywordflow">return</span> a;  <span class="comment">// return vector a back</span></div>
+<div class="line"><span class="lineno">  113</span>    }</div>
+<div class="line"><span class="lineno">  114</span> </div>
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+<div class="line"><span class="lineno">  116</span> </div>
+<div class="line"><span class="lineno">  117</span>    <span class="keywordflow">return</span> b * scalar;</div>
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-<p>Implementation of <a href="https://en.wikipedia.org/wiki/Segment_tree" target="_blank">Segment Tree</a> data structure.  
+<p>Implementation of [Segment Tree] (<a href="https://en.wikipedia.org/wiki/Segment_tree">https://en.wikipedia.org/wiki/Segment_tree</a>) data structure.  
 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;cassert&gt;</code><br />
 <code>#include &lt;cmath&gt;</code><br />
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+<div class="textblock"><p >Implementation of [Segment Tree] (<a href="https://en.wikipedia.org/wiki/Segment_tree">https://en.wikipedia.org/wiki/Segment_tree</a>) data structure. </p>
 <p >A segment tree, also known as a statistic tree, is a tree data structure used for storing information about intervals, or segments. Its classical version allows querying which of the stored segments contain a given point, but our modification allows us to perform (query) any binary operation on any range in the array in O(logN) time. Here, we have used addition (+). For range updates, we have used lazy propagation.</p>
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 <li>Space Complexity : O(NlogN) <br  />
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-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; choice;</div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>    <span class="keywordflow">if</span> (choice == 1) {</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter &quot;</span> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; numbers:\n&quot;</span>;</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt;= n; i++) {</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;: &quot;</span>;</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; arr[i];</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>        }</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>    }</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span> </div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>    <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#ae752659b7c1719d68fdb2ca538a93696">ConsTree</a>(arr, &amp;segtree, 0, n - 1, 0);</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span> </div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>    <span class="keywordflow">do</span> {</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nMake your choice:\n&quot;</span></div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>                     <span class="stringliteral">&quot;1: Range update (input)\n&quot;</span></div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>                     <span class="stringliteral">&quot;2: Range query (output)\n&quot;</span></div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>                     <span class="stringliteral">&quot;0: Exit\n&quot;</span>;</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; choice;</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span> </div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>        <span class="keywordflow">if</span> (choice == 1) {</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter 1-indexed lower bound, upper bound &amp; value:\n&quot;</span>;</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span> </div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>            uint64_t p = 1, q = 1, v = 0;</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; p &gt;&gt; q &gt;&gt; v;</div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>            <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>(&amp;segtree, &amp;lazy, p - 1, q - 1, v, 0, n - 1, 0);</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (choice == 2) {</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter 1-indexed lower bound &amp; upper bound:\n&quot;</span>;</div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span> </div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>            uint64_t p = 1, q = 1;</div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; p &gt;&gt; q;</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#a423a97ea0c7ea6e33b5844a6858d902d">query</a>(&amp;segtree, &amp;lazy, p - 1, q - 1, 0, n - 1, 0);</div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>        }</div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>    } <span class="keywordflow">while</span> (choice &gt; 0);</div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span> </div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  167</span>           {</div>
+<div class="line"><span class="lineno">  168</span>    <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
+<div class="line"><span class="lineno">  169</span> </div>
+<div class="line"><span class="lineno">  170</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter number of elements: &quot;</span>;</div>
+<div class="line"><span class="lineno">  171</span> </div>
+<div class="line"><span class="lineno">  172</span>    uint64_t n = 0;</div>
+<div class="line"><span class="lineno">  173</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
+<div class="line"><span class="lineno">  174</span> </div>
+<div class="line"><span class="lineno">  175</span>    <span class="keyword">auto</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">max</a> = <span class="keyword">static_cast&lt;</span>uint64_t<span class="keyword">&gt;</span>(2 * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(2, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/ceil.html">ceil</a>(log2(n))) - 1);</div>
+<div class="line"><span class="lineno">  176</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr(n), lazy(max), segtree(max);</div>
+<div class="line"><span class="lineno">  177</span> </div>
+<div class="line"><span class="lineno">  178</span>    <span class="keywordtype">int</span> choice = 0;</div>
+<div class="line"><span class="lineno">  179</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nDo you wish to enter each number?:\n&quot;</span></div>
+<div class="line"><span class="lineno">  180</span>                 <span class="stringliteral">&quot;1: Yes\n&quot;</span></div>
+<div class="line"><span class="lineno">  181</span>                 <span class="stringliteral">&quot;0: No (default initialize them to 0)\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  182</span> </div>
+<div class="line"><span class="lineno">  183</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; choice;</div>
+<div class="line"><span class="lineno">  184</span>    <span class="keywordflow">if</span> (choice == 1) {</div>
+<div class="line"><span class="lineno">  185</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter &quot;</span> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; numbers:\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  186</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt;= n; i++) {</div>
+<div class="line"><span class="lineno">  187</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;: &quot;</span>;</div>
+<div class="line"><span class="lineno">  188</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; arr[i];</div>
+<div class="line"><span class="lineno">  189</span>        }</div>
+<div class="line"><span class="lineno">  190</span>    }</div>
+<div class="line"><span class="lineno">  191</span> </div>
+<div class="line"><span class="lineno">  192</span>    <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#ae752659b7c1719d68fdb2ca538a93696">ConsTree</a>(arr, &amp;segtree, 0, n - 1, 0);</div>
+<div class="line"><span class="lineno">  193</span> </div>
+<div class="line"><span class="lineno">  194</span>    <span class="keywordflow">do</span> {</div>
+<div class="line"><span class="lineno">  195</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nMake your choice:\n&quot;</span></div>
+<div class="line"><span class="lineno">  196</span>                     <span class="stringliteral">&quot;1: Range update (input)\n&quot;</span></div>
+<div class="line"><span class="lineno">  197</span>                     <span class="stringliteral">&quot;2: Range query (output)\n&quot;</span></div>
+<div class="line"><span class="lineno">  198</span>                     <span class="stringliteral">&quot;0: Exit\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  199</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; choice;</div>
+<div class="line"><span class="lineno">  200</span> </div>
+<div class="line"><span class="lineno">  201</span>        <span class="keywordflow">if</span> (choice == 1) {</div>
+<div class="line"><span class="lineno">  202</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter 1-indexed lower bound, upper bound &amp; value:\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  203</span> </div>
+<div class="line"><span class="lineno">  204</span>            uint64_t p = 1, q = 1, v = 0;</div>
+<div class="line"><span class="lineno">  205</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; p &gt;&gt; q &gt;&gt; v;</div>
+<div class="line"><span class="lineno">  206</span>            <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>(&amp;segtree, &amp;lazy, p - 1, q - 1, v, 0, n - 1, 0);</div>
+<div class="line"><span class="lineno">  207</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (choice == 2) {</div>
+<div class="line"><span class="lineno">  208</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter 1-indexed lower bound &amp; upper bound:\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  209</span> </div>
+<div class="line"><span class="lineno">  210</span>            uint64_t p = 1, q = 1;</div>
+<div class="line"><span class="lineno">  211</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; p &gt;&gt; q;</div>
+<div class="line"><span class="lineno">  212</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#a423a97ea0c7ea6e33b5844a6858d902d">query</a>(&amp;segtree, &amp;lazy, p - 1, q - 1, 0, n - 1, 0);</div>
+<div class="line"><span class="lineno">  213</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  214</span>        }</div>
+<div class="line"><span class="lineno">  215</span>    } <span class="keywordflow">while</span> (choice &gt; 0);</div>
+<div class="line"><span class="lineno">  216</span> </div>
+<div class="line"><span class="lineno">  217</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  218</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aceil_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/ceil.html">std::ceil</a></div><div class="ttdeci">T ceil(T... args)</div></div>
@@ -299,7 +299,7 @@ Here is the call graph for this function:</div>
 <div class="ttc" id="asegtree_8cpp_html_a423a97ea0c7ea6e33b5844a6858d902d"><div class="ttname"><a href="../../d2/d45/segtree_8cpp.html#a423a97ea0c7ea6e33b5844a6858d902d">query</a></div><div class="ttdeci">int64_t query(std::vector&lt; int64_t &gt; *segtree, std::vector&lt; int64_t &gt; *lazy, uint64_t qlow, uint64_t qhigh, uint64_t low, uint64_t high, uint64_t pos)</div><div class="ttdoc">Returns the sum of all elements in a range.</div><div class="ttdef"><b>Definition:</b> segtree.cpp:62</div></div>
 <div class="ttc" id="asegtree_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d2/d45/segtree_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementation.</div><div class="ttdef"><b>Definition:</b> segtree.cpp:146</div></div>
 <div class="ttc" id="asegtree_8cpp_html_abd3e818681fb2e29cf08f4f60f82c8e0"><div class="ttname"><a href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a></div><div class="ttdeci">void update(std::vector&lt; int64_t &gt; *segtree, std::vector&lt; int64_t &gt; *lazy, int64_t start, int64_t end, int64_t delta, uint64_t low, uint64_t high, uint64_t pos)</div><div class="ttdoc">Updates a range of the segment tree.</div><div class="ttdef"><b>Definition:</b> segtree.cpp:102</div></div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int64_t &gt;</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -379,30 +379,30 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>result of the range query for this function call </dd></dl>
-<div class="fragment"><div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>                            {</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <span class="keywordflow">if</span> (low &gt; high || qlow &gt; high || low &gt; qhigh) {</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    }</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span> </div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    <span class="keywordflow">if</span> ((*lazy)[pos] != 0) {</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        (*segtree)[pos] += (*lazy)[pos] * (high - low + 1);</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span> </div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>        <span class="keywordflow">if</span> (low != high) {</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>            (*lazy)[2 * pos + 1] += (*lazy)[pos];</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>            (*lazy)[2 * pos + 2] += (*lazy)[pos];</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>        }</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        (*lazy)[pos] = 0;</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    }</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span> </div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <span class="keywordflow">if</span> (qlow &lt;= low &amp;&amp; qhigh &gt;= high) {</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>        <span class="keywordflow">return</span> (*segtree)[pos];</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    }</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span> </div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    uint64_t mid = (low + high) / 2;</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span> </div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#a423a97ea0c7ea6e33b5844a6858d902d">query</a>(segtree, lazy, qlow, qhigh, low, mid, 2 * pos + 1) +</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>           <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#a423a97ea0c7ea6e33b5844a6858d902d">query</a>(segtree, lazy, qlow, qhigh, mid + 1, high, 2 * pos + 2);</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   64</span>                            {</div>
+<div class="line"><span class="lineno">   65</span>    <span class="keywordflow">if</span> (low &gt; high || qlow &gt; high || low &gt; qhigh) {</div>
+<div class="line"><span class="lineno">   66</span>        <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">   67</span>    }</div>
+<div class="line"><span class="lineno">   68</span> </div>
+<div class="line"><span class="lineno">   69</span>    <span class="keywordflow">if</span> ((*lazy)[pos] != 0) {</div>
+<div class="line"><span class="lineno">   70</span>        (*segtree)[pos] += (*lazy)[pos] * (high - low + 1);</div>
+<div class="line"><span class="lineno">   71</span> </div>
+<div class="line"><span class="lineno">   72</span>        <span class="keywordflow">if</span> (low != high) {</div>
+<div class="line"><span class="lineno">   73</span>            (*lazy)[2 * pos + 1] += (*lazy)[pos];</div>
+<div class="line"><span class="lineno">   74</span>            (*lazy)[2 * pos + 2] += (*lazy)[pos];</div>
+<div class="line"><span class="lineno">   75</span>        }</div>
+<div class="line"><span class="lineno">   76</span>        (*lazy)[pos] = 0;</div>
+<div class="line"><span class="lineno">   77</span>    }</div>
+<div class="line"><span class="lineno">   78</span> </div>
+<div class="line"><span class="lineno">   79</span>    <span class="keywordflow">if</span> (qlow &lt;= low &amp;&amp; qhigh &gt;= high) {</div>
+<div class="line"><span class="lineno">   80</span>        <span class="keywordflow">return</span> (*segtree)[pos];</div>
+<div class="line"><span class="lineno">   81</span>    }</div>
+<div class="line"><span class="lineno">   82</span> </div>
+<div class="line"><span class="lineno">   83</span>    uint64_t mid = (low + high) / 2;</div>
+<div class="line"><span class="lineno">   84</span> </div>
+<div class="line"><span class="lineno">   85</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#a423a97ea0c7ea6e33b5844a6858d902d">query</a>(segtree, lazy, qlow, qhigh, low, mid, 2 * pos + 1) +</div>
+<div class="line"><span class="lineno">   86</span>           <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#a423a97ea0c7ea6e33b5844a6858d902d">query</a>(segtree, lazy, qlow, qhigh, mid + 1, high, 2 * pos + 2);</div>
+<div class="line"><span class="lineno">   87</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -437,21 +437,21 @@ Here is the call graph for this function:</div>
 
 <p>Self-test implementation. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>                   {</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    <span class="keyword">auto</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">max</a> = <span class="keyword">static_cast&lt;</span>int64_t<span class="keyword">&gt;</span>(2 * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(2, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/ceil.html">ceil</a>(log2(7))) - 1);</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>    assert(max == 15);</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span> </div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr{1, 2, 3, 4, 5, 6, 7}, lazy(max), segtree(max);</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#ae752659b7c1719d68fdb2ca538a93696">ConsTree</a>(arr, &amp;segtree, 0, 7 - 1, 0);</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span> </div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>    assert(<a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#a423a97ea0c7ea6e33b5844a6858d902d">query</a>(&amp;segtree, &amp;lazy, 1, 5, 0, 7 - 1, 0) == 2 + 3 + 4 + 5 + 6);</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span> </div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>    <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>(&amp;segtree, &amp;lazy, 2, 4, 1, 0, 7 - 1, 0);</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>    assert(<a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#a423a97ea0c7ea6e33b5844a6858d902d">query</a>(&amp;segtree, &amp;lazy, 1, 5, 0, 7 - 1, 0) == 2 + 4 + 5 + 6 + 6);</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span> </div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>(&amp;segtree, &amp;lazy, 0, 6, -2, 0, 7 - 1, 0);</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>    assert(<a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#a423a97ea0c7ea6e33b5844a6858d902d">query</a>(&amp;segtree, &amp;lazy, 0, 4, 0, 7 - 1, 0) == -1 + 0 + 2 + 3 + 4);</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  146</span>                   {</div>
+<div class="line"><span class="lineno">  147</span>    <span class="keyword">auto</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">max</a> = <span class="keyword">static_cast&lt;</span>int64_t<span class="keyword">&gt;</span>(2 * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(2, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/ceil.html">ceil</a>(log2(7))) - 1);</div>
+<div class="line"><span class="lineno">  148</span>    assert(max == 15);</div>
+<div class="line"><span class="lineno">  149</span> </div>
+<div class="line"><span class="lineno">  150</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr{1, 2, 3, 4, 5, 6, 7}, lazy(max), segtree(max);</div>
+<div class="line"><span class="lineno">  151</span>    <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#ae752659b7c1719d68fdb2ca538a93696">ConsTree</a>(arr, &amp;segtree, 0, 7 - 1, 0);</div>
+<div class="line"><span class="lineno">  152</span> </div>
+<div class="line"><span class="lineno">  153</span>    assert(<a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#a423a97ea0c7ea6e33b5844a6858d902d">query</a>(&amp;segtree, &amp;lazy, 1, 5, 0, 7 - 1, 0) == 2 + 3 + 4 + 5 + 6);</div>
+<div class="line"><span class="lineno">  154</span> </div>
+<div class="line"><span class="lineno">  155</span>    <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>(&amp;segtree, &amp;lazy, 2, 4, 1, 0, 7 - 1, 0);</div>
+<div class="line"><span class="lineno">  156</span>    assert(<a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#a423a97ea0c7ea6e33b5844a6858d902d">query</a>(&amp;segtree, &amp;lazy, 1, 5, 0, 7 - 1, 0) == 2 + 4 + 5 + 6 + 6);</div>
+<div class="line"><span class="lineno">  157</span> </div>
+<div class="line"><span class="lineno">  158</span>    <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>(&amp;segtree, &amp;lazy, 0, 6, -2, 0, 7 - 1, 0);</div>
+<div class="line"><span class="lineno">  159</span>    assert(<a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#a423a97ea0c7ea6e33b5844a6858d902d">query</a>(&amp;segtree, &amp;lazy, 0, 4, 0, 7 - 1, 0) == -1 + 0 + 2 + 3 + 4);</div>
+<div class="line"><span class="lineno">  160</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -538,42 +538,42 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>                                         {</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <span class="keywordflow">if</span> (low &gt; high) {</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>        <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    }</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span> </div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <span class="keywordflow">if</span> ((*lazy)[pos] != 0) {</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        (*segtree)[pos] += (*lazy)[pos] * (high - low + 1);</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span> </div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>        <span class="keywordflow">if</span> (low != high) {</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>            (*lazy)[2 * pos + 1] += (*lazy)[pos];</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>            (*lazy)[2 * pos + 2] += (*lazy)[pos];</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>        }</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>        (*lazy)[pos] = 0;</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    }</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span> </div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    <span class="keywordflow">if</span> (start &gt; high || end &lt; low) {</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    }</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span> </div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <span class="keywordflow">if</span> (start &lt;= low &amp;&amp; end &gt;= high) {</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>        (*segtree)[pos] += delta * (high - low + 1);</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span> </div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>        <span class="keywordflow">if</span> (low != high) {</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>            (*lazy)[2 * pos + 1] += delta;</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>            (*lazy)[2 * pos + 2] += delta;</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>        }</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span> </div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>        <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    }</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span> </div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    uint64_t mid = (low + high) / 2;</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span> </div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>(segtree, lazy, start, end, delta, low, mid, 2 * pos + 1);</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>(segtree, lazy, start, end, delta, mid + 1, high, 2 * pos + 2);</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    (*segtree)[pos] = (*segtree)[2 * pos + 1] + (*segtree)[2 * pos + 2];</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  104</span>                                         {</div>
+<div class="line"><span class="lineno">  105</span>    <span class="keywordflow">if</span> (low &gt; high) {</div>
+<div class="line"><span class="lineno">  106</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  107</span>    }</div>
+<div class="line"><span class="lineno">  108</span> </div>
+<div class="line"><span class="lineno">  109</span>    <span class="keywordflow">if</span> ((*lazy)[pos] != 0) {</div>
+<div class="line"><span class="lineno">  110</span>        (*segtree)[pos] += (*lazy)[pos] * (high - low + 1);</div>
+<div class="line"><span class="lineno">  111</span> </div>
+<div class="line"><span class="lineno">  112</span>        <span class="keywordflow">if</span> (low != high) {</div>
+<div class="line"><span class="lineno">  113</span>            (*lazy)[2 * pos + 1] += (*lazy)[pos];</div>
+<div class="line"><span class="lineno">  114</span>            (*lazy)[2 * pos + 2] += (*lazy)[pos];</div>
+<div class="line"><span class="lineno">  115</span>        }</div>
+<div class="line"><span class="lineno">  116</span>        (*lazy)[pos] = 0;</div>
+<div class="line"><span class="lineno">  117</span>    }</div>
+<div class="line"><span class="lineno">  118</span> </div>
+<div class="line"><span class="lineno">  119</span>    <span class="keywordflow">if</span> (start &gt; high || end &lt; low) {</div>
+<div class="line"><span class="lineno">  120</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  121</span>    }</div>
+<div class="line"><span class="lineno">  122</span> </div>
+<div class="line"><span class="lineno">  123</span>    <span class="keywordflow">if</span> (start &lt;= low &amp;&amp; end &gt;= high) {</div>
+<div class="line"><span class="lineno">  124</span>        (*segtree)[pos] += delta * (high - low + 1);</div>
+<div class="line"><span class="lineno">  125</span> </div>
+<div class="line"><span class="lineno">  126</span>        <span class="keywordflow">if</span> (low != high) {</div>
+<div class="line"><span class="lineno">  127</span>            (*lazy)[2 * pos + 1] += delta;</div>
+<div class="line"><span class="lineno">  128</span>            (*lazy)[2 * pos + 2] += delta;</div>
+<div class="line"><span class="lineno">  129</span>        }</div>
+<div class="line"><span class="lineno">  130</span> </div>
+<div class="line"><span class="lineno">  131</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  132</span>    }</div>
+<div class="line"><span class="lineno">  133</span> </div>
+<div class="line"><span class="lineno">  134</span>    uint64_t mid = (low + high) / 2;</div>
+<div class="line"><span class="lineno">  135</span> </div>
+<div class="line"><span class="lineno">  136</span>    <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>(segtree, lazy, start, end, delta, low, mid, 2 * pos + 1);</div>
+<div class="line"><span class="lineno">  137</span>    <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>(segtree, lazy, start, end, delta, mid + 1, high, 2 * pos + 2);</div>
+<div class="line"><span class="lineno">  138</span>    (*segtree)[pos] = (*segtree)[2 * pos + 1] + (*segtree)[2 * pos + 2];</div>
+<div class="line"><span class="lineno">  139</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -589,7 +589,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_074119ce3a874b57120c49a0cc4bb5ad.html">range_queries</a></li><li class="navelem"><a class="el" href="../../d2/d45/segtree_8cpp.html">segtree.cpp</a></li>
-    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.2 </li>
+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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diff --git a/d2/d52/heap__sort_8cpp.html b/d2/d52/heap__sort_8cpp.html
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@@ -30,8 +30,8 @@ MathJax.Hub.Config({
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- <tr style="height: 56px;">
-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
+  <td id="projectalign">
    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
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    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
 </table>
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-<!-- Generated by Doxygen 1.9.2 -->
+<!-- Generated by Doxygen 1.9.3 -->
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@@ -146,10 +146,10 @@ Functions</h2></td></tr>
       </table>
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 <p >Main function </p>
-<div class="fragment"><div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>           {</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    <a class="code hl_function" href="../../d2/d52/heap__sort_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>();</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  120</span>           {</div>
+<div class="line"><span class="lineno">  121</span>    <a class="code hl_function" href="../../d2/d52/heap__sort_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>();</div>
+<div class="line"><span class="lineno">  122</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  123</span>}</div>
 <div class="ttc" id="aheap__sort_8cpp_html_ae1a3968e7947464bee7714f6d43b7002"><div class="ttname"><a href="../../d2/d52/heap__sort_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a></div><div class="ttdeci">void test()</div><div class="ttdef"><b>Definition:</b> heap_sort.cpp:99</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -195,10 +195,10 @@ template&lt;typename T &gt; </div>
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@@ -218,25 +218,25 @@ template&lt;typename T &gt; </div>
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 <p >Test cases to test the program </p>
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-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1\n&quot;</span>;</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <span class="keywordtype">int</span> arr[] = {-10, 78, -1, -6, 7, 4, 94, 5, 99, 0};</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <span class="keywordtype">int</span> sz = <span class="keyword">sizeof</span>(arr) / <span class="keyword">sizeof</span>(arr[0]);  <span class="comment">// sz - size of array</span></div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <a class="code hl_function" href="../../d2/d52/heap__sort_8cpp.html#a9ed3e1510afdf3edd06cf2b68769a767">printArray</a>(arr, sz);  <span class="comment">// displaying the array before sorting</span></div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <a class="code hl_function" href="../../d5/d4c/group__sorting.html#ga29d28b140174dbdde7c9f5157758435f">heapSort</a>(arr, sz);    <span class="comment">// calling heapsort to sort the array</span></div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <a class="code hl_function" href="../../d2/d52/heap__sort_8cpp.html#a9ed3e1510afdf3edd06cf2b68769a767">printArray</a>(arr, sz);  <span class="comment">// display array after sorting</span></div>
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-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    sz = <span class="keyword">sizeof</span>(arr2) / <span class="keyword">sizeof</span>(arr2[0]);</div>
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+<div class="line"><span class="lineno">  116</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 passed\n&quot;</span>;</div>
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+<div class="textblock"><p >Implementation of [Multilayer Perceptron] (<a href="https://en.wikipedia.org/wiki/Multilayer_perceptron">https://en.wikipedia.org/wiki/Multilayer_perceptron</a>). </p>
 <dl class="section author"><dt>Author</dt><dd><a href="https://github.com/imdeep2905" target="_blank">Deep Raval</a></dd></dl>
 <p>A multilayer perceptron (MLP) is a class of feedforward artificial neural network (ANN). The term MLP is used ambiguously, sometimes loosely to any feedforward ANN, sometimes strictly to refer to networks composed of multiple layers of perceptrons (with threshold activation). Multilayer perceptrons are sometimes colloquially referred to as "vanilla" neural networks, especially when they have a single hidden layer.</p>
 <p >An MLP consists of at least three layers of nodes: an input layer, a hidden layer and an output layer. Except for the input nodes, each node is a neuron that uses a nonlinear activation function. MLP utilizes a supervised learning technique called backpropagation for training. Its multiple layers and non-linear activation distinguish MLP from a linear perceptron. It can distinguish data that is not linearly separable.</p>
@@ -197,7 +197,7 @@ Functions</h2></td></tr>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>derivative of relu(x) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>{ <span class="keywordflow">return</span> x &gt;= 0.0 ? 1.0 : 0.0; }</div>
+<div class="fragment"><div class="line"><span class="lineno">   81</span>{ <span class="keywordflow">return</span> x &gt;= 0.0 ? 1.0 : 0.0; }</div>
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   </dd>
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 <dl class="section return"><dt>Returns</dt><dd>Returns derivative of sigmoid(x) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>{ <span class="keywordflow">return</span> x * (1 - x); }</div>
+<div class="fragment"><div class="line"><span class="lineno">   67</span>{ <span class="keywordflow">return</span> x * (1 - x); }</div>
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   </dd>
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 <dl class="section return"><dt>Returns</dt><dd>Returns derivative of tanh(x) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>{ <span class="keywordflow">return</span> 1 - x * x; }</div>
+<div class="fragment"><div class="line"><span class="lineno">   95</span>{ <span class="keywordflow">return</span> 1 - x * x; }</div>
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 <dl class="section return"><dt>Returns</dt><dd>Returns x </dd></dl>
-<div class="fragment"><div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>{ <span class="keywordflow">return</span> x; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  112</span>{ <span class="keywordflow">return</span> x; }</div>
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 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00833" name="l00833"></a><span class="lineno">  833</span>           {</div>
-<div class="line"><a id="l00834" name="l00834"></a><span class="lineno">  834</span>    <span class="comment">// Testing</span></div>
-<div class="line"><a id="l00835" name="l00835"></a><span class="lineno">  835</span>    <a class="code hl_function" href="../../d2/d58/neural__network_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
-<div class="line"><a id="l00836" name="l00836"></a><span class="lineno">  836</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00837" name="l00837"></a><span class="lineno">  837</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  833</span>           {</div>
+<div class="line"><span class="lineno">  834</span>    <span class="comment">// Testing</span></div>
+<div class="line"><span class="lineno">  835</span>    <a class="code hl_function" href="../../d2/d58/neural__network_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
+<div class="line"><span class="lineno">  836</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  837</span>}</div>
 <div class="ttc" id="aneural__network_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d2/d58/neural__network_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdef"><b>Definition:</b> neural_network.cpp:805</div></div>
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   </dd>
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 <dl class="section return"><dt>Returns</dt><dd>relu(x) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>{ <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(0.0, x); }</div>
+<div class="fragment"><div class="line"><span class="lineno">   74</span>{ <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(0.0, x); }</div>
 <div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
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@@ -391,7 +391,7 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>Returns sigmoid(x) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>{ <span class="keywordflow">return</span> 1.0 / (1.0 + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">std::exp</a>(-x)); }</div>
+<div class="fragment"><div class="line"><span class="lineno">   60</span>{ <span class="keywordflow">return</span> 1.0 / (1.0 + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">std::exp</a>(-x)); }</div>
 <div class="ttc" id="aexp_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">std::exp</a></div><div class="ttdeci">T exp(T... args)</div></div>
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@@ -424,7 +424,7 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>Returns x * x </dd></dl>
-<div class="fragment"><div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>{ <span class="keywordflow">return</span> x * x; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  106</span>{ <span class="keywordflow">return</span> x * x; }</div>
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   </dd>
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 <dl class="section return"><dt>Returns</dt><dd>Returns tanh(x) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>{ <span class="keywordflow">return</span> 2 / (1 + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">std::exp</a>(-2 * x)) - 1; }</div>
+<div class="fragment"><div class="line"><span class="lineno">   88</span>{ <span class="keywordflow">return</span> 2 / (1 + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">std::exp</a>(-2 * x)) - 1; }</div>
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 <p >Function to test neural network </p><dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
-<div class="fragment"><div class="line"><a id="l00805" name="l00805"></a><span class="lineno">  805</span>                   {</div>
-<div class="line"><a id="l00806" name="l00806"></a><span class="lineno">  806</span>    <span class="comment">// Creating network with 3 layers for &quot;iris.csv&quot;</span></div>
-<div class="line"><a id="l00807" name="l00807"></a><span class="lineno">  807</span>    <a class="code hl_class" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html">machine_learning::neural_network::NeuralNetwork</a> myNN =</div>
-<div class="line"><a id="l00808" name="l00808"></a><span class="lineno">  808</span>        <a class="code hl_class" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html">machine_learning::neural_network::NeuralNetwork</a>({</div>
-<div class="line"><a id="l00809" name="l00809"></a><span class="lineno">  809</span>            {4, <span class="stringliteral">&quot;none&quot;</span>},  <span class="comment">// First layer with 3 neurons and &quot;none&quot; as activation</span></div>
-<div class="line"><a id="l00810" name="l00810"></a><span class="lineno">  810</span>            {6,</div>
-<div class="line"><a id="l00811" name="l00811"></a><span class="lineno">  811</span>             <span class="stringliteral">&quot;relu&quot;</span>},  <span class="comment">// Second layer with 6 neurons and &quot;relu&quot; as activation</span></div>
-<div class="line"><a id="l00812" name="l00812"></a><span class="lineno">  812</span>            {3, <span class="stringliteral">&quot;sigmoid&quot;</span>}  <span class="comment">// Third layer with 3 neurons and &quot;sigmoid&quot; as</span></div>
-<div class="line"><a id="l00813" name="l00813"></a><span class="lineno">  813</span>                            <span class="comment">// activation</span></div>
-<div class="line"><a id="l00814" name="l00814"></a><span class="lineno">  814</span>        });</div>
-<div class="line"><a id="l00815" name="l00815"></a><span class="lineno">  815</span>    <span class="comment">// Printing summary of model</span></div>
-<div class="line"><a id="l00816" name="l00816"></a><span class="lineno">  816</span>    myNN.<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a61d30113d13304c664057118b92a5931">summary</a>();</div>
-<div class="line"><a id="l00817" name="l00817"></a><span class="lineno">  817</span>    <span class="comment">// Training Model</span></div>
-<div class="line"><a id="l00818" name="l00818"></a><span class="lineno">  818</span>    myNN.<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a5172a6791b9bd24f4232bab8d6b81fff">fit_from_csv</a>(<span class="stringliteral">&quot;iris.csv&quot;</span>, <span class="keyword">true</span>, 100, 0.3, <span class="keyword">false</span>, 2, 32, <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00819" name="l00819"></a><span class="lineno">  819</span>    <span class="comment">// Testing predictions of model</span></div>
-<div class="line"><a id="l00820" name="l00820"></a><span class="lineno">  820</span>    assert(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a50480fccfb39de20ca47f1bf51ecb6ec">machine_learning::argmax</a>(</div>
-<div class="line"><a id="l00821" name="l00821"></a><span class="lineno">  821</span>               myNN.<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a3b9eac1824d365dce715fb17c33cb96f">single_predict</a>({{5, 3.4, 1.6, 0.4}})) == 0);</div>
-<div class="line"><a id="l00822" name="l00822"></a><span class="lineno">  822</span>    assert(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a50480fccfb39de20ca47f1bf51ecb6ec">machine_learning::argmax</a>(</div>
-<div class="line"><a id="l00823" name="l00823"></a><span class="lineno">  823</span>               myNN.<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a3b9eac1824d365dce715fb17c33cb96f">single_predict</a>({{6.4, 2.9, 4.3, 1.3}})) == 1);</div>
-<div class="line"><a id="l00824" name="l00824"></a><span class="lineno">  824</span>    assert(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a50480fccfb39de20ca47f1bf51ecb6ec">machine_learning::argmax</a>(</div>
-<div class="line"><a id="l00825" name="l00825"></a><span class="lineno">  825</span>               myNN.<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a3b9eac1824d365dce715fb17c33cb96f">single_predict</a>({{6.2, 3.4, 5.4, 2.3}})) == 2);</div>
-<div class="line"><a id="l00826" name="l00826"></a><span class="lineno">  826</span>    <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00827" name="l00827"></a><span class="lineno">  827</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  805</span>                   {</div>
+<div class="line"><span class="lineno">  806</span>    <span class="comment">// Creating network with 3 layers for &quot;iris.csv&quot;</span></div>
+<div class="line"><span class="lineno">  807</span>    <a class="code hl_class" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html">machine_learning::neural_network::NeuralNetwork</a> myNN =</div>
+<div class="line"><span class="lineno">  808</span>        <a class="code hl_class" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html">machine_learning::neural_network::NeuralNetwork</a>({</div>
+<div class="line"><span class="lineno">  809</span>            {4, <span class="stringliteral">&quot;none&quot;</span>},  <span class="comment">// First layer with 3 neurons and &quot;none&quot; as activation</span></div>
+<div class="line"><span class="lineno">  810</span>            {6,</div>
+<div class="line"><span class="lineno">  811</span>             <span class="stringliteral">&quot;relu&quot;</span>},  <span class="comment">// Second layer with 6 neurons and &quot;relu&quot; as activation</span></div>
+<div class="line"><span class="lineno">  812</span>            {3, <span class="stringliteral">&quot;sigmoid&quot;</span>}  <span class="comment">// Third layer with 3 neurons and &quot;sigmoid&quot; as</span></div>
+<div class="line"><span class="lineno">  813</span>                            <span class="comment">// activation</span></div>
+<div class="line"><span class="lineno">  814</span>        });</div>
+<div class="line"><span class="lineno">  815</span>    <span class="comment">// Printing summary of model</span></div>
+<div class="line"><span class="lineno">  816</span>    myNN.<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a61d30113d13304c664057118b92a5931">summary</a>();</div>
+<div class="line"><span class="lineno">  817</span>    <span class="comment">// Training Model</span></div>
+<div class="line"><span class="lineno">  818</span>    myNN.<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a5172a6791b9bd24f4232bab8d6b81fff">fit_from_csv</a>(<span class="stringliteral">&quot;iris.csv&quot;</span>, <span class="keyword">true</span>, 100, 0.3, <span class="keyword">false</span>, 2, 32, <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  819</span>    <span class="comment">// Testing predictions of model</span></div>
+<div class="line"><span class="lineno">  820</span>    assert(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a50480fccfb39de20ca47f1bf51ecb6ec">machine_learning::argmax</a>(</div>
+<div class="line"><span class="lineno">  821</span>               myNN.<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a3b9eac1824d365dce715fb17c33cb96f">single_predict</a>({{5, 3.4, 1.6, 0.4}})) == 0);</div>
+<div class="line"><span class="lineno">  822</span>    assert(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a50480fccfb39de20ca47f1bf51ecb6ec">machine_learning::argmax</a>(</div>
+<div class="line"><span class="lineno">  823</span>               myNN.<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a3b9eac1824d365dce715fb17c33cb96f">single_predict</a>({{6.4, 2.9, 4.3, 1.3}})) == 1);</div>
+<div class="line"><span class="lineno">  824</span>    assert(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a50480fccfb39de20ca47f1bf51ecb6ec">machine_learning::argmax</a>(</div>
+<div class="line"><span class="lineno">  825</span>               myNN.<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a3b9eac1824d365dce715fb17c33cb96f">single_predict</a>({{6.2, 3.4, 5.4, 2.3}})) == 2);</div>
+<div class="line"><span class="lineno">  826</span>    <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  827</span>}</div>
 <div class="ttc" id="aclassmachine__learning_1_1neural__network_1_1_neural_network_html"><div class="ttname"><a href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html">machine_learning::neural_network::NeuralNetwork</a></div><div class="ttdef"><b>Definition:</b> neural_network.cpp:247</div></div>
 <div class="ttc" id="aclassmachine__learning_1_1neural__network_1_1_neural_network_html_a3b9eac1824d365dce715fb17c33cb96f"><div class="ttname"><a href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a3b9eac1824d365dce715fb17c33cb96f">machine_learning::neural_network::NeuralNetwork::single_predict</a></div><div class="ttdeci">std::vector&lt; std::valarray&lt; double &gt; &gt; single_predict(const std::vector&lt; std::valarray&lt; double &gt; &gt; &amp;X)</div><div class="ttdef"><b>Definition:</b> neural_network.cpp:451</div></div>
 <div class="ttc" id="aclassmachine__learning_1_1neural__network_1_1_neural_network_html_a5172a6791b9bd24f4232bab8d6b81fff"><div class="ttname"><a href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a5172a6791b9bd24f4232bab8d6b81fff">machine_learning::neural_network::NeuralNetwork::fit_from_csv</a></div><div class="ttdeci">void fit_from_csv(const std::string &amp;file_name, const bool &amp;last_label, const int &amp;epochs, const double &amp;learning_rate, const bool &amp;normalize, const int &amp;slip_lines=1, const size_t &amp;batch_size=32, const bool &amp;shuffle=true)</div><div class="ttdef"><b>Definition:</b> neural_network.cpp:587</div></div>
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@@ -152,10 +152,10 @@ Functions</h2></td></tr>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>           {</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <a class="code hl_function" href="../../d2/d5a/subset__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  103</span>           {</div>
+<div class="line"><span class="lineno">  104</span>    <a class="code hl_function" href="../../d2/d5a/subset__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
+<div class="line"><span class="lineno">  105</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  106</span>}</div>
 <div class="ttc" id="asubset__sum_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d2/d5a/subset__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Test implementations.</div><div class="ttdef"><b>Definition:</b> subset_sum.cpp:57</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -201,23 +201,23 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>count of the number of subsets with required sum </dd></dl>
-<div class="fragment"><div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>                                                                          {</div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>    int32_t nelement = in_arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    uint64_t count_of_subset = 0;</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span> </div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    <span class="keywordflow">for</span> (int32_t i = 0; i &lt; (1 &lt;&lt; (nelement)); i++) {</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>        int32_t <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">check</a> = 0;</div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>        <span class="keywordflow">for</span> (int32_t j = 0; j &lt; nelement; j++) {</div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>            <span class="keywordflow">if</span> (i &amp; (1 &lt;&lt; j)) {</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>                <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">check</a> += (in_arr[j]);</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>            }</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>        }</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>        <span class="keywordflow">if</span> (check == <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>) {</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>            count_of_subset++;</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>        }</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>    }</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <span class="keywordflow">return</span> count_of_subset;</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   33</span>                                                                          {</div>
+<div class="line"><span class="lineno">   34</span>    int32_t nelement = in_arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   35</span>    uint64_t count_of_subset = 0;</div>
+<div class="line"><span class="lineno">   36</span> </div>
+<div class="line"><span class="lineno">   37</span>    <span class="keywordflow">for</span> (int32_t i = 0; i &lt; (1 &lt;&lt; (nelement)); i++) {</div>
+<div class="line"><span class="lineno">   38</span>        int32_t <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">check</a> = 0;</div>
+<div class="line"><span class="lineno">   39</span>        <span class="keywordflow">for</span> (int32_t j = 0; j &lt; nelement; j++) {</div>
+<div class="line"><span class="lineno">   40</span>            <span class="keywordflow">if</span> (i &amp; (1 &lt;&lt; j)) {</div>
+<div class="line"><span class="lineno">   41</span>                <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">check</a> += (in_arr[j]);</div>
+<div class="line"><span class="lineno">   42</span>            }</div>
+<div class="line"><span class="lineno">   43</span>        }</div>
+<div class="line"><span class="lineno">   44</span>        <span class="keywordflow">if</span> (check == <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>) {</div>
+<div class="line"><span class="lineno">   45</span>            count_of_subset++;</div>
+<div class="line"><span class="lineno">   46</span>        }</div>
+<div class="line"><span class="lineno">   47</span>    }</div>
+<div class="line"><span class="lineno">   48</span>    <span class="keywordflow">return</span> count_of_subset;</div>
+<div class="line"><span class="lineno">   49</span>}</div>
 <div class="ttc" id="anamespacemachine__learning_html_a6f1c98c016ad34ff3d9f39372161bd35"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">machine_learning::sum</a></div><div class="ttdeci">T sum(const std::vector&lt; std::valarray&lt; T &gt; &gt; &amp;A)</div><div class="ttdef"><b>Definition:</b> vector_ops.hpp:232</div></div>
 <div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
 <div class="ttc" id="aword__break_8cpp_html_a272b0f5cdb4e41fd6dee4538b808c06a"><div class="ttname"><a href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">dynamic_programming::word_break::check</a></div><div class="ttdeci">bool check(const std::string &amp;s, const std::unordered_set&lt; std::string &gt; &amp;strSet, int pos, std::vector&lt; int &gt; *dp)</div><div class="ttdoc">Function that checks if the string passed in param can be segmented from position 'pos',...</div><div class="ttdef"><b>Definition:</b> word_break.cpp:80</div></div>
@@ -255,47 +255,47 @@ Here is the call graph for this function:</div>
 
 <p>Test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>                   {</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <span class="comment">// 1st test</span></div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test &quot;</span>;</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> array1 = {-7, -3, -2, 5, 8};  <span class="comment">// input array</span></div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    assert(backtracking::subset_sum::number_of_subsets(0, array1) ==</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>           2);  <span class="comment">// first argument in subset_sum function is the required sum and</span></div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>                <span class="comment">// second is the input array</span></div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span> </div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <span class="comment">// 2nd test</span></div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test &quot;</span>;</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> array2 = {1, 2, 3, 3};</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    assert(backtracking::subset_sum::number_of_subsets(6, array2) ==</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>           3);  <span class="comment">// here we are expecting 3 subsets which sum up to 6 i.e.</span></div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>                <span class="comment">// {(1,2,3),(1,2,3),(3,3)}</span></div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span> </div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    <span class="comment">// 3rd test</span></div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3rd test &quot;</span>;</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> array3 = {1, 1, 1, 1};</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    assert(backtracking::subset_sum::number_of_subsets(1, array3) ==</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>           4);  <span class="comment">// here we are expecting 4 subsets which sum up to 1 i.e.</span></div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>                <span class="comment">// {(1),(1),(1),(1)}</span></div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span> </div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <span class="comment">// 4th test</span></div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4th test &quot;</span>;</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> array4 = {3, 3, 3, 3};</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    assert(backtracking::subset_sum::number_of_subsets(6, array4) ==</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>           6);  <span class="comment">// here we are expecting 6 subsets which sum up to 6 i.e.</span></div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>                <span class="comment">// {(3,3),(3,3),(3,3),(3,3),(3,3),(3,3)}</span></div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span> </div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    <span class="comment">// Test 5</span></div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;5th test &quot;</span>;</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> array5 = {};</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    assert(backtracking::subset_sum::number_of_subsets(6, array5) ==</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>           0);  <span class="comment">// here we are expecting 0 subsets which sum up to 6 i.e. we</span></div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>                <span class="comment">// cannot select anything from an empty array</span></div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   57</span>                   {</div>
+<div class="line"><span class="lineno">   58</span>    <span class="comment">// 1st test</span></div>
+<div class="line"><span class="lineno">   59</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test &quot;</span>;</div>
+<div class="line"><span class="lineno">   60</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> array1 = {-7, -3, -2, 5, 8};  <span class="comment">// input array</span></div>
+<div class="line"><span class="lineno">   61</span>    assert(backtracking::subset_sum::number_of_subsets(0, array1) ==</div>
+<div class="line"><span class="lineno">   62</span>           2);  <span class="comment">// first argument in subset_sum function is the required sum and</span></div>
+<div class="line"><span class="lineno">   63</span>                <span class="comment">// second is the input array</span></div>
+<div class="line"><span class="lineno">   64</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   65</span> </div>
+<div class="line"><span class="lineno">   66</span>    <span class="comment">// 2nd test</span></div>
+<div class="line"><span class="lineno">   67</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test &quot;</span>;</div>
+<div class="line"><span class="lineno">   68</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> array2 = {1, 2, 3, 3};</div>
+<div class="line"><span class="lineno">   69</span>    assert(backtracking::subset_sum::number_of_subsets(6, array2) ==</div>
+<div class="line"><span class="lineno">   70</span>           3);  <span class="comment">// here we are expecting 3 subsets which sum up to 6 i.e.</span></div>
+<div class="line"><span class="lineno">   71</span>                <span class="comment">// {(1,2,3),(1,2,3),(3,3)}</span></div>
+<div class="line"><span class="lineno">   72</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   73</span> </div>
+<div class="line"><span class="lineno">   74</span>    <span class="comment">// 3rd test</span></div>
+<div class="line"><span class="lineno">   75</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3rd test &quot;</span>;</div>
+<div class="line"><span class="lineno">   76</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> array3 = {1, 1, 1, 1};</div>
+<div class="line"><span class="lineno">   77</span>    assert(backtracking::subset_sum::number_of_subsets(1, array3) ==</div>
+<div class="line"><span class="lineno">   78</span>           4);  <span class="comment">// here we are expecting 4 subsets which sum up to 1 i.e.</span></div>
+<div class="line"><span class="lineno">   79</span>                <span class="comment">// {(1),(1),(1),(1)}</span></div>
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+<div class="line"><span class="lineno">   81</span> </div>
+<div class="line"><span class="lineno">   82</span>    <span class="comment">// 4th test</span></div>
+<div class="line"><span class="lineno">   83</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4th test &quot;</span>;</div>
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+<div class="line"><span class="lineno">   89</span> </div>
+<div class="line"><span class="lineno">   90</span>    <span class="comment">// Test 5</span></div>
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-<div class="line"><a id="l00440" name="l00440"></a><span class="lineno">  440</span>    <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">h_parent</a>.resize(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">Tree&lt;X&gt;::t_nodes</a>);</div>
-<div class="line"><a id="l00441" name="l00441"></a><span class="lineno">  441</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/iota.html">iota</a>(<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">h_parent</a>.begin(), <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">h_parent</a>.end(), 0);</div>
-<div class="line"><a id="l00442" name="l00442"></a><span class="lineno">  442</span>  }</div>
+<div class="fragment"><div class="line"><span class="lineno">  435</span>                             : Tree&lt;X&gt;(nodes), SG&lt;X&gt;(nodes) {</div>
+<div class="line"><span class="lineno">  436</span>    <span class="comment">/* Initialization and resize vectors */</span></div>
+<div class="line"><span class="lineno">  437</span>    <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a722cc7cf2c3e4d15583601a48b09776f">label</a> = 0;</div>
+<div class="line"><span class="lineno">  438</span>    <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#aa86a91ae0cd7898990a8170a2f2c9cda">h_label</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/assign.html">assign</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">Tree&lt;X&gt;::t_nodes</a>, -1);</div>
+<div class="line"><span class="lineno">  439</span>    <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a84424f180f12b514eaab57a6aa20b104">h_heavychlid</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/assign.html">assign</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">Tree&lt;X&gt;::t_nodes</a>, -1);</div>
+<div class="line"><span class="lineno">  440</span>    <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">h_parent</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/resize.html">resize</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">Tree&lt;X&gt;::t_nodes</a>);</div>
+<div class="line"><span class="lineno">  441</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/iota.html">iota</a>(<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">h_parent</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">h_parent</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>(), 0);</div>
+<div class="line"><span class="lineno">  442</span>  }</div>
+<div class="ttc" id="aassign_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/assign.html">std::vector::assign</a></div><div class="ttdeci">T assign(T... args)</div></div>
+<div class="ttc" id="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/begin.html">std::vector::begin</a></div><div class="ttdeci">T begin(T... args)</div></div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_h_l_d_html_a1b336474d17eff1aa4be73d4068dc725"><div class="ttname"><a href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">range_queries::heavy_light_decomposition::HLD::h_parent</a></div><div class="ttdeci">std::vector&lt; int &gt; h_parent</div><div class="ttdoc">stores the top of the heavy chain from a node</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:341</div></div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_h_l_d_html_a722cc7cf2c3e4d15583601a48b09776f"><div class="ttname"><a href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a722cc7cf2c3e4d15583601a48b09776f">range_queries::heavy_light_decomposition::HLD::label</a></div><div class="ttdeci">int label</div><div class="ttdoc">utility member to assign labels in dfs_labels()</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:338</div></div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_h_l_d_html_a84424f180f12b514eaab57a6aa20b104"><div class="ttname"><a href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a84424f180f12b514eaab57a6aa20b104">range_queries::heavy_light_decomposition::HLD::h_heavychlid</a></div><div class="ttdeci">std::vector&lt; int &gt; h_heavychlid</div><div class="ttdoc">stores the heavy child of a node</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:340</div></div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_h_l_d_html_aa86a91ae0cd7898990a8170a2f2c9cda"><div class="ttname"><a href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#aa86a91ae0cd7898990a8170a2f2c9cda">range_queries::heavy_light_decomposition::HLD::h_label</a></div><div class="ttdeci">std::vector&lt; int &gt; h_label</div><div class="ttdoc">stores the label of a node</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:339</div></div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_ae4630fa70a80a1dc65a875488a67178a"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">range_queries::heavy_light_decomposition::Tree::t_nodes</a></div><div class="ttdeci">const int t_nodes</div><div class="ttdoc">number of nodes</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:84</div></div>
+<div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/end.html">std::vector::end</a></div><div class="ttdeci">T end(T... args)</div></div>
 <div class="ttc" id="aiota_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/iota.html">std::iota</a></div><div class="ttdeci">T iota(T... args)</div></div>
+<div class="ttc" id="aresize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/resize.html">std::vector::resize</a></div><div class="ttdeci">T resize(T... args)</div></div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -294,25 +298,25 @@ template&lt;typename X &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>the sum of ndoe values in the simple path from a to b </dd></dl>
-<div class="fragment"><div class="line"><a id="l00409" name="l00409"></a><span class="lineno">  409</span>                              {</div>
-<div class="line"><a id="l00410" name="l00410"></a><span class="lineno">  410</span>    X ret = <a class="code hl_variable" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#aa7f93971a9f891e0bbb7023081f379d5">SG&lt;X&gt;::sret_init</a>;</div>
-<div class="line"><a id="l00411" name="l00411"></a><span class="lineno">  411</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">Tree&lt;X&gt;::t_depth</a>[a] &lt; <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">Tree&lt;X&gt;::t_depth</a>[b]) {</div>
-<div class="line"><a id="l00412" name="l00412"></a><span class="lineno">  412</span>      <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(a, b);</div>
-<div class="line"><a id="l00413" name="l00413"></a><span class="lineno">  413</span>    }</div>
-<div class="line"><a id="l00414" name="l00414"></a><span class="lineno">  414</span>    <span class="keywordflow">while</span> (<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">Tree&lt;X&gt;::t_depth</a>[a] &gt;= <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">Tree&lt;X&gt;::t_depth</a>[b]) {</div>
-<div class="line"><a id="l00415" name="l00415"></a><span class="lineno">  415</span>      <span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> = <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#aa86a91ae0cd7898990a8170a2f2c9cda">h_label</a>[<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">h_parent</a>[a]];</div>
-<div class="line"><a id="l00416" name="l00416"></a><span class="lineno">  416</span>      <span class="keywordtype">int</span> r = <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#aa86a91ae0cd7898990a8170a2f2c9cda">h_label</a>[a];</div>
-<div class="line"><a id="l00417" name="l00417"></a><span class="lineno">  417</span>      <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">Tree&lt;X&gt;::t_depth</a>[<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">h_parent</a>[a]] &lt; <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">Tree&lt;X&gt;::t_depth</a>[b]) {</div>
-<div class="line"><a id="l00418" name="l00418"></a><span class="lineno">  418</span>        <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> += <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">Tree&lt;X&gt;::t_depth</a>[b] - <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">Tree&lt;X&gt;::t_depth</a>[<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">h_parent</a>[a]];</div>
-<div class="line"><a id="l00419" name="l00419"></a><span class="lineno">  419</span>      }</div>
-<div class="line"><a id="l00420" name="l00420"></a><span class="lineno">  420</span>      ret = <a class="code hl_function" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#a41c733f5f5e262b308f7cb95c88c1e74">SG&lt;X&gt;::combine</a>(ret, <a class="code hl_function" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#a1fda852e6e522707fd97f61cdb0a2591">SG&lt;X&gt;::query</a>(l, r));</div>
-<div class="line"><a id="l00421" name="l00421"></a><span class="lineno">  421</span>      a = <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">Tree&lt;X&gt;::t_par</a>[<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">h_parent</a>[a]][0];</div>
-<div class="line"><a id="l00422" name="l00422"></a><span class="lineno">  422</span>      <span class="keywordflow">if</span> (a == -1) {</div>
-<div class="line"><a id="l00423" name="l00423"></a><span class="lineno">  423</span>        <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00424" name="l00424"></a><span class="lineno">  424</span>      }</div>
-<div class="line"><a id="l00425" name="l00425"></a><span class="lineno">  425</span>    }</div>
-<div class="line"><a id="l00426" name="l00426"></a><span class="lineno">  426</span>    <span class="keywordflow">return</span> ret;</div>
-<div class="line"><a id="l00427" name="l00427"></a><span class="lineno">  427</span>  }</div>
+<div class="fragment"><div class="line"><span class="lineno">  409</span>                              {</div>
+<div class="line"><span class="lineno">  410</span>    X ret = <a class="code hl_variable" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#aa7f93971a9f891e0bbb7023081f379d5">SG&lt;X&gt;::sret_init</a>;</div>
+<div class="line"><span class="lineno">  411</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">Tree&lt;X&gt;::t_depth</a>[a] &lt; <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">Tree&lt;X&gt;::t_depth</a>[b]) {</div>
+<div class="line"><span class="lineno">  412</span>      <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(a, b);</div>
+<div class="line"><span class="lineno">  413</span>    }</div>
+<div class="line"><span class="lineno">  414</span>    <span class="keywordflow">while</span> (<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">Tree&lt;X&gt;::t_depth</a>[a] &gt;= <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">Tree&lt;X&gt;::t_depth</a>[b]) {</div>
+<div class="line"><span class="lineno">  415</span>      <span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> = <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#aa86a91ae0cd7898990a8170a2f2c9cda">h_label</a>[<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">h_parent</a>[a]];</div>
+<div class="line"><span class="lineno">  416</span>      <span class="keywordtype">int</span> r = <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#aa86a91ae0cd7898990a8170a2f2c9cda">h_label</a>[a];</div>
+<div class="line"><span class="lineno">  417</span>      <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">Tree&lt;X&gt;::t_depth</a>[<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">h_parent</a>[a]] &lt; <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">Tree&lt;X&gt;::t_depth</a>[b]) {</div>
+<div class="line"><span class="lineno">  418</span>        <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> += <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">Tree&lt;X&gt;::t_depth</a>[b] - <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">Tree&lt;X&gt;::t_depth</a>[<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">h_parent</a>[a]];</div>
+<div class="line"><span class="lineno">  419</span>      }</div>
+<div class="line"><span class="lineno">  420</span>      ret = <a class="code hl_function" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#a41c733f5f5e262b308f7cb95c88c1e74">SG&lt;X&gt;::combine</a>(ret, <a class="code hl_function" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#a1fda852e6e522707fd97f61cdb0a2591">SG&lt;X&gt;::query</a>(l, r));</div>
+<div class="line"><span class="lineno">  421</span>      a = <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">Tree&lt;X&gt;::t_par</a>[<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">h_parent</a>[a]][0];</div>
+<div class="line"><span class="lineno">  422</span>      <span class="keywordflow">if</span> (a == -1) {</div>
+<div class="line"><span class="lineno">  423</span>        <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  424</span>      }</div>
+<div class="line"><span class="lineno">  425</span>    }</div>
+<div class="line"><span class="lineno">  426</span>    <span class="keywordflow">return</span> ret;</div>
+<div class="line"><span class="lineno">  427</span>  }</div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_s_g_html_a1fda852e6e522707fd97f61cdb0a2591"><div class="ttname"><a href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#a1fda852e6e522707fd97f61cdb0a2591">range_queries::heavy_light_decomposition::SG::query</a></div><div class="ttdeci">X query(int l, int r)</div><div class="ttdoc">Make a range query from node label l to node label r.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:305</div></div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_s_g_html_a41c733f5f5e262b308f7cb95c88c1e74"><div class="ttname"><a href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#a41c733f5f5e262b308f7cb95c88c1e74">range_queries::heavy_light_decomposition::SG::combine</a></div><div class="ttdeci">X combine(X lhs, X rhs)</div><div class="ttdoc">Function that specifies the type of operation involved when segments are combined.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:274</div></div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_s_g_html_aa7f93971a9f891e0bbb7023081f379d5"><div class="ttname"><a href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#aa7f93971a9f891e0bbb7023081f379d5">range_queries::heavy_light_decomposition::SG::sret_init</a></div><div class="ttdeci">X sret_init</div><div class="ttdoc">inital query return value</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:264</div></div>
@@ -374,19 +378,19 @@ template&lt;typename X &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00350" name="l00350"></a><span class="lineno">  350</span>                                 {</div>
-<div class="line"><a id="l00351" name="l00351"></a><span class="lineno">  351</span>    <span class="keywordtype">int</span> hc_size = -1, hc_id = -1;</div>
-<div class="line"><a id="l00352" name="l00352"></a><span class="lineno">  352</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> &amp;v : <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab1aeaefa1bd97b867c652ba916fbdb43">Tree&lt;X&gt;::t_adj</a>[u]) {</div>
-<div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span>      <span class="keywordflow">if</span> (v ^ p) {</div>
-<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span>        <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#af64848d6630c39d0f09ce2359cc7c4f8">dfs_hc</a>(v, u);</div>
-<div class="line"><a id="l00355" name="l00355"></a><span class="lineno">  355</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ada1494fccbc7f1f07b2f9be9f7e07ad5">Tree&lt;X&gt;::t_size</a>[v] &gt; hc_size) {</div>
-<div class="line"><a id="l00356" name="l00356"></a><span class="lineno">  356</span>          hc_size = <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ada1494fccbc7f1f07b2f9be9f7e07ad5">Tree&lt;X&gt;::t_size</a>[v];</div>
-<div class="line"><a id="l00357" name="l00357"></a><span class="lineno">  357</span>          hc_id = v;</div>
-<div class="line"><a id="l00358" name="l00358"></a><span class="lineno">  358</span>        }</div>
-<div class="line"><a id="l00359" name="l00359"></a><span class="lineno">  359</span>      }</div>
-<div class="line"><a id="l00360" name="l00360"></a><span class="lineno">  360</span>    }</div>
-<div class="line"><a id="l00361" name="l00361"></a><span class="lineno">  361</span>    <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a84424f180f12b514eaab57a6aa20b104">h_heavychlid</a>[u] = hc_id;</div>
-<div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span>  }</div>
+<div class="fragment"><div class="line"><span class="lineno">  350</span>                                 {</div>
+<div class="line"><span class="lineno">  351</span>    <span class="keywordtype">int</span> hc_size = -1, hc_id = -1;</div>
+<div class="line"><span class="lineno">  352</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> &amp;v : <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab1aeaefa1bd97b867c652ba916fbdb43">Tree&lt;X&gt;::t_adj</a>[u]) {</div>
+<div class="line"><span class="lineno">  353</span>      <span class="keywordflow">if</span> (v ^ p) {</div>
+<div class="line"><span class="lineno">  354</span>        <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#af64848d6630c39d0f09ce2359cc7c4f8">dfs_hc</a>(v, u);</div>
+<div class="line"><span class="lineno">  355</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ada1494fccbc7f1f07b2f9be9f7e07ad5">Tree&lt;X&gt;::t_size</a>[v] &gt; hc_size) {</div>
+<div class="line"><span class="lineno">  356</span>          hc_size = <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ada1494fccbc7f1f07b2f9be9f7e07ad5">Tree&lt;X&gt;::t_size</a>[v];</div>
+<div class="line"><span class="lineno">  357</span>          hc_id = v;</div>
+<div class="line"><span class="lineno">  358</span>        }</div>
+<div class="line"><span class="lineno">  359</span>      }</div>
+<div class="line"><span class="lineno">  360</span>    }</div>
+<div class="line"><span class="lineno">  361</span>    <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a84424f180f12b514eaab57a6aa20b104">h_heavychlid</a>[u] = hc_id;</div>
+<div class="line"><span class="lineno">  362</span>  }</div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_h_l_d_html_af64848d6630c39d0f09ce2359cc7c4f8"><div class="ttname"><a href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#af64848d6630c39d0f09ce2359cc7c4f8">range_queries::heavy_light_decomposition::HLD::dfs_hc</a></div><div class="ttdeci">void dfs_hc(int u, int p=-1)</div><div class="ttdoc">Utility function to assign heavy child to each node (-1 for a leaf node)</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:350</div></div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_ab1aeaefa1bd97b867c652ba916fbdb43"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab1aeaefa1bd97b867c652ba916fbdb43">range_queries::heavy_light_decomposition::Tree::t_adj</a></div><div class="ttdeci">std::vector&lt; std::list&lt; int &gt; &gt; t_adj</div><div class="ttdoc">an adjacency list to stores the tree edges</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:83</div></div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_ada1494fccbc7f1f07b2f9be9f7e07ad5"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ada1494fccbc7f1f07b2f9be9f7e07ad5">range_queries::heavy_light_decomposition::Tree::t_size</a></div><div class="ttdeci">std::vector&lt; int &gt; t_size</div><div class="ttdoc">a vector to store the subtree size rooted at node</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:89</div></div>
@@ -444,17 +448,17 @@ template&lt;typename X &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00390" name="l00390"></a><span class="lineno">  390</span>                                     {</div>
-<div class="line"><a id="l00391" name="l00391"></a><span class="lineno">  391</span>    <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#aa86a91ae0cd7898990a8170a2f2c9cda">h_label</a>[u] = <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a722cc7cf2c3e4d15583601a48b09776f">label</a>++;</div>
-<div class="line"><a id="l00392" name="l00392"></a><span class="lineno">  392</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a84424f180f12b514eaab57a6aa20b104">h_heavychlid</a>[u] != -1) {</div>
-<div class="line"><a id="l00393" name="l00393"></a><span class="lineno">  393</span>      <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a0579062b384e54b611b80c6337c7f2c8">dfs_labels</a>(<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a84424f180f12b514eaab57a6aa20b104">h_heavychlid</a>[u], u);</div>
-<div class="line"><a id="l00394" name="l00394"></a><span class="lineno">  394</span>    }</div>
-<div class="line"><a id="l00395" name="l00395"></a><span class="lineno">  395</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> &amp;v : <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab1aeaefa1bd97b867c652ba916fbdb43">Tree&lt;X&gt;::t_adj</a>[u]) {</div>
-<div class="line"><a id="l00396" name="l00396"></a><span class="lineno">  396</span>      <span class="keywordflow">if</span> (v ^ p and v ^ <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a84424f180f12b514eaab57a6aa20b104">h_heavychlid</a>[u]) {</div>
-<div class="line"><a id="l00397" name="l00397"></a><span class="lineno">  397</span>        <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a0579062b384e54b611b80c6337c7f2c8">dfs_labels</a>(v, u);</div>
-<div class="line"><a id="l00398" name="l00398"></a><span class="lineno">  398</span>      }</div>
-<div class="line"><a id="l00399" name="l00399"></a><span class="lineno">  399</span>    }</div>
-<div class="line"><a id="l00400" name="l00400"></a><span class="lineno">  400</span>  }</div>
+<div class="fragment"><div class="line"><span class="lineno">  390</span>                                     {</div>
+<div class="line"><span class="lineno">  391</span>    <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#aa86a91ae0cd7898990a8170a2f2c9cda">h_label</a>[u] = <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a722cc7cf2c3e4d15583601a48b09776f">label</a>++;</div>
+<div class="line"><span class="lineno">  392</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a84424f180f12b514eaab57a6aa20b104">h_heavychlid</a>[u] != -1) {</div>
+<div class="line"><span class="lineno">  393</span>      <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a0579062b384e54b611b80c6337c7f2c8">dfs_labels</a>(<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a84424f180f12b514eaab57a6aa20b104">h_heavychlid</a>[u], u);</div>
+<div class="line"><span class="lineno">  394</span>    }</div>
+<div class="line"><span class="lineno">  395</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> &amp;v : <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab1aeaefa1bd97b867c652ba916fbdb43">Tree&lt;X&gt;::t_adj</a>[u]) {</div>
+<div class="line"><span class="lineno">  396</span>      <span class="keywordflow">if</span> (v ^ p and v ^ <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a84424f180f12b514eaab57a6aa20b104">h_heavychlid</a>[u]) {</div>
+<div class="line"><span class="lineno">  397</span>        <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a0579062b384e54b611b80c6337c7f2c8">dfs_labels</a>(v, u);</div>
+<div class="line"><span class="lineno">  398</span>      }</div>
+<div class="line"><span class="lineno">  399</span>    }</div>
+<div class="line"><span class="lineno">  400</span>  }</div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_h_l_d_html_a0579062b384e54b611b80c6337c7f2c8"><div class="ttname"><a href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a0579062b384e54b611b80c6337c7f2c8">range_queries::heavy_light_decomposition::HLD::dfs_labels</a></div><div class="ttdeci">void dfs_labels(int u, int p=-1)</div><div class="ttdoc">Utility function to lable the nodes so that heavy chains have a contigous lable.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:390</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -510,17 +514,17 @@ template&lt;typename X &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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-<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>      <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">h_parent</a>[<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a84424f180f12b514eaab57a6aa20b104">h_heavychlid</a>[u]] = <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">h_parent</a>[u];</div>
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-<div class="line"><a id="l00376" name="l00376"></a><span class="lineno">  376</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> &amp;v : <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab1aeaefa1bd97b867c652ba916fbdb43">Tree&lt;X&gt;::t_adj</a>[u]) {</div>
-<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span>      <span class="keywordflow">if</span> (v ^ p and v ^ <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a84424f180f12b514eaab57a6aa20b104">h_heavychlid</a>[u]) {</div>
-<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span>        <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a2dfbda148aad0bfaba2ebfda9ebc915a">dfs_par</a>(v, u);</div>
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+<div class="fragment"><div class="line"><span class="lineno">  371</span>                                  {</div>
+<div class="line"><span class="lineno">  372</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a84424f180f12b514eaab57a6aa20b104">h_heavychlid</a>[u] != -1) {</div>
+<div class="line"><span class="lineno">  373</span>      <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">h_parent</a>[<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a84424f180f12b514eaab57a6aa20b104">h_heavychlid</a>[u]] = <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a1b336474d17eff1aa4be73d4068dc725">h_parent</a>[u];</div>
+<div class="line"><span class="lineno">  374</span>      <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a2dfbda148aad0bfaba2ebfda9ebc915a">dfs_par</a>(<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a84424f180f12b514eaab57a6aa20b104">h_heavychlid</a>[u], u);</div>
+<div class="line"><span class="lineno">  375</span>    }</div>
+<div class="line"><span class="lineno">  376</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> &amp;v : <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab1aeaefa1bd97b867c652ba916fbdb43">Tree&lt;X&gt;::t_adj</a>[u]) {</div>
+<div class="line"><span class="lineno">  377</span>      <span class="keywordflow">if</span> (v ^ p and v ^ <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a84424f180f12b514eaab57a6aa20b104">h_heavychlid</a>[u]) {</div>
+<div class="line"><span class="lineno">  378</span>        <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a2dfbda148aad0bfaba2ebfda9ebc915a">dfs_par</a>(v, u);</div>
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+<div class="line"><span class="lineno">  380</span>    }</div>
+<div class="line"><span class="lineno">  381</span>  }</div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_h_l_d_html_a2dfbda148aad0bfaba2ebfda9ebc915a"><div class="ttname"><a href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a2dfbda148aad0bfaba2ebfda9ebc915a">range_queries::heavy_light_decomposition::HLD::dfs_par</a></div><div class="ttdeci">void dfs_par(int u, int p=-1)</div><div class="ttdoc">Utility function to assign highest parent that can be reached though heavy chains.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:371</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -558,24 +562,24 @@ template&lt;typename X &gt; </div>
 
 <p>This function must be called after the tree adjacency list and node values are populated The function initializes the required parametes, and populates the segment tree. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00450" name="l00450"></a><span class="lineno">  450</span>              {</div>
-<div class="line"><a id="l00451" name="l00451"></a><span class="lineno">  451</span>    <a class="code hl_function" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ad22d760a5a33545a70e7ea5e1786c8dc">Tree&lt;X&gt;::init</a>();</div>
-<div class="line"><a id="l00452" name="l00452"></a><span class="lineno">  452</span> </div>
-<div class="line"><a id="l00453" name="l00453"></a><span class="lineno">  453</span>    <span class="comment">// Fill the heavy child, greatest parent, and labels</span></div>
-<div class="line"><a id="l00454" name="l00454"></a><span class="lineno">  454</span>    <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a722cc7cf2c3e4d15583601a48b09776f">label</a> = 0;</div>
-<div class="line"><a id="l00455" name="l00455"></a><span class="lineno">  455</span>    <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#af64848d6630c39d0f09ce2359cc7c4f8">dfs_hc</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa6c37e840355b9fb2105181c578694e8">Tree&lt;X&gt;::t_root</a>);</div>
-<div class="line"><a id="l00456" name="l00456"></a><span class="lineno">  456</span>    <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a2dfbda148aad0bfaba2ebfda9ebc915a">dfs_par</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa6c37e840355b9fb2105181c578694e8">Tree&lt;X&gt;::t_root</a>);</div>
-<div class="line"><a id="l00457" name="l00457"></a><span class="lineno">  457</span>    <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a0579062b384e54b611b80c6337c7f2c8">dfs_labels</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa6c37e840355b9fb2105181c578694e8">Tree&lt;X&gt;::t_root</a>);</div>
-<div class="line"><a id="l00458" name="l00458"></a><span class="lineno">  458</span> </div>
-<div class="line"><a id="l00459" name="l00459"></a><span class="lineno">  459</span>    <span class="comment">// Segment Tree Initialization</span></div>
-<div class="line"><a id="l00460" name="l00460"></a><span class="lineno">  460</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; Tree&lt;X&gt;::t_nodes; i++) {</div>
-<div class="line"><a id="l00461" name="l00461"></a><span class="lineno">  461</span>      <a class="code hl_variable" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#afbf8a9cb9449d5ca844f4e141a801e6a">SG&lt;X&gt;::s_tree</a>[<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#aa86a91ae0cd7898990a8170a2f2c9cda">h_label</a>[i] + <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">Tree&lt;X&gt;::t_nodes</a>] = <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a135b7952593c9b1aae38fcaf1cc1abf7">Tree&lt;X&gt;::t_val</a>[i];</div>
-<div class="line"><a id="l00462" name="l00462"></a><span class="lineno">  462</span>    }</div>
-<div class="line"><a id="l00463" name="l00463"></a><span class="lineno">  463</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">Tree&lt;X&gt;::t_nodes</a> - 1; i &gt; 0; i--) {</div>
-<div class="line"><a id="l00464" name="l00464"></a><span class="lineno">  464</span>      <a class="code hl_variable" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#afbf8a9cb9449d5ca844f4e141a801e6a">SG&lt;X&gt;::s_tree</a>[i] =</div>
-<div class="line"><a id="l00465" name="l00465"></a><span class="lineno">  465</span>          <a class="code hl_function" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#a41c733f5f5e262b308f7cb95c88c1e74">SG&lt;X&gt;::combine</a>(<a class="code hl_variable" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#afbf8a9cb9449d5ca844f4e141a801e6a">SG&lt;X&gt;::s_tree</a>[i &lt;&lt; 1], <a class="code hl_variable" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#afbf8a9cb9449d5ca844f4e141a801e6a">SG&lt;X&gt;::s_tree</a>[i &lt;&lt; 1 | 1]);</div>
-<div class="line"><a id="l00466" name="l00466"></a><span class="lineno">  466</span>    }</div>
-<div class="line"><a id="l00467" name="l00467"></a><span class="lineno">  467</span>  }</div>
+<div class="fragment"><div class="line"><span class="lineno">  450</span>              {</div>
+<div class="line"><span class="lineno">  451</span>    <a class="code hl_function" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ad22d760a5a33545a70e7ea5e1786c8dc">Tree&lt;X&gt;::init</a>();</div>
+<div class="line"><span class="lineno">  452</span> </div>
+<div class="line"><span class="lineno">  453</span>    <span class="comment">// Fill the heavy child, greatest parent, and labels</span></div>
+<div class="line"><span class="lineno">  454</span>    <a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a722cc7cf2c3e4d15583601a48b09776f">label</a> = 0;</div>
+<div class="line"><span class="lineno">  455</span>    <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#af64848d6630c39d0f09ce2359cc7c4f8">dfs_hc</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa6c37e840355b9fb2105181c578694e8">Tree&lt;X&gt;::t_root</a>);</div>
+<div class="line"><span class="lineno">  456</span>    <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a2dfbda148aad0bfaba2ebfda9ebc915a">dfs_par</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa6c37e840355b9fb2105181c578694e8">Tree&lt;X&gt;::t_root</a>);</div>
+<div class="line"><span class="lineno">  457</span>    <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a0579062b384e54b611b80c6337c7f2c8">dfs_labels</a>(<a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa6c37e840355b9fb2105181c578694e8">Tree&lt;X&gt;::t_root</a>);</div>
+<div class="line"><span class="lineno">  458</span> </div>
+<div class="line"><span class="lineno">  459</span>    <span class="comment">// Segment Tree Initialization</span></div>
+<div class="line"><span class="lineno">  460</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; Tree&lt;X&gt;::t_nodes; i++) {</div>
+<div class="line"><span class="lineno">  461</span>      <a class="code hl_variable" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#afbf8a9cb9449d5ca844f4e141a801e6a">SG&lt;X&gt;::s_tree</a>[<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#aa86a91ae0cd7898990a8170a2f2c9cda">h_label</a>[i] + <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">Tree&lt;X&gt;::t_nodes</a>] = <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a135b7952593c9b1aae38fcaf1cc1abf7">Tree&lt;X&gt;::t_val</a>[i];</div>
+<div class="line"><span class="lineno">  462</span>    }</div>
+<div class="line"><span class="lineno">  463</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae4630fa70a80a1dc65a875488a67178a">Tree&lt;X&gt;::t_nodes</a> - 1; i &gt; 0; i--) {</div>
+<div class="line"><span class="lineno">  464</span>      <a class="code hl_variable" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#afbf8a9cb9449d5ca844f4e141a801e6a">SG&lt;X&gt;::s_tree</a>[i] =</div>
+<div class="line"><span class="lineno">  465</span>          <a class="code hl_function" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#a41c733f5f5e262b308f7cb95c88c1e74">SG&lt;X&gt;::combine</a>(<a class="code hl_variable" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#afbf8a9cb9449d5ca844f4e141a801e6a">SG&lt;X&gt;::s_tree</a>[i &lt;&lt; 1], <a class="code hl_variable" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#afbf8a9cb9449d5ca844f4e141a801e6a">SG&lt;X&gt;::s_tree</a>[i &lt;&lt; 1 | 1]);</div>
+<div class="line"><span class="lineno">  466</span>    }</div>
+<div class="line"><span class="lineno">  467</span>  }</div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_s_g_html_afbf8a9cb9449d5ca844f4e141a801e6a"><div class="ttname"><a href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#afbf8a9cb9449d5ca844f4e141a801e6a">range_queries::heavy_light_decomposition::SG::s_tree</a></div><div class="ttdeci">std::vector&lt; X &gt; s_tree</div><div class="ttdoc">Everything here is private, and can only be accessed through the methods, in the derived class (HLD)</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:262</div></div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_a135b7952593c9b1aae38fcaf1cc1abf7"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a135b7952593c9b1aae38fcaf1cc1abf7">range_queries::heavy_light_decomposition::Tree::t_val</a></div><div class="ttdeci">std::vector&lt; X &gt; t_val</div><div class="ttdoc">values of nodes</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:92</div></div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_aa6c37e840355b9fb2105181c578694e8"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa6c37e840355b9fb2105181c578694e8">range_queries::heavy_light_decomposition::Tree::t_root</a></div><div class="ttdeci">int t_root</div><div class="ttdoc">the root of the tree</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:91</div></div>
@@ -601,7 +605,7 @@ template&lt;typename X &gt; </div>
   <td class="mlabels-left">
       <table class="memname">
         <tr>
-          <td class="memname">X <a class="el" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html">range_queries::heavy_light_decomposition::HLD</a>&lt; X &gt;::<a class="el" href="../../dd/d1b/structquery.html">query</a> </td>
+          <td class="memname">X <a class="el" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html">range_queries::heavy_light_decomposition::HLD</a>&lt; X &gt;<a class="el" href="../../dd/d1b/structquery.html">::query</a> </td>
           <td>(</td>
           <td class="paramtype">int&#160;</td>
           <td class="paramname"><em>a</em>, </td>
@@ -634,14 +638,14 @@ template&lt;typename X &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>the sum of node values in the simple path from a to b </dd></dl>
-<div class="fragment"><div class="line"><a id="l00489" name="l00489"></a><span class="lineno">  489</span>                        {</div>
-<div class="line"><a id="l00490" name="l00490"></a><span class="lineno">  490</span>    <span class="keywordtype">int</span> lc = <a class="code hl_function" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae2b407e64aaf9878fbee7ee6efe9c7d4">Tree&lt;X&gt;::lca</a>(a, b);</div>
-<div class="line"><a id="l00491" name="l00491"></a><span class="lineno">  491</span>    X ret = <a class="code hl_variable" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#aa7f93971a9f891e0bbb7023081f379d5">SG&lt;X&gt;::sret_init</a>;</div>
-<div class="line"><a id="l00492" name="l00492"></a><span class="lineno">  492</span>    assert(lc != -1);</div>
-<div class="line"><a id="l00493" name="l00493"></a><span class="lineno">  493</span>    ret += <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a7d5b40c076347a6aabfb37a0590f2f24">chain_query</a>(a, lc);</div>
-<div class="line"><a id="l00494" name="l00494"></a><span class="lineno">  494</span>    ret += <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a7d5b40c076347a6aabfb37a0590f2f24">chain_query</a>(b, lc);</div>
-<div class="line"><a id="l00495" name="l00495"></a><span class="lineno">  495</span>    <span class="keywordflow">return</span> ret - <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a135b7952593c9b1aae38fcaf1cc1abf7">Tree&lt;X&gt;::t_val</a>[lc];</div>
-<div class="line"><a id="l00496" name="l00496"></a><span class="lineno">  496</span>  }</div>
+<div class="fragment"><div class="line"><span class="lineno">  489</span>                        {</div>
+<div class="line"><span class="lineno">  490</span>    <span class="keywordtype">int</span> lc = <a class="code hl_function" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae2b407e64aaf9878fbee7ee6efe9c7d4">Tree&lt;X&gt;::lca</a>(a, b);</div>
+<div class="line"><span class="lineno">  491</span>    X ret = <a class="code hl_variable" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#aa7f93971a9f891e0bbb7023081f379d5">SG&lt;X&gt;::sret_init</a>;</div>
+<div class="line"><span class="lineno">  492</span>    assert(lc != -1);</div>
+<div class="line"><span class="lineno">  493</span>    ret += <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a7d5b40c076347a6aabfb37a0590f2f24">chain_query</a>(a, lc);</div>
+<div class="line"><span class="lineno">  494</span>    ret += <a class="code hl_function" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a7d5b40c076347a6aabfb37a0590f2f24">chain_query</a>(b, lc);</div>
+<div class="line"><span class="lineno">  495</span>    <span class="keywordflow">return</span> ret - <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a135b7952593c9b1aae38fcaf1cc1abf7">Tree&lt;X&gt;::t_val</a>[lc];</div>
+<div class="line"><span class="lineno">  496</span>  }</div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_h_l_d_html_a7d5b40c076347a6aabfb37a0590f2f24"><div class="ttname"><a href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a7d5b40c076347a6aabfb37a0590f2f24">range_queries::heavy_light_decomposition::HLD::chain_query</a></div><div class="ttdeci">X chain_query(int a, int b)</div><div class="ttdoc">Utility function to break down a path query into two chain queries.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:409</div></div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_ae2b407e64aaf9878fbee7ee6efe9c7d4"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae2b407e64aaf9878fbee7ee6efe9c7d4">range_queries::heavy_light_decomposition::Tree::lca</a></div><div class="ttdeci">int lca(int a, int b)</div><div class="ttdoc">The function returns the least common ancestor of two nodes.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:229</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -698,11 +702,11 @@ template&lt;typename X &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00475" name="l00475"></a><span class="lineno">  475</span>                               {</div>
-<div class="line"><a id="l00476" name="l00476"></a><span class="lineno">  476</span>    X diff = val - <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a135b7952593c9b1aae38fcaf1cc1abf7">Tree&lt;X&gt;::t_val</a>[<a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>];</div>
-<div class="line"><a id="l00477" name="l00477"></a><span class="lineno">  477</span>    <a class="code hl_function" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#a3c75bf5770790f8eba8cc92227b5400c">SG&lt;X&gt;::update</a>(<a class="code hl_variable" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#aa86a91ae0cd7898990a8170a2f2c9cda">h_label</a>[<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>], diff);</div>
-<div class="line"><a id="l00478" name="l00478"></a><span class="lineno">  478</span>    <a class="code hl_variable" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a135b7952593c9b1aae38fcaf1cc1abf7">Tree&lt;X&gt;::t_val</a>[<a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>] = val;</div>
-<div class="line"><a id="l00479" name="l00479"></a><span class="lineno">  479</span>  }</div>
+<div class="fragment"><div class="line"><span class="lineno">  475</span>                               {</div>
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+<div class="line"><span class="lineno">  533</span>      <span class="keywordtype">int</span> a = q[1], b = q[2];</div>
+<div class="line"><span class="lineno">  534</span>      code_result.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(hld.query(a - 1, b - 1));</div>
+<div class="line"><span class="lineno">  535</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  536</span>      <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno">  537</span>    }</div>
+<div class="line"><span class="lineno">  538</span>  }</div>
+<div class="line"><span class="lineno">  539</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; static_cast&lt;int&gt;(expected_result.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()); i++) {</div>
+<div class="line"><span class="lineno">  540</span>    assert(expected_result[i] == code_result[i]);</div>
+<div class="line"><span class="lineno">  541</span>  }</div>
+<div class="line"><span class="lineno">  542</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nTest 1 passed!\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  543</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_h_l_d_html"><div class="ttname"><a href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html">range_queries::heavy_light_decomposition::HLD</a></div><div class="ttdoc">The Heavy-Light Decomposition class.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:336</div></div>
 <div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
 <div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int64_t &gt;</a></div></div>
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 <p >Second test implementations </p><dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00549" name="l00549"></a><span class="lineno">  549</span>                     {</div>
-<div class="line"><a id="l00550" name="l00550"></a><span class="lineno">  550</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2:\n&quot;</span>;</div>
-<div class="line"><a id="l00551" name="l00551"></a><span class="lineno">  551</span> </div>
-<div class="line"><a id="l00552" name="l00552"></a><span class="lineno">  552</span>  <span class="comment">// Test details (Bamboo)</span></div>
-<div class="line"><a id="l00553" name="l00553"></a><span class="lineno">  553</span>  <span class="keywordtype">int</span> n = 10;</div>
-<div class="line"><a id="l00554" name="l00554"></a><span class="lineno">  554</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> node_values = {1, 8, 6, 8, 6, 2, 9, 2, 3, 2};</div>
-<div class="line"><a id="l00555" name="l00555"></a><span class="lineno">  555</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a>&gt; edges = {</div>
-<div class="line"><a id="l00556" name="l00556"></a><span class="lineno">  556</span>      {10, 5}, {6, 2}, {10, 7}, {5, 2}, {3, 9}, {8, 3}, {1, 4}, {6, 4}, {8, 7}};</div>
-<div class="line"><a id="l00557" name="l00557"></a><span class="lineno">  557</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a>&gt; queries = {</div>
-<div class="line"><a id="l00558" name="l00558"></a><span class="lineno">  558</span>      {2, 1, 10}, {2, 1, 6}, {1, 3, 4}, {2, 1, 9}, {1, 5, 3},</div>
-<div class="line"><a id="l00559" name="l00559"></a><span class="lineno">  559</span>      {1, 7, 8},  {2, 1, 4}, {2, 1, 8}, {1, 1, 4}, {1, 2, 7}};</div>
-<div class="line"><a id="l00560" name="l00560"></a><span class="lineno">  560</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> expected_result = {27, 11, 45, 9, 34};</div>
-<div class="line"><a id="l00561" name="l00561"></a><span class="lineno">  561</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> code_result;</div>
-<div class="line"><a id="l00562" name="l00562"></a><span class="lineno">  562</span> </div>
-<div class="line"><a id="l00563" name="l00563"></a><span class="lineno">  563</span>  <a class="code hl_class" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html">range_queries::heavy_light_decomposition::HLD&lt;int64_t&gt;</a> hld(n);</div>
-<div class="line"><a id="l00564" name="l00564"></a><span class="lineno">  564</span>  hld.set_node_val(node_values);</div>
-<div class="line"><a id="l00565" name="l00565"></a><span class="lineno">  565</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n - 1; i++) {</div>
-<div class="line"><a id="l00566" name="l00566"></a><span class="lineno">  566</span>    <span class="keywordtype">int</span> u = edges[i][0], v = edges[i][1];</div>
-<div class="line"><a id="l00567" name="l00567"></a><span class="lineno">  567</span>    hld.add_edge(u - 1, v - 1);</div>
-<div class="line"><a id="l00568" name="l00568"></a><span class="lineno">  568</span>  }</div>
-<div class="line"><a id="l00569" name="l00569"></a><span class="lineno">  569</span>  hld.init();</div>
-<div class="line"><a id="l00570" name="l00570"></a><span class="lineno">  570</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;q : queries) {</div>
-<div class="line"><a id="l00571" name="l00571"></a><span class="lineno">  571</span>    <span class="keywordtype">int</span> type = q[0];</div>
-<div class="line"><a id="l00572" name="l00572"></a><span class="lineno">  572</span>    <span class="keywordflow">if</span> (type == 1) {</div>
-<div class="line"><a id="l00573" name="l00573"></a><span class="lineno">  573</span>      <span class="keywordtype">int</span> p = q[1], x = q[2];</div>
-<div class="line"><a id="l00574" name="l00574"></a><span class="lineno">  574</span>      hld.update(p - 1, x);</div>
-<div class="line"><a id="l00575" name="l00575"></a><span class="lineno">  575</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (type == 2) {</div>
-<div class="line"><a id="l00576" name="l00576"></a><span class="lineno">  576</span>      <span class="keywordtype">int</span> a = q[1], b = q[2];</div>
-<div class="line"><a id="l00577" name="l00577"></a><span class="lineno">  577</span>      code_result.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(hld.query(a - 1, b - 1));</div>
-<div class="line"><a id="l00578" name="l00578"></a><span class="lineno">  578</span>    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00579" name="l00579"></a><span class="lineno">  579</span>      <span class="keywordflow">continue</span>;</div>
-<div class="line"><a id="l00580" name="l00580"></a><span class="lineno">  580</span>    }</div>
-<div class="line"><a id="l00581" name="l00581"></a><span class="lineno">  581</span>  }</div>
-<div class="line"><a id="l00582" name="l00582"></a><span class="lineno">  582</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; static_cast&lt;int&gt;(expected_result.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()); i++) {</div>
-<div class="line"><a id="l00583" name="l00583"></a><span class="lineno">  583</span>    assert(expected_result[i] == code_result[i]);</div>
-<div class="line"><a id="l00584" name="l00584"></a><span class="lineno">  584</span>  }</div>
-<div class="line"><a id="l00585" name="l00585"></a><span class="lineno">  585</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nTest2 passed!\n&quot;</span>;</div>
-<div class="line"><a id="l00586" name="l00586"></a><span class="lineno">  586</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  549</span>                     {</div>
+<div class="line"><span class="lineno">  550</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2:\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  551</span> </div>
+<div class="line"><span class="lineno">  552</span>  <span class="comment">// Test details (Bamboo)</span></div>
+<div class="line"><span class="lineno">  553</span>  <span class="keywordtype">int</span> n = 10;</div>
+<div class="line"><span class="lineno">  554</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> node_values = {1, 8, 6, 8, 6, 2, 9, 2, 3, 2};</div>
+<div class="line"><span class="lineno">  555</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a>&gt; edges = {</div>
+<div class="line"><span class="lineno">  556</span>      {10, 5}, {6, 2}, {10, 7}, {5, 2}, {3, 9}, {8, 3}, {1, 4}, {6, 4}, {8, 7}};</div>
+<div class="line"><span class="lineno">  557</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a>&gt; queries = {</div>
+<div class="line"><span class="lineno">  558</span>      {2, 1, 10}, {2, 1, 6}, {1, 3, 4}, {2, 1, 9}, {1, 5, 3},</div>
+<div class="line"><span class="lineno">  559</span>      {1, 7, 8},  {2, 1, 4}, {2, 1, 8}, {1, 1, 4}, {1, 2, 7}};</div>
+<div class="line"><span class="lineno">  560</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> expected_result = {27, 11, 45, 9, 34};</div>
+<div class="line"><span class="lineno">  561</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> code_result;</div>
+<div class="line"><span class="lineno">  562</span> </div>
+<div class="line"><span class="lineno">  563</span>  <a class="code hl_class" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html">range_queries::heavy_light_decomposition::HLD&lt;int64_t&gt;</a> hld(n);</div>
+<div class="line"><span class="lineno">  564</span>  hld.set_node_val(node_values);</div>
+<div class="line"><span class="lineno">  565</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n - 1; i++) {</div>
+<div class="line"><span class="lineno">  566</span>    <span class="keywordtype">int</span> u = edges[i][0], v = edges[i][1];</div>
+<div class="line"><span class="lineno">  567</span>    hld.add_edge(u - 1, v - 1);</div>
+<div class="line"><span class="lineno">  568</span>  }</div>
+<div class="line"><span class="lineno">  569</span>  hld.init();</div>
+<div class="line"><span class="lineno">  570</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;q : queries) {</div>
+<div class="line"><span class="lineno">  571</span>    <span class="keywordtype">int</span> type = q[0];</div>
+<div class="line"><span class="lineno">  572</span>    <span class="keywordflow">if</span> (type == 1) {</div>
+<div class="line"><span class="lineno">  573</span>      <span class="keywordtype">int</span> p = q[1], x = q[2];</div>
+<div class="line"><span class="lineno">  574</span>      hld.update(p - 1, x);</div>
+<div class="line"><span class="lineno">  575</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (type == 2) {</div>
+<div class="line"><span class="lineno">  576</span>      <span class="keywordtype">int</span> a = q[1], b = q[2];</div>
+<div class="line"><span class="lineno">  577</span>      code_result.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(hld.query(a - 1, b - 1));</div>
+<div class="line"><span class="lineno">  578</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  579</span>      <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno">  580</span>    }</div>
+<div class="line"><span class="lineno">  581</span>  }</div>
+<div class="line"><span class="lineno">  582</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; static_cast&lt;int&gt;(expected_result.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()); i++) {</div>
+<div class="line"><span class="lineno">  583</span>    assert(expected_result[i] == code_result[i]);</div>
+<div class="line"><span class="lineno">  584</span>  }</div>
+<div class="line"><span class="lineno">  585</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nTest2 passed!\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  586</span>}</div>
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@@ -371,44 +371,44 @@ Here is the call graph for this function:</div>
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 <p >Third test implementations </p><dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00592" name="l00592"></a><span class="lineno">  592</span>                     {</div>
-<div class="line"><a id="l00593" name="l00593"></a><span class="lineno">  593</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3:\n&quot;</span>;</div>
-<div class="line"><a id="l00594" name="l00594"></a><span class="lineno">  594</span> </div>
-<div class="line"><a id="l00595" name="l00595"></a><span class="lineno">  595</span>  <span class="comment">// Test details</span></div>
-<div class="line"><a id="l00596" name="l00596"></a><span class="lineno">  596</span>  <span class="keywordtype">int</span> n = 8;</div>
-<div class="line"><a id="l00597" name="l00597"></a><span class="lineno">  597</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> node_values = {1, 8, 6, 8, 6, 2, 9, 2};</div>
-<div class="line"><a id="l00598" name="l00598"></a><span class="lineno">  598</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a>&gt; edges = {{1, 2}, {2, 3}, {3, 4}, {1, 5},</div>
-<div class="line"><a id="l00599" name="l00599"></a><span class="lineno">  599</span>                                         {6, 3}, {7, 5}, {8, 7}};</div>
-<div class="line"><a id="l00600" name="l00600"></a><span class="lineno">  600</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a>&gt; queries = {</div>
-<div class="line"><a id="l00601" name="l00601"></a><span class="lineno">  601</span>      {2, 6, 8}, {2, 3, 6}, {1, 3, 4}, {2, 7, 1}, {1, 5, 3},</div>
-<div class="line"><a id="l00602" name="l00602"></a><span class="lineno">  602</span>      {1, 7, 8}, {2, 6, 4}, {2, 7, 8}, {1, 1, 4}, {1, 2, 7}};</div>
-<div class="line"><a id="l00603" name="l00603"></a><span class="lineno">  603</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> expected_result = {34, 8, 16, 14, 10};</div>
-<div class="line"><a id="l00604" name="l00604"></a><span class="lineno">  604</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> code_result;</div>
-<div class="line"><a id="l00605" name="l00605"></a><span class="lineno">  605</span> </div>
-<div class="line"><a id="l00606" name="l00606"></a><span class="lineno">  606</span>  <a class="code hl_class" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html">range_queries::heavy_light_decomposition::HLD&lt;int64_t&gt;</a> hld(n);</div>
-<div class="line"><a id="l00607" name="l00607"></a><span class="lineno">  607</span>  hld.set_node_val(node_values);</div>
-<div class="line"><a id="l00608" name="l00608"></a><span class="lineno">  608</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n - 1; i++) {</div>
-<div class="line"><a id="l00609" name="l00609"></a><span class="lineno">  609</span>    <span class="keywordtype">int</span> u = edges[i][0], v = edges[i][1];</div>
-<div class="line"><a id="l00610" name="l00610"></a><span class="lineno">  610</span>    hld.add_edge(u - 1, v - 1);</div>
-<div class="line"><a id="l00611" name="l00611"></a><span class="lineno">  611</span>  }</div>
-<div class="line"><a id="l00612" name="l00612"></a><span class="lineno">  612</span>  hld.init();</div>
-<div class="line"><a id="l00613" name="l00613"></a><span class="lineno">  613</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;q : queries) {</div>
-<div class="line"><a id="l00614" name="l00614"></a><span class="lineno">  614</span>    <span class="keywordtype">int</span> type = q[0];</div>
-<div class="line"><a id="l00615" name="l00615"></a><span class="lineno">  615</span>    <span class="keywordflow">if</span> (type == 1) {</div>
-<div class="line"><a id="l00616" name="l00616"></a><span class="lineno">  616</span>      <span class="keywordtype">int</span> p = q[1], x = q[2];</div>
-<div class="line"><a id="l00617" name="l00617"></a><span class="lineno">  617</span>      hld.update(p - 1, x);</div>
-<div class="line"><a id="l00618" name="l00618"></a><span class="lineno">  618</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (type == 2) {</div>
-<div class="line"><a id="l00619" name="l00619"></a><span class="lineno">  619</span>      <span class="keywordtype">int</span> a = q[1], b = q[2];</div>
-<div class="line"><a id="l00620" name="l00620"></a><span class="lineno">  620</span>      code_result.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(hld.query(a - 1, b - 1));</div>
-<div class="line"><a id="l00621" name="l00621"></a><span class="lineno">  621</span>    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00622" name="l00622"></a><span class="lineno">  622</span>      <span class="keywordflow">continue</span>;</div>
-<div class="line"><a id="l00623" name="l00623"></a><span class="lineno">  623</span>    }</div>
-<div class="line"><a id="l00624" name="l00624"></a><span class="lineno">  624</span>  }</div>
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+<div class="line"><span class="lineno">  594</span> </div>
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+<div class="line"><span class="lineno">   56</span>    dy[0][0] = y[0][1];                   <span class="comment">// x dot</span></div>
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+<div class="line"><span class="lineno">  167</span>    <span class="keywordflow">do</span> {</div>
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-<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;element? &quot;</span>;</div>
-<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; a[i][j];</div>
-<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>        }</div>
-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>    }</div>
-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span> </div>
-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>    <span class="comment">// counts the zero&#39;s</span></div>
-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; m; i++) {</div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>            <span class="keywordflow">if</span> (a[i][j] == 0)</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>                counterZeros++;  <span class="comment">// Counting number of zeroes</span></div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>        }</div>
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-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>    <span class="comment">// makes sure the matrix is a sparse matrix</span></div>
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+<div class="line"><span class="lineno">   27</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; a[i][j];</div>
+<div class="line"><span class="lineno">   28</span>        }</div>
+<div class="line"><span class="lineno">   29</span>    }</div>
+<div class="line"><span class="lineno">   30</span> </div>
+<div class="line"><span class="lineno">   31</span>    <span class="comment">// counts the zero&#39;s</span></div>
+<div class="line"><span class="lineno">   32</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; m; i++) {</div>
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+<div class="line"><span class="lineno">   37</span>    }</div>
+<div class="line"><span class="lineno">   38</span> </div>
+<div class="line"><span class="lineno">   39</span>    <span class="comment">// makes sure the matrix is a sparse matrix</span></div>
+<div class="line"><span class="lineno">   40</span>    <span class="keywordflow">if</span> (counterZeros &gt; ((m * n) / 2))  <span class="comment">// Checking for sparse matrix</span></div>
+<div class="line"><span class="lineno">   41</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Sparse matrix&quot;</span>;</div>
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+<div class="line"><span class="lineno">   45</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; m; i++) <span class="keyword">delete</span>[] a[i];</div>
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@@ -152,10 +152,10 @@ Functions</h2></td></tr>
 
 <p>Main function. </p>
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-<div class="fragment"><div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>           {</div>
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 Here is the call graph for this function:</div>
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 <dl class="section return"><dt>Returns</dt><dd>An <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a> of with row and column populated within it, if the element is present. </dd>
 <dd>
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-<div class="fragment"><div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>                                                {</div>
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-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>                                           <span class="comment">// matrix is less than the element,</span></div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>                                           <span class="comment">// move left.</span></div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>            ++left_index;</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (element &lt;</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>                   <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a>[left_index]</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>                         [right_index]) {  <span class="comment">// Else if value on this position of</span></div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>                                           <span class="comment">// matrix is greater than the</span></div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>                                           <span class="comment">// element, move down.</span></div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>            <span class="keywordflow">if</span>(!right_index)</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>            <span class="keywordflow">else</span> --right_index;</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>        }</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    }</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        0, 0);  <span class="comment">// If the program reaches here, that means one of the index</span></div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>                  <span class="comment">// went out of index, hence no element present.</span></div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   34</span>                                                {</div>
+<div class="line"><span class="lineno">   35</span>    uint32_t left_index = 0;</div>
+<div class="line"><span class="lineno">   36</span>    uint32_t right_index = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a>[0].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() - 1;  <span class="comment">// Start from top right corner</span></div>
+<div class="line"><span class="lineno">   37</span>    <span class="keywordflow">while</span> (left_index &lt; <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) {  <span class="comment">// Exit once the value of indexes get out of range.</span></div>
+<div class="line"><span class="lineno">   38</span>        <span class="keywordflow">if</span> (element ==</div>
+<div class="line"><span class="lineno">   39</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a>[left_index]</div>
+<div class="line"><span class="lineno">   40</span>                  [right_index]) {  <span class="comment">// If value on this position of matrix is</span></div>
+<div class="line"><span class="lineno">   41</span>                                    <span class="comment">// equal to element, return (row, column).</span></div>
+<div class="line"><span class="lineno">   42</span>            <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(left_index+1, right_index+1);</div>
+<div class="line"><span class="lineno">   43</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (element &gt;</div>
+<div class="line"><span class="lineno">   44</span>                   <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a>[left_index]</div>
+<div class="line"><span class="lineno">   45</span>                         [right_index]) {  <span class="comment">// Else if value on this position of</span></div>
+<div class="line"><span class="lineno">   46</span>                                           <span class="comment">// matrix is less than the element,</span></div>
+<div class="line"><span class="lineno">   47</span>                                           <span class="comment">// move left.</span></div>
+<div class="line"><span class="lineno">   48</span>            ++left_index;</div>
+<div class="line"><span class="lineno">   49</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (element &lt;</div>
+<div class="line"><span class="lineno">   50</span>                   <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a>[left_index]</div>
+<div class="line"><span class="lineno">   51</span>                         [right_index]) {  <span class="comment">// Else if value on this position of</span></div>
+<div class="line"><span class="lineno">   52</span>                                           <span class="comment">// matrix is greater than the</span></div>
+<div class="line"><span class="lineno">   53</span>                                           <span class="comment">// element, move down.</span></div>
+<div class="line"><span class="lineno">   54</span>            <span class="keywordflow">if</span>(!right_index)</div>
+<div class="line"><span class="lineno">   55</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">   56</span>            <span class="keywordflow">else</span> --right_index;</div>
+<div class="line"><span class="lineno">   57</span>        }</div>
+<div class="line"><span class="lineno">   58</span>    }</div>
+<div class="line"><span class="lineno">   59</span>    <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(</div>
+<div class="line"><span class="lineno">   60</span>        0, 0);  <span class="comment">// If the program reaches here, that means one of the index</span></div>
+<div class="line"><span class="lineno">   61</span>                  <span class="comment">// went out of index, hence no element present.</span></div>
+<div class="line"><span class="lineno">   62</span>}</div>
 <div class="ttc" id="amake_pair_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a></div><div class="ttdeci">T make_pair(T... args)</div></div>
 <div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
 <div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
@@ -267,34 +267,34 @@ Here is the call graph for this function:</div>
 
 <p>Test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>                   {</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int32_t&gt;</a>&gt; <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a> = {{1, 10, 100, 1000, 10000},</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>                                            {2, 20, 200, 2000, 20000},</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>                                            {3, 30, 300, 3000, 30000},</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>                                            {4, 40, 400, 4000, 40000},</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>                                            {5, 50, 500, 5000, 50000}};</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span> </div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint32_t, uint32_t&gt;</a> not_found = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(0, 0);</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint32_t, uint32_t&gt;</a> test_answer;</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <span class="comment">// Test 1</span></div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint32_t, uint32_t&gt;</a> answer1 = <a class="code hl_function" href="../../d3/d22/saddleback__search_8cpp.html#ad1e0ca34797d88490747c08eca70a2e6">search::saddleback::saddleback</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a>, 123);</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    assert(not_found == answer1);</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <span class="comment">// Test 2</span></div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    answer1 = <a class="code hl_function" href="../../d3/d22/saddleback__search_8cpp.html#ad1e0ca34797d88490747c08eca70a2e6">search::saddleback::saddleback</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a>, 0);</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    assert(not_found == answer1);</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    <span class="comment">// Test 3</span></div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>    answer1 = <a class="code hl_function" href="../../d3/d22/saddleback__search_8cpp.html#ad1e0ca34797d88490747c08eca70a2e6">search::saddleback::saddleback</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a>, 1);</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    test_answer = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(1, 1);</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    assert(test_answer == answer1);</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    <span class="comment">// Test 4</span></div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    answer1 = <a class="code hl_function" href="../../d3/d22/saddleback__search_8cpp.html#ad1e0ca34797d88490747c08eca70a2e6">search::saddleback::saddleback</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a>, 50000);</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    test_answer = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(5, 5);</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    assert(test_answer == answer1);</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    <span class="comment">// Test 5</span></div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>    answer1 = <a class="code hl_function" href="../../d3/d22/saddleback__search_8cpp.html#ad1e0ca34797d88490747c08eca70a2e6">search::saddleback::saddleback</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a>, 300);</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>    test_answer = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(3, 3);</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    assert(test_answer == answer1);</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   70</span>                   {</div>
+<div class="line"><span class="lineno">   71</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int32_t&gt;</a>&gt; <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a> = {{1, 10, 100, 1000, 10000},</div>
+<div class="line"><span class="lineno">   72</span>                                            {2, 20, 200, 2000, 20000},</div>
+<div class="line"><span class="lineno">   73</span>                                            {3, 30, 300, 3000, 30000},</div>
+<div class="line"><span class="lineno">   74</span>                                            {4, 40, 400, 4000, 40000},</div>
+<div class="line"><span class="lineno">   75</span>                                            {5, 50, 500, 5000, 50000}};</div>
+<div class="line"><span class="lineno">   76</span> </div>
+<div class="line"><span class="lineno">   77</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint32_t, uint32_t&gt;</a> not_found = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(0, 0);</div>
+<div class="line"><span class="lineno">   78</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint32_t, uint32_t&gt;</a> test_answer;</div>
+<div class="line"><span class="lineno">   79</span>    <span class="comment">// Test 1</span></div>
+<div class="line"><span class="lineno">   80</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint32_t, uint32_t&gt;</a> answer1 = <a class="code hl_function" href="../../d3/d22/saddleback__search_8cpp.html#ad1e0ca34797d88490747c08eca70a2e6">search::saddleback::saddleback</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a>, 123);</div>
+<div class="line"><span class="lineno">   81</span>    assert(not_found == answer1);</div>
+<div class="line"><span class="lineno">   82</span>    <span class="comment">// Test 2</span></div>
+<div class="line"><span class="lineno">   83</span>    answer1 = <a class="code hl_function" href="../../d3/d22/saddleback__search_8cpp.html#ad1e0ca34797d88490747c08eca70a2e6">search::saddleback::saddleback</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a>, 0);</div>
+<div class="line"><span class="lineno">   84</span>    assert(not_found == answer1);</div>
+<div class="line"><span class="lineno">   85</span>    <span class="comment">// Test 3</span></div>
+<div class="line"><span class="lineno">   86</span>    answer1 = <a class="code hl_function" href="../../d3/d22/saddleback__search_8cpp.html#ad1e0ca34797d88490747c08eca70a2e6">search::saddleback::saddleback</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a>, 1);</div>
+<div class="line"><span class="lineno">   87</span>    test_answer = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(1, 1);</div>
+<div class="line"><span class="lineno">   88</span>    assert(test_answer == answer1);</div>
+<div class="line"><span class="lineno">   89</span>    <span class="comment">// Test 4</span></div>
+<div class="line"><span class="lineno">   90</span>    answer1 = <a class="code hl_function" href="../../d3/d22/saddleback__search_8cpp.html#ad1e0ca34797d88490747c08eca70a2e6">search::saddleback::saddleback</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a>, 50000);</div>
+<div class="line"><span class="lineno">   91</span>    test_answer = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(5, 5);</div>
+<div class="line"><span class="lineno">   92</span>    assert(test_answer == answer1);</div>
+<div class="line"><span class="lineno">   93</span>    <span class="comment">// Test 5</span></div>
+<div class="line"><span class="lineno">   94</span>    answer1 = <a class="code hl_function" href="../../d3/d22/saddleback__search_8cpp.html#ad1e0ca34797d88490747c08eca70a2e6">search::saddleback::saddleback</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a>, 300);</div>
+<div class="line"><span class="lineno">   95</span>    test_answer = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(3, 3);</div>
+<div class="line"><span class="lineno">   96</span>    assert(test_answer == answer1);</div>
+<div class="line"><span class="lineno">   97</span>}</div>
 <div class="ttc" id="apair_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a></div></div>
 <div class="ttc" id="asaddleback__search_8cpp_html_ad1e0ca34797d88490747c08eca70a2e6"><div class="ttname"><a href="../../d3/d22/saddleback__search_8cpp.html#ad1e0ca34797d88490747c08eca70a2e6">search::saddleback::saddleback</a></div><div class="ttdeci">std::pair&lt; uint32_t, uint32_t &gt; saddleback(std::vector&lt; std::vector&lt; int32_t &gt; &gt; matrix, int32_t element)</div><div class="ttdef"><b>Definition:</b> saddleback_search.cpp:33</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -312,7 +312,7 @@ Here is the call graph for this function:</div>
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   <ul>
     <li class="navelem"><a class="el" href="../../dir_19b2bf9199a15c634a08b1ede1dd896a.html">search</a></li><li class="navelem"><a class="el" href="../../d3/d22/saddleback__search_8cpp.html">saddleback_search.cpp</a></li>
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-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>            temp-&gt;val = x;</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>            temp-&gt;left = NULL;</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>            temp-&gt;right = NULL;</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>            n-&gt;right = temp;</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>            Insert(n-&gt;right, x);</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        }</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    }</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   29</span>                            {</div>
+<div class="line"><span class="lineno">   30</span>    <span class="keywordflow">if</span> (x &lt; n-&gt;val) {</div>
+<div class="line"><span class="lineno">   31</span>        <span class="keywordflow">if</span> (n-&gt;left == NULL) {</div>
+<div class="line"><span class="lineno">   32</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *temp = <span class="keyword">new</span> <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
+<div class="line"><span class="lineno">   33</span>            temp-&gt;val = x;</div>
+<div class="line"><span class="lineno">   34</span>            temp-&gt;left = NULL;</div>
+<div class="line"><span class="lineno">   35</span>            temp-&gt;right = NULL;</div>
+<div class="line"><span class="lineno">   36</span>            n-&gt;left = temp;</div>
+<div class="line"><span class="lineno">   37</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   38</span>            Insert(n-&gt;left, x);</div>
+<div class="line"><span class="lineno">   39</span>        }</div>
+<div class="line"><span class="lineno">   40</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   41</span>        <span class="keywordflow">if</span> (n-&gt;right == NULL) {</div>
+<div class="line"><span class="lineno">   42</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *temp = <span class="keyword">new</span> <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
+<div class="line"><span class="lineno">   43</span>            temp-&gt;val = x;</div>
+<div class="line"><span class="lineno">   44</span>            temp-&gt;left = NULL;</div>
+<div class="line"><span class="lineno">   45</span>            temp-&gt;right = NULL;</div>
+<div class="line"><span class="lineno">   46</span>            n-&gt;right = temp;</div>
+<div class="line"><span class="lineno">   47</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   48</span>            Insert(n-&gt;right, x);</div>
+<div class="line"><span class="lineno">   49</span>        }</div>
+<div class="line"><span class="lineno">   50</span>    }</div>
+<div class="line"><span class="lineno">   51</span>}</div>
 <div class="ttc" id="ahash__search_8cpp_html_a8ca8dcb494104d273679e219e53d0555"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a></div><div class="ttdeci">struct list node</div></div>
 <div class="ttc" id="astructnode_html"><div class="ttname"><a href="../../d5/da1/structnode.html">node</a></div><div class="ttdef"><b>Definition:</b> avltree.cpp:13</div></div>
 </div><!-- fragment -->
@@ -332,56 +332,56 @@ Variables</h2></td></tr>
         </tr>
       </table>
 </div><div class="memdoc">
-<div class="fragment"><div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>           {</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    <a class="code hl_class" href="../../db/da9/classqueue.html">queue</a>.<a class="code hl_function" href="../../db/da9/classqueue.html#a36d47fdbedc199609818385110d9f922">front</a> = 0;</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    <a class="code hl_class" href="../../db/da9/classqueue.html">queue</a>.rear = 0;</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    <span class="keywordtype">int</span> value;</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    <span class="keywordtype">int</span> ch;</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *root = <span class="keyword">new</span> <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEnter the value of root node :&quot;</span>;</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; value;</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    root-&gt;val = value;</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    root-&gt;left = NULL;</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    root-&gt;right = NULL;</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    <span class="keywordflow">do</span> {</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n1. Insert&quot;</span></div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>                  &lt;&lt; <span class="stringliteral">&quot;\n2. Delete&quot;</span></div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>                  &lt;&lt; <span class="stringliteral">&quot;\n3. Breadth First&quot;</span></div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>                  &lt;&lt; <span class="stringliteral">&quot;\n4. Preorder Depth First&quot;</span></div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>                  &lt;&lt; <span class="stringliteral">&quot;\n5. Inorder Depth First&quot;</span></div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>                  &lt;&lt; <span class="stringliteral">&quot;\n6. Postorder Depth First&quot;</span>;</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span> </div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEnter Your Choice : &quot;</span>;</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; ch;</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>        <span class="keywordtype">int</span> x;</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>        <span class="keywordflow">switch</span> (ch) {</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>        <span class="keywordflow">case</span> 1:</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEnter the value to be Inserted : &quot;</span>;</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; x;</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>            Insert(root, x);</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>            <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>        <span class="keywordflow">case</span> 2:</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEnter the value to be Deleted : &quot;</span>;</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; x;</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>            Remove(root, root, x);</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>            <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>        <span class="keywordflow">case</span> 3:</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>            BFT(root);</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>            <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>        <span class="keywordflow">case</span> 4:</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>            Pre(root);</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>            <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>        <span class="keywordflow">case</span> 5:</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>            In(root);</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>            <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>        <span class="keywordflow">case</span> 6:</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>            Post(root);</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>            <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>        }</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>    } <span class="keywordflow">while</span> (ch != 0);</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span> </div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  125</span>           {</div>
+<div class="line"><span class="lineno">  126</span>    <a class="code hl_class" href="../../db/da9/classqueue.html">queue</a>.<a class="code hl_function" href="../../db/da9/classqueue.html#a36d47fdbedc199609818385110d9f922">front</a> = 0;</div>
+<div class="line"><span class="lineno">  127</span>    <a class="code hl_class" href="../../db/da9/classqueue.html">queue</a>.rear = 0;</div>
+<div class="line"><span class="lineno">  128</span>    <span class="keywordtype">int</span> value;</div>
+<div class="line"><span class="lineno">  129</span>    <span class="keywordtype">int</span> ch;</div>
+<div class="line"><span class="lineno">  130</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *root = <span class="keyword">new</span> <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
+<div class="line"><span class="lineno">  131</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEnter the value of root node :&quot;</span>;</div>
+<div class="line"><span class="lineno">  132</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; value;</div>
+<div class="line"><span class="lineno">  133</span>    root-&gt;val = value;</div>
+<div class="line"><span class="lineno">  134</span>    root-&gt;left = NULL;</div>
+<div class="line"><span class="lineno">  135</span>    root-&gt;right = NULL;</div>
+<div class="line"><span class="lineno">  136</span>    <span class="keywordflow">do</span> {</div>
+<div class="line"><span class="lineno">  137</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n1. Insert&quot;</span></div>
+<div class="line"><span class="lineno">  138</span>                  &lt;&lt; <span class="stringliteral">&quot;\n2. Delete&quot;</span></div>
+<div class="line"><span class="lineno">  139</span>                  &lt;&lt; <span class="stringliteral">&quot;\n3. Breadth First&quot;</span></div>
+<div class="line"><span class="lineno">  140</span>                  &lt;&lt; <span class="stringliteral">&quot;\n4. Preorder Depth First&quot;</span></div>
+<div class="line"><span class="lineno">  141</span>                  &lt;&lt; <span class="stringliteral">&quot;\n5. Inorder Depth First&quot;</span></div>
+<div class="line"><span class="lineno">  142</span>                  &lt;&lt; <span class="stringliteral">&quot;\n6. Postorder Depth First&quot;</span>;</div>
+<div class="line"><span class="lineno">  143</span> </div>
+<div class="line"><span class="lineno">  144</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEnter Your Choice : &quot;</span>;</div>
+<div class="line"><span class="lineno">  145</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; ch;</div>
+<div class="line"><span class="lineno">  146</span>        <span class="keywordtype">int</span> x;</div>
+<div class="line"><span class="lineno">  147</span>        <span class="keywordflow">switch</span> (ch) {</div>
+<div class="line"><span class="lineno">  148</span>        <span class="keywordflow">case</span> 1:</div>
+<div class="line"><span class="lineno">  149</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEnter the value to be Inserted : &quot;</span>;</div>
+<div class="line"><span class="lineno">  150</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; x;</div>
+<div class="line"><span class="lineno">  151</span>            Insert(root, x);</div>
+<div class="line"><span class="lineno">  152</span>            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  153</span>        <span class="keywordflow">case</span> 2:</div>
+<div class="line"><span class="lineno">  154</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEnter the value to be Deleted : &quot;</span>;</div>
+<div class="line"><span class="lineno">  155</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; x;</div>
+<div class="line"><span class="lineno">  156</span>            Remove(root, root, x);</div>
+<div class="line"><span class="lineno">  157</span>            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  158</span>        <span class="keywordflow">case</span> 3:</div>
+<div class="line"><span class="lineno">  159</span>            BFT(root);</div>
+<div class="line"><span class="lineno">  160</span>            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  161</span>        <span class="keywordflow">case</span> 4:</div>
+<div class="line"><span class="lineno">  162</span>            Pre(root);</div>
+<div class="line"><span class="lineno">  163</span>            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  164</span>        <span class="keywordflow">case</span> 5:</div>
+<div class="line"><span class="lineno">  165</span>            In(root);</div>
+<div class="line"><span class="lineno">  166</span>            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  167</span>        <span class="keywordflow">case</span> 6:</div>
+<div class="line"><span class="lineno">  168</span>            Post(root);</div>
+<div class="line"><span class="lineno">  169</span>            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  170</span>        }</div>
+<div class="line"><span class="lineno">  171</span>    } <span class="keywordflow">while</span> (ch != 0);</div>
+<div class="line"><span class="lineno">  172</span> </div>
+<div class="line"><span class="lineno">  173</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  174</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
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@@ -401,13 +401,13 @@ Variables</h2></td></tr>
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       </table>
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-<div class="fragment"><div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>                   {</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    <span class="keywordflow">if</span> (n != NULL) {</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        Post(n-&gt;left);</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        Post(n-&gt;right);</div>
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-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    }</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  117</span>                   {</div>
+<div class="line"><span class="lineno">  118</span>    <span class="keywordflow">if</span> (n != NULL) {</div>
+<div class="line"><span class="lineno">  119</span>        Post(n-&gt;left);</div>
+<div class="line"><span class="lineno">  120</span>        Post(n-&gt;right);</div>
+<div class="line"><span class="lineno">  121</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; n-&gt;val &lt;&lt; <span class="stringliteral">&quot;  &quot;</span>;</div>
+<div class="line"><span class="lineno">  122</span>    }</div>
+<div class="line"><span class="lineno">  123</span>}</div>
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@@ -426,13 +426,13 @@ Variables</h2></td></tr>
         </tr>
       </table>
 </div><div class="memdoc">
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  <a href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#details">More...</a></p>
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+<div class="line"><span class="lineno">  138</span>        <span class="comment">// or prefix in the line</span></div>
+<div class="line"><span class="lineno">  139</span>        <span class="keywordflow">if</span> (nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/stack/top.html">top</a>()-&gt;word_end) {</div>
+<div class="line"><span class="lineno">  140</span>            nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/stack/top.html">top</a>()-&gt;word_end = <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  141</span>        }</div>
+<div class="line"><span class="lineno">  142</span>        <span class="comment">// Delete only when it has no children after</span></div>
+<div class="line"><span class="lineno">  143</span>        <span class="comment">// and also no prefix in the line</span></div>
+<div class="line"><span class="lineno">  144</span>        <span class="keywordflow">while</span> (!(nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/stack/top.html">top</a>()-&gt;word_end) &amp;&amp; nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/stack/top.html">top</a>()-&gt;children.empty()) {</div>
+<div class="line"><span class="lineno">  145</span>            nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/stack/pop.html">pop</a>();</div>
+<div class="line"><span class="lineno">  146</span>            nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/stack/top.html">top</a>()-&gt;children.erase(word.back());</div>
+<div class="line"><span class="lineno">  147</span>            word.pop_back();</div>
+<div class="line"><span class="lineno">  148</span>        }</div>
+<div class="line"><span class="lineno">  149</span>    }</div>
 <div class="ttc" id="aclassdata__structures_1_1trie__using__hashmap_1_1_trie_html_a832072498abeaa52ad43c4fc99cba248"><div class="ttname"><a href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#a832072498abeaa52ad43c4fc99cba248">data_structures::trie_using_hashmap::Trie::root_node</a></div><div class="ttdeci">std::shared_ptr&lt; Node &gt; root_node</div><div class="ttdoc">declaring root node of trie</div><div class="ttdef"><b>Definition:</b> trie_using_hashmap.cpp:51</div></div>
 <div class="ttc" id="apop_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/stack/pop.html">std::stack::pop</a></div><div class="ttdeci">T pop(T... args)</div></div>
 <div class="ttc" id="apush_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/stack/push.html">std::stack::push</a></div><div class="ttdeci">T push(T... args)</div></div>
-<div class="ttc" id="ashared_ptr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr</a></div></div>
+<div class="ttc" id="ashared_ptr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt; Node &gt;</a></div></div>
 <div class="ttc" id="astack_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/stack.html">std::stack</a></div></div>
+<div class="ttc" id="astructdata__structures_1_1trie__using__hashmap_1_1_trie_1_1_node_html_a08212cdc99164b59da91b81f45e2f88e"><div class="ttname"><a href="../../d5/d12/structdata__structures_1_1trie__using__hashmap_1_1_trie_1_1_node.html#a08212cdc99164b59da91b81f45e2f88e">data_structures::trie_using_hashmap::Trie::Node::children</a></div><div class="ttdeci">std::unordered_map&lt; char16_t, std::shared_ptr&lt; Node &gt; &gt; children</div><div class="ttdef"><b>Definition:</b> trie_using_hashmap.cpp:46</div></div>
+<div class="ttc" id="astructdata__structures_1_1trie__using__hashmap_1_1_trie_1_1_node_html_a3cdb077745d3dc97212d693132371219"><div class="ttname"><a href="../../d5/d12/structdata__structures_1_1trie__using__hashmap_1_1_trie_1_1_node.html#a3cdb077745d3dc97212d693132371219">data_structures::trie_using_hashmap::Trie::Node::word_end</a></div><div class="ttdeci">bool word_end</div><div class="ttdoc">boolean variable to represent the node end</div><div class="ttdef"><b>Definition:</b> trie_using_hashmap.cpp:48</div></div>
 <div class="ttc" id="atop_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/stack/top.html">std::stack::top</a></div><div class="ttdeci">T top(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -266,26 +274,26 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>list of recommended words </dd></dl>
-<div class="fragment"><div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>                                                             {</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>        <span class="keywordflow">if</span> (element-&gt;word_end) {</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>            results.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(prefix);</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>        }</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>        <span class="keywordflow">if</span> (element-&gt;children.empty()) {</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>            <span class="keywordflow">return</span> results;</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>        }</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>        <span class="keywordflow">for</span> (<span class="keyword">auto</span> <span class="keyword">const</span>&amp; x : element-&gt;children) {</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> key = <span class="stringliteral">&quot;&quot;</span>;</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>            key = x.first;</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>            prefix += key;</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span> </div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>            results =</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>                <a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#a7bbe538c8015e8ce158e7ed43f605ebd">get_all_words</a>(results, element-&gt;children[x.first], prefix);</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span> </div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>            prefix.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/pop_back.html">pop_back</a>();</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>        }</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span> </div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>        <span class="keywordflow">return</span> results;</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  162</span>                                                             {</div>
+<div class="line"><span class="lineno">  163</span>        <span class="keywordflow">if</span> (element-&gt;<a class="code hl_variable" href="../../d5/d12/structdata__structures_1_1trie__using__hashmap_1_1_trie_1_1_node.html#a3cdb077745d3dc97212d693132371219">word_end</a>) {</div>
+<div class="line"><span class="lineno">  164</span>            results.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(prefix);</div>
+<div class="line"><span class="lineno">  165</span>        }</div>
+<div class="line"><span class="lineno">  166</span>        <span class="keywordflow">if</span> (element-&gt;<a class="code hl_variable" href="../../d5/d12/structdata__structures_1_1trie__using__hashmap_1_1_trie_1_1_node.html#a08212cdc99164b59da91b81f45e2f88e">children</a>.empty()) {</div>
+<div class="line"><span class="lineno">  167</span>            <span class="keywordflow">return</span> results;</div>
+<div class="line"><span class="lineno">  168</span>        }</div>
+<div class="line"><span class="lineno">  169</span>        <span class="keywordflow">for</span> (<span class="keyword">auto</span> <span class="keyword">const</span>&amp; x : element-&gt;<a class="code hl_variable" href="../../d5/d12/structdata__structures_1_1trie__using__hashmap_1_1_trie_1_1_node.html#a08212cdc99164b59da91b81f45e2f88e">children</a>) {</div>
+<div class="line"><span class="lineno">  170</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> key = <span class="stringliteral">&quot;&quot;</span>;</div>
+<div class="line"><span class="lineno">  171</span>            key = x.first;</div>
+<div class="line"><span class="lineno">  172</span>            prefix += key;</div>
+<div class="line"><span class="lineno">  173</span> </div>
+<div class="line"><span class="lineno">  174</span>            results =</div>
+<div class="line"><span class="lineno">  175</span>                <a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#a7bbe538c8015e8ce158e7ed43f605ebd">get_all_words</a>(results, element-&gt;<a class="code hl_variable" href="../../d5/d12/structdata__structures_1_1trie__using__hashmap_1_1_trie_1_1_node.html#a08212cdc99164b59da91b81f45e2f88e">children</a>[x.first], prefix);</div>
+<div class="line"><span class="lineno">  176</span> </div>
+<div class="line"><span class="lineno">  177</span>            prefix.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/pop_back.html">pop_back</a>();</div>
+<div class="line"><span class="lineno">  178</span>        }</div>
+<div class="line"><span class="lineno">  179</span> </div>
+<div class="line"><span class="lineno">  180</span>        <span class="keywordflow">return</span> results;</div>
+<div class="line"><span class="lineno">  181</span>    }</div>
 <div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
 <div class="ttc" id="aclassdata__structures_1_1trie__using__hashmap_1_1_trie_html_a7bbe538c8015e8ce158e7ed43f605ebd"><div class="ttname"><a href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#a7bbe538c8015e8ce158e7ed43f605ebd">data_structures::trie_using_hashmap::Trie::get_all_words</a></div><div class="ttdeci">std::vector&lt; std::string &gt; get_all_words(std::vector&lt; std::string &gt; results, const std::shared_ptr&lt; Node &gt; &amp;element, std::string prefix)</div><div class="ttdoc">helper function to predict/recommend words that starts with a given prefix from the end of prefix's n...</div><div class="ttdef"><b>Definition:</b> trie_using_hashmap.cpp:160</div></div>
 <div class="ttc" id="apop_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/pop_back.html">std::string::pop_back</a></div><div class="ttdeci">T pop_back(T... args)</div></div>
@@ -330,19 +338,19 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>                                       {</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Node&gt;</a> curr = <a class="code hl_variable" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#a832072498abeaa52ad43c4fc99cba248">root_node</a>;</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        <span class="keywordflow">for</span> (<span class="keywordtype">char</span> ch : word) {</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>            <span class="keywordflow">if</span> (curr-&gt;children.find(ch) == curr-&gt;children.end()) {</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>                curr-&gt;children[ch] = std::make_shared&lt;Node&gt;();</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>            }</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>            curr = curr-&gt;children[ch];</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        }</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span> </div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        <span class="keywordflow">if</span> (!curr-&gt;word_end &amp;&amp; curr != <a class="code hl_variable" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#a832072498abeaa52ad43c4fc99cba248">root_node</a>) {</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>            curr-&gt;word_end = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>        }</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   62</span>                                       {</div>
+<div class="line"><span class="lineno">   63</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Node&gt;</a> curr = <a class="code hl_variable" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#a832072498abeaa52ad43c4fc99cba248">root_node</a>;</div>
+<div class="line"><span class="lineno">   64</span>        <span class="keywordflow">for</span> (<span class="keywordtype">char</span> ch : word) {</div>
+<div class="line"><span class="lineno">   65</span>            <span class="keywordflow">if</span> (curr-&gt;<a class="code hl_variable" href="../../d5/d12/structdata__structures_1_1trie__using__hashmap_1_1_trie_1_1_node.html#a08212cdc99164b59da91b81f45e2f88e">children</a>.find(ch) == curr-&gt;<a class="code hl_variable" href="../../d5/d12/structdata__structures_1_1trie__using__hashmap_1_1_trie_1_1_node.html#a08212cdc99164b59da91b81f45e2f88e">children</a>.end()) {</div>
+<div class="line"><span class="lineno">   66</span>                curr-&gt;<a class="code hl_variable" href="../../d5/d12/structdata__structures_1_1trie__using__hashmap_1_1_trie_1_1_node.html#a08212cdc99164b59da91b81f45e2f88e">children</a>[ch] = std::make_shared&lt;Node&gt;();</div>
+<div class="line"><span class="lineno">   67</span>            }</div>
+<div class="line"><span class="lineno">   68</span>            curr = curr-&gt;<a class="code hl_variable" href="../../d5/d12/structdata__structures_1_1trie__using__hashmap_1_1_trie_1_1_node.html#a08212cdc99164b59da91b81f45e2f88e">children</a>[ch];</div>
+<div class="line"><span class="lineno">   69</span>        }</div>
+<div class="line"><span class="lineno">   70</span> </div>
+<div class="line"><span class="lineno">   71</span>        <span class="keywordflow">if</span> (!curr-&gt;<a class="code hl_variable" href="../../d5/d12/structdata__structures_1_1trie__using__hashmap_1_1_trie_1_1_node.html#a3cdb077745d3dc97212d693132371219">word_end</a> &amp;&amp; curr != <a class="code hl_variable" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#a832072498abeaa52ad43c4fc99cba248">root_node</a>) {</div>
+<div class="line"><span class="lineno">   72</span>            curr-&gt;<a class="code hl_variable" href="../../d5/d12/structdata__structures_1_1trie__using__hashmap_1_1_trie_1_1_node.html#a3cdb077745d3dc97212d693132371219">word_end</a> = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   73</span>        }</div>
+<div class="line"><span class="lineno">   74</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -379,31 +387,31 @@ Here is the call graph for this function:</div>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>list of recommended words </dd></dl>
 <p >&lt; iteratively and recursively get the recommended words</p>
-<div class="fragment"><div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>                                                                {</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::string&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Node&gt;</a> curr = <a class="code hl_variable" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#a832072498abeaa52ad43c4fc99cba248">root_node</a>;</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>        <span class="comment">// traversing until the end of the given prefix in trie</span></div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span> </div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>        <span class="keywordflow">for</span> (<span class="keywordtype">char</span> ch : prefix) {</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>            <span class="keywordflow">if</span> (curr-&gt;children.find(ch) == curr-&gt;children.end()) {</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>                <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>            }</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span> </div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>            curr = curr-&gt;children[ch];</div>
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-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span> </div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>        <span class="comment">// if the given prefix is the only word without children</span></div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>        <span class="keywordflow">if</span> (curr-&gt;word_end &amp;&amp; curr-&gt;children.empty()) {</div>
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-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span> </div>
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-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>            result, curr,</div>
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+<div class="line"><span class="lineno">  191</span>        <span class="comment">// traversing until the end of the given prefix in trie</span></div>
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+<div class="line"><span class="lineno">  201</span>        <span class="comment">// if the given prefix is the only word without children</span></div>
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+<div class="line"><span class="lineno">  208</span>            result, curr,</div>
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 <dl class="section return"><dt>Returns</dt><dd>the largest palindromic substring </dd></dl>
-<div class="fragment"><div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>                                               {</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    <span class="keywordflow">if</span> (prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() &gt; 0) {</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>        <span class="comment">// stuffing characters between the input string to handle cases with</span></div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>        <span class="comment">// even length palindrome</span></div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> stuffed_string = <span class="stringliteral">&quot;&quot;</span>;</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>        <span class="keywordflow">for</span> (<span class="keyword">auto</span> str : prototype) {</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>            stuffed_string += str;</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>            stuffed_string += <span class="stringliteral">&quot;#&quot;</span>;</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>        }</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        stuffed_string = <span class="stringliteral">&quot;@#&quot;</span> + stuffed_string + <span class="stringliteral">&quot;&amp;&quot;</span>;</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span> </div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> palindrome_max_half_length(</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>            stuffed_string.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>(),</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>            0);  <span class="comment">// this array will consist of largest possible half length of</span></div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>                 <span class="comment">// palindrome centered at index (say i with respect to the</span></div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>                 <span class="comment">// stuffed string). This value will be lower bound of half</span></div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>                 <span class="comment">// length since single character is a palindrome in itself.</span></div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span> </div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>        uint64_t bigger_center =</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>            0;  <span class="comment">// this is the index of the center of palindromic</span></div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>                <span class="comment">// substring which would be considered as the larger</span></div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>                <span class="comment">// palindrome, having symmetric halves</span></div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span> </div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        uint64_t <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> = 0;  <span class="comment">// this is the maximum length of the palindrome</span></div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>                             <span class="comment">// from &#39;bigger_center&#39; to the rightmost end</span></div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span> </div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="comment">// i is considered as center lying within one half of the palindrone</span></div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        <span class="comment">// which is centered at &#39;bigger_center&#39;</span></div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        <span class="keywordflow">for</span> (uint64_t i = 1; i &lt; stuffed_string.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - 1; i++) {</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>            <span class="keywordflow">if</span> (i &lt; right) {  <span class="comment">// when i is before right end, considering</span></div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>                              <span class="comment">// &#39;bigger_center&#39; as center of palindrome</span></div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>                uint64_t opposite_to_i =</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>                    2 * bigger_center -</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>                    i;  <span class="comment">// this is the opposite end of string, if</span></div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>                        <span class="comment">// centered at center, and having one end as i</span></div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span> </div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>                <span class="comment">// finding the minimum possible half length among</span></div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>                <span class="comment">// the palindrome on having center at opposite end,</span></div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>                <span class="comment">// and the string between i and right end,</span></div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>                <span class="comment">// considering &#39;bigger_center&#39; as center of palindrome</span></div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>                palindrome_max_half_length[i] = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>                    palindrome_max_half_length[opposite_to_i], right - i);</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>            }</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span> </div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>            <span class="comment">// expanding the palindrome across the maximum stored length in the</span></div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>            <span class="comment">// array, centered at i</span></div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>            <span class="keywordflow">while</span> (stuffed_string[i + (palindrome_max_half_length[i] + 1)] ==</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>                   stuffed_string[i - (palindrome_max_half_length[i] + 1)]) {</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>                palindrome_max_half_length[i]++;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>            }</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span> </div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>            <span class="comment">// if palindrome centered at i exceeds the rightmost end of</span></div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>            <span class="comment">// palindrome centered at &#39;bigger_center&#39;, then i will be made the</span></div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>            <span class="comment">// &#39;bigger_center&#39; and right value will also be updated with respect</span></div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>            <span class="comment">// to center i</span></div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>            <span class="keywordflow">if</span> (i + palindrome_max_half_length[i] &gt; right) {</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>                bigger_center = i;</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> = i + palindrome_max_half_length[i];</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>            }</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>        }</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span> </div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>        <span class="comment">// now extracting the first largest palindrome</span></div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>        uint64_t half_length = 0;   <span class="comment">// half length of the largest palindrome</span></div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        uint64_t center_index = 0;  <span class="comment">// index of center of the largest palindrome</span></div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span> </div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>        <span class="keywordflow">for</span> (uint64_t i = 1; i &lt; stuffed_string.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - 1; i++) {</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>            <span class="keywordflow">if</span> (palindrome_max_half_length[i] &gt; half_length) {</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>                half_length = palindrome_max_half_length[i];</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>                center_index = i;</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>            }</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        }</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span> </div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> palindromic_substring =</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>            <span class="stringliteral">&quot;&quot;</span>;  <span class="comment">// contains the resulting largest palindrome</span></div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span> </div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>        <span class="keywordflow">if</span> (half_length &gt; 0) {</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>            <span class="comment">// extra information: when &#39;#&#39; is the center, then palindromic</span></div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>            <span class="comment">// substring will have even length, else palindromic substring will</span></div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>            <span class="comment">// have odd length</span></div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span> </div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>            uint64_t start =</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>                center_index - half_length +</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>                1;  <span class="comment">// index of first character of palindromic substring</span></div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>            uint64_t <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> =</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>                center_index + half_length -</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>                1;  <span class="comment">// index of last character of palindromic substring</span></div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>            <span class="keywordflow">for</span> (uint64_t index = start; index &lt;= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a>; index += 2) {</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>                palindromic_substring += stuffed_string[index];</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>            }</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>            <span class="comment">// if length = 0, then there does not exist any palindrome of length</span></div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>            <span class="comment">// &gt; 1 so we can assign any character of length 1 from string as the</span></div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>            <span class="comment">// palindromic substring</span></div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>            palindromic_substring = prototype[0];</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>        }</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>        <span class="keywordflow">return</span> palindromic_substring;</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span> </div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>        <span class="comment">// handling case when string is empty</span></div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        <span class="keywordflow">return</span> <span class="stringliteral">&quot;&quot;</span>;</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>    }</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   40</span>                                               {</div>
+<div class="line"><span class="lineno">   41</span>    <span class="keywordflow">if</span> (prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() &gt; 0) {</div>
+<div class="line"><span class="lineno">   42</span>        <span class="comment">// stuffing characters between the input string to handle cases with</span></div>
+<div class="line"><span class="lineno">   43</span>        <span class="comment">// even length palindrome</span></div>
+<div class="line"><span class="lineno">   44</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> stuffed_string = <span class="stringliteral">&quot;&quot;</span>;</div>
+<div class="line"><span class="lineno">   45</span>        <span class="keywordflow">for</span> (<span class="keyword">auto</span> str : prototype) {</div>
+<div class="line"><span class="lineno">   46</span>            stuffed_string += str;</div>
+<div class="line"><span class="lineno">   47</span>            stuffed_string += <span class="stringliteral">&quot;#&quot;</span>;</div>
+<div class="line"><span class="lineno">   48</span>        }</div>
+<div class="line"><span class="lineno">   49</span>        stuffed_string = <span class="stringliteral">&quot;@#&quot;</span> + stuffed_string + <span class="stringliteral">&quot;&amp;&quot;</span>;</div>
+<div class="line"><span class="lineno">   50</span> </div>
+<div class="line"><span class="lineno">   51</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> palindrome_max_half_length(</div>
+<div class="line"><span class="lineno">   52</span>            stuffed_string.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>(),</div>
+<div class="line"><span class="lineno">   53</span>            0);  <span class="comment">// this array will consist of largest possible half length of</span></div>
+<div class="line"><span class="lineno">   54</span>                 <span class="comment">// palindrome centered at index (say i with respect to the</span></div>
+<div class="line"><span class="lineno">   55</span>                 <span class="comment">// stuffed string). This value will be lower bound of half</span></div>
+<div class="line"><span class="lineno">   56</span>                 <span class="comment">// length since single character is a palindrome in itself.</span></div>
+<div class="line"><span class="lineno">   57</span> </div>
+<div class="line"><span class="lineno">   58</span>        uint64_t bigger_center =</div>
+<div class="line"><span class="lineno">   59</span>            0;  <span class="comment">// this is the index of the center of palindromic</span></div>
+<div class="line"><span class="lineno">   60</span>                <span class="comment">// substring which would be considered as the larger</span></div>
+<div class="line"><span class="lineno">   61</span>                <span class="comment">// palindrome, having symmetric halves</span></div>
+<div class="line"><span class="lineno">   62</span> </div>
+<div class="line"><span class="lineno">   63</span>        uint64_t <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> = 0;  <span class="comment">// this is the maximum length of the palindrome</span></div>
+<div class="line"><span class="lineno">   64</span>                             <span class="comment">// from &#39;bigger_center&#39; to the rightmost end</span></div>
+<div class="line"><span class="lineno">   65</span> </div>
+<div class="line"><span class="lineno">   66</span>        <span class="comment">// i is considered as center lying within one half of the palindrone</span></div>
+<div class="line"><span class="lineno">   67</span>        <span class="comment">// which is centered at &#39;bigger_center&#39;</span></div>
+<div class="line"><span class="lineno">   68</span>        <span class="keywordflow">for</span> (uint64_t i = 1; i &lt; stuffed_string.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - 1; i++) {</div>
+<div class="line"><span class="lineno">   69</span>            <span class="keywordflow">if</span> (i &lt; right) {  <span class="comment">// when i is before right end, considering</span></div>
+<div class="line"><span class="lineno">   70</span>                              <span class="comment">// &#39;bigger_center&#39; as center of palindrome</span></div>
+<div class="line"><span class="lineno">   71</span>                uint64_t opposite_to_i =</div>
+<div class="line"><span class="lineno">   72</span>                    2 * bigger_center -</div>
+<div class="line"><span class="lineno">   73</span>                    i;  <span class="comment">// this is the opposite end of string, if</span></div>
+<div class="line"><span class="lineno">   74</span>                        <span class="comment">// centered at center, and having one end as i</span></div>
+<div class="line"><span class="lineno">   75</span> </div>
+<div class="line"><span class="lineno">   76</span>                <span class="comment">// finding the minimum possible half length among</span></div>
+<div class="line"><span class="lineno">   77</span>                <span class="comment">// the palindrome on having center at opposite end,</span></div>
+<div class="line"><span class="lineno">   78</span>                <span class="comment">// and the string between i and right end,</span></div>
+<div class="line"><span class="lineno">   79</span>                <span class="comment">// considering &#39;bigger_center&#39; as center of palindrome</span></div>
+<div class="line"><span class="lineno">   80</span>                palindrome_max_half_length[i] = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(</div>
+<div class="line"><span class="lineno">   81</span>                    palindrome_max_half_length[opposite_to_i], right - i);</div>
+<div class="line"><span class="lineno">   82</span>            }</div>
+<div class="line"><span class="lineno">   83</span> </div>
+<div class="line"><span class="lineno">   84</span>            <span class="comment">// expanding the palindrome across the maximum stored length in the</span></div>
+<div class="line"><span class="lineno">   85</span>            <span class="comment">// array, centered at i</span></div>
+<div class="line"><span class="lineno">   86</span>            <span class="keywordflow">while</span> (stuffed_string[i + (palindrome_max_half_length[i] + 1)] ==</div>
+<div class="line"><span class="lineno">   87</span>                   stuffed_string[i - (palindrome_max_half_length[i] + 1)]) {</div>
+<div class="line"><span class="lineno">   88</span>                palindrome_max_half_length[i]++;</div>
+<div class="line"><span class="lineno">   89</span>            }</div>
+<div class="line"><span class="lineno">   90</span> </div>
+<div class="line"><span class="lineno">   91</span>            <span class="comment">// if palindrome centered at i exceeds the rightmost end of</span></div>
+<div class="line"><span class="lineno">   92</span>            <span class="comment">// palindrome centered at &#39;bigger_center&#39;, then i will be made the</span></div>
+<div class="line"><span class="lineno">   93</span>            <span class="comment">// &#39;bigger_center&#39; and right value will also be updated with respect</span></div>
+<div class="line"><span class="lineno">   94</span>            <span class="comment">// to center i</span></div>
+<div class="line"><span class="lineno">   95</span>            <span class="keywordflow">if</span> (i + palindrome_max_half_length[i] &gt; right) {</div>
+<div class="line"><span class="lineno">   96</span>                bigger_center = i;</div>
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+<div class="line"><span class="lineno">   98</span>            }</div>
+<div class="line"><span class="lineno">   99</span>        }</div>
+<div class="line"><span class="lineno">  100</span> </div>
+<div class="line"><span class="lineno">  101</span>        <span class="comment">// now extracting the first largest palindrome</span></div>
+<div class="line"><span class="lineno">  102</span>        uint64_t half_length = 0;   <span class="comment">// half length of the largest palindrome</span></div>
+<div class="line"><span class="lineno">  103</span>        uint64_t center_index = 0;  <span class="comment">// index of center of the largest palindrome</span></div>
+<div class="line"><span class="lineno">  104</span> </div>
+<div class="line"><span class="lineno">  105</span>        <span class="keywordflow">for</span> (uint64_t i = 1; i &lt; stuffed_string.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - 1; i++) {</div>
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+<div class="line"><span class="lineno">  107</span>                half_length = palindrome_max_half_length[i];</div>
+<div class="line"><span class="lineno">  108</span>                center_index = i;</div>
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+<div class="line"><span class="lineno">  110</span>        }</div>
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+<div class="line"><span class="lineno">  113</span>            <span class="stringliteral">&quot;&quot;</span>;  <span class="comment">// contains the resulting largest palindrome</span></div>
+<div class="line"><span class="lineno">  114</span> </div>
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+<div class="line"><span class="lineno">  134</span>        }</div>
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 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>                   {</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;&quot;</span>) == <span class="stringliteral">&quot;&quot;</span>);</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;abababc&quot;</span>) == <span class="stringliteral">&quot;ababa&quot;</span>);</div>
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-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;DedzefDeD&quot;</span>) == <span class="stringliteral">&quot;DeD&quot;</span>);</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;XZYYXXYZXX&quot;</span>) == <span class="stringliteral">&quot;YXXY&quot;</span>);</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;1sm222m10abc&quot;</span>) == <span class="stringliteral">&quot;m222m&quot;</span>);</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;798989591&quot;</span>) == <span class="stringliteral">&quot;98989&quot;</span>);</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;xacdedcax&quot;</span>) == <span class="stringliteral">&quot;xacdedcax&quot;</span>);</div>
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+<div class="line"><span class="lineno">  151</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;&quot;</span>) == <span class="stringliteral">&quot;&quot;</span>);</div>
+<div class="line"><span class="lineno">  152</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;abababc&quot;</span>) == <span class="stringliteral">&quot;ababa&quot;</span>);</div>
+<div class="line"><span class="lineno">  153</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;cbaabd&quot;</span>) == <span class="stringliteral">&quot;baab&quot;</span>);</div>
+<div class="line"><span class="lineno">  154</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;DedzefDeD&quot;</span>) == <span class="stringliteral">&quot;DeD&quot;</span>);</div>
+<div class="line"><span class="lineno">  155</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;XZYYXXYZXX&quot;</span>) == <span class="stringliteral">&quot;YXXY&quot;</span>);</div>
+<div class="line"><span class="lineno">  156</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;1sm222m10abc&quot;</span>) == <span class="stringliteral">&quot;m222m&quot;</span>);</div>
+<div class="line"><span class="lineno">  157</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;798989591&quot;</span>) == <span class="stringliteral">&quot;98989&quot;</span>);</div>
+<div class="line"><span class="lineno">  158</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;xacdedcax&quot;</span>) == <span class="stringliteral">&quot;xacdedcax&quot;</span>);</div>
+<div class="line"><span class="lineno">  159</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;xaccax&quot;</span>) == <span class="stringliteral">&quot;xaccax&quot;</span>);</div>
+<div class="line"><span class="lineno">  160</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;a&quot;</span>) == <span class="stringliteral">&quot;a&quot;</span>);</div>
+<div class="line"><span class="lineno">  161</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;xy&quot;</span>) == <span class="stringliteral">&quot;x&quot;</span>);</div>
+<div class="line"><span class="lineno">  162</span>    assert(strings::manacher::manacher(<span class="stringliteral">&quot;abced&quot;</span>) == <span class="stringliteral">&quot;a&quot;</span>);</div>
+<div class="line"><span class="lineno">  163</span> </div>
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 <dl class="section return"><dt>Returns</dt><dd>new decrypted text </dd></dl>
-<div class="fragment"><div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>                                                                  {</div>
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+<div class="line"><span class="lineno">   63</span>            <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;c : text) { <span class="comment">// Going through each character</span></div>
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+<div class="line"><span class="lineno">   52</span>            }</div>
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-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> decrypted1 = <a class="code hl_function" href="../../d3/d4c/xor__cipher_8cpp.html#a6099b7e0f1793f418d2c1befca8355a4">ciphers::XOR::decrypt</a>(encrypted1, 17);</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    assert(text1 == decrypted1);</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Original text : &quot;</span> &lt;&lt; text1;</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; , Encrypted text (with key = 17) : &quot;</span> &lt;&lt; encrypted1;</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; , Decrypted text : &quot;</span>&lt;&lt; decrypted1 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><span class="lineno">   76</span>    <span class="comment">// matching_indexes1 gets the indexes where pattern1 exists in text1</span></div>
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+<div class="line"><span class="lineno">   78</span>    assert((matching_indexes1 == <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>{10, 14, 18, 30, 33}));</div>
+<div class="line"><span class="lineno">   79</span> </div>
+<div class="line"><span class="lineno">   80</span>    <span class="comment">// corner case</span></div>
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+<div class="line"><span class="lineno">   82</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> pattern2 = <span class="stringliteral">&quot;abc&quot;</span>;</div>
+<div class="line"><span class="lineno">   83</span> </div>
+<div class="line"><span class="lineno">   84</span>    <span class="comment">// matching_indexes2 gets the indexes where pattern2 exists in text2</span></div>
+<div class="line"><span class="lineno">   85</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> matching_indexes2 = <a class="code hl_function" href="../../d3/d80/z__function_8cpp.html#ac186ca3ac3a69b5e52543bb13fe46db8">find_pat_in_text</a>(pattern2, text2);</div>
+<div class="line"><span class="lineno">   86</span>    assert((matching_indexes2 == <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>{}));</div>
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 <p >Example 3: Input: s = "catsandog", wordDict = ["cats", "dog", "sand", "and", "cat"] Output: false</p>
-<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/axayjha" target="_blank">Akshay Anand</a> </dd></dl>
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 <dd>
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 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>           {</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>    <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// call the test function :)</span></div>
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-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>    <span class="comment">// the complete string</span></div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s = <span class="stringliteral">&quot;applepenapple&quot;</span>;</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>    <span class="comment">// the dictionary to be used</span></div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::string&gt;</a> wordDict = {<span class="stringliteral">&quot;apple&quot;</span>, <span class="stringliteral">&quot;pen&quot;</span>};</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span> </div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>    <span class="comment">// should return true, as applepenapple can be segmented as apple + pen +</span></div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>    <span class="comment">// apple</span></div>
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-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>}</div>
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+<div class="line"><span class="lineno">  175</span>    <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// call the test function :)</span></div>
+<div class="line"><span class="lineno">  176</span> </div>
+<div class="line"><span class="lineno">  177</span>    <span class="comment">// the complete string</span></div>
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+<div class="line"><span class="lineno">  179</span>    <span class="comment">// the dictionary to be used</span></div>
+<div class="line"><span class="lineno">  180</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::string&gt;</a> wordDict = {<span class="stringliteral">&quot;apple&quot;</span>, <span class="stringliteral">&quot;pen&quot;</span>};</div>
+<div class="line"><span class="lineno">  181</span> </div>
+<div class="line"><span class="lineno">  182</span>    <span class="comment">// should return true, as applepenapple can be segmented as apple + pen +</span></div>
+<div class="line"><span class="lineno">  183</span>    <span class="comment">// apple</span></div>
+<div class="line"><span class="lineno">  184</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#afe4dcd6fd5282e535685361cba645d7c">dynamic_programming::word_break::wordBreak</a>(s, wordDict)</div>
+<div class="line"><span class="lineno">  185</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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 <p>Test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>                   {</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>    <span class="comment">// the complete string</span></div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s = <span class="stringliteral">&quot;applepenapple&quot;</span>;</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>    <span class="comment">// the dictionary to be used</span></div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::string&gt;</a> wordDict = {<span class="stringliteral">&quot;apple&quot;</span>, <span class="stringliteral">&quot;pen&quot;</span>};</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span> </div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>    assert(dynamic_programming::word_break::wordBreak(s, wordDict));</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span> </div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>    <span class="comment">// should return true, as applepenapple can be segmented as apple + pen +</span></div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>    <span class="comment">// apple</span></div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#afe4dcd6fd5282e535685361cba645d7c">dynamic_programming::word_break::wordBreak</a>(s, wordDict)</div>
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-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test implementation passed!\n&quot;</span>;</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  156</span>                   {</div>
+<div class="line"><span class="lineno">  157</span>    <span class="comment">// the complete string</span></div>
+<div class="line"><span class="lineno">  158</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s = <span class="stringliteral">&quot;applepenapple&quot;</span>;</div>
+<div class="line"><span class="lineno">  159</span>    <span class="comment">// the dictionary to be used</span></div>
+<div class="line"><span class="lineno">  160</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::string&gt;</a> wordDict = {<span class="stringliteral">&quot;apple&quot;</span>, <span class="stringliteral">&quot;pen&quot;</span>};</div>
+<div class="line"><span class="lineno">  161</span> </div>
+<div class="line"><span class="lineno">  162</span>    assert(dynamic_programming::word_break::wordBreak(s, wordDict));</div>
+<div class="line"><span class="lineno">  163</span> </div>
+<div class="line"><span class="lineno">  164</span>    <span class="comment">// should return true, as applepenapple can be segmented as apple + pen +</span></div>
+<div class="line"><span class="lineno">  165</span>    <span class="comment">// apple</span></div>
+<div class="line"><span class="lineno">  166</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#afe4dcd6fd5282e535685361cba645d7c">dynamic_programming::word_break::wordBreak</a>(s, wordDict)</div>
+<div class="line"><span class="lineno">  167</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  168</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test implementation passed!\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  169</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -432,23 +432,23 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if s can be formed by a combination of strings present in wordDict </dd>
 <dd>
 <code>false</code> otherwise </dd></dl>
-<div class="fragment"><div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>                                                                         {</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    <span class="comment">// unordered set to store words in the dictionary for constant time</span></div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    <span class="comment">// search</span></div>
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-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    }</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    <span class="comment">// a vector to be used for memoization, whose value at index i will</span></div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>    <span class="comment">// tell if the string s can be segmented (correctly) at position i.</span></div>
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-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    <span class="comment">// calling check method with position = 0, to check from left</span></div>
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+<div class="line"><span class="lineno">  132</span>    <span class="comment">// unordered set to store words in the dictionary for constant time</span></div>
+<div class="line"><span class="lineno">  133</span>    <span class="comment">// search</span></div>
+<div class="line"><span class="lineno">  134</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_set.html">std::unordered_set&lt;std::string&gt;</a> strSet;</div>
+<div class="line"><span class="lineno">  135</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;s : wordDict) {</div>
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+<div class="line"><span class="lineno">  137</span>    }</div>
+<div class="line"><span class="lineno">  138</span>    <span class="comment">// a vector to be used for memoization, whose value at index i will</span></div>
+<div class="line"><span class="lineno">  139</span>    <span class="comment">// tell if the string s can be segmented (correctly) at position i.</span></div>
+<div class="line"><span class="lineno">  140</span>    <span class="comment">// initializing it with INT_MAX (which will denote no solution)</span></div>
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+<div class="line"><span class="lineno">  143</span>    <span class="comment">// calling check method with position = 0, to check from left</span></div>
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+<div class="line"><span class="lineno">  145</span>    <span class="comment">// manner</span></div>
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-<div class="line"><a id="l00684" name="l00684"></a><span class="lineno">  684</span>    <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00685" name="l00685"></a><span class="lineno">  685</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  663</span>                                              {</div>
+<div class="line"><span class="lineno">  664</span>    assert(tree != <span class="keyword">nullptr</span>);</div>
+<div class="line"><span class="lineno">  665</span> </div>
+<div class="line"><span class="lineno">  666</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/unique_ptr.html">std::unique_ptr&lt;Node&gt;</a> split_node;</div>
+<div class="line"><span class="lineno">  667</span> </div>
+<div class="line"><span class="lineno">  668</span>    <span class="keywordflow">if</span> (tree-&gt;Contains(item)) {</div>
+<div class="line"><span class="lineno">  669</span>        <span class="comment">// return nullptr indicate current node not overflow</span></div>
+<div class="line"><span class="lineno">  670</span>        <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  671</span>    }</div>
+<div class="line"><span class="lineno">  672</span> </div>
+<div class="line"><span class="lineno">  673</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *next_node = tree-&gt;GetNextPossibleChild(item);</div>
+<div class="line"><span class="lineno">  674</span>    <span class="keywordflow">if</span> (next_node) {</div>
+<div class="line"><span class="lineno">  675</span>        split_node.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/unique_ptr/reset.html">reset</a>(<a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a6749ebb40710c9752a2771eda03c6b3e">Insert</a>(next_node, item));</div>
+<div class="line"><span class="lineno">  676</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  677</span>        split_node.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/unique_ptr/reset.html">reset</a>(<span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>(item));</div>
+<div class="line"><span class="lineno">  678</span>    }</div>
+<div class="line"><span class="lineno">  679</span> </div>
+<div class="line"><span class="lineno">  680</span>    <span class="keywordflow">if</span> (split_node) {</div>
+<div class="line"><span class="lineno">  681</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a11f0d016dff7f7e62b3dddb9fdf47805">MergeNode</a>(tree, split_node.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/unique_ptr/get.html">get</a>());</div>
+<div class="line"><span class="lineno">  682</span>    }</div>
+<div class="line"><span class="lineno">  683</span> </div>
+<div class="line"><span class="lineno">  684</span>    <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  685</span>}</div>
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 <div class="ttc" id="aclassdata__structures_1_1tree__234_1_1_tree234_html_a6749ebb40710c9752a2771eda03c6b3e"><div class="ttname"><a href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a6749ebb40710c9752a2771eda03c6b3e">data_structures::tree_234::Tree234::Insert</a></div><div class="ttdeci">void Insert(int64_t item)</div><div class="ttdoc">Insert item to tree.</div><div class="ttdef"><b>Definition:</b> tree_234.cpp:655</div></div>
 <div class="ttc" id="aget_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/memory/unique_ptr/get.html">std::unique_ptr::get</a></div><div class="ttdeci">T get(T... args)</div></div>
@@ -522,19 +522,19 @@ Here is the call graph for this function:</div>
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-<div class="fragment"><div class="line"><a id="l00637" name="l00637"></a><span class="lineno">  637</span>                                          {</div>
-<div class="line"><a id="l00638" name="l00638"></a><span class="lineno">  638</span>    <span class="keywordflow">if</span> (!<a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>) {</div>
-<div class="line"><a id="l00639" name="l00639"></a><span class="lineno">  639</span>        <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a> = <span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>(item);</div>
-<div class="line"><a id="l00640" name="l00640"></a><span class="lineno">  640</span>        <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00641" name="l00641"></a><span class="lineno">  641</span>    }</div>
-<div class="line"><a id="l00642" name="l00642"></a><span class="lineno">  642</span> </div>
-<div class="line"><a id="l00643" name="l00643"></a><span class="lineno">  643</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *split_node = <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a6749ebb40710c9752a2771eda03c6b3e">Insert</a>(<a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>, item);</div>
-<div class="line"><a id="l00644" name="l00644"></a><span class="lineno">  644</span> </div>
-<div class="line"><a id="l00645" name="l00645"></a><span class="lineno">  645</span>    <span class="comment">// if root has split, then update root_</span></div>
-<div class="line"><a id="l00646" name="l00646"></a><span class="lineno">  646</span>    <span class="keywordflow">if</span> (split_node) {</div>
-<div class="line"><a id="l00647" name="l00647"></a><span class="lineno">  647</span>        <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a> = split_node;</div>
-<div class="line"><a id="l00648" name="l00648"></a><span class="lineno">  648</span>    }</div>
-<div class="line"><a id="l00649" name="l00649"></a><span class="lineno">  649</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  637</span>                                          {</div>
+<div class="line"><span class="lineno">  638</span>    <span class="keywordflow">if</span> (!<a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>) {</div>
+<div class="line"><span class="lineno">  639</span>        <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a> = <span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>(item);</div>
+<div class="line"><span class="lineno">  640</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  641</span>    }</div>
+<div class="line"><span class="lineno">  642</span> </div>
+<div class="line"><span class="lineno">  643</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *split_node = <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a6749ebb40710c9752a2771eda03c6b3e">Insert</a>(<a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>, item);</div>
+<div class="line"><span class="lineno">  644</span> </div>
+<div class="line"><span class="lineno">  645</span>    <span class="comment">// if root has split, then update root_</span></div>
+<div class="line"><span class="lineno">  646</span>    <span class="keywordflow">if</span> (split_node) {</div>
+<div class="line"><span class="lineno">  647</span>        <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a> = split_node;</div>
+<div class="line"><span class="lineno">  648</span>    }</div>
+<div class="line"><span class="lineno">  649</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -575,53 +575,53 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00585" name="l00585"></a><span class="lineno">  585</span>                                         {</div>
-<div class="line"><a id="l00586" name="l00586"></a><span class="lineno">  586</span>    <span class="keywordflow">if</span> (!<a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>) {</div>
-<div class="line"><a id="l00587" name="l00587"></a><span class="lineno">  587</span>        <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a> = <span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>(item);</div>
-<div class="line"><a id="l00588" name="l00588"></a><span class="lineno">  588</span>        <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00589" name="l00589"></a><span class="lineno">  589</span>    }</div>
-<div class="line"><a id="l00590" name="l00590"></a><span class="lineno">  590</span> </div>
-<div class="line"><a id="l00591" name="l00591"></a><span class="lineno">  591</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *parent = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00592" name="l00592"></a><span class="lineno">  592</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>;</div>
-<div class="line"><a id="l00593" name="l00593"></a><span class="lineno">  593</span> </div>
-<div class="line"><a id="l00594" name="l00594"></a><span class="lineno">  594</span>    <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
-<div class="line"><a id="l00595" name="l00595"></a><span class="lineno">  595</span>        <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>) {</div>
-<div class="line"><a id="l00596" name="l00596"></a><span class="lineno">  596</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/unique_ptr.html">std::unique_ptr&lt;Node&gt;</a> tmp(<span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>(item));</div>
-<div class="line"><a id="l00597" name="l00597"></a><span class="lineno">  597</span>            <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#ad37e29e2a4a6cc0eb65cbd5595e1da95">MergeNodeNotFull</a>(parent, tmp.get());</div>
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-<div class="line"><a id="l00601" name="l00601"></a><span class="lineno">  601</span>        <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;Contains(item)) {</div>
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-<div class="line"><a id="l00605" name="l00605"></a><span class="lineno">  605</span>        <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;IsFull()) {</div>
-<div class="line"><a id="l00606" name="l00606"></a><span class="lineno">  606</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a370b625ca9f16bbef2b65e024ef78ea9">SplitNode</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>);</div>
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-<div class="line"><a id="l00608" name="l00608"></a><span class="lineno">  608</span>            <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *cur_node = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00609" name="l00609"></a><span class="lineno">  609</span> </div>
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-<div class="line"><a id="l00615" name="l00615"></a><span class="lineno">  615</span> </div>
-<div class="line"><a id="l00616" name="l00616"></a><span class="lineno">  616</span>            <span class="keywordflow">if</span> (!parent) {</div>
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-<div class="line"><a id="l00624" name="l00624"></a><span class="lineno">  624</span> </div>
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-<div class="line"><a id="l00627" name="l00627"></a><span class="lineno">  627</span> </div>
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+<div class="line"><span class="lineno">  604</span> </div>
+<div class="line"><span class="lineno">  605</span>        <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;IsFull()) {</div>
+<div class="line"><span class="lineno">  606</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a370b625ca9f16bbef2b65e024ef78ea9">SplitNode</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>);</div>
+<div class="line"><span class="lineno">  607</span> </div>
+<div class="line"><span class="lineno">  608</span>            <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *cur_node = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  609</span> </div>
+<div class="line"><span class="lineno">  610</span>            <span class="keywordflow">if</span> (item &lt; node-&gt;GetItem(0)) {</div>
+<div class="line"><span class="lineno">  611</span>                cur_node = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetChild(0);</div>
+<div class="line"><span class="lineno">  612</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  613</span>                cur_node = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetChild(1);</div>
+<div class="line"><span class="lineno">  614</span>            }</div>
+<div class="line"><span class="lineno">  615</span> </div>
+<div class="line"><span class="lineno">  616</span>            <span class="keywordflow">if</span> (!parent) {</div>
+<div class="line"><span class="lineno">  617</span>                <span class="comment">// for the root node parent is nullptr, we simply assign the</span></div>
+<div class="line"><span class="lineno">  618</span>                <span class="comment">// split parent to root_</span></div>
+<div class="line"><span class="lineno">  619</span>                <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a> = <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
+<div class="line"><span class="lineno">  620</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  621</span>                <span class="comment">// merge the split parent to its origin parent</span></div>
+<div class="line"><span class="lineno">  622</span>                <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#ad37e29e2a4a6cc0eb65cbd5595e1da95">MergeNodeNotFull</a>(parent, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>);</div>
+<div class="line"><span class="lineno">  623</span>            }</div>
+<div class="line"><span class="lineno">  624</span> </div>
+<div class="line"><span class="lineno">  625</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = cur_node;</div>
+<div class="line"><span class="lineno">  626</span>        }</div>
+<div class="line"><span class="lineno">  627</span> </div>
+<div class="line"><span class="lineno">  628</span>        parent = <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
+<div class="line"><span class="lineno">  629</span>        <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = parent-&gt;GetNextPossibleChild(item);</div>
+<div class="line"><span class="lineno">  630</span>    }</div>
+<div class="line"><span class="lineno">  631</span>}</div>
 <div class="ttc" id="aclassdata__structures_1_1tree__234_1_1_tree234_html_a370b625ca9f16bbef2b65e024ef78ea9"><div class="ttname"><a href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a370b625ca9f16bbef2b65e024ef78ea9">data_structures::tree_234::Tree234::SplitNode</a></div><div class="ttdeci">Node * SplitNode(Node *node)</div><div class="ttdoc">Split a 4-node to 1 parent and 2 children, and return the parent node.</div><div class="ttdef"><b>Definition:</b> tree_234.cpp:745</div></div>
 <div class="ttc" id="aclassdata__structures_1_1tree__234_1_1_tree234_html_ad37e29e2a4a6cc0eb65cbd5595e1da95"><div class="ttname"><a href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#ad37e29e2a4a6cc0eb65cbd5595e1da95">data_structures::tree_234::Tree234::MergeNodeNotFull</a></div><div class="ttdeci">void MergeNodeNotFull(Node *dst_node, Node *node)</div><div class="ttdoc">Merge node to a not-full target node.</div><div class="ttdef"><b>Definition:</b> tree_234.cpp:730</div></div>
 <div class="ttc" id="ahash__search_8cpp_html_a8ca8dcb494104d273679e219e53d0555"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a></div><div class="ttdeci">struct list node</div></div>
@@ -672,18 +672,18 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00869" name="l00869"></a><span class="lineno">  869</span>                                                   {</div>
-<div class="line"><a id="l00870" name="l00870"></a><span class="lineno">  870</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> = parent-&gt;GetItemLeftChild(index);</div>
-<div class="line"><a id="l00871" name="l00871"></a><span class="lineno">  871</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> = parent-&gt;GetItemRightChild(index);</div>
-<div class="line"><a id="l00872" name="l00872"></a><span class="lineno">  872</span> </div>
-<div class="line"><a id="l00873" name="l00873"></a><span class="lineno">  873</span>    assert(right &amp;&amp; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>-&gt;Is34Node());</div>
-<div class="line"><a id="l00874" name="l00874"></a><span class="lineno">  874</span>    assert(left &amp;&amp; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>-&gt;Is2Node());</div>
-<div class="line"><a id="l00875" name="l00875"></a><span class="lineno">  875</span> </div>
-<div class="line"><a id="l00876" name="l00876"></a><span class="lineno">  876</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>-&gt;InsertItemByIndex(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>-&gt;GetCount(), parent-&gt;GetItem(index),</div>
-<div class="line"><a id="l00877" name="l00877"></a><span class="lineno">  877</span>                            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>-&gt;GetLeftmostChild(), <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00878" name="l00878"></a><span class="lineno">  878</span>    parent-&gt;SetItem(index, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>-&gt;GetMinItem());</div>
-<div class="line"><a id="l00879" name="l00879"></a><span class="lineno">  879</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>-&gt;RemoveItemByIndex(0, <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00880" name="l00880"></a><span class="lineno">  880</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  869</span>                                                   {</div>
+<div class="line"><span class="lineno">  870</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> = parent-&gt;GetItemLeftChild(index);</div>
+<div class="line"><span class="lineno">  871</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> = parent-&gt;GetItemRightChild(index);</div>
+<div class="line"><span class="lineno">  872</span> </div>
+<div class="line"><span class="lineno">  873</span>    assert(right &amp;&amp; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>-&gt;Is34Node());</div>
+<div class="line"><span class="lineno">  874</span>    assert(left &amp;&amp; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>-&gt;Is2Node());</div>
+<div class="line"><span class="lineno">  875</span> </div>
+<div class="line"><span class="lineno">  876</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>-&gt;InsertItemByIndex(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>-&gt;GetCount(), parent-&gt;GetItem(index),</div>
+<div class="line"><span class="lineno">  877</span>                            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>-&gt;GetLeftmostChild(), <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  878</span>    parent-&gt;SetItem(index, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>-&gt;GetMinItem());</div>
+<div class="line"><span class="lineno">  879</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>-&gt;RemoveItemByIndex(0, <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  880</span>}</div>
 <div class="ttc" id="aleft_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::left</a></div><div class="ttdeci">T left(T... args)</div></div>
 </div><!-- fragment -->
 </div>
@@ -732,34 +732,34 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>the merged 4-node </dd></dl>
-<div class="fragment"><div class="line"><a id="l00895" name="l00895"></a><span class="lineno">  895</span>                                               {</div>
-<div class="line"><a id="l00896" name="l00896"></a><span class="lineno">  896</span>    assert(parent);</div>
-<div class="line"><a id="l00897" name="l00897"></a><span class="lineno">  897</span> </div>
-<div class="line"><a id="l00898" name="l00898"></a><span class="lineno">  898</span>    <span class="comment">// bool is_parent_2node = parent-&gt;Is2Node();</span></div>
-<div class="line"><a id="l00899" name="l00899"></a><span class="lineno">  899</span> </div>
-<div class="line"><a id="l00900" name="l00900"></a><span class="lineno">  900</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *left_child = parent-&gt;GetItemLeftChild(index);</div>
-<div class="line"><a id="l00901" name="l00901"></a><span class="lineno">  901</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *right_child = parent-&gt;GetItemRightChild(index);</div>
-<div class="line"><a id="l00902" name="l00902"></a><span class="lineno">  902</span> </div>
-<div class="line"><a id="l00903" name="l00903"></a><span class="lineno">  903</span>    assert(left_child-&gt;Is2Node() &amp;&amp; right_child-&gt;Is2Node());</div>
-<div class="line"><a id="l00904" name="l00904"></a><span class="lineno">  904</span> </div>
-<div class="line"><a id="l00905" name="l00905"></a><span class="lineno">  905</span>    int64_t item = parent-&gt;GetItem(index);</div>
-<div class="line"><a id="l00906" name="l00906"></a><span class="lineno">  906</span> </div>
-<div class="line"><a id="l00907" name="l00907"></a><span class="lineno">  907</span>    <span class="comment">// 1. merge parent&#39;s item and right child to left child</span></div>
-<div class="line"><a id="l00908" name="l00908"></a><span class="lineno">  908</span>    left_child-&gt;SetItem(1, item);</div>
-<div class="line"><a id="l00909" name="l00909"></a><span class="lineno">  909</span>    left_child-&gt;SetItem(2, right_child-&gt;GetItem(0));</div>
-<div class="line"><a id="l00910" name="l00910"></a><span class="lineno">  910</span>    left_child-&gt;SetChild(2, right_child-&gt;GetChild(0));</div>
-<div class="line"><a id="l00911" name="l00911"></a><span class="lineno">  911</span>    left_child-&gt;SetChild(3, right_child-&gt;GetChild(1));</div>
-<div class="line"><a id="l00912" name="l00912"></a><span class="lineno">  912</span> </div>
-<div class="line"><a id="l00913" name="l00913"></a><span class="lineno">  913</span>    left_child-&gt;SetCount(3);</div>
-<div class="line"><a id="l00914" name="l00914"></a><span class="lineno">  914</span> </div>
-<div class="line"><a id="l00915" name="l00915"></a><span class="lineno">  915</span>    <span class="comment">// 2. remove the parent&#39;s item</span></div>
-<div class="line"><a id="l00916" name="l00916"></a><span class="lineno">  916</span>    parent-&gt;RemoveItemByIndex(index, <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00917" name="l00917"></a><span class="lineno">  917</span> </div>
-<div class="line"><a id="l00918" name="l00918"></a><span class="lineno">  918</span>    <span class="comment">// 3. delete the unused right child</span></div>
-<div class="line"><a id="l00919" name="l00919"></a><span class="lineno">  919</span>    <span class="keyword">delete</span> right_child;</div>
-<div class="line"><a id="l00920" name="l00920"></a><span class="lineno">  920</span> </div>
-<div class="line"><a id="l00921" name="l00921"></a><span class="lineno">  921</span>    <span class="keywordflow">return</span> left_child;</div>
-<div class="line"><a id="l00922" name="l00922"></a><span class="lineno">  922</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  895</span>                                               {</div>
+<div class="line"><span class="lineno">  896</span>    assert(parent);</div>
+<div class="line"><span class="lineno">  897</span> </div>
+<div class="line"><span class="lineno">  898</span>    <span class="comment">// bool is_parent_2node = parent-&gt;Is2Node();</span></div>
+<div class="line"><span class="lineno">  899</span> </div>
+<div class="line"><span class="lineno">  900</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *left_child = parent-&gt;GetItemLeftChild(index);</div>
+<div class="line"><span class="lineno">  901</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *right_child = parent-&gt;GetItemRightChild(index);</div>
+<div class="line"><span class="lineno">  902</span> </div>
+<div class="line"><span class="lineno">  903</span>    assert(left_child-&gt;Is2Node() &amp;&amp; right_child-&gt;Is2Node());</div>
+<div class="line"><span class="lineno">  904</span> </div>
+<div class="line"><span class="lineno">  905</span>    int64_t item = parent-&gt;GetItem(index);</div>
+<div class="line"><span class="lineno">  906</span> </div>
+<div class="line"><span class="lineno">  907</span>    <span class="comment">// 1. merge parent&#39;s item and right child to left child</span></div>
+<div class="line"><span class="lineno">  908</span>    left_child-&gt;SetItem(1, item);</div>
+<div class="line"><span class="lineno">  909</span>    left_child-&gt;SetItem(2, right_child-&gt;GetItem(0));</div>
+<div class="line"><span class="lineno">  910</span>    left_child-&gt;SetChild(2, right_child-&gt;GetChild(0));</div>
+<div class="line"><span class="lineno">  911</span>    left_child-&gt;SetChild(3, right_child-&gt;GetChild(1));</div>
+<div class="line"><span class="lineno">  912</span> </div>
+<div class="line"><span class="lineno">  913</span>    left_child-&gt;SetCount(3);</div>
+<div class="line"><span class="lineno">  914</span> </div>
+<div class="line"><span class="lineno">  915</span>    <span class="comment">// 2. remove the parent&#39;s item</span></div>
+<div class="line"><span class="lineno">  916</span>    parent-&gt;RemoveItemByIndex(index, <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  917</span> </div>
+<div class="line"><span class="lineno">  918</span>    <span class="comment">// 3. delete the unused right child</span></div>
+<div class="line"><span class="lineno">  919</span>    <span class="keyword">delete</span> right_child;</div>
+<div class="line"><span class="lineno">  920</span> </div>
+<div class="line"><span class="lineno">  921</span>    <span class="keywordflow">return</span> left_child;</div>
+<div class="line"><span class="lineno">  922</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -807,25 +807,25 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>overflow node of this level </dd></dl>
-<div class="fragment"><div class="line"><a id="l00700" name="l00700"></a><span class="lineno">  700</span>                                                   {</div>
-<div class="line"><a id="l00701" name="l00701"></a><span class="lineno">  701</span>    assert(dst_node != <span class="keyword">nullptr</span> &amp;&amp; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> != <span class="keyword">nullptr</span>);</div>
-<div class="line"><a id="l00702" name="l00702"></a><span class="lineno">  702</span> </div>
-<div class="line"><a id="l00703" name="l00703"></a><span class="lineno">  703</span>    <span class="keywordflow">if</span> (!dst_node-&gt;IsFull()) {</div>
-<div class="line"><a id="l00704" name="l00704"></a><span class="lineno">  704</span>        <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#ad37e29e2a4a6cc0eb65cbd5595e1da95">MergeNodeNotFull</a>(dst_node, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>);</div>
-<div class="line"><a id="l00705" name="l00705"></a><span class="lineno">  705</span>        <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00706" name="l00706"></a><span class="lineno">  706</span>    }</div>
-<div class="line"><a id="l00707" name="l00707"></a><span class="lineno">  707</span> </div>
-<div class="line"><a id="l00708" name="l00708"></a><span class="lineno">  708</span>    dst_node = <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a370b625ca9f16bbef2b65e024ef78ea9">SplitNode</a>(dst_node);</div>
-<div class="line"><a id="l00709" name="l00709"></a><span class="lineno">  709</span> </div>
-<div class="line"><a id="l00710" name="l00710"></a><span class="lineno">  710</span>    <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(0) &lt; dst_node-&gt;GetItem(0)) {</div>
-<div class="line"><a id="l00711" name="l00711"></a><span class="lineno">  711</span>        <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#ad37e29e2a4a6cc0eb65cbd5595e1da95">MergeNodeNotFull</a>(dst_node-&gt;GetChild(0), <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>);</div>
-<div class="line"><a id="l00712" name="l00712"></a><span class="lineno">  712</span> </div>
-<div class="line"><a id="l00713" name="l00713"></a><span class="lineno">  713</span>    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00714" name="l00714"></a><span class="lineno">  714</span>        <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#ad37e29e2a4a6cc0eb65cbd5595e1da95">MergeNodeNotFull</a>(dst_node-&gt;GetChild(1), <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>);</div>
-<div class="line"><a id="l00715" name="l00715"></a><span class="lineno">  715</span>    }</div>
-<div class="line"><a id="l00716" name="l00716"></a><span class="lineno">  716</span> </div>
-<div class="line"><a id="l00717" name="l00717"></a><span class="lineno">  717</span>    <span class="keywordflow">return</span> dst_node;</div>
-<div class="line"><a id="l00718" name="l00718"></a><span class="lineno">  718</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  700</span>                                                   {</div>
+<div class="line"><span class="lineno">  701</span>    assert(dst_node != <span class="keyword">nullptr</span> &amp;&amp; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> != <span class="keyword">nullptr</span>);</div>
+<div class="line"><span class="lineno">  702</span> </div>
+<div class="line"><span class="lineno">  703</span>    <span class="keywordflow">if</span> (!dst_node-&gt;IsFull()) {</div>
+<div class="line"><span class="lineno">  704</span>        <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#ad37e29e2a4a6cc0eb65cbd5595e1da95">MergeNodeNotFull</a>(dst_node, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>);</div>
+<div class="line"><span class="lineno">  705</span>        <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  706</span>    }</div>
+<div class="line"><span class="lineno">  707</span> </div>
+<div class="line"><span class="lineno">  708</span>    dst_node = <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a370b625ca9f16bbef2b65e024ef78ea9">SplitNode</a>(dst_node);</div>
+<div class="line"><span class="lineno">  709</span> </div>
+<div class="line"><span class="lineno">  710</span>    <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(0) &lt; dst_node-&gt;GetItem(0)) {</div>
+<div class="line"><span class="lineno">  711</span>        <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#ad37e29e2a4a6cc0eb65cbd5595e1da95">MergeNodeNotFull</a>(dst_node-&gt;GetChild(0), <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>);</div>
+<div class="line"><span class="lineno">  712</span> </div>
+<div class="line"><span class="lineno">  713</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  714</span>        <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#ad37e29e2a4a6cc0eb65cbd5595e1da95">MergeNodeNotFull</a>(dst_node-&gt;GetChild(1), <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>);</div>
+<div class="line"><span class="lineno">  715</span>    }</div>
+<div class="line"><span class="lineno">  716</span> </div>
+<div class="line"><span class="lineno">  717</span>    <span class="keywordflow">return</span> dst_node;</div>
+<div class="line"><span class="lineno">  718</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -878,14 +878,14 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00730" name="l00730"></a><span class="lineno">  730</span>                                                         {</div>
-<div class="line"><a id="l00731" name="l00731"></a><span class="lineno">  731</span>    assert(dst_node &amp;&amp; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> &amp;&amp; !dst_node-&gt;IsFull() &amp;&amp; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;Is2Node());</div>
-<div class="line"><a id="l00732" name="l00732"></a><span class="lineno">  732</span> </div>
-<div class="line"><a id="l00733" name="l00733"></a><span class="lineno">  733</span>    int8_t i = dst_node-&gt;InsertItem(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(0));</div>
-<div class="line"><a id="l00734" name="l00734"></a><span class="lineno">  734</span> </div>
-<div class="line"><a id="l00735" name="l00735"></a><span class="lineno">  735</span>    dst_node-&gt;SetChild(i, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetChild(0));</div>
-<div class="line"><a id="l00736" name="l00736"></a><span class="lineno">  736</span>    dst_node-&gt;SetChild(i + 1, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetChild(1));</div>
-<div class="line"><a id="l00737" name="l00737"></a><span class="lineno">  737</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  730</span>                                                         {</div>
+<div class="line"><span class="lineno">  731</span>    assert(dst_node &amp;&amp; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> &amp;&amp; !dst_node-&gt;IsFull() &amp;&amp; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;Is2Node());</div>
+<div class="line"><span class="lineno">  732</span> </div>
+<div class="line"><span class="lineno">  733</span>    int8_t i = dst_node-&gt;InsertItem(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(0));</div>
+<div class="line"><span class="lineno">  734</span> </div>
+<div class="line"><span class="lineno">  735</span>    dst_node-&gt;SetChild(i, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetChild(0));</div>
+<div class="line"><span class="lineno">  736</span>    dst_node-&gt;SetChild(i + 1, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetChild(1));</div>
+<div class="line"><span class="lineno">  737</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -921,87 +921,87 @@ Here is the call graph for this function:</div>
 <p >This is a helper structure to do a level order traversal to print the tree.</p>
 <p >&lt; tree node</p>
 <p >&lt; node index of level order that used when draw the link between child and parent</p>
-<div class="fragment"><div class="line"><a id="l01131" name="l01131"></a><span class="lineno"> 1131</span>                                         {</div>
-<div class="line"><a id="l01132" name="l01132"></a><span class="lineno"> 1132</span>    <span class="keywordflow">if</span> (!file_name) {</div>
-<div class="line"><a id="l01133" name="l01133"></a><span class="lineno"> 1133</span>        file_name = <span class="stringliteral">&quot;out.dot&quot;</span>;</div>
-<div class="line"><a id="l01134" name="l01134"></a><span class="lineno"> 1134</span>    }</div>
-<div class="line"><a id="l01135" name="l01135"></a><span class="lineno"> 1135</span> </div>
-<div class="line"><a id="l01136" name="l01136"></a><span class="lineno"> 1136</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> ofs;</div>
-<div class="line"><a id="l01137" name="l01137"></a><span class="lineno"> 1137</span> </div>
-<div class="line"><a id="l01138" name="l01138"></a><span class="lineno"> 1138</span>    ofs.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">open</a>(file_name);</div>
-<div class="line"><a id="l01139" name="l01139"></a><span class="lineno"> 1139</span>    <span class="keywordflow">if</span> (!ofs) {</div>
-<div class="line"><a id="l01140" name="l01140"></a><span class="lineno"> 1140</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;create tree dot file failed, &quot;</span> &lt;&lt; file_name &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l01141" name="l01141"></a><span class="lineno"> 1141</span>        <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l01142" name="l01142"></a><span class="lineno"> 1142</span>    }</div>
-<div class="line"><a id="l01143" name="l01143"></a><span class="lineno"> 1143</span> </div>
-<div class="line"><a id="l01144" name="l01144"></a><span class="lineno"> 1144</span>    ofs &lt;&lt; <span class="stringliteral">&quot;digraph G {\n&quot;</span>;</div>
-<div class="line"><a id="l01145" name="l01145"></a><span class="lineno"> 1145</span>    ofs &lt;&lt; <span class="stringliteral">&quot;node [shape=record]\n&quot;</span>;</div>
-<div class="line"><a id="l01146" name="l01146"></a><span class="lineno"> 1146</span> </div>
-<div class="line"><a id="l01147" name="l01147"></a><span class="lineno"> 1147</span>    int64_t index = 0;</div>
-<div class="line"><a id="l01148" name="l01148"></a><span class="lineno"> 1148</span><span class="comment"></span> </div>
-<div class="line"><a id="l01149" name="l01149"></a><span class="lineno"> 1149</span><span class="comment">    /** @brief This is a helper structure to do a level order traversal to print</span></div>
-<div class="line"><a id="l01150" name="l01150"></a><span class="lineno"> 1150</span><span class="comment">     * the tree. */</span></div>
-<div class="line"><a id="l01151" name="l01151"></a><span class="lineno"> 1151</span>    <span class="keyword">struct </span>NodeInfo {</div>
-<div class="line"><a id="l01152" name="l01152"></a><span class="lineno"> 1152</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;     <span class="comment">///&lt; tree node</span></div>
-<div class="line"><a id="l01153" name="l01153"></a><span class="lineno"> 1153</span>        int64_t index;  <span class="comment">///&lt; node index of level order that used when draw the</span><span class="comment"></span></div>
-<div class="line"><a id="l01154" name="l01154"></a><span class="lineno"> 1154</span><span class="comment">                        ///&lt; link between child and parent</span></div>
-<div class="line"><a id="l01155" name="l01155"></a><span class="lineno"> 1155</span><span class="comment"></span>    };</div>
-<div class="line"><a id="l01156" name="l01156"></a><span class="lineno"> 1156</span> </div>
-<div class="line"><a id="l01157" name="l01157"></a><span class="lineno"> 1157</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue&lt;NodeInfo&gt;</a> q;</div>
-<div class="line"><a id="l01158" name="l01158"></a><span class="lineno"> 1158</span> </div>
-<div class="line"><a id="l01159" name="l01159"></a><span class="lineno"> 1159</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>) {</div>
-<div class="line"><a id="l01160" name="l01160"></a><span class="lineno"> 1160</span>        <span class="comment">// print root node</span></div>
-<div class="line"><a id="l01161" name="l01161"></a><span class="lineno"> 1161</span>        <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#af260f0760344771bf8fce4fc9b1739be">PrintNode</a>(ofs, <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>, -1, index, 0);</div>
-<div class="line"><a id="l01162" name="l01162"></a><span class="lineno"> 1162</span> </div>
-<div class="line"><a id="l01163" name="l01163"></a><span class="lineno"> 1163</span>        NodeInfo ni{};</div>
-<div class="line"><a id="l01164" name="l01164"></a><span class="lineno"> 1164</span>        ni.node = <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>;</div>
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-<div class="line"><a id="l01166" name="l01166"></a><span class="lineno"> 1166</span> </div>
-<div class="line"><a id="l01167" name="l01167"></a><span class="lineno"> 1167</span>        q.push(ni);</div>
-<div class="line"><a id="l01168" name="l01168"></a><span class="lineno"> 1168</span> </div>
-<div class="line"><a id="l01169" name="l01169"></a><span class="lineno"> 1169</span>        <span class="keywordflow">while</span> (!q.empty()) {</div>
-<div class="line"><a id="l01170" name="l01170"></a><span class="lineno"> 1170</span>            NodeInfo node_info = q.front();</div>
-<div class="line"><a id="l01171" name="l01171"></a><span class="lineno"> 1171</span>            q.pop();</div>
-<div class="line"><a id="l01172" name="l01172"></a><span class="lineno"> 1172</span> </div>
-<div class="line"><a id="l01173" name="l01173"></a><span class="lineno"> 1173</span>            assert(node_info.node-&gt;GetCount() &gt; 0);</div>
-<div class="line"><a id="l01174" name="l01174"></a><span class="lineno"> 1174</span> </div>
-<div class="line"><a id="l01175" name="l01175"></a><span class="lineno"> 1175</span>            <span class="keywordflow">if</span> (!node_info.node-&gt;IsLeaf()) {</div>
-<div class="line"><a id="l01176" name="l01176"></a><span class="lineno"> 1176</span>                <span class="keywordflow">if</span> (node_info.node-&gt;GetCount() &gt; 0) {</div>
-<div class="line"><a id="l01177" name="l01177"></a><span class="lineno"> 1177</span>                    <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#af260f0760344771bf8fce4fc9b1739be">PrintNode</a>(ofs, node_info.node-&gt;GetChild(0), node_info.index,</div>
-<div class="line"><a id="l01178" name="l01178"></a><span class="lineno"> 1178</span>                              ++index, 0);</div>
-<div class="line"><a id="l01179" name="l01179"></a><span class="lineno"> 1179</span>                    ni.node = node_info.node-&gt;GetChild(0);</div>
-<div class="line"><a id="l01180" name="l01180"></a><span class="lineno"> 1180</span>                    ni.index = index;</div>
-<div class="line"><a id="l01181" name="l01181"></a><span class="lineno"> 1181</span>                    q.push(ni);</div>
-<div class="line"><a id="l01182" name="l01182"></a><span class="lineno"> 1182</span> </div>
-<div class="line"><a id="l01183" name="l01183"></a><span class="lineno"> 1183</span>                    <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#af260f0760344771bf8fce4fc9b1739be">PrintNode</a>(ofs, node_info.node-&gt;GetChild(1), node_info.index,</div>
-<div class="line"><a id="l01184" name="l01184"></a><span class="lineno"> 1184</span>                              ++index, 1);</div>
-<div class="line"><a id="l01185" name="l01185"></a><span class="lineno"> 1185</span>                    ni.node = node_info.node-&gt;GetChild(1);</div>
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-<div class="line"><a id="l01188" name="l01188"></a><span class="lineno"> 1188</span>                }</div>
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-<div class="line"><a id="l01190" name="l01190"></a><span class="lineno"> 1190</span>                <span class="keywordflow">if</span> (node_info.node-&gt;GetCount() &gt; 1) {</div>
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-<div class="line"><a id="l01192" name="l01192"></a><span class="lineno"> 1192</span>                              ++index, 2);</div>
-<div class="line"><a id="l01193" name="l01193"></a><span class="lineno"> 1193</span>                    ni.node = node_info.node-&gt;GetChild(2);</div>
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-<div class="line"><a id="l01197" name="l01197"></a><span class="lineno"> 1197</span> </div>
-<div class="line"><a id="l01198" name="l01198"></a><span class="lineno"> 1198</span>                <span class="keywordflow">if</span> (node_info.node-&gt;GetCount() &gt; 2) {</div>
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-<div class="line"><a id="l01200" name="l01200"></a><span class="lineno"> 1200</span>                              ++index, 3);</div>
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-<div class="line"><a id="l01211" name="l01211"></a><span class="lineno"> 1211</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno"> 1131</span>                                         {</div>
+<div class="line"><span class="lineno"> 1132</span>    <span class="keywordflow">if</span> (!file_name) {</div>
+<div class="line"><span class="lineno"> 1133</span>        file_name = <span class="stringliteral">&quot;out.dot&quot;</span>;</div>
+<div class="line"><span class="lineno"> 1134</span>    }</div>
+<div class="line"><span class="lineno"> 1135</span> </div>
+<div class="line"><span class="lineno"> 1136</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> ofs;</div>
+<div class="line"><span class="lineno"> 1137</span> </div>
+<div class="line"><span class="lineno"> 1138</span>    ofs.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">open</a>(file_name);</div>
+<div class="line"><span class="lineno"> 1139</span>    <span class="keywordflow">if</span> (!ofs) {</div>
+<div class="line"><span class="lineno"> 1140</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;create tree dot file failed, &quot;</span> &lt;&lt; file_name &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno"> 1141</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno"> 1142</span>    }</div>
+<div class="line"><span class="lineno"> 1143</span> </div>
+<div class="line"><span class="lineno"> 1144</span>    ofs &lt;&lt; <span class="stringliteral">&quot;digraph G {\n&quot;</span>;</div>
+<div class="line"><span class="lineno"> 1145</span>    ofs &lt;&lt; <span class="stringliteral">&quot;node [shape=record]\n&quot;</span>;</div>
+<div class="line"><span class="lineno"> 1146</span> </div>
+<div class="line"><span class="lineno"> 1147</span>    int64_t index = 0;</div>
+<div class="line"><span class="lineno"> 1148</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno"> 1149</span><span class="comment">    /** @brief This is a helper structure to do a level order traversal to print</span></div>
+<div class="line"><span class="lineno"> 1150</span><span class="comment">     * the tree. */</span></div>
+<div class="line"><span class="lineno"> 1151</span>    <span class="keyword">struct </span>NodeInfo {</div>
+<div class="line"><span class="lineno"> 1152</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;     <span class="comment">///&lt; tree node</span></div>
+<div class="line"><span class="lineno"> 1153</span>        int64_t index;  <span class="comment">///&lt; node index of level order that used when draw the</span><span class="comment"></span></div>
+<div class="line"><span class="lineno"> 1154</span><span class="comment">                        ///&lt; link between child and parent</span></div>
+<div class="line"><span class="lineno"> 1155</span><span class="comment"></span>    };</div>
+<div class="line"><span class="lineno"> 1156</span> </div>
+<div class="line"><span class="lineno"> 1157</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue&lt;NodeInfo&gt;</a> q;</div>
+<div class="line"><span class="lineno"> 1158</span> </div>
+<div class="line"><span class="lineno"> 1159</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>) {</div>
+<div class="line"><span class="lineno"> 1160</span>        <span class="comment">// print root node</span></div>
+<div class="line"><span class="lineno"> 1161</span>        <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#af260f0760344771bf8fce4fc9b1739be">PrintNode</a>(ofs, <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>, -1, index, 0);</div>
+<div class="line"><span class="lineno"> 1162</span> </div>
+<div class="line"><span class="lineno"> 1163</span>        NodeInfo ni{};</div>
+<div class="line"><span class="lineno"> 1164</span>        ni.node = <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>;</div>
+<div class="line"><span class="lineno"> 1165</span>        ni.index = index;</div>
+<div class="line"><span class="lineno"> 1166</span> </div>
+<div class="line"><span class="lineno"> 1167</span>        q.push(ni);</div>
+<div class="line"><span class="lineno"> 1168</span> </div>
+<div class="line"><span class="lineno"> 1169</span>        <span class="keywordflow">while</span> (!q.empty()) {</div>
+<div class="line"><span class="lineno"> 1170</span>            NodeInfo node_info = q.front();</div>
+<div class="line"><span class="lineno"> 1171</span>            q.pop();</div>
+<div class="line"><span class="lineno"> 1172</span> </div>
+<div class="line"><span class="lineno"> 1173</span>            assert(node_info.node-&gt;GetCount() &gt; 0);</div>
+<div class="line"><span class="lineno"> 1174</span> </div>
+<div class="line"><span class="lineno"> 1175</span>            <span class="keywordflow">if</span> (!node_info.node-&gt;IsLeaf()) {</div>
+<div class="line"><span class="lineno"> 1176</span>                <span class="keywordflow">if</span> (node_info.node-&gt;GetCount() &gt; 0) {</div>
+<div class="line"><span class="lineno"> 1177</span>                    <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#af260f0760344771bf8fce4fc9b1739be">PrintNode</a>(ofs, node_info.node-&gt;GetChild(0), node_info.index,</div>
+<div class="line"><span class="lineno"> 1178</span>                              ++index, 0);</div>
+<div class="line"><span class="lineno"> 1179</span>                    ni.node = node_info.node-&gt;GetChild(0);</div>
+<div class="line"><span class="lineno"> 1180</span>                    ni.index = index;</div>
+<div class="line"><span class="lineno"> 1181</span>                    q.push(ni);</div>
+<div class="line"><span class="lineno"> 1182</span> </div>
+<div class="line"><span class="lineno"> 1183</span>                    <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#af260f0760344771bf8fce4fc9b1739be">PrintNode</a>(ofs, node_info.node-&gt;GetChild(1), node_info.index,</div>
+<div class="line"><span class="lineno"> 1184</span>                              ++index, 1);</div>
+<div class="line"><span class="lineno"> 1185</span>                    ni.node = node_info.node-&gt;GetChild(1);</div>
+<div class="line"><span class="lineno"> 1186</span>                    ni.index = index;</div>
+<div class="line"><span class="lineno"> 1187</span>                    q.push(ni);</div>
+<div class="line"><span class="lineno"> 1188</span>                }</div>
+<div class="line"><span class="lineno"> 1189</span> </div>
+<div class="line"><span class="lineno"> 1190</span>                <span class="keywordflow">if</span> (node_info.node-&gt;GetCount() &gt; 1) {</div>
+<div class="line"><span class="lineno"> 1191</span>                    <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#af260f0760344771bf8fce4fc9b1739be">PrintNode</a>(ofs, node_info.node-&gt;GetChild(2), node_info.index,</div>
+<div class="line"><span class="lineno"> 1192</span>                              ++index, 2);</div>
+<div class="line"><span class="lineno"> 1193</span>                    ni.node = node_info.node-&gt;GetChild(2);</div>
+<div class="line"><span class="lineno"> 1194</span>                    ni.index = index;</div>
+<div class="line"><span class="lineno"> 1195</span>                    q.push(ni);</div>
+<div class="line"><span class="lineno"> 1196</span>                }</div>
+<div class="line"><span class="lineno"> 1197</span> </div>
+<div class="line"><span class="lineno"> 1198</span>                <span class="keywordflow">if</span> (node_info.node-&gt;GetCount() &gt; 2) {</div>
+<div class="line"><span class="lineno"> 1199</span>                    <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#af260f0760344771bf8fce4fc9b1739be">PrintNode</a>(ofs, node_info.node-&gt;GetChild(3), node_info.index,</div>
+<div class="line"><span class="lineno"> 1200</span>                              ++index, 3);</div>
+<div class="line"><span class="lineno"> 1201</span>                    ni.node = node_info.node-&gt;GetChild(3);</div>
+<div class="line"><span class="lineno"> 1202</span>                    ni.index = index;</div>
+<div class="line"><span class="lineno"> 1203</span>                    q.push(ni);</div>
+<div class="line"><span class="lineno"> 1204</span>                }</div>
+<div class="line"><span class="lineno"> 1205</span>            }</div>
+<div class="line"><span class="lineno"> 1206</span>        }</div>
+<div class="line"><span class="lineno"> 1207</span>    }</div>
+<div class="line"><span class="lineno"> 1208</span> </div>
+<div class="line"><span class="lineno"> 1209</span>    ofs &lt;&lt; <span class="stringliteral">&quot;}\n&quot;</span>;</div>
+<div class="line"><span class="lineno"> 1210</span>    ofs.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/close.html">close</a>();</div>
+<div class="line"><span class="lineno"> 1211</span>}</div>
 <div class="ttc" id="abasic_ofstream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aclassdata__structures_1_1tree__234_1_1_tree234_html_af260f0760344771bf8fce4fc9b1739be"><div class="ttname"><a href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#af260f0760344771bf8fce4fc9b1739be">data_structures::tree_234::Tree234::PrintNode</a></div><div class="ttdeci">void PrintNode(std::ofstream &amp;ofs, Node *node, int64_t parent_index, int64_t index, int8_t parent_child_index)</div><div class="ttdoc">Print the tree to a dot file. You can convert it to picture with graphviz.</div><div class="ttdef"><b>Definition:</b> tree_234.cpp:1226</div></div>
@@ -1081,36 +1081,36 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l01227" name="l01227"></a><span class="lineno"> 1227</span>                                                                  {</div>
-<div class="line"><a id="l01228" name="l01228"></a><span class="lineno"> 1228</span>    assert(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>);</div>
-<div class="line"><a id="l01229" name="l01229"></a><span class="lineno"> 1229</span> </div>
-<div class="line"><a id="l01230" name="l01230"></a><span class="lineno"> 1230</span>    <span class="keywordflow">switch</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetCount()) {</div>
-<div class="line"><a id="l01231" name="l01231"></a><span class="lineno"> 1231</span>        <span class="keywordflow">case</span> 1:</div>
-<div class="line"><a id="l01232" name="l01232"></a><span class="lineno"> 1232</span>            ofs &lt;&lt; <span class="stringliteral">&quot;node_&quot;</span> &lt;&lt; index &lt;&lt; <span class="stringliteral">&quot; [label=\&quot;&lt;f0&gt; &quot;</span> &lt;&lt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(0)</div>
-<div class="line"><a id="l01233" name="l01233"></a><span class="lineno"> 1233</span>                &lt;&lt; <span class="stringliteral">&quot;\&quot;]\n&quot;</span>;</div>
-<div class="line"><a id="l01234" name="l01234"></a><span class="lineno"> 1234</span>            <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l01235" name="l01235"></a><span class="lineno"> 1235</span>        <span class="keywordflow">case</span> 2:</div>
-<div class="line"><a id="l01236" name="l01236"></a><span class="lineno"> 1236</span>            ofs &lt;&lt; <span class="stringliteral">&quot;node_&quot;</span> &lt;&lt; index &lt;&lt; <span class="stringliteral">&quot; [label=\&quot;&lt;f0&gt; &quot;</span> &lt;&lt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(0)</div>
-<div class="line"><a id="l01237" name="l01237"></a><span class="lineno"> 1237</span>                &lt;&lt; <span class="stringliteral">&quot; | &lt;f1&gt; &quot;</span> &lt;&lt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(1) &lt;&lt; <span class="stringliteral">&quot;\&quot;]\n&quot;</span>;</div>
-<div class="line"><a id="l01238" name="l01238"></a><span class="lineno"> 1238</span>            <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l01239" name="l01239"></a><span class="lineno"> 1239</span>        <span class="keywordflow">case</span> 3:</div>
-<div class="line"><a id="l01240" name="l01240"></a><span class="lineno"> 1240</span>            ofs &lt;&lt; <span class="stringliteral">&quot;node_&quot;</span> &lt;&lt; index &lt;&lt; <span class="stringliteral">&quot; [label=\&quot;&lt;f0&gt; &quot;</span> &lt;&lt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(0)</div>
-<div class="line"><a id="l01241" name="l01241"></a><span class="lineno"> 1241</span>                &lt;&lt; <span class="stringliteral">&quot; | &lt;f1&gt; &quot;</span> &lt;&lt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(1) &lt;&lt; <span class="stringliteral">&quot;| &lt;f2&gt; &quot;</span></div>
-<div class="line"><a id="l01242" name="l01242"></a><span class="lineno"> 1242</span>                &lt;&lt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(2) &lt;&lt; <span class="stringliteral">&quot;\&quot;]\n&quot;</span>;</div>
-<div class="line"><a id="l01243" name="l01243"></a><span class="lineno"> 1243</span>            <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l01244" name="l01244"></a><span class="lineno"> 1244</span> </div>
-<div class="line"><a id="l01245" name="l01245"></a><span class="lineno"> 1245</span>        <span class="keywordflow">default</span>:</div>
-<div class="line"><a id="l01246" name="l01246"></a><span class="lineno"> 1246</span>            <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l01247" name="l01247"></a><span class="lineno"> 1247</span>    }</div>
-<div class="line"><a id="l01248" name="l01248"></a><span class="lineno"> 1248</span> </div>
-<div class="line"><a id="l01249" name="l01249"></a><span class="lineno"> 1249</span>    <span class="comment">// draw the edge</span></div>
-<div class="line"><a id="l01250" name="l01250"></a><span class="lineno"> 1250</span>    <span class="keywordflow">if</span> (parent_index &gt;= 0) {</div>
-<div class="line"><a id="l01251" name="l01251"></a><span class="lineno"> 1251</span>        ofs &lt;&lt; <span class="stringliteral">&quot;node_&quot;</span> &lt;&lt; parent_index &lt;&lt; <span class="stringliteral">&quot;:f&quot;</span></div>
-<div class="line"><a id="l01252" name="l01252"></a><span class="lineno"> 1252</span>            &lt;&lt; (parent_child_index == 0 ? 0 : parent_child_index - 1) &lt;&lt; <span class="stringliteral">&quot;:&quot;</span></div>
-<div class="line"><a id="l01253" name="l01253"></a><span class="lineno"> 1253</span>            &lt;&lt; (parent_child_index == 0 ? <span class="stringliteral">&quot;sw&quot;</span> : <span class="stringliteral">&quot;se&quot;</span>) &lt;&lt; <span class="stringliteral">&quot; -&gt; node_&quot;</span> &lt;&lt; index</div>
-<div class="line"><a id="l01254" name="l01254"></a><span class="lineno"> 1254</span>            &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l01255" name="l01255"></a><span class="lineno"> 1255</span>    }</div>
-<div class="line"><a id="l01256" name="l01256"></a><span class="lineno"> 1256</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno"> 1227</span>                                                                  {</div>
+<div class="line"><span class="lineno"> 1228</span>    assert(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>);</div>
+<div class="line"><span class="lineno"> 1229</span> </div>
+<div class="line"><span class="lineno"> 1230</span>    <span class="keywordflow">switch</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetCount()) {</div>
+<div class="line"><span class="lineno"> 1231</span>        <span class="keywordflow">case</span> 1:</div>
+<div class="line"><span class="lineno"> 1232</span>            ofs &lt;&lt; <span class="stringliteral">&quot;node_&quot;</span> &lt;&lt; index &lt;&lt; <span class="stringliteral">&quot; [label=\&quot;&lt;f0&gt; &quot;</span> &lt;&lt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(0)</div>
+<div class="line"><span class="lineno"> 1233</span>                &lt;&lt; <span class="stringliteral">&quot;\&quot;]\n&quot;</span>;</div>
+<div class="line"><span class="lineno"> 1234</span>            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno"> 1235</span>        <span class="keywordflow">case</span> 2:</div>
+<div class="line"><span class="lineno"> 1236</span>            ofs &lt;&lt; <span class="stringliteral">&quot;node_&quot;</span> &lt;&lt; index &lt;&lt; <span class="stringliteral">&quot; [label=\&quot;&lt;f0&gt; &quot;</span> &lt;&lt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(0)</div>
+<div class="line"><span class="lineno"> 1237</span>                &lt;&lt; <span class="stringliteral">&quot; | &lt;f1&gt; &quot;</span> &lt;&lt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(1) &lt;&lt; <span class="stringliteral">&quot;\&quot;]\n&quot;</span>;</div>
+<div class="line"><span class="lineno"> 1238</span>            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno"> 1239</span>        <span class="keywordflow">case</span> 3:</div>
+<div class="line"><span class="lineno"> 1240</span>            ofs &lt;&lt; <span class="stringliteral">&quot;node_&quot;</span> &lt;&lt; index &lt;&lt; <span class="stringliteral">&quot; [label=\&quot;&lt;f0&gt; &quot;</span> &lt;&lt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(0)</div>
+<div class="line"><span class="lineno"> 1241</span>                &lt;&lt; <span class="stringliteral">&quot; | &lt;f1&gt; &quot;</span> &lt;&lt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(1) &lt;&lt; <span class="stringliteral">&quot;| &lt;f2&gt; &quot;</span></div>
+<div class="line"><span class="lineno"> 1242</span>                &lt;&lt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(2) &lt;&lt; <span class="stringliteral">&quot;\&quot;]\n&quot;</span>;</div>
+<div class="line"><span class="lineno"> 1243</span>            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno"> 1244</span> </div>
+<div class="line"><span class="lineno"> 1245</span>        <span class="keywordflow">default</span>:</div>
+<div class="line"><span class="lineno"> 1246</span>            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno"> 1247</span>    }</div>
+<div class="line"><span class="lineno"> 1248</span> </div>
+<div class="line"><span class="lineno"> 1249</span>    <span class="comment">// draw the edge</span></div>
+<div class="line"><span class="lineno"> 1250</span>    <span class="keywordflow">if</span> (parent_index &gt;= 0) {</div>
+<div class="line"><span class="lineno"> 1251</span>        ofs &lt;&lt; <span class="stringliteral">&quot;node_&quot;</span> &lt;&lt; parent_index &lt;&lt; <span class="stringliteral">&quot;:f&quot;</span></div>
+<div class="line"><span class="lineno"> 1252</span>            &lt;&lt; (parent_child_index == 0 ? 0 : parent_child_index - 1) &lt;&lt; <span class="stringliteral">&quot;:&quot;</span></div>
+<div class="line"><span class="lineno"> 1253</span>            &lt;&lt; (parent_child_index == 0 ? <span class="stringliteral">&quot;sw&quot;</span> : <span class="stringliteral">&quot;se&quot;</span>) &lt;&lt; <span class="stringliteral">&quot; -&gt; node_&quot;</span> &lt;&lt; index</div>
+<div class="line"><span class="lineno"> 1254</span>            &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno"> 1255</span>    }</div>
+<div class="line"><span class="lineno"> 1256</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1138,7 +1138,7 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if item found and removed, false otherwise </dd></dl>
-<div class="fragment"><div class="line"><a id="l00929" name="l00929"></a><span class="lineno">  929</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a61dd051a74e5f36c8dc03dae8dca6ef4">RemovePreMerge</a>(<a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>, item); }</div>
+<div class="fragment"><div class="line"><span class="lineno">  929</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a61dd051a74e5f36c8dc03dae8dca6ef4">RemovePreMerge</a>(<a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>, item); }</div>
 <div class="ttc" id="aclassdata__structures_1_1tree__234_1_1_tree234_html_a61dd051a74e5f36c8dc03dae8dca6ef4"><div class="ttname"><a href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a61dd051a74e5f36c8dc03dae8dca6ef4">data_structures::tree_234::Tree234::RemovePreMerge</a></div><div class="ttdeci">bool RemovePreMerge(Node *node, int64_t item)</div><div class="ttdoc">Main function implement the pre-merge remove operation.</div><div class="ttdef"><b>Definition:</b> tree_234.cpp:937</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -1192,161 +1192,161 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if remove success, false otherwise </dd></dl>
-<div class="fragment"><div class="line"><a id="l00937" name="l00937"></a><span class="lineno">  937</span>                                                     {</div>
-<div class="line"><a id="l00938" name="l00938"></a><span class="lineno">  938</span>    <span class="keywordflow">while</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>) {</div>
-<div class="line"><a id="l00939" name="l00939"></a><span class="lineno">  939</span>        <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;IsLeaf()) {</div>
-<div class="line"><a id="l00940" name="l00940"></a><span class="lineno">  940</span>            <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;Contains(item)) {</div>
-<div class="line"><a id="l00941" name="l00941"></a><span class="lineno">  941</span>                <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;Is2Node()) {</div>
-<div class="line"><a id="l00942" name="l00942"></a><span class="lineno">  942</span>                    <span class="comment">// node must be root</span></div>
-<div class="line"><a id="l00943" name="l00943"></a><span class="lineno">  943</span>                    <span class="keyword">delete</span> <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
-<div class="line"><a id="l00944" name="l00944"></a><span class="lineno">  944</span>                    <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a> = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00945" name="l00945"></a><span class="lineno">  945</span>                } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00946" name="l00946"></a><span class="lineno">  946</span>                    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;RemoveItemByIndex(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemIndex(item), <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00947" name="l00947"></a><span class="lineno">  947</span>                }</div>
-<div class="line"><a id="l00948" name="l00948"></a><span class="lineno">  948</span>                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00949" name="l00949"></a><span class="lineno">  949</span>            }</div>
-<div class="line"><a id="l00950" name="l00950"></a><span class="lineno">  950</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00951" name="l00951"></a><span class="lineno">  951</span>        }</div>
-<div class="line"><a id="l00952" name="l00952"></a><span class="lineno">  952</span> </div>
-<div class="line"><a id="l00953" name="l00953"></a><span class="lineno">  953</span>        <span class="comment">// node is internal</span></div>
-<div class="line"><a id="l00954" name="l00954"></a><span class="lineno">  954</span>        <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;Contains(item)) {</div>
-<div class="line"><a id="l00955" name="l00955"></a><span class="lineno">  955</span>            int8_t index = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemIndex(item);</div>
-<div class="line"><a id="l00956" name="l00956"></a><span class="lineno">  956</span> </div>
-<div class="line"><a id="l00957" name="l00957"></a><span class="lineno">  957</span>            <span class="comment">// Here is important!!! What we do next depend on its children&#39;s</span></div>
-<div class="line"><a id="l00958" name="l00958"></a><span class="lineno">  958</span>            <span class="comment">// state. Why?</span></div>
-<div class="line"><a id="l00959" name="l00959"></a><span class="lineno">  959</span>            <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *left_child = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemLeftChild(index);</div>
-<div class="line"><a id="l00960" name="l00960"></a><span class="lineno">  960</span>            <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *right_child = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemRightChild(index);</div>
-<div class="line"><a id="l00961" name="l00961"></a><span class="lineno">  961</span>            assert(left_child &amp;&amp; right_child);</div>
-<div class="line"><a id="l00962" name="l00962"></a><span class="lineno">  962</span> </div>
-<div class="line"><a id="l00963" name="l00963"></a><span class="lineno">  963</span>            <span class="keywordflow">if</span> (left_child-&gt;Is2Node() &amp;&amp; right_child-&gt;Is2Node()) {</div>
-<div class="line"><a id="l00964" name="l00964"></a><span class="lineno">  964</span>                <span class="comment">// both left and right child are 2-node,we should not modify</span></div>
-<div class="line"><a id="l00965" name="l00965"></a><span class="lineno">  965</span>                <span class="comment">// current node in this situation. Because we are going to do</span></div>
-<div class="line"><a id="l00966" name="l00966"></a><span class="lineno">  966</span>                <span class="comment">// merge with its children which will move target item to next</span></div>
-<div class="line"><a id="l00967" name="l00967"></a><span class="lineno">  967</span>                <span class="comment">// layer. so if we replace the item with successor or</span></div>
-<div class="line"><a id="l00968" name="l00968"></a><span class="lineno">  968</span>                <span class="comment">// predecessor now, when we do the recursive remove with</span></div>
-<div class="line"><a id="l00969" name="l00969"></a><span class="lineno">  969</span>                <span class="comment">// successor or predecessor, we will result in removing the just</span></div>
-<div class="line"><a id="l00970" name="l00970"></a><span class="lineno">  970</span>                <span class="comment">// replaced one in the merged node. That&#39;s not what we want.</span></div>
-<div class="line"><a id="l00971" name="l00971"></a><span class="lineno">  971</span> </div>
-<div class="line"><a id="l00972" name="l00972"></a><span class="lineno">  972</span>                <span class="comment">// we need to convert the child 2-node to 3-node or 4-node</span></div>
-<div class="line"><a id="l00973" name="l00973"></a><span class="lineno">  973</span>                <span class="comment">// first. First we try to see if any of them can convert to</span></div>
-<div class="line"><a id="l00974" name="l00974"></a><span class="lineno">  974</span>                <span class="comment">// 3-node by rotate. By using rotate we keep the empty house for</span></div>
-<div class="line"><a id="l00975" name="l00975"></a><span class="lineno">  975</span>                <span class="comment">// the future insertion which will be more efficient than merge.</span></div>
-<div class="line"><a id="l00976" name="l00976"></a><span class="lineno">  976</span>                <span class="comment">//</span></div>
-<div class="line"><a id="l00977" name="l00977"></a><span class="lineno">  977</span>                <span class="comment">//            | ? | node | ? |</span></div>
-<div class="line"><a id="l00978" name="l00978"></a><span class="lineno">  978</span>                <span class="comment">//           /    |      |    \</span></div>
-<div class="line"><a id="l00979" name="l00979"></a><span class="lineno">  979</span><span class="comment">                //          /     |      |     \</span></div>
-<div class="line"><a id="l00980" name="l00980"></a><span class="lineno">  980</span><span class="comment">                //         /      |      |      \</span></div>
-<div class="line"><a id="l00981" name="l00981"></a><span class="lineno">  981</span><span class="comment">                //        /       |      |       \</span></div>
-<div class="line"><a id="l00982" name="l00982"></a><span class="lineno">  982</span><span class="comment">                //       /        |      |        \</span></div>
-<div class="line"><a id="l00983" name="l00983"></a><span class="lineno">  983</span><span class="comment">                //      /         |      |         \</span></div>
-<div class="line"><a id="l00984" name="l00984"></a><span class="lineno">  984</span><span class="comment">                //     ?  left_child  right_child   ?</span></div>
-<div class="line"><a id="l00985" name="l00985"></a><span class="lineno">  985</span>                <span class="comment">//</span></div>
-<div class="line"><a id="l00986" name="l00986"></a><span class="lineno">  986</span> </div>
-<div class="line"><a id="l00987" name="l00987"></a><span class="lineno">  987</span>                <span class="comment">// node must be the root</span></div>
-<div class="line"><a id="l00988" name="l00988"></a><span class="lineno">  988</span>                <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;Is2Node()) {</div>
-<div class="line"><a id="l00989" name="l00989"></a><span class="lineno">  989</span>                    <span class="comment">// this means we can&#39;t avoid merging the target item into</span></div>
-<div class="line"><a id="l00990" name="l00990"></a><span class="lineno">  990</span>                    <span class="comment">// next layer, and this will cause us do different process</span></div>
-<div class="line"><a id="l00991" name="l00991"></a><span class="lineno">  991</span>                    <span class="comment">// compared with other cases</span></div>
-<div class="line"><a id="l00992" name="l00992"></a><span class="lineno">  992</span>                    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *new_root = <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a36f4d5f603f7edb7db7c73fb53ba14e9">Merge</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, index);</div>
-<div class="line"><a id="l00993" name="l00993"></a><span class="lineno">  993</span>                    <span class="keyword">delete</span> <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>;</div>
-<div class="line"><a id="l00994" name="l00994"></a><span class="lineno">  994</span>                    <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a> = new_root;</div>
-<div class="line"><a id="l00995" name="l00995"></a><span class="lineno">  995</span>                    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>;</div>
-<div class="line"><a id="l00996" name="l00996"></a><span class="lineno">  996</span> </div>
-<div class="line"><a id="l00997" name="l00997"></a><span class="lineno">  997</span>                    <span class="comment">// now node point to the</span></div>
-<div class="line"><a id="l00998" name="l00998"></a><span class="lineno">  998</span>                    <span class="keywordflow">continue</span>;</div>
-<div class="line"><a id="l00999" name="l00999"></a><span class="lineno">  999</span>                }</div>
-<div class="line"><a id="l01000" name="l01000"></a><span class="lineno"> 1000</span> </div>
-<div class="line"><a id="l01001" name="l01001"></a><span class="lineno"> 1001</span>                <span class="comment">// here means we can avoid merging the target item into next</span></div>
-<div class="line"><a id="l01002" name="l01002"></a><span class="lineno"> 1002</span>                <span class="comment">// layer. So we convert one of its left or right child to 3-node</span></div>
-<div class="line"><a id="l01003" name="l01003"></a><span class="lineno"> 1003</span>                <span class="comment">// and then do the successor or predecessor swap and recursive</span></div>
-<div class="line"><a id="l01004" name="l01004"></a><span class="lineno"> 1004</span>                <span class="comment">// remove the next layer will successor or predecessor.</span></div>
-<div class="line"><a id="l01005" name="l01005"></a><span class="lineno"> 1005</span>                <span class="keywordflow">do</span> {</div>
-<div class="line"><a id="l01006" name="l01006"></a><span class="lineno"> 1006</span>                    <span class="keywordflow">if</span> (index &gt; 0) {</div>
-<div class="line"><a id="l01007" name="l01007"></a><span class="lineno"> 1007</span>                        <span class="comment">// left_child has left-sibling, we check if we can do a</span></div>
-<div class="line"><a id="l01008" name="l01008"></a><span class="lineno"> 1008</span>                        <span class="comment">// rotate</span></div>
-<div class="line"><a id="l01009" name="l01009"></a><span class="lineno"> 1009</span>                        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *left_sibling = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemLeftChild(index - 1);</div>
-<div class="line"><a id="l01010" name="l01010"></a><span class="lineno"> 1010</span>                        <span class="keywordflow">if</span> (left_sibling-&gt;Is34Node()) {</div>
-<div class="line"><a id="l01011" name="l01011"></a><span class="lineno"> 1011</span>                            <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#ae68f8e62be02657c1287def6b38d7cc9">RightRotate</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, index - 1);</div>
-<div class="line"><a id="l01012" name="l01012"></a><span class="lineno"> 1012</span>                            <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l01013" name="l01013"></a><span class="lineno"> 1013</span>                        }</div>
-<div class="line"><a id="l01014" name="l01014"></a><span class="lineno"> 1014</span>                    }</div>
-<div class="line"><a id="l01015" name="l01015"></a><span class="lineno"> 1015</span> </div>
-<div class="line"><a id="l01016" name="l01016"></a><span class="lineno"> 1016</span>                    <span class="keywordflow">if</span> (index &lt; node-&gt;GetCount() - 1) {</div>
-<div class="line"><a id="l01017" name="l01017"></a><span class="lineno"> 1017</span>                        <span class="comment">// right_child has right-sibling, we check if we can do</span></div>
-<div class="line"><a id="l01018" name="l01018"></a><span class="lineno"> 1018</span>                        <span class="comment">// a rotate</span></div>
-<div class="line"><a id="l01019" name="l01019"></a><span class="lineno"> 1019</span>                        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *right_sibling =</div>
-<div class="line"><a id="l01020" name="l01020"></a><span class="lineno"> 1020</span>                            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemRightChild(index + 1);</div>
-<div class="line"><a id="l01021" name="l01021"></a><span class="lineno"> 1021</span>                        <span class="keywordflow">if</span> (right_sibling-&gt;Is34Node()) {</div>
-<div class="line"><a id="l01022" name="l01022"></a><span class="lineno"> 1022</span>                            <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#ae58dca20f08eaf9313f6e7b0869c2d0e">LeftRotate</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, index + 1);</div>
-<div class="line"><a id="l01023" name="l01023"></a><span class="lineno"> 1023</span>                            <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l01024" name="l01024"></a><span class="lineno"> 1024</span>                        }</div>
-<div class="line"><a id="l01025" name="l01025"></a><span class="lineno"> 1025</span>                    }</div>
-<div class="line"><a id="l01026" name="l01026"></a><span class="lineno"> 1026</span> </div>
-<div class="line"><a id="l01027" name="l01027"></a><span class="lineno"> 1027</span>                    <span class="comment">// we do a merge. We avoid merging the target item, which</span></div>
-<div class="line"><a id="l01028" name="l01028"></a><span class="lineno"> 1028</span>                    <span class="comment">// may trigger another merge in the recursion process.</span></div>
-<div class="line"><a id="l01029" name="l01029"></a><span class="lineno"> 1029</span>                    <span class="keywordflow">if</span> (index &gt; 0) {</div>
-<div class="line"><a id="l01030" name="l01030"></a><span class="lineno"> 1030</span>                        <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a36f4d5f603f7edb7db7c73fb53ba14e9">Merge</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, index - 1);</div>
-<div class="line"><a id="l01031" name="l01031"></a><span class="lineno"> 1031</span>                        <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l01032" name="l01032"></a><span class="lineno"> 1032</span>                    }</div>
-<div class="line"><a id="l01033" name="l01033"></a><span class="lineno"> 1033</span> </div>
-<div class="line"><a id="l01034" name="l01034"></a><span class="lineno"> 1034</span>                    <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a36f4d5f603f7edb7db7c73fb53ba14e9">Merge</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, index + 1);</div>
-<div class="line"><a id="l01035" name="l01035"></a><span class="lineno"> 1035</span> </div>
-<div class="line"><a id="l01036" name="l01036"></a><span class="lineno"> 1036</span>                } <span class="keywordflow">while</span> (<span class="keyword">false</span>);</div>
-<div class="line"><a id="l01037" name="l01037"></a><span class="lineno"> 1037</span>            }</div>
-<div class="line"><a id="l01038" name="l01038"></a><span class="lineno"> 1038</span> </div>
-<div class="line"><a id="l01039" name="l01039"></a><span class="lineno"> 1039</span>            <span class="comment">// refresh the left_child and right_child since they may be invalid</span></div>
-<div class="line"><a id="l01040" name="l01040"></a><span class="lineno"> 1040</span>            <span class="comment">// because of merge</span></div>
-<div class="line"><a id="l01041" name="l01041"></a><span class="lineno"> 1041</span>            left_child = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemLeftChild(index);</div>
-<div class="line"><a id="l01042" name="l01042"></a><span class="lineno"> 1042</span>            right_child = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemRightChild(index);</div>
-<div class="line"><a id="l01043" name="l01043"></a><span class="lineno"> 1043</span> </div>
-<div class="line"><a id="l01044" name="l01044"></a><span class="lineno"> 1044</span>            <span class="keywordflow">if</span> (left_child-&gt;Is34Node()) {</div>
-<div class="line"><a id="l01045" name="l01045"></a><span class="lineno"> 1045</span>                int64_t predecessor_item = <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#ac85ba5abfd6d34dcd908b2afe6464657">GetTreeMaxItem</a>(left_child);</div>
-<div class="line"><a id="l01046" name="l01046"></a><span class="lineno"> 1046</span>                <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;SetItem(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemIndex(item), predecessor_item);</div>
-<div class="line"><a id="l01047" name="l01047"></a><span class="lineno"> 1047</span> </div>
-<div class="line"><a id="l01048" name="l01048"></a><span class="lineno"> 1048</span>                <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = left_child;</div>
-<div class="line"><a id="l01049" name="l01049"></a><span class="lineno"> 1049</span>                item = predecessor_item;</div>
-<div class="line"><a id="l01050" name="l01050"></a><span class="lineno"> 1050</span>                <span class="keywordflow">continue</span>;</div>
-<div class="line"><a id="l01051" name="l01051"></a><span class="lineno"> 1051</span>            }</div>
-<div class="line"><a id="l01052" name="l01052"></a><span class="lineno"> 1052</span> </div>
-<div class="line"><a id="l01053" name="l01053"></a><span class="lineno"> 1053</span>            <span class="keywordflow">if</span> (right_child-&gt;Is34Node()) {</div>
-<div class="line"><a id="l01054" name="l01054"></a><span class="lineno"> 1054</span>                int64_t successor_item = <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a65a1235659356166a3e9b451c64fcc36">GetTreeMinItem</a>(right_child);</div>
-<div class="line"><a id="l01055" name="l01055"></a><span class="lineno"> 1055</span>                <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;SetItem(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemIndex(item), successor_item);</div>
-<div class="line"><a id="l01056" name="l01056"></a><span class="lineno"> 1056</span>                <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = right_child;</div>
-<div class="line"><a id="l01057" name="l01057"></a><span class="lineno"> 1057</span>                item = successor_item;</div>
-<div class="line"><a id="l01058" name="l01058"></a><span class="lineno"> 1058</span>                <span class="keywordflow">continue</span>;</div>
-<div class="line"><a id="l01059" name="l01059"></a><span class="lineno"> 1059</span>            }</div>
-<div class="line"><a id="l01060" name="l01060"></a><span class="lineno"> 1060</span>        }</div>
-<div class="line"><a id="l01061" name="l01061"></a><span class="lineno"> 1061</span> </div>
-<div class="line"><a id="l01062" name="l01062"></a><span class="lineno"> 1062</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *next_node = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetNextPossibleChild(item);</div>
-<div class="line"><a id="l01063" name="l01063"></a><span class="lineno"> 1063</span> </div>
-<div class="line"><a id="l01064" name="l01064"></a><span class="lineno"> 1064</span>        <span class="keywordflow">if</span> (next_node-&gt;Is34Node()) {</div>
-<div class="line"><a id="l01065" name="l01065"></a><span class="lineno"> 1065</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = next_node;</div>
-<div class="line"><a id="l01066" name="l01066"></a><span class="lineno"> 1066</span>            <span class="keywordflow">continue</span>;</div>
-<div class="line"><a id="l01067" name="l01067"></a><span class="lineno"> 1067</span>        }</div>
-<div class="line"><a id="l01068" name="l01068"></a><span class="lineno"> 1068</span> </div>
-<div class="line"><a id="l01069" name="l01069"></a><span class="lineno"> 1069</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#aec0642d1d151521ca7c70ea85cdb15d3">TryRightRotate</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, next_node)) {</div>
-<div class="line"><a id="l01070" name="l01070"></a><span class="lineno"> 1070</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = next_node;</div>
-<div class="line"><a id="l01071" name="l01071"></a><span class="lineno"> 1071</span>            <span class="keywordflow">continue</span>;</div>
-<div class="line"><a id="l01072" name="l01072"></a><span class="lineno"> 1072</span>        }</div>
-<div class="line"><a id="l01073" name="l01073"></a><span class="lineno"> 1073</span> </div>
-<div class="line"><a id="l01074" name="l01074"></a><span class="lineno"> 1074</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#ac5361479dd996eb331759f33808657d9">TryLeftRotate</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, next_node)) {</div>
-<div class="line"><a id="l01075" name="l01075"></a><span class="lineno"> 1075</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = next_node;</div>
-<div class="line"><a id="l01076" name="l01076"></a><span class="lineno"> 1076</span>            <span class="keywordflow">continue</span>;</div>
-<div class="line"><a id="l01077" name="l01077"></a><span class="lineno"> 1077</span>        }</div>
-<div class="line"><a id="l01078" name="l01078"></a><span class="lineno"> 1078</span> </div>
-<div class="line"><a id="l01079" name="l01079"></a><span class="lineno"> 1079</span>        <span class="comment">// get here means both left sibling and right sibling of next_node is</span></div>
-<div class="line"><a id="l01080" name="l01080"></a><span class="lineno"> 1080</span>        <span class="comment">// 2-node, so we do merge</span></div>
-<div class="line"><a id="l01081" name="l01081"></a><span class="lineno"> 1081</span>        int8_t child_index = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetChildIndex(next_node);</div>
-<div class="line"><a id="l01082" name="l01082"></a><span class="lineno"> 1082</span>        <span class="keywordflow">if</span> (child_index &gt; 0) {</div>
-<div class="line"><a id="l01083" name="l01083"></a><span class="lineno"> 1083</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a36f4d5f603f7edb7db7c73fb53ba14e9">Merge</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, child_index - 1);</div>
-<div class="line"><a id="l01084" name="l01084"></a><span class="lineno"> 1084</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l01085" name="l01085"></a><span class="lineno"> 1085</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a36f4d5f603f7edb7db7c73fb53ba14e9">Merge</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, child_index);</div>
-<div class="line"><a id="l01086" name="l01086"></a><span class="lineno"> 1086</span>        }</div>
-<div class="line"><a id="l01087" name="l01087"></a><span class="lineno"> 1087</span> </div>
-<div class="line"><a id="l01088" name="l01088"></a><span class="lineno"> 1088</span>    }  <span class="comment">// while</span></div>
-<div class="line"><a id="l01089" name="l01089"></a><span class="lineno"> 1089</span> </div>
-<div class="line"><a id="l01090" name="l01090"></a><span class="lineno"> 1090</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l01091" name="l01091"></a><span class="lineno"> 1091</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  937</span>                                                     {</div>
+<div class="line"><span class="lineno">  938</span>    <span class="keywordflow">while</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>) {</div>
+<div class="line"><span class="lineno">  939</span>        <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;IsLeaf()) {</div>
+<div class="line"><span class="lineno">  940</span>            <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;Contains(item)) {</div>
+<div class="line"><span class="lineno">  941</span>                <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;Is2Node()) {</div>
+<div class="line"><span class="lineno">  942</span>                    <span class="comment">// node must be root</span></div>
+<div class="line"><span class="lineno">  943</span>                    <span class="keyword">delete</span> <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
+<div class="line"><span class="lineno">  944</span>                    <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a> = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  945</span>                } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  946</span>                    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;RemoveItemByIndex(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemIndex(item), <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  947</span>                }</div>
+<div class="line"><span class="lineno">  948</span>                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  949</span>            }</div>
+<div class="line"><span class="lineno">  950</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  951</span>        }</div>
+<div class="line"><span class="lineno">  952</span> </div>
+<div class="line"><span class="lineno">  953</span>        <span class="comment">// node is internal</span></div>
+<div class="line"><span class="lineno">  954</span>        <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;Contains(item)) {</div>
+<div class="line"><span class="lineno">  955</span>            int8_t index = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemIndex(item);</div>
+<div class="line"><span class="lineno">  956</span> </div>
+<div class="line"><span class="lineno">  957</span>            <span class="comment">// Here is important!!! What we do next depend on its children&#39;s</span></div>
+<div class="line"><span class="lineno">  958</span>            <span class="comment">// state. Why?</span></div>
+<div class="line"><span class="lineno">  959</span>            <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *left_child = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemLeftChild(index);</div>
+<div class="line"><span class="lineno">  960</span>            <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *right_child = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemRightChild(index);</div>
+<div class="line"><span class="lineno">  961</span>            assert(left_child &amp;&amp; right_child);</div>
+<div class="line"><span class="lineno">  962</span> </div>
+<div class="line"><span class="lineno">  963</span>            <span class="keywordflow">if</span> (left_child-&gt;Is2Node() &amp;&amp; right_child-&gt;Is2Node()) {</div>
+<div class="line"><span class="lineno">  964</span>                <span class="comment">// both left and right child are 2-node,we should not modify</span></div>
+<div class="line"><span class="lineno">  965</span>                <span class="comment">// current node in this situation. Because we are going to do</span></div>
+<div class="line"><span class="lineno">  966</span>                <span class="comment">// merge with its children which will move target item to next</span></div>
+<div class="line"><span class="lineno">  967</span>                <span class="comment">// layer. so if we replace the item with successor or</span></div>
+<div class="line"><span class="lineno">  968</span>                <span class="comment">// predecessor now, when we do the recursive remove with</span></div>
+<div class="line"><span class="lineno">  969</span>                <span class="comment">// successor or predecessor, we will result in removing the just</span></div>
+<div class="line"><span class="lineno">  970</span>                <span class="comment">// replaced one in the merged node. That&#39;s not what we want.</span></div>
+<div class="line"><span class="lineno">  971</span> </div>
+<div class="line"><span class="lineno">  972</span>                <span class="comment">// we need to convert the child 2-node to 3-node or 4-node</span></div>
+<div class="line"><span class="lineno">  973</span>                <span class="comment">// first. First we try to see if any of them can convert to</span></div>
+<div class="line"><span class="lineno">  974</span>                <span class="comment">// 3-node by rotate. By using rotate we keep the empty house for</span></div>
+<div class="line"><span class="lineno">  975</span>                <span class="comment">// the future insertion which will be more efficient than merge.</span></div>
+<div class="line"><span class="lineno">  976</span>                <span class="comment">//</span></div>
+<div class="line"><span class="lineno">  977</span>                <span class="comment">//            | ? | node | ? |</span></div>
+<div class="line"><span class="lineno">  978</span>                <span class="comment">//           /    |      |    \</span></div>
+<div class="line"><span class="lineno">  979</span><span class="comment">                //          /     |      |     \</span></div>
+<div class="line"><span class="lineno">  980</span><span class="comment">                //         /      |      |      \</span></div>
+<div class="line"><span class="lineno">  981</span><span class="comment">                //        /       |      |       \</span></div>
+<div class="line"><span class="lineno">  982</span><span class="comment">                //       /        |      |        \</span></div>
+<div class="line"><span class="lineno">  983</span><span class="comment">                //      /         |      |         \</span></div>
+<div class="line"><span class="lineno">  984</span><span class="comment">                //     ?  left_child  right_child   ?</span></div>
+<div class="line"><span class="lineno">  985</span>                <span class="comment">//</span></div>
+<div class="line"><span class="lineno">  986</span> </div>
+<div class="line"><span class="lineno">  987</span>                <span class="comment">// node must be the root</span></div>
+<div class="line"><span class="lineno">  988</span>                <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;Is2Node()) {</div>
+<div class="line"><span class="lineno">  989</span>                    <span class="comment">// this means we can&#39;t avoid merging the target item into</span></div>
+<div class="line"><span class="lineno">  990</span>                    <span class="comment">// next layer, and this will cause us do different process</span></div>
+<div class="line"><span class="lineno">  991</span>                    <span class="comment">// compared with other cases</span></div>
+<div class="line"><span class="lineno">  992</span>                    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *new_root = <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a36f4d5f603f7edb7db7c73fb53ba14e9">Merge</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, index);</div>
+<div class="line"><span class="lineno">  993</span>                    <span class="keyword">delete</span> <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>;</div>
+<div class="line"><span class="lineno">  994</span>                    <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a> = new_root;</div>
+<div class="line"><span class="lineno">  995</span>                    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>;</div>
+<div class="line"><span class="lineno">  996</span> </div>
+<div class="line"><span class="lineno">  997</span>                    <span class="comment">// now node point to the</span></div>
+<div class="line"><span class="lineno">  998</span>                    <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno">  999</span>                }</div>
+<div class="line"><span class="lineno"> 1000</span> </div>
+<div class="line"><span class="lineno"> 1001</span>                <span class="comment">// here means we can avoid merging the target item into next</span></div>
+<div class="line"><span class="lineno"> 1002</span>                <span class="comment">// layer. So we convert one of its left or right child to 3-node</span></div>
+<div class="line"><span class="lineno"> 1003</span>                <span class="comment">// and then do the successor or predecessor swap and recursive</span></div>
+<div class="line"><span class="lineno"> 1004</span>                <span class="comment">// remove the next layer will successor or predecessor.</span></div>
+<div class="line"><span class="lineno"> 1005</span>                <span class="keywordflow">do</span> {</div>
+<div class="line"><span class="lineno"> 1006</span>                    <span class="keywordflow">if</span> (index &gt; 0) {</div>
+<div class="line"><span class="lineno"> 1007</span>                        <span class="comment">// left_child has left-sibling, we check if we can do a</span></div>
+<div class="line"><span class="lineno"> 1008</span>                        <span class="comment">// rotate</span></div>
+<div class="line"><span class="lineno"> 1009</span>                        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *left_sibling = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemLeftChild(index - 1);</div>
+<div class="line"><span class="lineno"> 1010</span>                        <span class="keywordflow">if</span> (left_sibling-&gt;Is34Node()) {</div>
+<div class="line"><span class="lineno"> 1011</span>                            <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#ae68f8e62be02657c1287def6b38d7cc9">RightRotate</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, index - 1);</div>
+<div class="line"><span class="lineno"> 1012</span>                            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno"> 1013</span>                        }</div>
+<div class="line"><span class="lineno"> 1014</span>                    }</div>
+<div class="line"><span class="lineno"> 1015</span> </div>
+<div class="line"><span class="lineno"> 1016</span>                    <span class="keywordflow">if</span> (index &lt; node-&gt;GetCount() - 1) {</div>
+<div class="line"><span class="lineno"> 1017</span>                        <span class="comment">// right_child has right-sibling, we check if we can do</span></div>
+<div class="line"><span class="lineno"> 1018</span>                        <span class="comment">// a rotate</span></div>
+<div class="line"><span class="lineno"> 1019</span>                        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *right_sibling =</div>
+<div class="line"><span class="lineno"> 1020</span>                            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemRightChild(index + 1);</div>
+<div class="line"><span class="lineno"> 1021</span>                        <span class="keywordflow">if</span> (right_sibling-&gt;Is34Node()) {</div>
+<div class="line"><span class="lineno"> 1022</span>                            <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#ae58dca20f08eaf9313f6e7b0869c2d0e">LeftRotate</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, index + 1);</div>
+<div class="line"><span class="lineno"> 1023</span>                            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno"> 1024</span>                        }</div>
+<div class="line"><span class="lineno"> 1025</span>                    }</div>
+<div class="line"><span class="lineno"> 1026</span> </div>
+<div class="line"><span class="lineno"> 1027</span>                    <span class="comment">// we do a merge. We avoid merging the target item, which</span></div>
+<div class="line"><span class="lineno"> 1028</span>                    <span class="comment">// may trigger another merge in the recursion process.</span></div>
+<div class="line"><span class="lineno"> 1029</span>                    <span class="keywordflow">if</span> (index &gt; 0) {</div>
+<div class="line"><span class="lineno"> 1030</span>                        <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a36f4d5f603f7edb7db7c73fb53ba14e9">Merge</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, index - 1);</div>
+<div class="line"><span class="lineno"> 1031</span>                        <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno"> 1032</span>                    }</div>
+<div class="line"><span class="lineno"> 1033</span> </div>
+<div class="line"><span class="lineno"> 1034</span>                    <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a36f4d5f603f7edb7db7c73fb53ba14e9">Merge</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, index + 1);</div>
+<div class="line"><span class="lineno"> 1035</span> </div>
+<div class="line"><span class="lineno"> 1036</span>                } <span class="keywordflow">while</span> (<span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno"> 1037</span>            }</div>
+<div class="line"><span class="lineno"> 1038</span> </div>
+<div class="line"><span class="lineno"> 1039</span>            <span class="comment">// refresh the left_child and right_child since they may be invalid</span></div>
+<div class="line"><span class="lineno"> 1040</span>            <span class="comment">// because of merge</span></div>
+<div class="line"><span class="lineno"> 1041</span>            left_child = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemLeftChild(index);</div>
+<div class="line"><span class="lineno"> 1042</span>            right_child = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemRightChild(index);</div>
+<div class="line"><span class="lineno"> 1043</span> </div>
+<div class="line"><span class="lineno"> 1044</span>            <span class="keywordflow">if</span> (left_child-&gt;Is34Node()) {</div>
+<div class="line"><span class="lineno"> 1045</span>                int64_t predecessor_item = <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#ac85ba5abfd6d34dcd908b2afe6464657">GetTreeMaxItem</a>(left_child);</div>
+<div class="line"><span class="lineno"> 1046</span>                <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;SetItem(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemIndex(item), predecessor_item);</div>
+<div class="line"><span class="lineno"> 1047</span> </div>
+<div class="line"><span class="lineno"> 1048</span>                <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = left_child;</div>
+<div class="line"><span class="lineno"> 1049</span>                item = predecessor_item;</div>
+<div class="line"><span class="lineno"> 1050</span>                <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno"> 1051</span>            }</div>
+<div class="line"><span class="lineno"> 1052</span> </div>
+<div class="line"><span class="lineno"> 1053</span>            <span class="keywordflow">if</span> (right_child-&gt;Is34Node()) {</div>
+<div class="line"><span class="lineno"> 1054</span>                int64_t successor_item = <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a65a1235659356166a3e9b451c64fcc36">GetTreeMinItem</a>(right_child);</div>
+<div class="line"><span class="lineno"> 1055</span>                <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;SetItem(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItemIndex(item), successor_item);</div>
+<div class="line"><span class="lineno"> 1056</span>                <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = right_child;</div>
+<div class="line"><span class="lineno"> 1057</span>                item = successor_item;</div>
+<div class="line"><span class="lineno"> 1058</span>                <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno"> 1059</span>            }</div>
+<div class="line"><span class="lineno"> 1060</span>        }</div>
+<div class="line"><span class="lineno"> 1061</span> </div>
+<div class="line"><span class="lineno"> 1062</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *next_node = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetNextPossibleChild(item);</div>
+<div class="line"><span class="lineno"> 1063</span> </div>
+<div class="line"><span class="lineno"> 1064</span>        <span class="keywordflow">if</span> (next_node-&gt;Is34Node()) {</div>
+<div class="line"><span class="lineno"> 1065</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = next_node;</div>
+<div class="line"><span class="lineno"> 1066</span>            <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno"> 1067</span>        }</div>
+<div class="line"><span class="lineno"> 1068</span> </div>
+<div class="line"><span class="lineno"> 1069</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#aec0642d1d151521ca7c70ea85cdb15d3">TryRightRotate</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, next_node)) {</div>
+<div class="line"><span class="lineno"> 1070</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = next_node;</div>
+<div class="line"><span class="lineno"> 1071</span>            <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno"> 1072</span>        }</div>
+<div class="line"><span class="lineno"> 1073</span> </div>
+<div class="line"><span class="lineno"> 1074</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#ac5361479dd996eb331759f33808657d9">TryLeftRotate</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, next_node)) {</div>
+<div class="line"><span class="lineno"> 1075</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = next_node;</div>
+<div class="line"><span class="lineno"> 1076</span>            <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno"> 1077</span>        }</div>
+<div class="line"><span class="lineno"> 1078</span> </div>
+<div class="line"><span class="lineno"> 1079</span>        <span class="comment">// get here means both left sibling and right sibling of next_node is</span></div>
+<div class="line"><span class="lineno"> 1080</span>        <span class="comment">// 2-node, so we do merge</span></div>
+<div class="line"><span class="lineno"> 1081</span>        int8_t child_index = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetChildIndex(next_node);</div>
+<div class="line"><span class="lineno"> 1082</span>        <span class="keywordflow">if</span> (child_index &gt; 0) {</div>
+<div class="line"><span class="lineno"> 1083</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a36f4d5f603f7edb7db7c73fb53ba14e9">Merge</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, child_index - 1);</div>
+<div class="line"><span class="lineno"> 1084</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno"> 1085</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a36f4d5f603f7edb7db7c73fb53ba14e9">Merge</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, child_index);</div>
+<div class="line"><span class="lineno"> 1086</span>        }</div>
+<div class="line"><span class="lineno"> 1087</span> </div>
+<div class="line"><span class="lineno"> 1088</span>    }  <span class="comment">// while</span></div>
+<div class="line"><span class="lineno"> 1089</span> </div>
+<div class="line"><span class="lineno"> 1090</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno"> 1091</span>}</div>
 <div class="ttc" id="aclassdata__structures_1_1tree__234_1_1_tree234_html_a36f4d5f603f7edb7db7c73fb53ba14e9"><div class="ttname"><a href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a36f4d5f603f7edb7db7c73fb53ba14e9">data_structures::tree_234::Tree234::Merge</a></div><div class="ttdeci">Node * Merge(Node *parent, int8_t index)</div><div class="ttdoc">Merge the item at index of the parent node, and its left and right child.</div><div class="ttdef"><b>Definition:</b> tree_234.cpp:895</div></div>
 <div class="ttc" id="aclassdata__structures_1_1tree__234_1_1_tree234_html_a65a1235659356166a3e9b451c64fcc36"><div class="ttname"><a href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a65a1235659356166a3e9b451c64fcc36">data_structures::tree_234::Tree234::GetTreeMinItem</a></div><div class="ttdeci">int64_t GetTreeMinItem(Node *tree)</div><div class="ttdoc">Get the min item of the tree.</div><div class="ttdef"><b>Definition:</b> tree_234.cpp:1115</div></div>
 <div class="ttc" id="aclassdata__structures_1_1tree__234_1_1_tree234_html_ac5361479dd996eb331759f33808657d9"><div class="ttname"><a href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#ac5361479dd996eb331759f33808657d9">data_structures::tree_234::Tree234::TryLeftRotate</a></div><div class="ttdeci">bool TryLeftRotate(Node *parent, Node *to_child)</div><div class="ttdoc">A handy function to try if we can do a left rotate to the target node.</div><div class="ttdef"><b>Definition:</b> tree_234.cpp:778</div></div>
@@ -1406,18 +1406,18 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00845" name="l00845"></a><span class="lineno">  845</span>                                                    {</div>
-<div class="line"><a id="l00846" name="l00846"></a><span class="lineno">  846</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> = parent-&gt;GetItemLeftChild(index);</div>
-<div class="line"><a id="l00847" name="l00847"></a><span class="lineno">  847</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> = parent-&gt;GetItemRightChild(index);</div>
-<div class="line"><a id="l00848" name="l00848"></a><span class="lineno">  848</span> </div>
-<div class="line"><a id="l00849" name="l00849"></a><span class="lineno">  849</span>    assert(left &amp;&amp; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>-&gt;Is34Node());</div>
-<div class="line"><a id="l00850" name="l00850"></a><span class="lineno">  850</span>    assert(right &amp;&amp; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>-&gt;Is2Node());</div>
-<div class="line"><a id="l00851" name="l00851"></a><span class="lineno">  851</span> </div>
-<div class="line"><a id="l00852" name="l00852"></a><span class="lineno">  852</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>-&gt;InsertItemByIndex(0, parent-&gt;GetItem(index),</div>
-<div class="line"><a id="l00853" name="l00853"></a><span class="lineno">  853</span>                             <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>-&gt;GetRightmostChild(), <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00854" name="l00854"></a><span class="lineno">  854</span>    parent-&gt;SetItem(index, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>-&gt;GetMaxItem());</div>
-<div class="line"><a id="l00855" name="l00855"></a><span class="lineno">  855</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>-&gt;RemoveItemByIndex(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>-&gt;GetCount() - 1, <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00856" name="l00856"></a><span class="lineno">  856</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  845</span>                                                    {</div>
+<div class="line"><span class="lineno">  846</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> = parent-&gt;GetItemLeftChild(index);</div>
+<div class="line"><span class="lineno">  847</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> = parent-&gt;GetItemRightChild(index);</div>
+<div class="line"><span class="lineno">  848</span> </div>
+<div class="line"><span class="lineno">  849</span>    assert(left &amp;&amp; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>-&gt;Is34Node());</div>
+<div class="line"><span class="lineno">  850</span>    assert(right &amp;&amp; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>-&gt;Is2Node());</div>
+<div class="line"><span class="lineno">  851</span> </div>
+<div class="line"><span class="lineno">  852</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>-&gt;InsertItemByIndex(0, parent-&gt;GetItem(index),</div>
+<div class="line"><span class="lineno">  853</span>                             <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>-&gt;GetRightmostChild(), <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  854</span>    parent-&gt;SetItem(index, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>-&gt;GetMaxItem());</div>
+<div class="line"><span class="lineno">  855</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>-&gt;RemoveItemByIndex(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>-&gt;GetCount() - 1, <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  856</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1453,23 +1453,23 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>split parent node </dd></dl>
-<div class="fragment"><div class="line"><a id="l00745" name="l00745"></a><span class="lineno">  745</span>                                   {</div>
-<div class="line"><a id="l00746" name="l00746"></a><span class="lineno">  746</span>    assert(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetCount() == 3);</div>
-<div class="line"><a id="l00747" name="l00747"></a><span class="lineno">  747</span> </div>
-<div class="line"><a id="l00748" name="l00748"></a><span class="lineno">  748</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> = <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
-<div class="line"><a id="l00749" name="l00749"></a><span class="lineno">  749</span> </div>
-<div class="line"><a id="l00750" name="l00750"></a><span class="lineno">  750</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> = <span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(2));</div>
-<div class="line"><a id="l00751" name="l00751"></a><span class="lineno">  751</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>-&gt;SetChild(0, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetChild(2));</div>
-<div class="line"><a id="l00752" name="l00752"></a><span class="lineno">  752</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>-&gt;SetChild(1, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetChild(3));</div>
-<div class="line"><a id="l00753" name="l00753"></a><span class="lineno">  753</span> </div>
-<div class="line"><a id="l00754" name="l00754"></a><span class="lineno">  754</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *parent = <span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(1));</div>
-<div class="line"><a id="l00755" name="l00755"></a><span class="lineno">  755</span>    parent-&gt;SetChild(0, left);</div>
-<div class="line"><a id="l00756" name="l00756"></a><span class="lineno">  756</span>    parent-&gt;SetChild(1, right);</div>
-<div class="line"><a id="l00757" name="l00757"></a><span class="lineno">  757</span> </div>
-<div class="line"><a id="l00758" name="l00758"></a><span class="lineno">  758</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>-&gt;SetCount(1);</div>
-<div class="line"><a id="l00759" name="l00759"></a><span class="lineno">  759</span> </div>
-<div class="line"><a id="l00760" name="l00760"></a><span class="lineno">  760</span>    <span class="keywordflow">return</span> parent;</div>
-<div class="line"><a id="l00761" name="l00761"></a><span class="lineno">  761</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  745</span>                                   {</div>
+<div class="line"><span class="lineno">  746</span>    assert(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetCount() == 3);</div>
+<div class="line"><span class="lineno">  747</span> </div>
+<div class="line"><span class="lineno">  748</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> = <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
+<div class="line"><span class="lineno">  749</span> </div>
+<div class="line"><span class="lineno">  750</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> = <span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(2));</div>
+<div class="line"><span class="lineno">  751</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>-&gt;SetChild(0, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetChild(2));</div>
+<div class="line"><span class="lineno">  752</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>-&gt;SetChild(1, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetChild(3));</div>
+<div class="line"><span class="lineno">  753</span> </div>
+<div class="line"><span class="lineno">  754</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *parent = <span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(1));</div>
+<div class="line"><span class="lineno">  755</span>    parent-&gt;SetChild(0, left);</div>
+<div class="line"><span class="lineno">  756</span>    parent-&gt;SetChild(1, right);</div>
+<div class="line"><span class="lineno">  757</span> </div>
+<div class="line"><span class="lineno">  758</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>-&gt;SetCount(1);</div>
+<div class="line"><span class="lineno">  759</span> </div>
+<div class="line"><span class="lineno">  760</span>    <span class="keywordflow">return</span> parent;</div>
+<div class="line"><span class="lineno">  761</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1496,10 +1496,10 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00562" name="l00562"></a><span class="lineno">  562</span>                       {</div>
-<div class="line"><a id="l00563" name="l00563"></a><span class="lineno">  563</span>    <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a84ab7b4fe7442b5e2eeed8c050bb86bd">Traverse</a>(<a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>);</div>
-<div class="line"><a id="l00564" name="l00564"></a><span class="lineno">  564</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00565" name="l00565"></a><span class="lineno">  565</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  562</span>                       {</div>
+<div class="line"><span class="lineno">  563</span>    <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a84ab7b4fe7442b5e2eeed8c050bb86bd">Traverse</a>(<a class="code hl_variable" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a348ea76c7629b2dcf740be062f970a36">root_</a>);</div>
+<div class="line"><span class="lineno">  564</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  565</span>}</div>
 <div class="ttc" id="aclassdata__structures_1_1tree__234_1_1_tree234_html_a84ab7b4fe7442b5e2eeed8c050bb86bd"><div class="ttname"><a href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a84ab7b4fe7442b5e2eeed8c050bb86bd">data_structures::tree_234::Tree234::Traverse</a></div><div class="ttdeci">void Traverse()</div><div class="ttdoc">In-order traverse.</div><div class="ttdef"><b>Definition:</b> tree_234.cpp:562</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -1541,19 +1541,19 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00567" name="l00567"></a><span class="lineno">  567</span>                                 {</div>
-<div class="line"><a id="l00568" name="l00568"></a><span class="lineno">  568</span>    <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>) {</div>
-<div class="line"><a id="l00569" name="l00569"></a><span class="lineno">  569</span>        <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00570" name="l00570"></a><span class="lineno">  570</span>    }</div>
-<div class="line"><a id="l00571" name="l00571"></a><span class="lineno">  571</span> </div>
-<div class="line"><a id="l00572" name="l00572"></a><span class="lineno">  572</span>    int8_t i = 0;</div>
-<div class="line"><a id="l00573" name="l00573"></a><span class="lineno">  573</span>    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetCount(); i++) {</div>
-<div class="line"><a id="l00574" name="l00574"></a><span class="lineno">  574</span>        <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a84ab7b4fe7442b5e2eeed8c050bb86bd">Traverse</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetChild(i));</div>
-<div class="line"><a id="l00575" name="l00575"></a><span class="lineno">  575</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetItem(i) &lt;&lt; <span class="stringliteral">&quot;, &quot;</span>;</div>
-<div class="line"><a id="l00576" name="l00576"></a><span class="lineno">  576</span>    }</div>
-<div class="line"><a id="l00577" name="l00577"></a><span class="lineno">  577</span> </div>
-<div class="line"><a id="l00578" name="l00578"></a><span class="lineno">  578</span>    <a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a84ab7b4fe7442b5e2eeed8c050bb86bd">Traverse</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;GetChild(i));</div>
-<div class="line"><a id="l00579" name="l00579"></a><span class="lineno">  579</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  567</span>                                 {</div>
+<div class="line"><span class="lineno">  568</span>    <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>) {</div>
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+<div class="line"><span class="lineno">  571</span> </div>
+<div class="line"><span class="lineno">  572</span>    int8_t i = 0;</div>
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-<div class="fragment"><div class="line"><a id="l00778" name="l00778"></a><span class="lineno">  778</span>                                                        {</div>
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+<div class="line"><span class="lineno">  781</span>    <span class="comment">// child is right most, can not do left rotate to it</span></div>
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 <dl class="section see"><dt>See also</dt><dd><a class="el" href="../../df/d28/dsu__union__rank_8cpp.html" title="DSU (Disjoint sets)">dsu_union_rank.cpp</a> </dd></dl>
 </div><h2 class="groupheader">Function Documentation</h2>
 <a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
@@ -152,15 +153,15 @@ Functions</h2></td></tr>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
 <p >&lt; number of items</p>
 <p >&lt; object of class disjoint sets</p>
-<div class="fragment"><div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>           {</div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    uint64_t n = 10;  <span class="comment">///&lt; number of items</span></div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>    <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1);     <span class="comment">///&lt; object of class disjoint sets</span></div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span> </div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>    <a class="code hl_function" href="../../d3/dae/dsu__path__compression_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a>();  <span class="comment">// run 1st test case</span></div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>    <a class="code hl_function" href="../../d3/dae/dsu__path__compression_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a>();  <span class="comment">// run 2nd test case</span></div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span> </div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  205</span>           {</div>
+<div class="line"><span class="lineno">  206</span>    uint64_t n = 10;  <span class="comment">///&lt; number of items</span></div>
+<div class="line"><span class="lineno">  207</span>    <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1);     <span class="comment">///&lt; object of class disjoint sets</span></div>
+<div class="line"><span class="lineno">  208</span> </div>
+<div class="line"><span class="lineno">  209</span>    <a class="code hl_function" href="../../d3/dae/dsu__path__compression_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a>();  <span class="comment">// run 1st test case</span></div>
+<div class="line"><span class="lineno">  210</span>    <a class="code hl_function" href="../../d3/dae/dsu__path__compression_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a>();  <span class="comment">// run 2nd test case</span></div>
+<div class="line"><span class="lineno">  211</span> </div>
+<div class="line"><span class="lineno">  212</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  213</span>}</div>
 <div class="ttc" id="aclassdsu_html"><div class="ttname"><a href="../../dd/d1f/classdsu.html">dsu</a></div><div class="ttdoc">Disjoint sets union data structure, class based representation.</div><div class="ttdef"><b>Definition:</b> dsu_path_compression.cpp:33</div></div>
 <div class="ttc" id="adsu__path__compression_8cpp_html_a45d94ead4cf4e1ff9f87c38bc99f59ae"><div class="ttname"><a href="../../d3/dae/dsu__path__compression_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a></div><div class="ttdeci">static void test2()</div><div class="ttdoc">Self-implementations, 2nd test.</div><div class="ttdef"><b>Definition:</b> dsu_path_compression.cpp:186</div></div>
 <div class="ttc" id="adsu__path__compression_8cpp_html_ae7880ce913f3058a35ff106d5be9e243"><div class="ttname"><a href="../../d3/dae/dsu__path__compression_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a></div><div class="ttdeci">static void test1()</div><div class="ttdoc">Self-test implementations, 1st test.</div><div class="ttdef"><b>Definition:</b> dsu_path_compression.cpp:169</div></div>
@@ -200,19 +201,19 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
 <p >&lt; number of items</p>
 <p >&lt; object of class disjoint sets</p>
-<div class="fragment"><div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>                    {</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>    <span class="comment">// the minimum, maximum, and size of the set</span></div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>    uint64_t n = 10;  <span class="comment">///&lt; number of items</span></div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>    <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1);     <span class="comment">///&lt; object of class disjoint sets</span></div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>    <span class="comment">// set 1</span></div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>    d.UnionSet(1, 2);  <span class="comment">// performs union operation on 1 and 2</span></div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>    d.UnionSet(1, 4);  <span class="comment">// performs union operation on 1 and 4</span></div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = {1, 4, 3};</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>    <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.size(); i++) {</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>        assert(d.get(4).at(i) == <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>[i]);  <span class="comment">// makes sure algorithm works fine</span></div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>    }</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test passed!&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  169</span>                    {</div>
+<div class="line"><span class="lineno">  170</span>    <span class="comment">// the minimum, maximum, and size of the set</span></div>
+<div class="line"><span class="lineno">  171</span>    uint64_t n = 10;  <span class="comment">///&lt; number of items</span></div>
+<div class="line"><span class="lineno">  172</span>    <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1);     <span class="comment">///&lt; object of class disjoint sets</span></div>
+<div class="line"><span class="lineno">  173</span>    <span class="comment">// set 1</span></div>
+<div class="line"><span class="lineno">  174</span>    d.UnionSet(1, 2);  <span class="comment">// performs union operation on 1 and 2</span></div>
+<div class="line"><span class="lineno">  175</span>    d.UnionSet(1, 4);  <span class="comment">// performs union operation on 1 and 4</span></div>
+<div class="line"><span class="lineno">  176</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = {1, 4, 3};</div>
+<div class="line"><span class="lineno">  177</span>    <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.size(); i++) {</div>
+<div class="line"><span class="lineno">  178</span>        assert(d.get(4).at(i) == <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>[i]);  <span class="comment">// makes sure algorithm works fine</span></div>
+<div class="line"><span class="lineno">  179</span>    }</div>
+<div class="line"><span class="lineno">  180</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test passed!&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
+<div class="line"><span class="lineno">  181</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="amatrix__exponentiation_8cpp_html_a600eaf353befc174637855795f12d258"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a></div><div class="ttdeci">#define endl</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:36</div></div>
 <div class="ttc" id="amatrix__exponentiation_8cpp_html_ad8389ed58fd0ec66df248014775ad1fa"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a></div><div class="ttdeci">ll ans(ll n)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:91</div></div>
@@ -253,20 +254,20 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
 <p >&lt; number of items</p>
 <p >&lt; object of class disjoint sets</p>
-<div class="fragment"><div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>                    {</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>    <span class="comment">// the minimum, maximum, and size of the set</span></div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>    uint64_t n = 10;  <span class="comment">///&lt; number of items</span></div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>    <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1);     <span class="comment">///&lt; object of class disjoint sets</span></div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>    <span class="comment">// set 1</span></div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>    d.UnionSet(3, 5);</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>    d.UnionSet(5, 6);</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>    d.UnionSet(5, 7);</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = {3, 7, 4};</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>    <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.size(); i++) {</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>        assert(d.get(3).at(i) == <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>[i]);  <span class="comment">// makes sure algorithm works fine</span></div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>    }</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test passed!&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  186</span>                    {</div>
+<div class="line"><span class="lineno">  187</span>    <span class="comment">// the minimum, maximum, and size of the set</span></div>
+<div class="line"><span class="lineno">  188</span>    uint64_t n = 10;  <span class="comment">///&lt; number of items</span></div>
+<div class="line"><span class="lineno">  189</span>    <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1);     <span class="comment">///&lt; object of class disjoint sets</span></div>
+<div class="line"><span class="lineno">  190</span>    <span class="comment">// set 1</span></div>
+<div class="line"><span class="lineno">  191</span>    d.UnionSet(3, 5);</div>
+<div class="line"><span class="lineno">  192</span>    d.UnionSet(5, 6);</div>
+<div class="line"><span class="lineno">  193</span>    d.UnionSet(5, 7);</div>
+<div class="line"><span class="lineno">  194</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = {3, 7, 4};</div>
+<div class="line"><span class="lineno">  195</span>    <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.size(); i++) {</div>
+<div class="line"><span class="lineno">  196</span>        assert(d.get(3).at(i) == <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>[i]);  <span class="comment">// makes sure algorithm works fine</span></div>
+<div class="line"><span class="lineno">  197</span>    }</div>
+<div class="line"><span class="lineno">  198</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test passed!&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
+<div class="line"><span class="lineno">  199</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -282,7 +283,7 @@ Here is the call graph for this function:</div>
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-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Running Test-1...&quot;</span>);</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span> </div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>    <a class="code hl_class" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html">others::lru_cache::LRUCache</a> cache(4);</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    cache.refer(1);</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>    cache.refer(2);</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    cache.refer(5);</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>    cache.refer(1);</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>    cache.refer(4);</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>    cache.refer(5);</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span> </div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Checking assert statement...&quot;</span>);</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>    assert(cache.getHits() == expected_hits &amp;&amp;</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>           cache.getPageFault() == expected_pageFault);</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Assert successful!&quot;</span>);</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Test-1 complete!&quot;</span>);</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  159</span>                     {</div>
+<div class="line"><span class="lineno">  160</span>    uint64_t expected_hits = 2;</div>
+<div class="line"><span class="lineno">  161</span>    uint64_t expected_pageFault = 4;</div>
+<div class="line"><span class="lineno">  162</span> </div>
+<div class="line"><span class="lineno">  163</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Running Test-1...&quot;</span>);</div>
+<div class="line"><span class="lineno">  164</span> </div>
+<div class="line"><span class="lineno">  165</span>    <a class="code hl_class" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html">others::lru_cache::LRUCache</a> cache(4);</div>
+<div class="line"><span class="lineno">  166</span>    cache.refer(1);</div>
+<div class="line"><span class="lineno">  167</span>    cache.refer(2);</div>
+<div class="line"><span class="lineno">  168</span>    cache.refer(5);</div>
+<div class="line"><span class="lineno">  169</span>    cache.refer(1);</div>
+<div class="line"><span class="lineno">  170</span>    cache.refer(4);</div>
+<div class="line"><span class="lineno">  171</span>    cache.refer(5);</div>
+<div class="line"><span class="lineno">  172</span> </div>
+<div class="line"><span class="lineno">  173</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Checking assert statement...&quot;</span>);</div>
+<div class="line"><span class="lineno">  174</span>    assert(cache.getHits() == expected_hits &amp;&amp;</div>
+<div class="line"><span class="lineno">  175</span>           cache.getPageFault() == expected_pageFault);</div>
+<div class="line"><span class="lineno">  176</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Assert successful!&quot;</span>);</div>
+<div class="line"><span class="lineno">  177</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Test-1 complete!&quot;</span>);</div>
+<div class="line"><span class="lineno">  178</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../d3/db3/lru__cache_8cpp_a6401e8f2d41d8cc9cd0e52ab381608d4_cgraph.svg" width="347" height="183"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d3/db3/lru__cache_8cpp_a6401e8f2d41d8cc9cd0e52ab381608d4_cgraph.svg" width="562" height="475"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
 </div>
 </div>
 
@@ -393,30 +393,30 @@ Here is the call graph for this function:</div>
 
 <p>A test case contains hits more than cache size The assert statement will check expected hist and miss to resultant hits and miss. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>                     {</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>    uint64_t expected_hits = 4;</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>    uint64_t expected_pageFault = 2;</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span> </div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Running Test-2...&quot;</span>);</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span> </div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>    <a class="code hl_class" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html">others::lru_cache::LRUCache</a> cache(4);</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>    cache.refer(1);</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>    cache.refer(1);</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>    cache.refer(1);</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>    cache.refer(1);</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>    cache.refer(1);</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>    cache.refer(5);</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span> </div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Checking assert statement...&quot;</span>);</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>    assert(cache.getHits() == expected_hits &amp;&amp;</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>           cache.getPageFault() == expected_pageFault);</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Assert successful!&quot;</span>);</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Test-2 complete!&quot;</span>);</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  186</span>                     {</div>
+<div class="line"><span class="lineno">  187</span>    uint64_t expected_hits = 4;</div>
+<div class="line"><span class="lineno">  188</span>    uint64_t expected_pageFault = 2;</div>
+<div class="line"><span class="lineno">  189</span> </div>
+<div class="line"><span class="lineno">  190</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Running Test-2...&quot;</span>);</div>
+<div class="line"><span class="lineno">  191</span> </div>
+<div class="line"><span class="lineno">  192</span>    <a class="code hl_class" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html">others::lru_cache::LRUCache</a> cache(4);</div>
+<div class="line"><span class="lineno">  193</span>    cache.refer(1);</div>
+<div class="line"><span class="lineno">  194</span>    cache.refer(1);</div>
+<div class="line"><span class="lineno">  195</span>    cache.refer(1);</div>
+<div class="line"><span class="lineno">  196</span>    cache.refer(1);</div>
+<div class="line"><span class="lineno">  197</span>    cache.refer(1);</div>
+<div class="line"><span class="lineno">  198</span>    cache.refer(5);</div>
+<div class="line"><span class="lineno">  199</span> </div>
+<div class="line"><span class="lineno">  200</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Checking assert statement...&quot;</span>);</div>
+<div class="line"><span class="lineno">  201</span>    assert(cache.getHits() == expected_hits &amp;&amp;</div>
+<div class="line"><span class="lineno">  202</span>           cache.getPageFault() == expected_pageFault);</div>
+<div class="line"><span class="lineno">  203</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Assert successful!&quot;</span>);</div>
+<div class="line"><span class="lineno">  204</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Test-2 complete!&quot;</span>);</div>
+<div class="line"><span class="lineno">  205</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../d3/db3/lru__cache_8cpp_a4b02e288a407876a8d6024f98a2a25ec_cgraph.svg" width="347" height="183"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d3/db3/lru__cache_8cpp_a4b02e288a407876a8d6024f98a2a25ec_cgraph.svg" width="562" height="475"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
 </div>
 </div>
 
@@ -447,30 +447,30 @@ Here is the call graph for this function:</div>
 
 <p>A simple test case The assert statement will check expected hist and miss to resultant hits and miss. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>                     {</div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>    uint64_t expected_hits = 1;</div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>    uint64_t expected_pageFault = 5;</div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span> </div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Running Test-3...&quot;</span>);</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span> </div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>    <a class="code hl_class" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html">others::lru_cache::LRUCache</a> cache(4);</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>    cache.refer(1);</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>    cache.refer(2);</div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>    cache.refer(3);</div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>    cache.refer(4);</div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    cache.refer(5);</div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>    cache.refer(5);</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span> </div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Checking assert statement...&quot;</span>);</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    assert(cache.getHits() == expected_hits &amp;&amp;</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>           cache.getPageFault() == expected_pageFault);</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Assert successful!&quot;</span>);</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Test-3 complete!&quot;</span>);</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  213</span>                     {</div>
+<div class="line"><span class="lineno">  214</span>    uint64_t expected_hits = 1;</div>
+<div class="line"><span class="lineno">  215</span>    uint64_t expected_pageFault = 5;</div>
+<div class="line"><span class="lineno">  216</span> </div>
+<div class="line"><span class="lineno">  217</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Running Test-3...&quot;</span>);</div>
+<div class="line"><span class="lineno">  218</span> </div>
+<div class="line"><span class="lineno">  219</span>    <a class="code hl_class" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html">others::lru_cache::LRUCache</a> cache(4);</div>
+<div class="line"><span class="lineno">  220</span>    cache.refer(1);</div>
+<div class="line"><span class="lineno">  221</span>    cache.refer(2);</div>
+<div class="line"><span class="lineno">  222</span>    cache.refer(3);</div>
+<div class="line"><span class="lineno">  223</span>    cache.refer(4);</div>
+<div class="line"><span class="lineno">  224</span>    cache.refer(5);</div>
+<div class="line"><span class="lineno">  225</span>    cache.refer(5);</div>
+<div class="line"><span class="lineno">  226</span> </div>
+<div class="line"><span class="lineno">  227</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Checking assert statement...&quot;</span>);</div>
+<div class="line"><span class="lineno">  228</span>    assert(cache.getHits() == expected_hits &amp;&amp;</div>
+<div class="line"><span class="lineno">  229</span>           cache.getPageFault() == expected_pageFault);</div>
+<div class="line"><span class="lineno">  230</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Assert successful!&quot;</span>);</div>
+<div class="line"><span class="lineno">  231</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(<span class="stringliteral">&quot;Test-3 complete!&quot;</span>);</div>
+<div class="line"><span class="lineno">  232</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../d3/db3/lru__cache_8cpp_a01ec21fc91ddafd964ae2035ba7892c0_cgraph.svg" width="347" height="183"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d3/db3/lru__cache_8cpp_a01ec21fc91ddafd964ae2035ba7892c0_cgraph.svg" width="562" height="475"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
 </div>
 </div>
 
@@ -482,7 +482,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_9510827d0b234b3cc54b29892f217477.html">others</a></li><li class="navelem"><a class="el" href="../../d3/db3/lru__cache_8cpp.html">lru_cache.cpp</a></li>
-    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.2 </li>
+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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diff --git a/d3/db3/lru__cache_8cpp_a01ec21fc91ddafd964ae2035ba7892c0_cgraph.map b/d3/db3/lru__cache_8cpp_a01ec21fc91ddafd964ae2035ba7892c0_cgraph.map
index 303bf6a33..363cacfbe 100644
--- a/d3/db3/lru__cache_8cpp_a01ec21fc91ddafd964ae2035ba7892c0_cgraph.map
+++ b/d3/db3/lru__cache_8cpp_a01ec21fc91ddafd964ae2035ba7892c0_cgraph.map
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-<div class="fragment"><div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>                                                {</div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>        <span class="keyword">auto</span> graphAjdList = <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.getAdjList();</div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>        <span class="keyword">auto</span> vertices = <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.getVertices();</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span> </div>
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-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>            <span class="keywordflow">for</span> (<span class="keyword">auto</span> <span class="keyword">const</span>&amp; child : children) {</div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>                indegree[child]++;</div>
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-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>            <span class="comment">// Decrease number of nodes that need to be traversed.</span></div>
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-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>            <span class="keyword">auto</span> it = graphAjdList.find(solved);</div>
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+<div class="line"><span class="lineno">  251</span>        <span class="keyword">auto</span> vertices = <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.getVertices();</div>
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+<div class="line"><span class="lineno">  267</span>                can_be_solved.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/emplace.html">emplace</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>);</div>
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+<div class="line"><span class="lineno">  275</span>            <span class="keyword">auto</span> solved = can_be_solved.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/front.html">front</a>();</div>
+<div class="line"><span class="lineno">  276</span>            <span class="comment">// Visit the node.</span></div>
+<div class="line"><span class="lineno">  277</span>            can_be_solved.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/pop.html">pop</a>();</div>
+<div class="line"><span class="lineno">  278</span>            <span class="comment">// Decrease number of nodes that need to be traversed.</span></div>
+<div class="line"><span class="lineno">  279</span>            remain--;</div>
+<div class="line"><span class="lineno">  280</span> </div>
+<div class="line"><span class="lineno">  281</span>            <span class="comment">// Visit all the children of the visited node.</span></div>
+<div class="line"><span class="lineno">  282</span>            <span class="keyword">auto</span> it = graphAjdList.find(solved);</div>
+<div class="line"><span class="lineno">  283</span>            <span class="keywordflow">if</span> (it != graphAjdList.end()) {</div>
+<div class="line"><span class="lineno">  284</span>                <span class="keywordflow">for</span> (<span class="keyword">auto</span> child : it-&gt;second) {</div>
+<div class="line"><span class="lineno">  285</span>                    <span class="comment">// Check if we can visited the node safely.</span></div>
+<div class="line"><span class="lineno">  286</span>                    <span class="keywordflow">if</span> (--indegree[child] == 0) {</div>
+<div class="line"><span class="lineno">  287</span>                        <span class="comment">// if node can be visited safely, then add that node to</span></div>
+<div class="line"><span class="lineno">  288</span>                        <span class="comment">// the visit queue.</span></div>
+<div class="line"><span class="lineno">  289</span>                        can_be_solved.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/emplace.html">emplace</a>(child);</div>
+<div class="line"><span class="lineno">  290</span>                    }</div>
+<div class="line"><span class="lineno">  291</span>                }</div>
+<div class="line"><span class="lineno">  292</span>            }</div>
+<div class="line"><span class="lineno">  293</span>        }</div>
+<div class="line"><span class="lineno">  294</span> </div>
+<div class="line"><span class="lineno">  295</span>        <span class="comment">// If there are still nodes that we can&#39;t visit, then it means that</span></div>
+<div class="line"><span class="lineno">  296</span>        <span class="comment">// there is a cycle and return true, else return false.</span></div>
+<div class="line"><span class="lineno">  297</span>        <span class="keywordflow">return</span> !(remain == 0);</div>
+<div class="line"><span class="lineno">  298</span>    }</div>
 <div class="ttc" id="aemplace_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue/emplace.html">std::queue::emplace</a></div><div class="ttdeci">T emplace(T... args)</div></div>
 <div class="ttc" id="aempty_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue/empty.html">std::queue::empty</a></div><div class="ttdeci">T empty(T... args)</div></div>
 <div class="ttc" id="afront_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue/front.html">std::queue::front</a></div><div class="ttdeci">T front(T... args)</div></div>
@@ -286,35 +286,35 @@ Here is the call graph for this function:</div>
 <p >State of the node.</p>
 <p >It is a vector of "nodeStates" which represents the state node is in. It can take only 3 values: "not_visited", "in_stack", and "visited".</p>
 <p >Initially, all nodes are in "not_visited" state.</p>
-<div class="fragment"><div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>                                                {</div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>        <span class="keyword">auto</span> vertices = <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.getVertices();</div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span><span class="comment"></span> </div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span><span class="comment">        /** State of the node.</span></div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span><span class="comment">         *</span></div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span><span class="comment">         * It is a vector of &quot;nodeStates&quot; which represents the state node is in.</span></div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span><span class="comment">         * It can take only 3 values: &quot;not_visited&quot;, &quot;in_stack&quot;, and &quot;visited&quot;.</span></div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span><span class="comment">         *</span></div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span><span class="comment">         * Initially, all nodes are in &quot;not_visited&quot; state.</span></div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span><span class="comment">         */</span></div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;nodeStates&gt;</a> state(vertices, not_visited);</div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span> </div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>        <span class="comment">// Start visiting each node.</span></div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>        <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = 0; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> &lt; vertices; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>++) {</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>            <span class="comment">// If a node is not visited, only then check for presence of cycle.</span></div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>            <span class="comment">// There is no need to check for presence of cycle for a visited</span></div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>            <span class="comment">// node as it has already been checked for presence of cycle.</span></div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>            <span class="keywordflow">if</span> (state[<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>] == not_visited) {</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>                <span class="comment">// Check for cycle.</span></div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>                <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d3/dbb/class_cycle_check.html#a2f4485c08b45e7a21a2e86f9c3f01d8b">isCyclicDFSHelper</a>(<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.getAdjList(), &amp;state, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>)) {</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>                    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>                }</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>            }</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>        }</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span> </div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>        <span class="comment">// All nodes have been safely traversed, that means there is no cycle in</span></div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>        <span class="comment">// the graph. Return false.</span></div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  212</span>                                                {</div>
+<div class="line"><span class="lineno">  213</span>        <span class="keyword">auto</span> vertices = <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.getVertices();</div>
+<div class="line"><span class="lineno">  214</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  215</span><span class="comment">        /** State of the node.</span></div>
+<div class="line"><span class="lineno">  216</span><span class="comment">         *</span></div>
+<div class="line"><span class="lineno">  217</span><span class="comment">         * It is a vector of &quot;nodeStates&quot; which represents the state node is in.</span></div>
+<div class="line"><span class="lineno">  218</span><span class="comment">         * It can take only 3 values: &quot;not_visited&quot;, &quot;in_stack&quot;, and &quot;visited&quot;.</span></div>
+<div class="line"><span class="lineno">  219</span><span class="comment">         *</span></div>
+<div class="line"><span class="lineno">  220</span><span class="comment">         * Initially, all nodes are in &quot;not_visited&quot; state.</span></div>
+<div class="line"><span class="lineno">  221</span><span class="comment">         */</span></div>
+<div class="line"><span class="lineno">  222</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;nodeStates&gt;</a> state(vertices, not_visited);</div>
+<div class="line"><span class="lineno">  223</span> </div>
+<div class="line"><span class="lineno">  224</span>        <span class="comment">// Start visiting each node.</span></div>
+<div class="line"><span class="lineno">  225</span>        <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = 0; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> &lt; vertices; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>++) {</div>
+<div class="line"><span class="lineno">  226</span>            <span class="comment">// If a node is not visited, only then check for presence of cycle.</span></div>
+<div class="line"><span class="lineno">  227</span>            <span class="comment">// There is no need to check for presence of cycle for a visited</span></div>
+<div class="line"><span class="lineno">  228</span>            <span class="comment">// node as it has already been checked for presence of cycle.</span></div>
+<div class="line"><span class="lineno">  229</span>            <span class="keywordflow">if</span> (state[<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>] == not_visited) {</div>
+<div class="line"><span class="lineno">  230</span>                <span class="comment">// Check for cycle.</span></div>
+<div class="line"><span class="lineno">  231</span>                <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d3/dbb/class_cycle_check.html#a2f4485c08b45e7a21a2e86f9c3f01d8b">isCyclicDFSHelper</a>(<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.getAdjList(), &amp;state, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>)) {</div>
+<div class="line"><span class="lineno">  232</span>                    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  233</span>                }</div>
+<div class="line"><span class="lineno">  234</span>            }</div>
+<div class="line"><span class="lineno">  235</span>        }</div>
+<div class="line"><span class="lineno">  236</span> </div>
+<div class="line"><span class="lineno">  237</span>        <span class="comment">// All nodes have been safely traversed, that means there is no cycle in</span></div>
+<div class="line"><span class="lineno">  238</span>        <span class="comment">// the graph. Return false.</span></div>
+<div class="line"><span class="lineno">  239</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  240</span>    }</div>
 <div class="ttc" id="aclass_cycle_check_html_a2f4485c08b45e7a21a2e86f9c3f01d8b"><div class="ttname"><a href="../../d3/dbb/class_cycle_check.html#a2f4485c08b45e7a21a2e86f9c3f01d8b">CycleCheck::isCyclicDFSHelper</a></div><div class="ttdeci">static bool isCyclicDFSHelper(AdjList const &amp;adjList, std::vector&lt; nodeStates &gt; *state, unsigned int node)</div><div class="ttdef"><b>Definition:</b> cycle_check_directed_graph.cpp:170</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -374,37 +374,37 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if graph has a cycle, else false. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>                                                     {</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>        <span class="comment">// Add node &quot;in_stack&quot; state.</span></div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>        (*state)[<a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>] = in_stack;</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span> </div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>        <span class="comment">// If the node has children, then recursively visit all children of the</span></div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>        <span class="comment">// node.</span></div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>        <span class="keyword">auto</span> <span class="keyword">const</span> it = adjList.find(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>);</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>        <span class="keywordflow">if</span> (it != adjList.end()) {</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>            <span class="keywordflow">for</span> (<span class="keyword">auto</span> child : it-&gt;second) {</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>                <span class="comment">// If state of child node is &quot;not_visited&quot;, evaluate that child</span></div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>                <span class="comment">// for presence of cycle.</span></div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>                <span class="keyword">auto</span> state_of_child = (*state)[child];</div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>                <span class="keywordflow">if</span> (state_of_child == not_visited) {</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>                    <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d3/dbb/class_cycle_check.html#a2f4485c08b45e7a21a2e86f9c3f01d8b">isCyclicDFSHelper</a>(adjList, state, child)) {</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>                        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>                    }</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>                } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (state_of_child == in_stack) {</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>                    <span class="comment">// If child node was &quot;in_stack&quot;, then that means that there</span></div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>                    <span class="comment">// is a cycle in the graph. Return true for presence of the</span></div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>                    <span class="comment">// cycle.</span></div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>                    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>                }</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>            }</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>        }</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span> </div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>        <span class="comment">// Current node has been evaluated for the presence of cycle and had no</span></div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>        <span class="comment">// cycle. Mark current node as &quot;visited&quot;.</span></div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>        (*state)[<a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>] = visited;</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>        <span class="comment">// Return that current node didn&#39;t result in any cycles.</span></div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  172</span>                                                     {</div>
+<div class="line"><span class="lineno">  173</span>        <span class="comment">// Add node &quot;in_stack&quot; state.</span></div>
+<div class="line"><span class="lineno">  174</span>        (*state)[<a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>] = in_stack;</div>
+<div class="line"><span class="lineno">  175</span> </div>
+<div class="line"><span class="lineno">  176</span>        <span class="comment">// If the node has children, then recursively visit all children of the</span></div>
+<div class="line"><span class="lineno">  177</span>        <span class="comment">// node.</span></div>
+<div class="line"><span class="lineno">  178</span>        <span class="keyword">auto</span> <span class="keyword">const</span> it = adjList.find(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>);</div>
+<div class="line"><span class="lineno">  179</span>        <span class="keywordflow">if</span> (it != adjList.end()) {</div>
+<div class="line"><span class="lineno">  180</span>            <span class="keywordflow">for</span> (<span class="keyword">auto</span> child : it-&gt;second) {</div>
+<div class="line"><span class="lineno">  181</span>                <span class="comment">// If state of child node is &quot;not_visited&quot;, evaluate that child</span></div>
+<div class="line"><span class="lineno">  182</span>                <span class="comment">// for presence of cycle.</span></div>
+<div class="line"><span class="lineno">  183</span>                <span class="keyword">auto</span> state_of_child = (*state)[child];</div>
+<div class="line"><span class="lineno">  184</span>                <span class="keywordflow">if</span> (state_of_child == not_visited) {</div>
+<div class="line"><span class="lineno">  185</span>                    <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d3/dbb/class_cycle_check.html#a2f4485c08b45e7a21a2e86f9c3f01d8b">isCyclicDFSHelper</a>(adjList, state, child)) {</div>
+<div class="line"><span class="lineno">  186</span>                        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  187</span>                    }</div>
+<div class="line"><span class="lineno">  188</span>                } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (state_of_child == in_stack) {</div>
+<div class="line"><span class="lineno">  189</span>                    <span class="comment">// If child node was &quot;in_stack&quot;, then that means that there</span></div>
+<div class="line"><span class="lineno">  190</span>                    <span class="comment">// is a cycle in the graph. Return true for presence of the</span></div>
+<div class="line"><span class="lineno">  191</span>                    <span class="comment">// cycle.</span></div>
+<div class="line"><span class="lineno">  192</span>                    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  193</span>                }</div>
+<div class="line"><span class="lineno">  194</span>            }</div>
+<div class="line"><span class="lineno">  195</span>        }</div>
+<div class="line"><span class="lineno">  196</span> </div>
+<div class="line"><span class="lineno">  197</span>        <span class="comment">// Current node has been evaluated for the presence of cycle and had no</span></div>
+<div class="line"><span class="lineno">  198</span>        <span class="comment">// cycle. Mark current node as &quot;visited&quot;.</span></div>
+<div class="line"><span class="lineno">  199</span>        (*state)[<a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>] = visited;</div>
+<div class="line"><span class="lineno">  200</span>        <span class="comment">// Return that current node didn&#39;t result in any cycles.</span></div>
+<div class="line"><span class="lineno">  201</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  202</span>    }</div>
 <div class="ttc" id="ahash__search_8cpp_html_a8ca8dcb494104d273679e219e53d0555"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a></div><div class="ttdeci">struct list node</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -424,7 +424,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>        temp = <a class="code hl_variable" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[temp].next;</div>
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-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   69</span>               {</div>
+<div class="line"><span class="lineno">   70</span>    <span class="keywordtype">int</span> temp = head;</div>
+<div class="line"><span class="lineno">   71</span>    <span class="keywordflow">while</span> (temp != -1) {</div>
+<div class="line"><span class="lineno">   72</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_variable" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[temp].data &lt;&lt; <span class="stringliteral">&quot;-&gt;&quot;</span>;</div>
+<div class="line"><span class="lineno">   73</span>        temp = <a class="code hl_variable" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[temp].next;</div>
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+<div class="line"><span class="lineno">   75</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;-1&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   76</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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@@ -194,10 +194,10 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>avail</b> = 0</td></tr
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 <p >This function when called will delete the node with the index presented as an argument, and will put back that node into the array. </p>
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-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   42</span>                                   {</div>
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+<div class="line"><span class="lineno">   44</span>    avail = nodeToBeDeleted;</div>
+<div class="line"><span class="lineno">   45</span>}</div>
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 <p >This will return the index of the first free node present in the avail list </p>
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-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    <span class="keywordflow">return</span> NodeIndexToBeReturned;</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   32</span>              {</div>
+<div class="line"><span class="lineno">   33</span>    <span class="keywordtype">int</span> NodeIndexToBeReturned = avail;</div>
+<div class="line"><span class="lineno">   34</span>    avail = <a class="code hl_variable" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[avail].next;</div>
+<div class="line"><span class="lineno">   35</span>    <span class="keywordflow">return</span> NodeIndexToBeReturned;</div>
+<div class="line"><span class="lineno">   36</span>}</div>
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-<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>    }</div>
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-<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   23</span>                       {</div>
+<div class="line"><span class="lineno">   24</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= 98; i++) {</div>
+<div class="line"><span class="lineno">   25</span>        <a class="code hl_variable" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[i].next = i + 1;</div>
+<div class="line"><span class="lineno">   26</span>    }</div>
+<div class="line"><span class="lineno">   27</span>    <a class="code hl_variable" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[99].next = -1;  <span class="comment">// indicating the end of the linked list.</span></div>
+<div class="line"><span class="lineno">   28</span>}</div>
 </div><!-- fragment -->
 </div>
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@@ -263,12 +263,12 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>avail</b> = 0</td></tr
       </table>
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 <p >The function will insert the given data into the front of the linked list. </p>
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-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    <a class="code hl_variable" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[newNode].data = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    <a class="code hl_variable" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[newNode].next = head;</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>    head = newNode;</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   50</span>                                    {</div>
+<div class="line"><span class="lineno">   51</span>    <span class="keywordtype">int</span> newNode = <a class="code hl_function" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#a73e11e0871f56342a30da93b6c93e8be">getnode</a>();</div>
+<div class="line"><span class="lineno">   52</span>    <a class="code hl_variable" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[newNode].data = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
+<div class="line"><span class="lineno">   53</span>    <a class="code hl_variable" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[newNode].next = head;</div>
+<div class="line"><span class="lineno">   54</span>    head = newNode;</div>
+<div class="line"><span class="lineno">   55</span>}</div>
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 <div class="ttc" id="alinkedlist__implentation__usingarray_8cpp_html_a73e11e0871f56342a30da93b6c93e8be"><div class="ttname"><a href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#a73e11e0871f56342a30da93b6c93e8be">getnode</a></div><div class="ttdeci">int getnode()</div><div class="ttdef"><b>Definition:</b> linkedlist_implentation_usingarray.cpp:32</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -295,17 +295,17 @@ Here is the call graph for this function:</div>
         </tr>
       </table>
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-<div class="fragment"><div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>                              {</div>
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+<div class="line"><span class="lineno">   59</span>    <span class="keywordtype">int</span> temp = head;</div>
+<div class="line"><span class="lineno">   60</span>    <span class="keywordflow">while</span> (<a class="code hl_variable" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[temp].next != -1) {</div>
+<div class="line"><span class="lineno">   61</span>        temp = <a class="code hl_variable" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[temp].next;</div>
+<div class="line"><span class="lineno">   62</span>    }</div>
+<div class="line"><span class="lineno">   63</span>    <span class="comment">// temp is now pointing to the end node.</span></div>
+<div class="line"><span class="lineno">   64</span>    <a class="code hl_variable" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[newNode].data = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
+<div class="line"><span class="lineno">   65</span>    <a class="code hl_variable" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[newNode].next = -1;</div>
+<div class="line"><span class="lineno">   66</span>    <a class="code hl_variable" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[temp].next = newNode;</div>
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 <p >Main function </p>
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-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(37);</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(63);</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    <span class="comment">// array populating ends</span></div>
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-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr)));</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; 1st test passed!\n&quot;</span>;</div>
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+<div class="line"><span class="lineno">   98</span>    <span class="keyword">const</span> uint64_t size = 6;</div>
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+<div class="line"><span class="lineno">  100</span>    <span class="comment">// populating the array</span></div>
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+<div class="line"><span class="lineno">  104</span>    arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(12);</div>
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+<div class="line"><span class="lineno">  107</span>    <span class="comment">// array populating ends</span></div>
+<div class="line"><span class="lineno">  108</span> </div>
+<div class="line"><span class="lineno">  109</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#ae3a775d99dbbb94c130a973df0cfddcf">sorting::recursive_bubble_sort</a>(&amp;arr, size);</div>
+<div class="line"><span class="lineno">  110</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr)));</div>
+<div class="line"><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; 1st test passed!\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  112</span>    <span class="comment">// printing the array</span></div>
+<div class="line"><span class="lineno">  113</span>    <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; size; i++) {</div>
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+<div class="line"><span class="lineno">  117</span> </div>
+<div class="line"><span class="lineno">  118</span>    <span class="comment">// 2nd example. Creating an array of type `double`.</span></div>
+<div class="line"><span class="lineno">  119</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test using doubles\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  120</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> double_arr;</div>
+<div class="line"><span class="lineno">  121</span> </div>
+<div class="line"><span class="lineno">  122</span>    <span class="comment">// populating the array</span></div>
+<div class="line"><span class="lineno">  123</span>    double_arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(20.4);</div>
+<div class="line"><span class="lineno">  124</span>    double_arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(62.7);</div>
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+<div class="line"><span class="lineno">  129</span>    <span class="comment">// array populating ends</span></div>
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+<div class="line"><span class="lineno">  135</span>    <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; size; i++) {</div>
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-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span> </div>
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-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>         i++) {  <span class="comment">// Checking all characters of prototype string</span></div>
-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>        <span class="keywordflow">if</span> (shiftTable.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/find.html">find</a>(prototype[i]) ==</div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>            shiftTable.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/end.html">end</a>()) {  <span class="comment">// If character does not exist in HashMap</span></div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>            <span class="keywordflow">if</span> (i != prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - 1) {</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>                shiftTable.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/insert.html">insert</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>                    prototype[i], prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - i -</div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>                                      1));  <span class="comment">// Insert the character as key and the size of prototype string - index of character - 1 as value</span></div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>                shiftTable.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/insert.html">insert</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(</div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>                    prototype[i],</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>                    prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>()));  <span class="comment">// Insert the character as key and the size of prototype string as value</span></div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>            }</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>            <span class="keywordflow">if</span> (i != prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - 1) {</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>                shiftTable[prototype[i]] = prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/size.html">size</a>() - i - 1;</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>            }</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>        }</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    }</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    <span class="keywordflow">return</span> shiftTable;</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   26</span>                                                                       {</div>
+<div class="line"><span class="lineno">   27</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map.html">std::unordered_map&lt;char, int&gt;</a></div>
+<div class="line"><span class="lineno">   28</span>        shiftTable;  <span class="comment">// A HashMap for shift table that has characters for keys and integers for values</span></div>
+<div class="line"><span class="lineno">   29</span> </div>
+<div class="line"><span class="lineno">   30</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   31</span>         i++) {  <span class="comment">// Checking all characters of prototype string</span></div>
+<div class="line"><span class="lineno">   32</span>        <span class="keywordflow">if</span> (shiftTable.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/find.html">find</a>(prototype[i]) ==</div>
+<div class="line"><span class="lineno">   33</span>            shiftTable.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/end.html">end</a>()) {  <span class="comment">// If character does not exist in HashMap</span></div>
+<div class="line"><span class="lineno">   34</span>            <span class="keywordflow">if</span> (i != prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - 1) {</div>
+<div class="line"><span class="lineno">   35</span>                shiftTable.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/insert.html">insert</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(</div>
+<div class="line"><span class="lineno">   36</span>                    prototype[i], prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - i -</div>
+<div class="line"><span class="lineno">   37</span>                                      1));  <span class="comment">// Insert the character as key and the size of prototype string - index of character - 1 as value</span></div>
+<div class="line"><span class="lineno">   38</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   39</span>                shiftTable.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/insert.html">insert</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(</div>
+<div class="line"><span class="lineno">   40</span>                    prototype[i],</div>
+<div class="line"><span class="lineno">   41</span>                    prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>()));  <span class="comment">// Insert the character as key and the size of prototype string as value</span></div>
+<div class="line"><span class="lineno">   42</span>            }</div>
+<div class="line"><span class="lineno">   43</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   44</span>            <span class="keywordflow">if</span> (i != prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - 1) {</div>
+<div class="line"><span class="lineno">   45</span>                shiftTable[prototype[i]] = prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/size.html">size</a>() - i - 1;</div>
+<div class="line"><span class="lineno">   46</span>            }</div>
+<div class="line"><span class="lineno">   47</span>        }</div>
+<div class="line"><span class="lineno">   48</span>    }</div>
+<div class="line"><span class="lineno">   49</span>    <span class="keywordflow">return</span> shiftTable;</div>
+<div class="line"><span class="lineno">   50</span>}</div>
 <div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/unordered_map/end.html">std::unordered_map::end</a></div><div class="ttdeci">T end(T... args)</div></div>
 <div class="ttc" id="afind_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/unordered_map/find.html">std::unordered_map::find</a></div><div class="ttdeci">T find(T... args)</div></div>
 <div class="ttc" id="ainsert_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/unordered_map/insert.html">std::unordered_map::insert</a></div><div class="ttdeci">T insert(T... args)</div></div>
@@ -232,40 +232,40 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd>true if text string contains prototype string </dd>
 <dd>
 false if text string does not contain prototype string </dd></dl>
-<div class="fragment"><div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>                                                                 {</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map.html">std::unordered_map&lt;char, int&gt;</a> shiftTable = <a class="code hl_function" href="../../d3/dfe/horspool_8cpp.html#a1a9c3aa55ccc79d0f47d50c580997336">findShiftTable</a>(</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        prototype);  <span class="comment">// Initialise shift table calling findShiftTable function</span></div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span> </div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    <span class="keywordtype">int</span> i = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() -</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        1);  <span class="comment">// Index that we shift in text to find the substring</span></div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <span class="keywordflow">while</span> (i &lt; text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>()) {</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        <span class="keywordtype">int</span> j = i, <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> = 0;</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        <span class="keywordtype">bool</span> flag = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span> </div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> z = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - 1); z &gt;= 0 &amp;&amp; flag;</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>             z--) {  <span class="comment">// Checking if all characters of substring are equal with all characters of string</span></div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>            <span class="keywordflow">if</span> (text[j] == prototype[z]) {</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++;</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>                j--;</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>                flag = <span class="keyword">false</span>;  <span class="comment">// If two characters are not equal set flag to false and break from loop</span></div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>            }</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        }</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span> </div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>        <span class="keywordflow">if</span> (k ==</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>            prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>()) {  <span class="comment">// If all characters match then return true</span></div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>            <span class="keywordflow">if</span> (shiftTable.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/find.html">find</a>(text[i]) != shiftTable.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/end.html">end</a>()) {</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>                i += shiftTable[text[i]];  <span class="comment">// If shift table contains the character then shift index as many steps as value</span></div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>                i += prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();  <span class="comment">// If character does not exist in shift table then shift index as many steps as size of prototype string</span></div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>            }</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        }</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    }</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   59</span>                                                                 {</div>
+<div class="line"><span class="lineno">   60</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map.html">std::unordered_map&lt;char, int&gt;</a> shiftTable = <a class="code hl_function" href="../../d3/dfe/horspool_8cpp.html#a1a9c3aa55ccc79d0f47d50c580997336">findShiftTable</a>(</div>
+<div class="line"><span class="lineno">   61</span>        prototype);  <span class="comment">// Initialise shift table calling findShiftTable function</span></div>
+<div class="line"><span class="lineno">   62</span> </div>
+<div class="line"><span class="lineno">   63</span>    <span class="keywordtype">int</span> i = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(</div>
+<div class="line"><span class="lineno">   64</span>        prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() -</div>
+<div class="line"><span class="lineno">   65</span>        1);  <span class="comment">// Index that we shift in text to find the substring</span></div>
+<div class="line"><span class="lineno">   66</span>    <span class="keywordflow">while</span> (i &lt; text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>()) {</div>
+<div class="line"><span class="lineno">   67</span>        <span class="keywordtype">int</span> j = i, <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> = 0;</div>
+<div class="line"><span class="lineno">   68</span>        <span class="keywordtype">bool</span> flag = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   69</span> </div>
+<div class="line"><span class="lineno">   70</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> z = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - 1); z &gt;= 0 &amp;&amp; flag;</div>
+<div class="line"><span class="lineno">   71</span>             z--) {  <span class="comment">// Checking if all characters of substring are equal with all characters of string</span></div>
+<div class="line"><span class="lineno">   72</span>            <span class="keywordflow">if</span> (text[j] == prototype[z]) {</div>
+<div class="line"><span class="lineno">   73</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++;</div>
+<div class="line"><span class="lineno">   74</span>                j--;</div>
+<div class="line"><span class="lineno">   75</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   76</span>                flag = <span class="keyword">false</span>;  <span class="comment">// If two characters are not equal set flag to false and break from loop</span></div>
+<div class="line"><span class="lineno">   77</span>            }</div>
+<div class="line"><span class="lineno">   78</span>        }</div>
+<div class="line"><span class="lineno">   79</span> </div>
+<div class="line"><span class="lineno">   80</span>        <span class="keywordflow">if</span> (k ==</div>
+<div class="line"><span class="lineno">   81</span>            prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>()) {  <span class="comment">// If all characters match then return true</span></div>
+<div class="line"><span class="lineno">   82</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   83</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   84</span>            <span class="keywordflow">if</span> (shiftTable.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/find.html">find</a>(text[i]) != shiftTable.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/end.html">end</a>()) {</div>
+<div class="line"><span class="lineno">   85</span>                i += shiftTable[text[i]];  <span class="comment">// If shift table contains the character then shift index as many steps as value</span></div>
+<div class="line"><span class="lineno">   86</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   87</span>                i += prototype.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();  <span class="comment">// If character does not exist in shift table then shift index as many steps as size of prototype string</span></div>
+<div class="line"><span class="lineno">   88</span>            }</div>
+<div class="line"><span class="lineno">   89</span>        }</div>
+<div class="line"><span class="lineno">   90</span>    }</div>
+<div class="line"><span class="lineno">   91</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   92</span>}</div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
 <div class="ttc" id="ahorspool_8cpp_html_a1a9c3aa55ccc79d0f47d50c580997336"><div class="ttname"><a href="../../d3/dfe/horspool_8cpp.html#a1a9c3aa55ccc79d0f47d50c580997336">strings::horspool::findShiftTable</a></div><div class="ttdeci">std::unordered_map&lt; char, int &gt; findShiftTable(const std::string &amp;prototype)</div><div class="ttdef"><b>Definition:</b> horspool.cpp:26</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -295,10 +295,10 @@ Here is the call graph for this function:</div>
 
 <p>Main Function that calls test function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>          {</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <a class="code hl_function" href="../../d3/dfe/horspool_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  119</span>          {</div>
+<div class="line"><span class="lineno">  120</span>    <a class="code hl_function" href="../../d3/dfe/horspool_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
+<div class="line"><span class="lineno">  121</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  122</span>}</div>
 <div class="ttc" id="ahorspool_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d3/dfe/horspool_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Function with test cases for Horspool's algorithm.</div><div class="ttdef"><b>Definition:</b> horspool.cpp:100</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -334,20 +334,20 @@ Here is the call graph for this function:</div>
 
 <p>Function with test cases for Horspool's algorithm. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>                  {</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;Hello World&quot;</span>,<span class="stringliteral">&quot;World&quot;</span>) == <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;Hello World&quot;</span>,<span class="stringliteral">&quot; World&quot;</span>) == <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;Hello World&quot;</span>,<span class="stringliteral">&quot;ello&quot;</span>) == <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;Hello World&quot;</span>,<span class="stringliteral">&quot;rld&quot;</span>) == <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;Hello&quot;</span>,<span class="stringliteral">&quot;Helo&quot;</span>) == <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;c++_algorithms&quot;</span>,<span class="stringliteral">&quot;c++_algorithms&quot;</span>) == <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;c++_algorithms&quot;</span>,<span class="stringliteral">&quot;c++_&quot;</span>) == <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;Hello&quot;</span>,<span class="stringliteral">&quot;Hello World&quot;</span>) == <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;c++_algorithms&quot;</span>,<span class="stringliteral">&quot;&quot;</span>) == <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;c++&quot;</span>,<span class="stringliteral">&quot;c&quot;</span>) == <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;3458934793&quot;</span>,<span class="stringliteral">&quot;4793&quot;</span>) == <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;3458934793&quot;</span>,<span class="stringliteral">&quot;123&quot;</span>) == <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  100</span>                  {</div>
+<div class="line"><span class="lineno">  101</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;Hello World&quot;</span>,<span class="stringliteral">&quot;World&quot;</span>) == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  102</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;Hello World&quot;</span>,<span class="stringliteral">&quot; World&quot;</span>) == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  103</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;Hello World&quot;</span>,<span class="stringliteral">&quot;ello&quot;</span>) == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  104</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;Hello World&quot;</span>,<span class="stringliteral">&quot;rld&quot;</span>) == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  105</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;Hello&quot;</span>,<span class="stringliteral">&quot;Helo&quot;</span>) == <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  106</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;c++_algorithms&quot;</span>,<span class="stringliteral">&quot;c++_algorithms&quot;</span>) == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  107</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;c++_algorithms&quot;</span>,<span class="stringliteral">&quot;c++_&quot;</span>) == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  108</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;Hello&quot;</span>,<span class="stringliteral">&quot;Hello World&quot;</span>) == <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  109</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;c++_algorithms&quot;</span>,<span class="stringliteral">&quot;&quot;</span>) == <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  110</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;c++&quot;</span>,<span class="stringliteral">&quot;c&quot;</span>) == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  111</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;3458934793&quot;</span>,<span class="stringliteral">&quot;4793&quot;</span>) == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  112</span>    assert(strings::horspool::horspool(<span class="stringliteral">&quot;3458934793&quot;</span>,<span class="stringliteral">&quot;123&quot;</span>) == <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  113</span>}</div>
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-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    <span class="comment">// If the result calculated is nan, then the user has given wrong input</span></div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>    <span class="comment">// interval.</span></div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    assert(!<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/isnan.html">std::isnan</a>(evaluate_integral) &amp;&amp;</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>           <span class="stringliteral">&quot;The definite integral can&#39;t be evaluated. Check the validity of &quot;</span></div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>           <span class="stringliteral">&quot;your input.\n&quot;</span>);</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <span class="comment">// Else return</span></div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <span class="keywordflow">return</span> evaluate_integral;</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   68</span>                                                                    {</div>
+<div class="line"><span class="lineno">   69</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map&lt;std::int32_t, double&gt;</a></div>
+<div class="line"><span class="lineno">   70</span>        data_table;  <span class="comment">// Contains the data points. key: i, value: f(xi)</span></div>
+<div class="line"><span class="lineno">   71</span>    <span class="keywordtype">double</span> xi = a;   <span class="comment">// Initialize xi to the starting point x0 = a</span></div>
+<div class="line"><span class="lineno">   72</span> </div>
+<div class="line"><span class="lineno">   73</span>    <span class="comment">// Create the data table</span></div>
+<div class="line"><span class="lineno">   74</span>    <span class="keywordtype">double</span> temp = NAN;</div>
+<div class="line"><span class="lineno">   75</span>    <span class="keywordflow">for</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int32_t</a> i = 0; i &lt;= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
+<div class="line"><span class="lineno">   76</span>        temp = func(xi);</div>
+<div class="line"><span class="lineno">   77</span>        data_table.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map/insert.html">insert</a>(</div>
+<div class="line"><span class="lineno">   78</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;std::int32_t, double&gt;</a>(i, temp));  <span class="comment">// add i and f(xi)</span></div>
+<div class="line"><span class="lineno">   79</span>        xi += <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>;  <span class="comment">// Get the next point xi for the next iteration</span></div>
+<div class="line"><span class="lineno">   80</span>    }</div>
+<div class="line"><span class="lineno">   81</span> </div>
+<div class="line"><span class="lineno">   82</span>    <span class="comment">// Evaluate the integral.</span></div>
+<div class="line"><span class="lineno">   83</span>    <span class="comment">// Remember: f(x0) + 4*f(x1) + 2*f(x2) + ... + 2*f(xN-2) + 4*f(xN-1) + f(xN)</span></div>
+<div class="line"><span class="lineno">   84</span>    <span class="keywordtype">double</span> evaluate_integral = 0;</div>
+<div class="line"><span class="lineno">   85</span>    <span class="keywordflow">for</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int32_t</a> i = 0; i &lt;= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
+<div class="line"><span class="lineno">   86</span>        <span class="keywordflow">if</span> (i == 0 || i == N) {</div>
+<div class="line"><span class="lineno">   87</span>            evaluate_integral += data_table.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map/at.html">at</a>(i);</div>
+<div class="line"><span class="lineno">   88</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (i % 2 == 1) {</div>
+<div class="line"><span class="lineno">   89</span>            evaluate_integral += 4 * data_table.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map/at.html">at</a>(i);</div>
+<div class="line"><span class="lineno">   90</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   91</span>            evaluate_integral += 2 * data_table.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map/at.html">at</a>(i);</div>
+<div class="line"><span class="lineno">   92</span>        }</div>
+<div class="line"><span class="lineno">   93</span>    }</div>
+<div class="line"><span class="lineno">   94</span> </div>
+<div class="line"><span class="lineno">   95</span>    <span class="comment">// Multiply by the coefficient h/3</span></div>
+<div class="line"><span class="lineno">   96</span>    evaluate_integral *= <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> / 3;</div>
+<div class="line"><span class="lineno">   97</span> </div>
+<div class="line"><span class="lineno">   98</span>    <span class="comment">// If the result calculated is nan, then the user has given wrong input</span></div>
+<div class="line"><span class="lineno">   99</span>    <span class="comment">// interval.</span></div>
+<div class="line"><span class="lineno">  100</span>    assert(!<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/isnan.html">std::isnan</a>(evaluate_integral) &amp;&amp;</div>
+<div class="line"><span class="lineno">  101</span>           <span class="stringliteral">&quot;The definite integral can&#39;t be evaluated. Check the validity of &quot;</span></div>
+<div class="line"><span class="lineno">  102</span>           <span class="stringliteral">&quot;your input.\n&quot;</span>);</div>
+<div class="line"><span class="lineno">  103</span>    <span class="comment">// Else return</span></div>
+<div class="line"><span class="lineno">  104</span>    <span class="keywordflow">return</span> evaluate_integral;</div>
+<div class="line"><span class="lineno">  105</span>}</div>
 <div class="ttc" id="aat_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/map/at.html">std::map::at</a></div><div class="ttdeci">T at(T... args)</div></div>
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 <div class="ttc" id="ahash__search_8cpp_html_a566eaf0ffafd50bc61e644561fd27001"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a></div><div class="ttdeci">int h(int key)</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:45</div></div>
@@ -268,7 +268,7 @@ Functions</h2></td></tr>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>the value of the dependent variable yi = f(xi) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>{ <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(x) + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">std::log</a>(x); }</div>
+<div class="fragment"><div class="line"><span class="lineno">  113</span>{ <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(x) + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">std::log</a>(x); }</div>
 <div class="ttc" id="alog_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/log.html">std::log</a></div><div class="ttdeci">T log(T... args)</div></div>
 <div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -297,7 +297,7 @@ Here is the call graph for this function:</div>
 </div><div class="memdoc">
 
 <p>Another test function. </p>
-<div class="fragment"><div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>{ <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">std::exp</a>(-x) * (4 - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(x, 2)); }</div>
+<div class="fragment"><div class="line"><span class="lineno">  115</span>{ <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">std::exp</a>(-x) * (4 - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(x, 2)); }</div>
 <div class="ttc" id="aexp_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">std::exp</a></div><div class="ttdeci">T exp(T... args)</div></div>
 <div class="ttc" id="apow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a></div><div class="ttdeci">T pow(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -328,7 +328,7 @@ Here is the call graph for this function:</div>
 <p>Another test function. </p>
 <dl class="section examples"><dt>Examples</dt><dd><a class="el" href="../../dc/dc4/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2numerical_methods_2rungekutta_8cpp-example.html#a4">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp</a>.</dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>{ <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(2 * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(x, 3) + 3); }</div>
+<div class="fragment"><div class="line"><span class="lineno">  117</span>{ <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(2 * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(x, 3) + 3); }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -355,7 +355,7 @@ Here is the call graph for this function:</div>
 </div><div class="memdoc">
 
 <p>Another test function. </p>
-<div class="fragment"><div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>{ <span class="keywordflow">return</span> x + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">std::log</a>(2 * x + 1); }</div>
+<div class="fragment"><div class="line"><span class="lineno">  119</span>{ <span class="keywordflow">return</span> x + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">std::log</a>(2 * x + 1); }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -403,43 +403,43 @@ Here is the call graph for this function:</div>
 <p >Number of intervals to divide the integration interval. MUST BE EVEN</p>
 <p >Starting and ending point of the integration in the real axis</p>
 <p >Step, calculated by a, b and N</p>
-<div class="fragment"><div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>                                {</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int32_t</a> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 16;  <span class="comment">/// Number of intervals to divide the integration</span><span class="comment"></span></div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span><span class="comment">                          /// interval. MUST BE EVEN</span></div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span><span class="comment"></span>    <span class="keywordtype">double</span> a = 1, b = 3;  <span class="comment">/// Starting and ending point of the integration in</span><span class="comment"></span></div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span><span class="comment">                          /// the real axis</span></div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span><span class="comment"></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> = NAN;       <span class="comment">/// Step, calculated by a, b and N</span></div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span> </div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>    <span class="keywordtype">bool</span> used_argv_parameters =</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>        <span class="keyword">false</span>;  <span class="comment">// If argv parameters are used then the assert must be omitted</span></div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>                <span class="comment">// for the tst cases</span></div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span> </div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>    <span class="comment">// Get user input (by the command line parameters or the console after</span></div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>    <span class="comment">// displaying messages)</span></div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>    <span class="keywordflow">if</span> (argc == 4) {</div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>        <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">std::atoi</a>(argv[1]);</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>        a = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a>(argv[2]);</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>        b = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a>(argv[3]);</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>        <span class="comment">// Check if a&lt;b else abort</span></div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>        assert(a &lt; b &amp;&amp; <span class="stringliteral">&quot;a has to be less than b&quot;</span>);</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>        assert(N &gt; 0 &amp;&amp; <span class="stringliteral">&quot;N has to be &gt; 0&quot;</span>);</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>        <span class="keywordflow">if</span> (N &lt; 16 || a != 1 || b != 3) {</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>            used_argv_parameters = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>        }</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;You selected N=&quot;</span> &lt;&lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> &lt;&lt; <span class="stringliteral">&quot;, a=&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, b=&quot;</span> &lt;&lt; b</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>                  &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>    } <span class="keywordflow">else</span> {</div>
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-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>                  &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span> </div>
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-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>    <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> = (b - a) / N;</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span> </div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>    <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2ae48a41e43dc6ab11b962742349646e">test</a>(N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, b, used_argv_parameters);  <span class="comment">// run self-test implementations</span></div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span> </div>
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+<div class="fragment"><div class="line"><span class="lineno">  170</span>                                {</div>
+<div class="line"><span class="lineno">  171</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int32_t</a> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 16;  <span class="comment">/// Number of intervals to divide the integration</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  172</span><span class="comment">                          /// interval. MUST BE EVEN</span></div>
+<div class="line"><span class="lineno">  173</span><span class="comment"></span>    <span class="keywordtype">double</span> a = 1, b = 3;  <span class="comment">/// Starting and ending point of the integration in</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  174</span><span class="comment">                          /// the real axis</span></div>
+<div class="line"><span class="lineno">  175</span><span class="comment"></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> = NAN;       <span class="comment">/// Step, calculated by a, b and N</span></div>
+<div class="line"><span class="lineno">  176</span> </div>
+<div class="line"><span class="lineno">  177</span>    <span class="keywordtype">bool</span> used_argv_parameters =</div>
+<div class="line"><span class="lineno">  178</span>        <span class="keyword">false</span>;  <span class="comment">// If argv parameters are used then the assert must be omitted</span></div>
+<div class="line"><span class="lineno">  179</span>                <span class="comment">// for the tst cases</span></div>
+<div class="line"><span class="lineno">  180</span> </div>
+<div class="line"><span class="lineno">  181</span>    <span class="comment">// Get user input (by the command line parameters or the console after</span></div>
+<div class="line"><span class="lineno">  182</span>    <span class="comment">// displaying messages)</span></div>
+<div class="line"><span class="lineno">  183</span>    <span class="keywordflow">if</span> (argc == 4) {</div>
+<div class="line"><span class="lineno">  184</span>        <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">std::atoi</a>(argv[1]);</div>
+<div class="line"><span class="lineno">  185</span>        a = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a>(argv[2]);</div>
+<div class="line"><span class="lineno">  186</span>        b = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a>(argv[3]);</div>
+<div class="line"><span class="lineno">  187</span>        <span class="comment">// Check if a&lt;b else abort</span></div>
+<div class="line"><span class="lineno">  188</span>        assert(a &lt; b &amp;&amp; <span class="stringliteral">&quot;a has to be less than b&quot;</span>);</div>
+<div class="line"><span class="lineno">  189</span>        assert(N &gt; 0 &amp;&amp; <span class="stringliteral">&quot;N has to be &gt; 0&quot;</span>);</div>
+<div class="line"><span class="lineno">  190</span>        <span class="keywordflow">if</span> (N &lt; 16 || a != 1 || b != 3) {</div>
+<div class="line"><span class="lineno">  191</span>            used_argv_parameters = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  192</span>        }</div>
+<div class="line"><span class="lineno">  193</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;You selected N=&quot;</span> &lt;&lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> &lt;&lt; <span class="stringliteral">&quot;, a=&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, b=&quot;</span> &lt;&lt; b</div>
+<div class="line"><span class="lineno">  194</span>                  &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  195</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  196</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Default N=&quot;</span> &lt;&lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> &lt;&lt; <span class="stringliteral">&quot;, a=&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, b=&quot;</span> &lt;&lt; b</div>
+<div class="line"><span class="lineno">  197</span>                  &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  198</span>    }</div>
+<div class="line"><span class="lineno">  199</span> </div>
+<div class="line"><span class="lineno">  200</span>    <span class="comment">// Find the step</span></div>
+<div class="line"><span class="lineno">  201</span>    <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> = (b - a) / N;</div>
+<div class="line"><span class="lineno">  202</span> </div>
+<div class="line"><span class="lineno">  203</span>    <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2ae48a41e43dc6ab11b962742349646e">test</a>(N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, b, used_argv_parameters);  <span class="comment">// run self-test implementations</span></div>
+<div class="line"><span class="lineno">  204</span> </div>
+<div class="line"><span class="lineno">  205</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  206</span>}</div>
 <div class="ttc" id="aatof_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a></div><div class="ttdeci">T atof(T... args)</div></div>
 <div class="ttc" id="aatoi_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">std::atoi</a></div><div class="ttdeci">T atoi(T... args)</div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
@@ -517,36 +517,36 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>                                            {</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    <span class="comment">// Call the functions and find the integral of each function</span></div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    <span class="keywordtype">double</span> result_f = numerical_methods::simpson_method::evaluate_by_simpson(</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>        N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::simpson_method::f);</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    assert((used_argv_parameters || (result_f &gt;= 4.09 &amp;&amp; result_f &lt;= 4.10)) &amp;&amp;</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>           <span class="stringliteral">&quot;The result of f(x) is wrong&quot;</span>);</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The result of integral f(x) on interval [&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; b</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>              &lt;&lt; <span class="stringliteral">&quot;] is equal to: &quot;</span> &lt;&lt; result_f &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span> </div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    <span class="keywordtype">double</span> result_g = numerical_methods::simpson_method::evaluate_by_simpson(</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>        N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::simpson_method::g);</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    assert((used_argv_parameters || (result_g &gt;= 0.27 &amp;&amp; result_g &lt;= 0.28)) &amp;&amp;</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>           <span class="stringliteral">&quot;The result of g(x) is wrong&quot;</span>);</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The result of integral g(x) on interval [&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; b</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>              &lt;&lt; <span class="stringliteral">&quot;] is equal to: &quot;</span> &lt;&lt; result_g &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span> </div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>    <span class="keywordtype">double</span> result_k = numerical_methods::simpson_method::evaluate_by_simpson(</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>        N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::simpson_method::k);</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    assert((used_argv_parameters || (result_k &gt;= 9.06 &amp;&amp; result_k &lt;= 9.07)) &amp;&amp;</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>           <span class="stringliteral">&quot;The result of k(x) is wrong&quot;</span>);</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The result of integral k(x) on interval [&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; b</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>              &lt;&lt; <span class="stringliteral">&quot;] is equal to: &quot;</span> &lt;&lt; result_k &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span> </div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>    <span class="keywordtype">double</span> result_l = numerical_methods::simpson_method::evaluate_by_simpson(</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>        N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::simpson_method::l);</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    assert((used_argv_parameters || (result_l &gt;= 7.16 &amp;&amp; result_l &lt;= 7.17)) &amp;&amp;</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>           <span class="stringliteral">&quot;The result of l(x) is wrong&quot;</span>);</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The result of integral l(x) on interval [&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; b</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>              &lt;&lt; <span class="stringliteral">&quot;] is equal to: &quot;</span> &lt;&lt; result_l &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  133</span>                                            {</div>
+<div class="line"><span class="lineno">  134</span>    <span class="comment">// Call the functions and find the integral of each function</span></div>
+<div class="line"><span class="lineno">  135</span>    <span class="keywordtype">double</span> result_f = numerical_methods::simpson_method::evaluate_by_simpson(</div>
+<div class="line"><span class="lineno">  136</span>        N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::simpson_method::f);</div>
+<div class="line"><span class="lineno">  137</span>    assert((used_argv_parameters || (result_f &gt;= 4.09 &amp;&amp; result_f &lt;= 4.10)) &amp;&amp;</div>
+<div class="line"><span class="lineno">  138</span>           <span class="stringliteral">&quot;The result of f(x) is wrong&quot;</span>);</div>
+<div class="line"><span class="lineno">  139</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The result of integral f(x) on interval [&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; b</div>
+<div class="line"><span class="lineno">  140</span>              &lt;&lt; <span class="stringliteral">&quot;] is equal to: &quot;</span> &lt;&lt; result_f &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  141</span> </div>
+<div class="line"><span class="lineno">  142</span>    <span class="keywordtype">double</span> result_g = numerical_methods::simpson_method::evaluate_by_simpson(</div>
+<div class="line"><span class="lineno">  143</span>        N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::simpson_method::g);</div>
+<div class="line"><span class="lineno">  144</span>    assert((used_argv_parameters || (result_g &gt;= 0.27 &amp;&amp; result_g &lt;= 0.28)) &amp;&amp;</div>
+<div class="line"><span class="lineno">  145</span>           <span class="stringliteral">&quot;The result of g(x) is wrong&quot;</span>);</div>
+<div class="line"><span class="lineno">  146</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The result of integral g(x) on interval [&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; b</div>
+<div class="line"><span class="lineno">  147</span>              &lt;&lt; <span class="stringliteral">&quot;] is equal to: &quot;</span> &lt;&lt; result_g &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  148</span> </div>
+<div class="line"><span class="lineno">  149</span>    <span class="keywordtype">double</span> result_k = numerical_methods::simpson_method::evaluate_by_simpson(</div>
+<div class="line"><span class="lineno">  150</span>        N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::simpson_method::k);</div>
+<div class="line"><span class="lineno">  151</span>    assert((used_argv_parameters || (result_k &gt;= 9.06 &amp;&amp; result_k &lt;= 9.07)) &amp;&amp;</div>
+<div class="line"><span class="lineno">  152</span>           <span class="stringliteral">&quot;The result of k(x) is wrong&quot;</span>);</div>
+<div class="line"><span class="lineno">  153</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The result of integral k(x) on interval [&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; b</div>
+<div class="line"><span class="lineno">  154</span>              &lt;&lt; <span class="stringliteral">&quot;] is equal to: &quot;</span> &lt;&lt; result_k &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  155</span> </div>
+<div class="line"><span class="lineno">  156</span>    <span class="keywordtype">double</span> result_l = numerical_methods::simpson_method::evaluate_by_simpson(</div>
+<div class="line"><span class="lineno">  157</span>        N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::simpson_method::l);</div>
+<div class="line"><span class="lineno">  158</span>    assert((used_argv_parameters || (result_l &gt;= 7.16 &amp;&amp; result_l &lt;= 7.17)) &amp;&amp;</div>
+<div class="line"><span class="lineno">  159</span>           <span class="stringliteral">&quot;The result of l(x) is wrong&quot;</span>);</div>
+<div class="line"><span class="lineno">  160</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The result of integral l(x) on interval [&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; b</div>
+<div class="line"><span class="lineno">  161</span>              &lt;&lt; <span class="stringliteral">&quot;] is equal to: &quot;</span> &lt;&lt; result_l &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  162</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -556,7 +556,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_9c6faab82c22511b50177aa2e38e2780.html">numerical_methods</a></li><li class="navelem"><a class="el" href="../../d4/d18/composite__simpson__rule_8cpp.html">composite_simpson_rule.cpp</a></li>
-    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.2 </li>
+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
   </ul>
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diff --git a/d4/d18/composite__simpson__rule_8cpp_a1b74d828b33760094906797042b89442_cgraph.map b/d4/d18/composite__simpson__rule_8cpp_a1b74d828b33760094906797042b89442_cgraph.map
index 8481f5c4d..f2011946c 100644
--- a/d4/d18/composite__simpson__rule_8cpp_a1b74d828b33760094906797042b89442_cgraph.map
+++ b/d4/d18/composite__simpson__rule_8cpp_a1b74d828b33760094906797042b89442_cgraph.map
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diff --git a/d4/d18/composite__simpson__rule_8cpp_a1b74d828b33760094906797042b89442_cgraph.md5 b/d4/d18/composite__simpson__rule_8cpp_a1b74d828b33760094906797042b89442_cgraph.md5
index 0eba06b45..2bc3ce523 100644
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 <p >Function for finding greatest common divisor of two numbers. @params two integers x and y whose gcd we want to find. </p><dl class="section return"><dt>Returns</dt><dd>greatest common divisor of x and y. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span>                                                 {</div>
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+<div class="line"><span class="lineno">   18</span>        <span class="keywordflow">return</span> y;</div>
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+<div class="line"><span class="lineno">   24</span>        <span class="keywordflow">return</span> x;</div>
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+<div class="line"><span class="lineno">   32</span>    <span class="comment">// Again the following is valid because we have checked whether x == 0</span></div>
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+<div class="line"><span class="lineno">   34</span>    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> temp = y / x;</div>
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 Here is the call graph for this function:</div>
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 <p >Function for finding the least common multiple of two numbers. @params integer x and y whose lcm we want to find. </p><dl class="section return"><dt>Returns</dt><dd>lcm of x and y using the relation x * y = gcd(x, y) * lcm(x, y) </dd></dl>
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+<div class="line"><span class="lineno">   44</span>  <span class="keywordflow">return</span> x / <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(x, y) * y;</div>
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 <p >Main function </p>
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-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   78</span>           {</div>
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+<div class="line"><span class="lineno">   80</span>    <span class="keywordflow">return</span> 0;</div>
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 Here is the call graph for this function:</div>
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 <p >Function for testing the <a class="el" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm()</a> functions with some assert statements. </p>
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-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>                  <span class="stringliteral">&quot;result.\n&quot;</span>,</div>
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-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;First assertion passes: LCM of 5 and 10 is &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(5, 10)</div>
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-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>        }</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>        <span class="keywordflow">return</span> successor;  <span class="comment">// Nodes with maximum vales will not have a successor</span></div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>    }</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  176</span>                                                    {</div>
+<div class="line"><span class="lineno">  177</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *current = <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a824cbf1814854824cf05f062eea07b95">getNode</a>(root, <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
+<div class="line"><span class="lineno">  178</span>    <span class="keywordflow">if</span> (current == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  179</span>        <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  180</span>    }</div>
+<div class="line"><span class="lineno">  181</span> </div>
+<div class="line"><span class="lineno">  182</span>    <span class="comment">// Case - 1</span></div>
+<div class="line"><span class="lineno">  183</span>    <span class="keywordflow">if</span> (current-&gt;right != <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  184</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a72483e3f6933e004a8d86371e8a990db">findMinNode</a>(current-&gt;right);</div>
+<div class="line"><span class="lineno">  185</span>    }</div>
+<div class="line"><span class="lineno">  186</span>    <span class="comment">// case - 2</span></div>
+<div class="line"><span class="lineno">  187</span>    <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  188</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *successor = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  189</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *ancestor = root;</div>
+<div class="line"><span class="lineno">  190</span> </div>
+<div class="line"><span class="lineno">  191</span>        <span class="keywordflow">while</span> (ancestor != current &amp;&amp; ancestor != <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  192</span>            <span class="comment">// This means my current node is in left of the root node</span></div>
+<div class="line"><span class="lineno">  193</span>            <span class="keywordflow">if</span> (current-&gt;data &lt; ancestor-&gt;data) {</div>
+<div class="line"><span class="lineno">  194</span>                successor = ancestor;</div>
+<div class="line"><span class="lineno">  195</span>                ancestor = ancestor-&gt;left;  <span class="comment">// keep going left</span></div>
+<div class="line"><span class="lineno">  196</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  197</span>                ancestor = ancestor-&gt;right;</div>
+<div class="line"><span class="lineno">  198</span>            }</div>
+<div class="line"><span class="lineno">  199</span>        }</div>
+<div class="line"><span class="lineno">  200</span>        <span class="keywordflow">return</span> successor;  <span class="comment">// Nodes with maximum vales will not have a successor</span></div>
+<div class="line"><span class="lineno">  201</span>    }</div>
+<div class="line"><span class="lineno">  202</span>}</div>
 <div class="ttc" id="ahash__search_8cpp_html_a6e1a77282bc65ad359d753d25df23243"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a></div><div class="ttdeci">int data[MAX]</div><div class="ttdoc">test data</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:24</div></div>
 <div class="ttc" id="ainorder__successor__of__bst_8cpp_html_a72483e3f6933e004a8d86371e8a990db"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a72483e3f6933e004a8d86371e8a990db">operations_on_datastructures::inorder_traversal_of_bst::findMinNode</a></div><div class="ttdeci">Node * findMinNode(Node *root)</div><div class="ttdoc">Finds and return the minimum node in BST.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:121</div></div>
 <div class="ttc" id="ainorder__successor__of__bst_8cpp_html_a824cbf1814854824cf05f062eea07b95"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a824cbf1814854824cf05f062eea07b95">operations_on_datastructures::inorder_traversal_of_bst::getNode</a></div><div class="ttdeci">Node * getNode(Node *root, int64_t data)</div><div class="ttdoc">Searches the given data in BST and returns the pointer to the node containing that data.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:100</div></div>
@@ -382,21 +382,22 @@ Here is the call graph for this function:</div>
 <p ><a class="el" href="../../db/d8b/struct_node.html">Node</a> found!</p>
 <p >Traverse right subtree recursively as the given data is greater than the data in root node, data must be present in right subtree.</p>
 <p >Traverse left subtree recursively as the given data is less than the data in root node, data must be present in left subtree.</p>
-<div class="fragment"><div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>                                        {</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <span class="keywordflow">if</span> (root == <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>        <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (root-&gt;data == <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>) {</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>        <span class="keywordflow">return</span> root;  <span class="comment">/// Node found!</span></div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a> &gt; root-&gt;data) {<span class="comment"></span></div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span><span class="comment">        /// Traverse right subtree recursively as the given data is greater than</span></div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span><span class="comment">        /// the data in root node, data must be present in right subtree.</span></div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span><span class="comment"></span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a824cbf1814854824cf05f062eea07b95">getNode</a>(root-&gt;right, <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    } <span class="keywordflow">else</span> {<span class="comment"></span></div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span><span class="comment">        /// Traverse left subtree recursively as the given data is less than the</span></div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span><span class="comment">        /// data in root node, data must be present in left subtree.</span></div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span><span class="comment"></span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a824cbf1814854824cf05f062eea07b95">getNode</a>(root-&gt;left, <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    }</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  100</span>                                        {</div>
+<div class="line"><span class="lineno">  101</span>    <span class="keywordflow">if</span> (root == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  102</span>        <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  103</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (root-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a> == <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>) {</div>
+<div class="line"><span class="lineno">  104</span>        <span class="keywordflow">return</span> root;  <span class="comment">/// Node found!</span></div>
+<div class="line"><span class="lineno">  105</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a> &gt; root-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a>) {<span class="comment"></span></div>
+<div class="line"><span class="lineno">  106</span><span class="comment">        /// Traverse right subtree recursively as the given data is greater than</span></div>
+<div class="line"><span class="lineno">  107</span><span class="comment">        /// the data in root node, data must be present in right subtree.</span></div>
+<div class="line"><span class="lineno">  108</span><span class="comment"></span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a824cbf1814854824cf05f062eea07b95">getNode</a>(root-&gt;right, <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
+<div class="line"><span class="lineno">  109</span>    } <span class="keywordflow">else</span> {<span class="comment"></span></div>
+<div class="line"><span class="lineno">  110</span><span class="comment">        /// Traverse left subtree recursively as the given data is less than the</span></div>
+<div class="line"><span class="lineno">  111</span><span class="comment">        /// data in root node, data must be present in left subtree.</span></div>
+<div class="line"><span class="lineno">  112</span><span class="comment"></span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a824cbf1814854824cf05f062eea07b95">getNode</a>(root-&gt;left, <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
+<div class="line"><span class="lineno">  113</span>    }</div>
+<div class="line"><span class="lineno">  114</span>}</div>
+<div class="ttc" id="adata_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/data.html">std::vector::data</a></div><div class="ttdeci">T data(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -441,16 +442,16 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>Node* Pointer to the root node. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>                                       {</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    <span class="keywordflow">if</span> (root == <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>        root = <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7f6f73a33beec448c27cc1d70b220702">makeNode</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (data &lt;= root-&gt;<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>) {</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>        root-&gt;left = Insert(root-&gt;left, <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        root-&gt;right = Insert(root-&gt;right, <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    }</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    <span class="keywordflow">return</span> root;</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   82</span>                                       {</div>
+<div class="line"><span class="lineno">   83</span>    <span class="keywordflow">if</span> (root == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">   84</span>        root = <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7f6f73a33beec448c27cc1d70b220702">makeNode</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
+<div class="line"><span class="lineno">   85</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (data &lt;= root-&gt;<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>) {</div>
+<div class="line"><span class="lineno">   86</span>        root-&gt;left = Insert(root-&gt;left, <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
+<div class="line"><span class="lineno">   87</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   88</span>        root-&gt;right = Insert(root-&gt;right, <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
+<div class="line"><span class="lineno">   89</span>    }</div>
+<div class="line"><span class="lineno">   90</span>    <span class="keywordflow">return</span> root;</div>
+<div class="line"><span class="lineno">   91</span>}</div>
 <div class="ttc" id="ainorder__successor__of__bst_8cpp_html_a7f6f73a33beec448c27cc1d70b220702"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7f6f73a33beec448c27cc1d70b220702">operations_on_datastructures::inorder_traversal_of_bst::makeNode</a></div><div class="ttdeci">Node * makeNode(int64_t data)</div><div class="ttdoc">Allocates a new node in heap for given data and returns it's pointer.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:68</div></div>
 </div><!-- fragment -->
 </div>
@@ -495,38 +496,38 @@ Here is the call graph for this function:</div>
 <p >&lt; An element to find inorder successor for.</p>
 <p >&lt; Making BST</p>
 <p >memory cleanup!</p>
-<div class="fragment"><div class="line"><a id="l00398" name="l00398"></a><span class="lineno">  398</span>                                 {</div>
-<div class="line"><a id="l00399" name="l00399"></a><span class="lineno">  399</span>    <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
-<div class="line"><a id="l00400" name="l00400"></a><span class="lineno">  400</span> </div>
-<div class="line"><a id="l00401" name="l00401"></a><span class="lineno">  401</span>    <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a> *root =</div>
-<div class="line"><a id="l00402" name="l00402"></a><span class="lineno">  402</span>        <span class="keyword">nullptr</span>;  <span class="comment">///&lt; root node of the bst</span></div>
-<div class="line"><a id="l00403" name="l00403"></a><span class="lineno">  403</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> node_data{3,  4, 5,</div>
-<div class="line"><a id="l00404" name="l00404"></a><span class="lineno">  404</span>                                   89, 1, 2};  <span class="comment">///&lt; Data to add nodes in BST</span></div>
-<div class="line"><a id="l00405" name="l00405"></a><span class="lineno">  405</span> </div>
-<div class="line"><a id="l00406" name="l00406"></a><span class="lineno">  406</span>    int64_t targetElement = 4;  <span class="comment">///&lt; An element to find inorder successor for.</span></div>
-<div class="line"><a id="l00407" name="l00407"></a><span class="lineno">  407</span>    root = <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a05fe8a029e155c43e4efa598d4d089d9">operations_on_datastructures::inorder_traversal_of_bst::makeBST</a>(</div>
-<div class="line"><a id="l00408" name="l00408"></a><span class="lineno">  408</span>        root, node_data);  <span class="comment">///&lt; Making BST</span></div>
-<div class="line"><a id="l00409" name="l00409"></a><span class="lineno">  409</span> </div>
-<div class="line"><a id="l00410" name="l00410"></a><span class="lineno">  410</span>    <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a></div>
-<div class="line"><a id="l00411" name="l00411"></a><span class="lineno">  411</span>        *inorderSuccessor = operations_on_datastructures::</div>
-<div class="line"><a id="l00412" name="l00412"></a><span class="lineno">  412</span>            inorder_traversal_of_bst::getInorderSuccessor(root, targetElement);</div>
-<div class="line"><a id="l00413" name="l00413"></a><span class="lineno">  413</span> </div>
-<div class="line"><a id="l00414" name="l00414"></a><span class="lineno">  414</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;In-order sequence is : &quot;</span>;</div>
-<div class="line"><a id="l00415" name="l00415"></a><span class="lineno">  415</span>    <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">operations_on_datastructures::inorder_traversal_of_bst::printInorder</a>(root);</div>
-<div class="line"><a id="l00416" name="l00416"></a><span class="lineno">  416</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00417" name="l00417"></a><span class="lineno">  417</span> </div>
-<div class="line"><a id="l00418" name="l00418"></a><span class="lineno">  418</span>    <span class="keywordflow">if</span> (inorderSuccessor == <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00419" name="l00419"></a><span class="lineno">  419</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Inorder successor for last node is NULL&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00420" name="l00420"></a><span class="lineno">  420</span>    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00421" name="l00421"></a><span class="lineno">  421</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Target element is : &quot;</span> &lt;&lt; targetElement &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00422" name="l00422"></a><span class="lineno">  422</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Inorder successor for target element is : &quot;</span></div>
-<div class="line"><a id="l00423" name="l00423"></a><span class="lineno">  423</span>                  &lt;&lt; inorderSuccessor-&gt;<a class="code hl_variable" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html#ae161f3e5ef33ade73429cab9291612e2">data</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00424" name="l00424"></a><span class="lineno">  424</span>    }</div>
-<div class="line"><a id="l00425" name="l00425"></a><span class="lineno">  425</span> </div>
-<div class="line"><a id="l00426" name="l00426"></a><span class="lineno">  426</span>    <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7b20eb99272665c1777949e26ab59589">deallocate</a>(root);  <span class="comment">/// memory cleanup!</span></div>
-<div class="line"><a id="l00427" name="l00427"></a><span class="lineno">  427</span> </div>
-<div class="line"><a id="l00428" name="l00428"></a><span class="lineno">  428</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00429" name="l00429"></a><span class="lineno">  429</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  398</span>                                 {</div>
+<div class="line"><span class="lineno">  399</span>    <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
+<div class="line"><span class="lineno">  400</span> </div>
+<div class="line"><span class="lineno">  401</span>    <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a> *root =</div>
+<div class="line"><span class="lineno">  402</span>        <span class="keyword">nullptr</span>;  <span class="comment">///&lt; root node of the bst</span></div>
+<div class="line"><span class="lineno">  403</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> node_data{3,  4, 5,</div>
+<div class="line"><span class="lineno">  404</span>                                   89, 1, 2};  <span class="comment">///&lt; Data to add nodes in BST</span></div>
+<div class="line"><span class="lineno">  405</span> </div>
+<div class="line"><span class="lineno">  406</span>    int64_t targetElement = 4;  <span class="comment">///&lt; An element to find inorder successor for.</span></div>
+<div class="line"><span class="lineno">  407</span>    root = <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a05fe8a029e155c43e4efa598d4d089d9">operations_on_datastructures::inorder_traversal_of_bst::makeBST</a>(</div>
+<div class="line"><span class="lineno">  408</span>        root, node_data);  <span class="comment">///&lt; Making BST</span></div>
+<div class="line"><span class="lineno">  409</span> </div>
+<div class="line"><span class="lineno">  410</span>    <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a></div>
+<div class="line"><span class="lineno">  411</span>        *inorderSuccessor = operations_on_datastructures::</div>
+<div class="line"><span class="lineno">  412</span>            inorder_traversal_of_bst::getInorderSuccessor(root, targetElement);</div>
+<div class="line"><span class="lineno">  413</span> </div>
+<div class="line"><span class="lineno">  414</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;In-order sequence is : &quot;</span>;</div>
+<div class="line"><span class="lineno">  415</span>    <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">operations_on_datastructures::inorder_traversal_of_bst::printInorder</a>(root);</div>
+<div class="line"><span class="lineno">  416</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  417</span> </div>
+<div class="line"><span class="lineno">  418</span>    <span class="keywordflow">if</span> (inorderSuccessor == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  419</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Inorder successor for last node is NULL&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  420</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  421</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Target element is : &quot;</span> &lt;&lt; targetElement &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  422</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Inorder successor for target element is : &quot;</span></div>
+<div class="line"><span class="lineno">  423</span>                  &lt;&lt; inorderSuccessor-&gt;<a class="code hl_variable" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html#ae161f3e5ef33ade73429cab9291612e2">data</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  424</span>    }</div>
+<div class="line"><span class="lineno">  425</span> </div>
+<div class="line"><span class="lineno">  426</span>    <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7b20eb99272665c1777949e26ab59589">deallocate</a>(root);  <span class="comment">/// memory cleanup!</span></div>
+<div class="line"><span class="lineno">  427</span> </div>
+<div class="line"><span class="lineno">  428</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  429</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aclassoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node_html"><div class="ttname"><a href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a></div><div class="ttdoc">A Node structure representing a single node in BST.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:56</div></div>
 <div class="ttc" id="aclassoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node_html_ae161f3e5ef33ade73429cab9291612e2"><div class="ttname"><a href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html#ae161f3e5ef33ade73429cab9291612e2">operations_on_datastructures::inorder_traversal_of_bst::Node::data</a></div><div class="ttdeci">int64_t data</div><div class="ttdoc">The key/value of the node.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:58</div></div>
@@ -534,7 +535,7 @@ Here is the call graph for this function:</div>
 <div class="ttc" id="ainorder__successor__of__bst_8cpp_html_a05fe8a029e155c43e4efa598d4d089d9"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a05fe8a029e155c43e4efa598d4d089d9">operations_on_datastructures::inorder_traversal_of_bst::makeBST</a></div><div class="ttdeci">Node * makeBST(Node *root, const std::vector&lt; int64_t &gt; &amp;data)</div><div class="ttdoc">This function is used in test cases to quickly create BST containing large data instead of hard codin...</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:155</div></div>
 <div class="ttc" id="ainorder__successor__of__bst_8cpp_html_a5d7266b934ca50c4f53e4f1e725d89a4"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">operations_on_datastructures::inorder_traversal_of_bst::printInorder</a></div><div class="ttdeci">void printInorder(Node *root)</div><div class="ttdoc">Prints the BST in inorder traversal using recursion.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:136</div></div>
 <div class="ttc" id="ainorder__successor__of__bst_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:387</div></div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int64_t &gt;</a></div></div>
 </div><!-- fragment --><div class="dynheader">
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@@ -579,12 +580,12 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd><a class="el" href="../../db/d8b/struct_node.html">Node</a> pointer to the root node. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>                                                          {</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>    <span class="keywordflow">for</span> (int64_t values : <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>) {</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>        root = Insert(root, values);</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    }</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>    <span class="keywordflow">return</span> root;</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  155</span>                                                          {</div>
+<div class="line"><span class="lineno">  156</span>    <span class="keywordflow">for</span> (int64_t values : <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>) {</div>
+<div class="line"><span class="lineno">  157</span>        root = Insert(root, values);</div>
+<div class="line"><span class="lineno">  158</span>    }</div>
+<div class="line"><span class="lineno">  159</span>    <span class="keywordflow">return</span> root;</div>
+<div class="line"><span class="lineno">  160</span>}</div>
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@@ -621,13 +622,13 @@ Here is the call graph for this function:</div>
 <p >&lt; setting data for node</p>
 <p >&lt; setting left child as null</p>
 <p >&lt; setting right child as null</p>
-<div class="fragment"><div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>                             {</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>();</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;data = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;      <span class="comment">///&lt; setting data for node</span></div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left = <span class="keyword">nullptr</span>;   <span class="comment">///&lt; setting left child as null</span></div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right = <span class="keyword">nullptr</span>;  <span class="comment">///&lt; setting right child as null</span></div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <span class="keywordflow">return</span> <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   68</span>                             {</div>
+<div class="line"><span class="lineno">   69</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>();</div>
+<div class="line"><span class="lineno">   70</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;data = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;      <span class="comment">///&lt; setting data for node</span></div>
+<div class="line"><span class="lineno">   71</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left = <span class="keyword">nullptr</span>;   <span class="comment">///&lt; setting left child as null</span></div>
+<div class="line"><span class="lineno">   72</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right = <span class="keyword">nullptr</span>;  <span class="comment">///&lt; setting right child as null</span></div>
+<div class="line"><span class="lineno">   73</span>    <span class="keywordflow">return</span> <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
+<div class="line"><span class="lineno">   74</span>}</div>
 <div class="ttc" id="ahash__search_8cpp_html_a8ca8dcb494104d273679e219e53d0555"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a></div><div class="ttdeci">struct list node</div></div>
 <div class="ttc" id="astructnode_html"><div class="ttname"><a href="../../d5/da1/structnode.html">node</a></div><div class="ttdef"><b>Definition:</b> avltree.cpp:13</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -665,15 +666,15 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
 <p >recursive call to left subtree</p>
 <p >recursive call to right subtree</p>
-<div class="fragment"><div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>                              {</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    <span class="keywordflow">if</span> (root == <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>        <span class="keywordflow">return</span>;</div>
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-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span> </div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">printInorder</a>(root-&gt;left);  <span class="comment">/// recursive call to left subtree</span></div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; root-&gt;data &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">printInorder</a>(root-&gt;right);  <span class="comment">/// recursive call to right subtree</span></div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  136</span>                              {</div>
+<div class="line"><span class="lineno">  137</span>    <span class="keywordflow">if</span> (root == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  138</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  139</span>    }</div>
+<div class="line"><span class="lineno">  140</span> </div>
+<div class="line"><span class="lineno">  141</span>    <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">printInorder</a>(root-&gt;left);  <span class="comment">/// recursive call to left subtree</span></div>
+<div class="line"><span class="lineno">  142</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; root-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a> &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">  143</span>    <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">printInorder</a>(root-&gt;right);  <span class="comment">/// recursive call to right subtree</span></div>
+<div class="line"><span class="lineno">  144</span>}</div>
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@@ -708,10 +709,10 @@ Here is the call graph for this function:</div>
 
 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00387" name="l00387"></a><span class="lineno">  387</span>                   {</div>
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-<div class="line"><a id="l00390" name="l00390"></a><span class="lineno">  390</span>}</div>
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@@ -189,30 +189,30 @@ template&lt;size_t n&gt; </div>
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-<div class="fragment"><div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>                            {</div>
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-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>            <span class="comment">// Recursive to place rest of the queens</span></div>
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+<div class="line"><span class="lineno">   93</span>        printSolution&lt;n&gt;(board);</div>
+<div class="line"><span class="lineno">   94</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">   95</span>    }</div>
+<div class="line"><span class="lineno">   96</span> </div>
+<div class="line"><span class="lineno">   97</span>    <span class="comment">// Consider this column and try placing</span></div>
+<div class="line"><span class="lineno">   98</span>    <span class="comment">// this queen in all rows one by one</span></div>
+<div class="line"><span class="lineno">   99</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">  100</span>        <span class="comment">// Check if queen can be placed</span></div>
+<div class="line"><span class="lineno">  101</span>        <span class="comment">// on board[i][col]</span></div>
+<div class="line"><span class="lineno">  102</span>        <span class="keywordflow">if</span> (isSafe&lt;n&gt;(board, i, col)) {</div>
+<div class="line"><span class="lineno">  103</span>            <span class="comment">// Place this queen in matrix</span></div>
+<div class="line"><span class="lineno">  104</span>            board[i][col] = 1;</div>
+<div class="line"><span class="lineno">  105</span> </div>
+<div class="line"><span class="lineno">  106</span>            <span class="comment">// Recursive to place rest of the queens</span></div>
+<div class="line"><span class="lineno">  107</span>            solveNQ&lt;n&gt;(board, col + 1);</div>
+<div class="line"><span class="lineno">  108</span> </div>
+<div class="line"><span class="lineno">  109</span>            board[i][col] = 0;  <span class="comment">// backtrack</span></div>
+<div class="line"><span class="lineno">  110</span>        }</div>
+<div class="line"><span class="lineno">  111</span>    }</div>
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-<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span>    <span class="keywordflow">if</span> (num1 &lt;= 0 | num2 &lt;= 0) {</div>
-<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span>        <span class="keywordflow">throw</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/domain_error.html">std::domain_error</a>(<span class="stringliteral">&quot;Euclidean algorithm domain is for ints &gt; 0&quot;</span>);</div>
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-<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>    <span class="comment">// Everything divides 0</span></div>
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-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>    <span class="comment">// base case</span></div>
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-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>}</div>
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+<div class="line"><span class="lineno">   16</span>        <span class="keywordflow">throw</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/domain_error.html">std::domain_error</a>(<span class="stringliteral">&quot;Euclidean algorithm domain is for ints &gt; 0&quot;</span>);</div>
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+<div class="line"><span class="lineno">   18</span> </div>
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+<div class="line"><span class="lineno">   23</span>    <span class="comment">// Everything divides 0</span></div>
+<div class="line"><span class="lineno">   24</span>    <span class="keywordflow">if</span> (num1 == 0)</div>
+<div class="line"><span class="lineno">   25</span>        <span class="keywordflow">return</span> num2;</div>
+<div class="line"><span class="lineno">   26</span>    <span class="keywordflow">if</span> (num2 == 0)</div>
+<div class="line"><span class="lineno">   27</span>        <span class="keywordflow">return</span> num1;</div>
+<div class="line"><span class="lineno">   28</span> </div>
+<div class="line"><span class="lineno">   29</span>    <span class="comment">// base case</span></div>
+<div class="line"><span class="lineno">   30</span>    <span class="keywordflow">if</span> (num1 == num2)</div>
+<div class="line"><span class="lineno">   31</span>        <span class="keywordflow">return</span> num1;</div>
+<div class="line"><span class="lineno">   32</span> </div>
+<div class="line"><span class="lineno">   33</span>    <span class="comment">// a is greater</span></div>
+<div class="line"><span class="lineno">   34</span>    <span class="keywordflow">if</span> (num1 &gt; num2)</div>
+<div class="line"><span class="lineno">   35</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>(num1 - num2, num2);</div>
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 <div class="ttc" id="adomain_error_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/error/domain_error.html">std::domain_error</a></div></div>
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+<div class="line"><span class="lineno">   44</span>    <span class="keywordflow">try</span> {</div>
+<div class="line"><span class="lineno">   45</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;gcd of -120,10 is &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>(-120, 10) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><span class="lineno">   35</span>    uint64_t count = 0;</div>
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+<div class="line"><span class="lineno">   37</span>        <span class="keywordflow">if</span> (value &amp; 1) {  <span class="comment">// check lower bit</span></div>
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+<div class="line"><span class="lineno">   40</span>        value &gt;&gt;= 1;  <span class="comment">// shift bits, removing lower bit</span></div>
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+<div class="line"><span class="lineno">   60</span>    assert(a.size() == b.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>());</div>
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 <p>Main function. </p>
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-<div class="fragment"><div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>           {</div>
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+<div class="line"><span class="lineno">  101</span>    uint64_t a = 11;  <span class="comment">// 1011 in binary</span></div>
+<div class="line"><span class="lineno">  102</span>    uint64_t b = 2;   <span class="comment">// 0010 in binary</span></div>
+<div class="line"><span class="lineno">  103</span> </div>
+<div class="line"><span class="lineno">  104</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hamming distance between &quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot; and &quot;</span> &lt;&lt; b &lt;&lt; <span class="stringliteral">&quot; is &quot;</span></div>
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+<div class="line"><span class="lineno">  106</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  107</span>}</div>
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 <p>Function to the test hamming distance. </p>
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-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>                                                                <span class="stringliteral">&quot;abcd&quot;</span>) == 0);</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;dcba&quot;</span>,</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>                                                                <span class="stringliteral">&quot;abcd&quot;</span>) == 4);</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   75</span>                   {</div>
+<div class="line"><span class="lineno">   76</span>    assert(bit_manipulation::hamming_distance::hamming_distance(11, 2) == 2);</div>
+<div class="line"><span class="lineno">   77</span>    assert(bit_manipulation::hamming_distance::hamming_distance(2, 0) == 1);</div>
+<div class="line"><span class="lineno">   78</span>    assert(bit_manipulation::hamming_distance::hamming_distance(11, 0) == 3);</div>
+<div class="line"><span class="lineno">   79</span> </div>
+<div class="line"><span class="lineno">   80</span>    assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;1101&quot;</span>,</div>
+<div class="line"><span class="lineno">   81</span>                                                                <span class="stringliteral">&quot;1111&quot;</span>) == 1);</div>
+<div class="line"><span class="lineno">   82</span>    assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;1111&quot;</span>,</div>
+<div class="line"><span class="lineno">   83</span>                                                                <span class="stringliteral">&quot;1111&quot;</span>) == 0);</div>
+<div class="line"><span class="lineno">   84</span>    assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;0000&quot;</span>,</div>
+<div class="line"><span class="lineno">   85</span>                                                                <span class="stringliteral">&quot;1111&quot;</span>) == 4);</div>
+<div class="line"><span class="lineno">   86</span> </div>
+<div class="line"><span class="lineno">   87</span>    assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;alpha&quot;</span>,</div>
+<div class="line"><span class="lineno">   88</span>                                                                <span class="stringliteral">&quot;alphb&quot;</span>) == 1);</div>
+<div class="line"><span class="lineno">   89</span>    assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;abcd&quot;</span>,</div>
+<div class="line"><span class="lineno">   90</span>                                                                <span class="stringliteral">&quot;abcd&quot;</span>) == 0);</div>
+<div class="line"><span class="lineno">   91</span>    assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;dcba&quot;</span>,</div>
+<div class="line"><span class="lineno">   92</span>                                                                <span class="stringliteral">&quot;abcd&quot;</span>) == 4);</div>
+<div class="line"><span class="lineno">   93</span>}</div>
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 <p >Function for testing the <a class="el" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong()</a> function with all the test cases. </p>
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-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <span class="comment">// is_armstrong(370) returns true.</span></div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    assert(<a class="code hl_function" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong</a>(370) == <span class="keyword">true</span>);</div>
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+<div class="line"><span class="lineno">   60</span>    <span class="comment">// is_armstrong(370) returns true.</span></div>
+<div class="line"><span class="lineno">   61</span>    assert(<a class="code hl_function" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong</a>(370) == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">   62</span>    <span class="comment">// is_armstrong(225) returns false.</span></div>
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+<div class="line"><span class="lineno">   64</span>    <span class="comment">// is_armstrong(-23) returns false.</span></div>
+<div class="line"><span class="lineno">   65</span>    assert(<a class="code hl_function" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong</a>(-23) == <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">   66</span>    <span class="comment">// is_armstrong(153) returns true.</span></div>
+<div class="line"><span class="lineno">   67</span>    assert(<a class="code hl_function" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong</a>(153) == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">   68</span>    <span class="comment">// is_armstrong(0) returns true.</span></div>
+<div class="line"><span class="lineno">   69</span>    assert(<a class="code hl_function" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong</a>(0) == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">   70</span>    <span class="comment">// is_armstrong(12) returns false.</span></div>
+<div class="line"><span class="lineno">   71</span>    assert(<a class="code hl_function" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong</a>(12) == <span class="keyword">false</span>);</div>
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    <div id="projectbrief">Set of algorithms implemented in C++.</div>
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@@ -177,19 +177,19 @@ template&lt;typename T &gt; </div>
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 <p >function to compare sorting using cstdlib's qsort </p>
-<div class="fragment"><div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>                                          {</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    T arg1 = *<span class="keyword">static_cast&lt;</span><span class="keyword">const </span>T *<span class="keyword">&gt;</span>(a);</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    T arg2 = *<span class="keyword">static_cast&lt;</span><span class="keyword">const </span>T *<span class="keyword">&gt;</span>(b);</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span> </div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    <span class="keywordflow">if</span> (arg1 &lt; arg2)</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>        <span class="keywordflow">return</span> -1;</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    <span class="keywordflow">if</span> (arg1 &gt; arg2)</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>        <span class="keywordflow">return</span> 1;</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span> </div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    <span class="comment">//  return (arg1 &gt; arg2) - (arg1 &lt; arg2); // possible shortcut</span></div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    <span class="comment">//  return arg1 - arg2; // erroneous shortcut (fails if INT_MIN is present)</span></div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   87</span>                                          {</div>
+<div class="line"><span class="lineno">   88</span>    T arg1 = *<span class="keyword">static_cast&lt;</span><span class="keyword">const </span>T *<span class="keyword">&gt;</span>(a);</div>
+<div class="line"><span class="lineno">   89</span>    T arg2 = *<span class="keyword">static_cast&lt;</span><span class="keyword">const </span>T *<span class="keyword">&gt;</span>(b);</div>
+<div class="line"><span class="lineno">   90</span> </div>
+<div class="line"><span class="lineno">   91</span>    <span class="keywordflow">if</span> (arg1 &lt; arg2)</div>
+<div class="line"><span class="lineno">   92</span>        <span class="keywordflow">return</span> -1;</div>
+<div class="line"><span class="lineno">   93</span>    <span class="keywordflow">if</span> (arg1 &gt; arg2)</div>
+<div class="line"><span class="lineno">   94</span>        <span class="keywordflow">return</span> 1;</div>
+<div class="line"><span class="lineno">   95</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">   96</span> </div>
+<div class="line"><span class="lineno">   97</span>    <span class="comment">//  return (arg1 &gt; arg2) - (arg1 &lt; arg2); // possible shortcut</span></div>
+<div class="line"><span class="lineno">   98</span>    <span class="comment">//  return arg1 - arg2; // erroneous shortcut (fails if INT_MIN is present)</span></div>
+<div class="line"><span class="lineno">   99</span>}</div>
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@@ -219,58 +219,58 @@ template&lt;typename T &gt; </div>
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 <p >Main function </p>
-<div class="fragment"><div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>                                 {</div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>    <span class="comment">// initialize random number generator - once per program</span></div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(NULL));</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span> </div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>    <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a895b313cb2671e8f712040460325573e">test_int</a>(100);  <span class="comment">// test with sorting random array of 100 values</span></div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 - 100 int values - passed. \n&quot;</span>;</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>    <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a895b313cb2671e8f712040460325573e">test_int</a>(1000);  <span class="comment">// test with sorting random array of 1000 values</span></div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 - 1000 int values - passed.\n&quot;</span>;</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>    <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a895b313cb2671e8f712040460325573e">test_int</a>(10000);  <span class="comment">// test with sorting random array of 10000 values</span></div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 - 10000 int values - passed.\n&quot;</span>;</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span> </div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>    <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a22ea0d1f7943ebb4371d31e44b465b6d">test_f</a>(100);  <span class="comment">// test with sorting random array of 100 values</span></div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 - 100 float values - passed. \n&quot;</span>;</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>    <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a22ea0d1f7943ebb4371d31e44b465b6d">test_f</a>(1000);  <span class="comment">// test with sorting random array of 1000 values</span></div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 - 1000 float values - passed.\n&quot;</span>;</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>    <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a22ea0d1f7943ebb4371d31e44b465b6d">test_f</a>(10000);  <span class="comment">// test with sorting random array of 10000 values</span></div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 - 10000 float values - passed.\n&quot;</span>;</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span> </div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>    <span class="keywordtype">int</span> i, NUM_DATA;</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span> </div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>    <span class="keywordflow">if</span> (argc == 2)</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>        NUM_DATA = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">atoi</a>(argv[1]);</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    <span class="keywordflow">else</span></div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>        NUM_DATA = 200;</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span> </div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    <span class="comment">// int array = new int[NUM_DATA];</span></div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>    <span class="keywordtype">int</span> *<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a> = <span class="keyword">new</span> <span class="keywordtype">int</span>[NUM_DATA];</div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>    <span class="comment">// int array2 = new int[NUM_DATA];</span></div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>    <span class="keywordtype">int</span> range = 1800;</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span> </div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">time</a>(NULL));</div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>    <span class="keywordflow">for</span> (i = 0; i &lt; NUM_DATA; i++) {</div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>        <span class="comment">// allocate random numbers in the given range</span></div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - (range &gt;&gt; 1);</div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>    }</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span> </div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Unsorted original data: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>    <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a951127aea9d7e1e53ea9ae0868633246">show_data</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">shell_sort</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);  <span class="comment">// perform sorting</span></div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span> </div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>              &lt;&lt; <span class="stringliteral">&quot;Data Sorted using custom implementation: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>    <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a951127aea9d7e1e53ea9ae0868633246">show_data</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span> </div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>    <span class="keywordtype">double</span> elapsed_time = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) * 1.f / CLOCKS_PER_SEC;</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time spent sorting: &quot;</span> &lt;&lt; elapsed_time &lt;&lt; <span class="stringliteral">&quot;s\n&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span> </div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>    <span class="keyword">delete</span>[] <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
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-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>}</div>
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+<div class="line"><span class="lineno">  184</span>    <span class="comment">// initialize random number generator - once per program</span></div>
+<div class="line"><span class="lineno">  185</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(NULL));</div>
+<div class="line"><span class="lineno">  186</span> </div>
+<div class="line"><span class="lineno">  187</span>    <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a895b313cb2671e8f712040460325573e">test_int</a>(100);  <span class="comment">// test with sorting random array of 100 values</span></div>
+<div class="line"><span class="lineno">  188</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 - 100 int values - passed. \n&quot;</span>;</div>
+<div class="line"><span class="lineno">  189</span>    <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a895b313cb2671e8f712040460325573e">test_int</a>(1000);  <span class="comment">// test with sorting random array of 1000 values</span></div>
+<div class="line"><span class="lineno">  190</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 - 1000 int values - passed.\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  191</span>    <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a895b313cb2671e8f712040460325573e">test_int</a>(10000);  <span class="comment">// test with sorting random array of 10000 values</span></div>
+<div class="line"><span class="lineno">  192</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 - 10000 int values - passed.\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  193</span> </div>
+<div class="line"><span class="lineno">  194</span>    <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a22ea0d1f7943ebb4371d31e44b465b6d">test_f</a>(100);  <span class="comment">// test with sorting random array of 100 values</span></div>
+<div class="line"><span class="lineno">  195</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 - 100 float values - passed. \n&quot;</span>;</div>
+<div class="line"><span class="lineno">  196</span>    <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a22ea0d1f7943ebb4371d31e44b465b6d">test_f</a>(1000);  <span class="comment">// test with sorting random array of 1000 values</span></div>
+<div class="line"><span class="lineno">  197</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 - 1000 float values - passed.\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  198</span>    <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a22ea0d1f7943ebb4371d31e44b465b6d">test_f</a>(10000);  <span class="comment">// test with sorting random array of 10000 values</span></div>
+<div class="line"><span class="lineno">  199</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 - 10000 float values - passed.\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  200</span> </div>
+<div class="line"><span class="lineno">  201</span>    <span class="keywordtype">int</span> i, NUM_DATA;</div>
+<div class="line"><span class="lineno">  202</span> </div>
+<div class="line"><span class="lineno">  203</span>    <span class="keywordflow">if</span> (argc == 2)</div>
+<div class="line"><span class="lineno">  204</span>        NUM_DATA = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">atoi</a>(argv[1]);</div>
+<div class="line"><span class="lineno">  205</span>    <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  206</span>        NUM_DATA = 200;</div>
+<div class="line"><span class="lineno">  207</span> </div>
+<div class="line"><span class="lineno">  208</span>    <span class="comment">// int array = new int[NUM_DATA];</span></div>
+<div class="line"><span class="lineno">  209</span>    <span class="keywordtype">int</span> *<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a> = <span class="keyword">new</span> <span class="keywordtype">int</span>[NUM_DATA];</div>
+<div class="line"><span class="lineno">  210</span>    <span class="comment">// int array2 = new int[NUM_DATA];</span></div>
+<div class="line"><span class="lineno">  211</span>    <span class="keywordtype">int</span> range = 1800;</div>
+<div class="line"><span class="lineno">  212</span> </div>
+<div class="line"><span class="lineno">  213</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">time</a>(NULL));</div>
+<div class="line"><span class="lineno">  214</span>    <span class="keywordflow">for</span> (i = 0; i &lt; NUM_DATA; i++) {</div>
+<div class="line"><span class="lineno">  215</span>        <span class="comment">// allocate random numbers in the given range</span></div>
+<div class="line"><span class="lineno">  216</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - (range &gt;&gt; 1);</div>
+<div class="line"><span class="lineno">  217</span>    }</div>
+<div class="line"><span class="lineno">  218</span> </div>
+<div class="line"><span class="lineno">  219</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Unsorted original data: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  220</span>    <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a951127aea9d7e1e53ea9ae0868633246">show_data</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);</div>
+<div class="line"><span class="lineno">  221</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  222</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">shell_sort</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);  <span class="comment">// perform sorting</span></div>
+<div class="line"><span class="lineno">  223</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  224</span> </div>
+<div class="line"><span class="lineno">  225</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
+<div class="line"><span class="lineno">  226</span>              &lt;&lt; <span class="stringliteral">&quot;Data Sorted using custom implementation: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  227</span>    <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a951127aea9d7e1e53ea9ae0868633246">show_data</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);</div>
+<div class="line"><span class="lineno">  228</span> </div>
+<div class="line"><span class="lineno">  229</span>    <span class="keywordtype">double</span> elapsed_time = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) * 1.f / CLOCKS_PER_SEC;</div>
+<div class="line"><span class="lineno">  230</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time spent sorting: &quot;</span> &lt;&lt; elapsed_time &lt;&lt; <span class="stringliteral">&quot;s\n&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  231</span> </div>
+<div class="line"><span class="lineno">  232</span>    <span class="keyword">delete</span>[] <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
+<div class="line"><span class="lineno">  233</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  234</span>}</div>
 <div class="ttc" id="aatoi_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">std::atoi</a></div><div class="ttdeci">T atoi(T... args)</div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aclock_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a></div><div class="ttdeci">T clock(T... args)</div></div>
@@ -328,14 +328,14 @@ template&lt;class T &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span>                                   {</div>
-<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span>    <span class="keywordtype">size_t</span> i;</div>
-<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span> </div>
-<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>    <span class="keywordflow">for</span> (i = 0; i &lt; LEN; i++) {</div>
-<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; arr[i] &lt;&lt; <span class="stringliteral">&quot;, &quot;</span>;</div>
-<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>    }</div>
-<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   18</span>                                   {</div>
+<div class="line"><span class="lineno">   19</span>    <span class="keywordtype">size_t</span> i;</div>
+<div class="line"><span class="lineno">   20</span> </div>
+<div class="line"><span class="lineno">   21</span>    <span class="keywordflow">for</span> (i = 0; i &lt; LEN; i++) {</div>
+<div class="line"><span class="lineno">   22</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; arr[i] &lt;&lt; <span class="stringliteral">&quot;, &quot;</span>;</div>
+<div class="line"><span class="lineno">   23</span>    }</div>
+<div class="line"><span class="lineno">   24</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   25</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -369,9 +369,9 @@ template&lt;typename T , size_t N&gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>                            {</div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>    <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a951127aea9d7e1e53ea9ae0868633246">show_data</a>(arr, N);</div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   32</span>                            {</div>
+<div class="line"><span class="lineno">   33</span>    <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a951127aea9d7e1e53ea9ae0868633246">show_data</a>(arr, N);</div>
+<div class="line"><span class="lineno">   34</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -397,42 +397,42 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Test implementation of shell_sort on float arrays by comparing results against <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/qsort.html">std::qsort</a>. </p>
-<div class="fragment"><div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>                                {</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    <span class="comment">// int array = new int[NUM_DATA];</span></div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    <span class="keywordtype">float</span> *<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a> = <span class="keyword">new</span> <span class="keywordtype">float</span>[NUM_DATA];</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>    <span class="keywordtype">float</span> *data2 = <span class="keyword">new</span> <span class="keywordtype">float</span>[NUM_DATA];</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>    <span class="comment">// int array2 = new int[NUM_DATA];</span></div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    <span class="keywordtype">int</span> range = 1000;</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span> </div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; NUM_DATA; i++) {</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] = data2[i] = ((<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - (range &gt;&gt; 1)) / 100.;</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>    }</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span> </div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>    <span class="comment">/* sort using our implementation */</span></div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">shell_sort</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>    <span class="keywordtype">double</span> elapsed_time = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) / CLOCKS_PER_SEC;</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time spent sorting using shell_sort2: &quot;</span> &lt;&lt; elapsed_time</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>              &lt;&lt; <span class="stringliteral">&quot;s\n&quot;</span>;</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span> </div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>    <span class="comment">/* sort using std::qsort */</span></div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>    start = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/qsort.html">std::qsort</a>(data2, NUM_DATA, <span class="keyword">sizeof</span>(data2[0]), <a class="code hl_struct" href="../../d1/db3/structcompare.html">compare&lt;float&gt;</a>);</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span> </div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>    elapsed_time = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) / CLOCKS_PER_SEC;</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time spent sorting using std::qsort: &quot;</span> &lt;&lt; elapsed_time</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>              &lt;&lt; <span class="stringliteral">&quot;s\n&quot;</span>;</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span> </div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; NUM_DATA; i++) {</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>        assert(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] == data2[i]);  <span class="comment">// ensure that our sorting results match</span></div>
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-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  145</span>                                {</div>
+<div class="line"><span class="lineno">  146</span>    <span class="comment">// int array = new int[NUM_DATA];</span></div>
+<div class="line"><span class="lineno">  147</span>    <span class="keywordtype">float</span> *<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a> = <span class="keyword">new</span> <span class="keywordtype">float</span>[NUM_DATA];</div>
+<div class="line"><span class="lineno">  148</span>    <span class="keywordtype">float</span> *data2 = <span class="keyword">new</span> <span class="keywordtype">float</span>[NUM_DATA];</div>
+<div class="line"><span class="lineno">  149</span>    <span class="comment">// int array2 = new int[NUM_DATA];</span></div>
+<div class="line"><span class="lineno">  150</span>    <span class="keywordtype">int</span> range = 1000;</div>
+<div class="line"><span class="lineno">  151</span> </div>
+<div class="line"><span class="lineno">  152</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; NUM_DATA; i++) {</div>
+<div class="line"><span class="lineno">  153</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] = data2[i] = ((<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - (range &gt;&gt; 1)) / 100.;</div>
+<div class="line"><span class="lineno">  154</span>    }</div>
+<div class="line"><span class="lineno">  155</span> </div>
+<div class="line"><span class="lineno">  156</span>    <span class="comment">/* sort using our implementation */</span></div>
+<div class="line"><span class="lineno">  157</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  158</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">shell_sort</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);</div>
+<div class="line"><span class="lineno">  159</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  160</span>    <span class="keywordtype">double</span> elapsed_time = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) / CLOCKS_PER_SEC;</div>
+<div class="line"><span class="lineno">  161</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time spent sorting using shell_sort2: &quot;</span> &lt;&lt; elapsed_time</div>
+<div class="line"><span class="lineno">  162</span>              &lt;&lt; <span class="stringliteral">&quot;s\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  163</span> </div>
+<div class="line"><span class="lineno">  164</span>    <span class="comment">/* sort using std::qsort */</span></div>
+<div class="line"><span class="lineno">  165</span>    start = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  166</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/qsort.html">std::qsort</a>(data2, NUM_DATA, <span class="keyword">sizeof</span>(data2[0]), <a class="code hl_struct" href="../../d1/db3/structcompare.html">compare&lt;float&gt;</a>);</div>
+<div class="line"><span class="lineno">  167</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  168</span> </div>
+<div class="line"><span class="lineno">  169</span>    elapsed_time = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) / CLOCKS_PER_SEC;</div>
+<div class="line"><span class="lineno">  170</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time spent sorting using std::qsort: &quot;</span> &lt;&lt; elapsed_time</div>
+<div class="line"><span class="lineno">  171</span>              &lt;&lt; <span class="stringliteral">&quot;s\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  172</span> </div>
+<div class="line"><span class="lineno">  173</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; NUM_DATA; i++) {</div>
+<div class="line"><span class="lineno">  174</span>        assert(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] == data2[i]);  <span class="comment">// ensure that our sorting results match</span></div>
+<div class="line"><span class="lineno">  175</span>                                      <span class="comment">// the standard results</span></div>
+<div class="line"><span class="lineno">  176</span>    }</div>
+<div class="line"><span class="lineno">  177</span> </div>
+<div class="line"><span class="lineno">  178</span>    <span class="keyword">delete</span>[] <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
+<div class="line"><span class="lineno">  179</span>    <span class="keyword">delete</span>[] data2;</div>
+<div class="line"><span class="lineno">  180</span>}</div>
 <div class="ttc" id="aqsort_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/qsort.html">std::qsort</a></div><div class="ttdeci">T qsort(T... args)</div></div>
 <div class="ttc" id="astructcompare_html"><div class="ttname"><a href="../../d1/db3/structcompare.html">compare</a></div><div class="ttdef"><b>Definition:</b> huffman.cpp:28</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -460,41 +460,41 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Test implementation of shell_sort on integer arrays by comparing results against <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/qsort.html">std::qsort</a>. </p>
-<div class="fragment"><div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>                                  {</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    <span class="comment">// int array = new int[NUM_DATA];</span></div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    <span class="keywordtype">int</span> *<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a> = <span class="keyword">new</span> <span class="keywordtype">int</span>[NUM_DATA];</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    <span class="keywordtype">int</span> *data2 = <span class="keyword">new</span> <span class="keywordtype">int</span>[NUM_DATA];</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <span class="comment">// int array2 = new int[NUM_DATA];</span></div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    <span class="keywordtype">int</span> range = 1800;</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span> </div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; NUM_DATA; i++)</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] = data2[i] = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - (range &gt;&gt; 1);</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span> </div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    <span class="comment">/* sort using our implementation */</span></div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">shell_sort</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    <span class="keywordtype">double</span> elapsed_time = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) / CLOCKS_PER_SEC;</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time spent sorting using shell_sort2: &quot;</span> &lt;&lt; elapsed_time</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>              &lt;&lt; <span class="stringliteral">&quot;s\n&quot;</span>;</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span> </div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <span class="comment">/* sort using std::qsort */</span></div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    start = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/qsort.html">std::qsort</a>(data2, NUM_DATA, <span class="keyword">sizeof</span>(data2[0]), <a class="code hl_struct" href="../../d1/db3/structcompare.html">compare&lt;int&gt;</a>);</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span> </div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    elapsed_time = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) / CLOCKS_PER_SEC;</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time spent sorting using std::qsort: &quot;</span> &lt;&lt; elapsed_time</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>              &lt;&lt; <span class="stringliteral">&quot;s\n&quot;</span>;</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span> </div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; NUM_DATA; i++) {</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>        assert(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] == data2[i]);  <span class="comment">// ensure that our sorting results match</span></div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>                                      <span class="comment">// the standard results</span></div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    }</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span> </div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    <span class="keyword">delete</span>[] <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    <span class="keyword">delete</span>[] data2;</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  105</span>                                  {</div>
+<div class="line"><span class="lineno">  106</span>    <span class="comment">// int array = new int[NUM_DATA];</span></div>
+<div class="line"><span class="lineno">  107</span>    <span class="keywordtype">int</span> *<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a> = <span class="keyword">new</span> <span class="keywordtype">int</span>[NUM_DATA];</div>
+<div class="line"><span class="lineno">  108</span>    <span class="keywordtype">int</span> *data2 = <span class="keyword">new</span> <span class="keywordtype">int</span>[NUM_DATA];</div>
+<div class="line"><span class="lineno">  109</span>    <span class="comment">// int array2 = new int[NUM_DATA];</span></div>
+<div class="line"><span class="lineno">  110</span>    <span class="keywordtype">int</span> range = 1800;</div>
+<div class="line"><span class="lineno">  111</span> </div>
+<div class="line"><span class="lineno">  112</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; NUM_DATA; i++)</div>
+<div class="line"><span class="lineno">  113</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] = data2[i] = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - (range &gt;&gt; 1);</div>
+<div class="line"><span class="lineno">  114</span> </div>
+<div class="line"><span class="lineno">  115</span>    <span class="comment">/* sort using our implementation */</span></div>
+<div class="line"><span class="lineno">  116</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  117</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">shell_sort</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);</div>
+<div class="line"><span class="lineno">  118</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  119</span>    <span class="keywordtype">double</span> elapsed_time = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) / CLOCKS_PER_SEC;</div>
+<div class="line"><span class="lineno">  120</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time spent sorting using shell_sort2: &quot;</span> &lt;&lt; elapsed_time</div>
+<div class="line"><span class="lineno">  121</span>              &lt;&lt; <span class="stringliteral">&quot;s\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  122</span> </div>
+<div class="line"><span class="lineno">  123</span>    <span class="comment">/* sort using std::qsort */</span></div>
+<div class="line"><span class="lineno">  124</span>    start = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  125</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/qsort.html">std::qsort</a>(data2, NUM_DATA, <span class="keyword">sizeof</span>(data2[0]), <a class="code hl_struct" href="../../d1/db3/structcompare.html">compare&lt;int&gt;</a>);</div>
+<div class="line"><span class="lineno">  126</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  127</span> </div>
+<div class="line"><span class="lineno">  128</span>    elapsed_time = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) / CLOCKS_PER_SEC;</div>
+<div class="line"><span class="lineno">  129</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time spent sorting using std::qsort: &quot;</span> &lt;&lt; elapsed_time</div>
+<div class="line"><span class="lineno">  130</span>              &lt;&lt; <span class="stringliteral">&quot;s\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  131</span> </div>
+<div class="line"><span class="lineno">  132</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; NUM_DATA; i++) {</div>
+<div class="line"><span class="lineno">  133</span>        assert(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] == data2[i]);  <span class="comment">// ensure that our sorting results match</span></div>
+<div class="line"><span class="lineno">  134</span>                                      <span class="comment">// the standard results</span></div>
+<div class="line"><span class="lineno">  135</span>    }</div>
+<div class="line"><span class="lineno">  136</span> </div>
+<div class="line"><span class="lineno">  137</span>    <span class="keyword">delete</span>[] <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
+<div class="line"><span class="lineno">  138</span>    <span class="keyword">delete</span>[] data2;</div>
+<div class="line"><span class="lineno">  139</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -510,7 +510,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_bb1b521853a9c46347182a9d10420771.html">sorting</a></li><li class="navelem"><a class="el" href="../../d4/d7a/shell__sort2_8cpp.html">shell_sort2.cpp</a></li>
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 <p >Function for testing the <a class="el" href="../../d4/d83/sum__of__digits_8cpp.html#a4619c78b6ad985713024f930f31c4395">sum_of_digits()</a> function with a first test case of 119765 and assert statement. </p>
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-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   40</span>             {</div>
+<div class="line"><span class="lineno">   41</span>    <span class="keywordtype">int</span> test_case_1 = <a class="code hl_function" href="../../d4/d83/sum__of__digits_8cpp.html#a4619c78b6ad985713024f930f31c4395">sum_of_digits</a>(119765);</div>
+<div class="line"><span class="lineno">   42</span>    assert(test_case_1 == 29);</div>
+<div class="line"><span class="lineno">   43</span>}</div>
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 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -278,10 +278,10 @@ Here is the call graph for this function:</div>
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 <p >Function for testing the <a class="el" href="../../d4/d83/sum__of__digits_8cpp.html#a4619c78b6ad985713024f930f31c4395">sum_of_digits()</a> function with a second test case of -12256 and assert statement. </p>
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-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   49</span>             {</div>
+<div class="line"><span class="lineno">   50</span>    <span class="keywordtype">int</span> test_case_2 = <a class="code hl_function" href="../../d4/d83/sum__of__digits_8cpp.html#a4619c78b6ad985713024f930f31c4395">sum_of_digits</a>(-12256);</div>
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@@ -97,6 +97,12 @@ $(document).ready(function(){initNavTree('d4/d90/classdata__structures_1_1_skip_
   <div class="headertitle"><div class="title">data_structures::SkipList Class Reference</div></div>
 </div><!--header-->
 <div class="contents">
+<div class="dynheader">
+Collaboration diagram for data_structures::SkipList:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d7/d0b/classdata__structures_1_1_skip_list__coll__graph.svg" width="422" height="260"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+<center><span class="legend">[<a target="top" href="../../graph_legend.html">legend</a>]</span></center></div>
 <table class="memberdecls">
 <tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
 Public Member Functions</h2></td></tr>
@@ -150,11 +156,11 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>level</b></td></tr>
 </table>
 </div><div class="memdoc">
 <p >Skip List constructor. Initializes header, start <a class="el" href="../../d9/d49/structdata__structures_1_1_node.html">Node</a> for searching in the list </p>
-<div class="fragment"><div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>               {</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a> = 0;</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="comment">// Header initialization</span></div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#ad7e392386d7db622185d6f7c718e4f16">header</a> = std::make_shared&lt;Node&gt;(-1, <a class="code hl_variable" href="../../d5/d3c/namespacedata__structures.html#ac0d7e0be24da9f41bcb19745873c436a">MAX_LEVEL</a>);</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   64</span>               {</div>
+<div class="line"><span class="lineno">   65</span>        <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a> = 0;</div>
+<div class="line"><span class="lineno">   66</span>        <span class="comment">// Header initialization</span></div>
+<div class="line"><span class="lineno">   67</span>        <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#ad7e392386d7db622185d6f7c718e4f16">header</a> = std::make_shared&lt;Node&gt;(-1, <a class="code hl_variable" href="../../d5/d3c/namespacedata__structures.html#ac0d7e0be24da9f41bcb19745873c436a">MAX_LEVEL</a>);</div>
+<div class="line"><span class="lineno">   68</span>    }</div>
 <div class="ttc" id="aclassdata__structures_1_1_skip_list_html_a3e249c2c35a8b7f5ffd2d77fee60d650"><div class="ttname"><a href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">data_structures::SkipList::level</a></div><div class="ttdeci">int level</div><div class="ttdoc">Maximum level of the skiplist.</div><div class="ttdef"><b>Definition:</b> skip_list.cpp:56</div></div>
 <div class="ttc" id="aclassdata__structures_1_1_skip_list_html_ad7e392386d7db622185d6f7c718e4f16"><div class="ttname"><a href="../../d4/d90/classdata__structures_1_1_skip_list.html#ad7e392386d7db622185d6f7c718e4f16">data_structures::SkipList::header</a></div><div class="ttdeci">std::shared_ptr&lt; Node &gt; header</div><div class="ttdoc">Pointer to the header node.</div><div class="ttdef"><b>Definition:</b> skip_list.cpp:57</div></div>
 <div class="ttc" id="anamespacedata__structures_html_ac0d7e0be24da9f41bcb19745873c436a"><div class="ttname"><a href="../../d5/d3c/namespacedata__structures.html#ac0d7e0be24da9f41bcb19745873c436a">data_structures::MAX_LEVEL</a></div><div class="ttdeci">constexpr int MAX_LEVEL</div><div class="ttdoc">Maximum level of skip list.</div><div class="ttdef"><b>Definition:</b> skip_list.cpp:27</div></div>
@@ -191,42 +197,42 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>level</b></td></tr>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>                                {</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Node&gt;</a> x = <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#ad7e392386d7db622185d6f7c718e4f16">header</a>;</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span> </div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::shared_ptr&lt;Node&gt;</a>, <a class="code hl_variable" href="../../d5/d3c/namespacedata__structures.html#ac0d7e0be24da9f41bcb19745873c436a">MAX_LEVEL</a> + 1&gt; <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>;</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>.fill(<span class="keyword">nullptr</span>);</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span> </div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a>; i &gt;= 0; i--) {</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>            <span class="keywordflow">while</span> (x-&gt;forward[i] != <span class="keyword">nullptr</span> &amp;&amp; x-&gt;forward[i]-&gt;key &lt; key) {</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>                x = x-&gt;forward[i];</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>            }</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>            <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>[i] = x;</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>        }</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span> </div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>        x = x-&gt;forward[0];</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span> </div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>        <span class="keywordtype">bool</span> doesnt_exist = (x == <span class="keyword">nullptr</span> || x-&gt;key != key);</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span> </div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>        <span class="keywordflow">if</span> (!doesnt_exist) {</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a>; i++) {</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>                <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>[i]-&gt;forward[i] != x) {</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>                    <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>                }</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>                <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>[i]-&gt;forward[i] = x-&gt;forward[i];</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>            }</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>            <span class="comment">/* Remove empty levels*/</span></div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>            <span class="keywordflow">while</span> (<a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a> &gt; 0 &amp;&amp; <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#ad7e392386d7db622185d6f7c718e4f16">header</a>-&gt;forward[<a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a>] == <span class="keyword">nullptr</span>) <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a>--;</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Deleted&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Doesn&#39;t exist&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>        }</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  133</span>                                {</div>
+<div class="line"><span class="lineno">  134</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Node&gt;</a> x = <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#ad7e392386d7db622185d6f7c718e4f16">header</a>;</div>
+<div class="line"><span class="lineno">  135</span> </div>
+<div class="line"><span class="lineno">  136</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::shared_ptr&lt;Node&gt;</a>, <a class="code hl_variable" href="../../d5/d3c/namespacedata__structures.html#ac0d7e0be24da9f41bcb19745873c436a">MAX_LEVEL</a> + 1&gt; <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>;</div>
+<div class="line"><span class="lineno">  137</span>        <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>.fill(<span class="keyword">nullptr</span>);</div>
+<div class="line"><span class="lineno">  138</span> </div>
+<div class="line"><span class="lineno">  139</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a>; i &gt;= 0; i--) {</div>
+<div class="line"><span class="lineno">  140</span>            <span class="keywordflow">while</span> (x-&gt;forward[i] != <span class="keyword">nullptr</span> &amp;&amp; x-&gt;forward[i]-&gt;key &lt; key) {</div>
+<div class="line"><span class="lineno">  141</span>                x = x-&gt;forward[i];</div>
+<div class="line"><span class="lineno">  142</span>            }</div>
+<div class="line"><span class="lineno">  143</span>            <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>[i] = x;</div>
+<div class="line"><span class="lineno">  144</span>        }</div>
+<div class="line"><span class="lineno">  145</span> </div>
+<div class="line"><span class="lineno">  146</span>        x = x-&gt;forward[0];</div>
+<div class="line"><span class="lineno">  147</span> </div>
+<div class="line"><span class="lineno">  148</span>        <span class="keywordtype">bool</span> doesnt_exist = (x == <span class="keyword">nullptr</span> || x-&gt;key != key);</div>
+<div class="line"><span class="lineno">  149</span> </div>
+<div class="line"><span class="lineno">  150</span>        <span class="keywordflow">if</span> (!doesnt_exist) {</div>
+<div class="line"><span class="lineno">  151</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a>; i++) {</div>
+<div class="line"><span class="lineno">  152</span>                <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>[i]-&gt;forward[i] != x) {</div>
+<div class="line"><span class="lineno">  153</span>                    <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  154</span>                }</div>
+<div class="line"><span class="lineno">  155</span>                <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>[i]-&gt;forward[i] = x-&gt;forward[i];</div>
+<div class="line"><span class="lineno">  156</span>            }</div>
+<div class="line"><span class="lineno">  157</span>            <span class="comment">/* Remove empty levels*/</span></div>
+<div class="line"><span class="lineno">  158</span>            <span class="keywordflow">while</span> (<a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a> &gt; 0 &amp;&amp; <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#ad7e392386d7db622185d6f7c718e4f16">header</a>-&gt;forward[<a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a>] == <span class="keyword">nullptr</span>) <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a>--;</div>
+<div class="line"><span class="lineno">  159</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Deleted&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  160</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  161</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Doesn&#39;t exist&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  162</span>        }</div>
+<div class="line"><span class="lineno">  163</span>    }</div>
 <div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
 <div class="ttc" id="asegtree_8cpp_html_abd3e818681fb2e29cf08f4f60f82c8e0"><div class="ttname"><a href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a></div><div class="ttdeci">void update(std::vector&lt; int64_t &gt; *segtree, std::vector&lt; int64_t &gt; *lazy, int64_t start, int64_t end, int64_t delta, uint64_t low, uint64_t high, uint64_t pos)</div><div class="ttdoc">Updates a range of the segment tree.</div><div class="ttdef"><b>Definition:</b> segtree.cpp:102</div></div>
-<div class="ttc" id="ashared_ptr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr</a></div></div>
+<div class="ttc" id="ashared_ptr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt; Node &gt;</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -259,18 +265,18 @@ Here is the call graph for this function:</div>
 </table>
 </div><div class="memdoc">
 <p >Display skip list level </p>
-<div class="fragment"><div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>                       {</div>
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-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a>; i++) {</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Node&gt;</a> <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#ad7e392386d7db622185d6f7c718e4f16">header</a>-&gt;forward[i];</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Level &quot;</span> &lt;&lt; (i) &lt;&lt; <span class="stringliteral">&quot;: &quot;</span>;</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>            <span class="keywordflow">while</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a> != <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;key &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>                <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;forward[i];</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>            }</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>        }</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  191</span>                       {</div>
+<div class="line"><span class="lineno">  192</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Displaying list:\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  193</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a>; i++) {</div>
+<div class="line"><span class="lineno">  194</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Node&gt;</a> <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#ad7e392386d7db622185d6f7c718e4f16">header</a>-&gt;forward[i];</div>
+<div class="line"><span class="lineno">  195</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Level &quot;</span> &lt;&lt; (i) &lt;&lt; <span class="stringliteral">&quot;: &quot;</span>;</div>
+<div class="line"><span class="lineno">  196</span>            <span class="keywordflow">while</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a> != <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  197</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;key &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">  198</span>                <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;forward[i];</div>
+<div class="line"><span class="lineno">  199</span>            }</div>
+<div class="line"><span class="lineno">  200</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  201</span>        }</div>
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 <div class="ttc" id="astructnode_html"><div class="ttname"><a href="../../d5/da1/structnode.html">node</a></div><div class="ttdef"><b>Definition:</b> avltree.cpp:13</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -321,44 +327,44 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>                                             {</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Inserting&quot;</span> &lt;&lt; key &lt;&lt; <span class="stringliteral">&quot;...&quot;</span>;</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Node&gt;</a> x = <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#ad7e392386d7db622185d6f7c718e4f16">header</a>;</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::shared_ptr&lt;Node&gt;</a>, <a class="code hl_variable" href="../../d5/d3c/namespacedata__structures.html#ac0d7e0be24da9f41bcb19745873c436a">MAX_LEVEL</a> + 1&gt; <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>;</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>        <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>.fill(<span class="keyword">nullptr</span>);</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span> </div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a>; i &gt;= 0; i--) {</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>            <span class="keywordflow">while</span> (x-&gt;forward[i] != <span class="keyword">nullptr</span> &amp;&amp; x-&gt;forward[i]-&gt;key &lt; key) {</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>                x = x-&gt;forward[i];</div>
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-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span> </div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        x = x-&gt;forward[0];</div>
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-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>        <span class="keywordflow">if</span> (doesnt_exist) {</div>
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-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span> </div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>            <span class="keywordflow">if</span> (rlevel &gt; <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a>) {</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>                <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a> + 1; i &lt; rlevel + 1; i++) <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>[i] = <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#ad7e392386d7db622185d6f7c718e4f16">header</a>;</div>
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-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Inserted&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><span class="lineno">   92</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Node&gt;</a> x = <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#ad7e392386d7db622185d6f7c718e4f16">header</a>;</div>
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+<div class="line"><span class="lineno">   94</span>        <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>.fill(<span class="keyword">nullptr</span>);</div>
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+<div class="line"><span class="lineno">   96</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a>; i &gt;= 0; i--) {</div>
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+<div class="line"><span class="lineno">  108</span> </div>
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+<div class="line"><span class="lineno">  110</span>                <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#a3e249c2c35a8b7f5ffd2d77fee60d650">level</a> + 1; i &lt; rlevel + 1; i++) <a class="code hl_function" href="../../d2/d45/segtree_8cpp.html#abd3e818681fb2e29cf08f4f60f82c8e0">update</a>[i] = <a class="code hl_variable" href="../../d4/d90/classdata__structures_1_1_skip_list.html#ad7e392386d7db622185d6f7c718e4f16">header</a>;</div>
+<div class="line"><span class="lineno">  111</span> </div>
+<div class="line"><span class="lineno">  112</span>                <span class="comment">// Update current level</span></div>
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 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -392,14 +398,14 @@ Here is the call graph for this function:</div>
 </table>
 </div><div class="memdoc">
 <p >Returns random level of the skip list. Every higher level is 2 times less likely. </p><dl class="section return"><dt>Returns</dt><dd>random level for skip list </dd></dl>
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+<div class="line"><span class="lineno">   95</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a> &gt;  table = <a class="code hl_function" href="../../d4/d96/range__queries_2sparse__table_8cpp.html#a803a2451e87021d14ae06f148383e6bc">range_queries::sparse_table::buildTable</a>(A, logs);</div>
+<div class="line"><span class="lineno">   96</span>    assert(range_queries::sparse_table::getMinimum(0, 0, logs, table) == 1);</div>
+<div class="line"><span class="lineno">   97</span>    assert(range_queries::sparse_table::getMinimum(0, 4, logs, table) == 0);</div>
+<div class="line"><span class="lineno">   98</span>    assert(range_queries::sparse_table::getMinimum(2, 4, logs, table) == 0);</div>
+<div class="line"><span class="lineno">   99</span>    <span class="keywordflow">return</span> 0;</div>
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 <div class="ttc" id="arange__queries_2sparse__table_8cpp_html_a803a2451e87021d14ae06f148383e6bc"><div class="ttname"><a href="../../d4/d96/range__queries_2sparse__table_8cpp.html#a803a2451e87021d14ae06f148383e6bc">range_queries::sparse_table::buildTable</a></div><div class="ttdeci">std::vector&lt; std::vector&lt; T &gt; &gt; buildTable(const std::vector&lt; T &gt; &amp;A, const std::vector&lt; T &gt; &amp;logs)</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:54</div></div>
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-<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>    <a class="code hl_function" href="../../d4/d9c/primes__up__to__billion_8cpp.html#a031cada84819ed6426f58e4f7e81261c">Sieve</a>(100000000);</div>
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-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d4/d9c/primes__up__to__billion_8cpp.html#ac0f4b77b901ddb15dab4c4dee1ac6e95">prime</a>[n] == <span class="charliteral">&#39;1&#39;</span>)</div>
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+<div class="line"><span class="lineno">   58</span>        <span class="keywordflow">return</span> current_position;</div>
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 <p>Main function. </p>
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+<div class="line"><span class="lineno">  185</span>    <span class="comment">// Load factor greater than 0.5 causes resizing</span></div>
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+<div class="line"><span class="lineno">  187</span>        <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#ada6f1f44f7e83b0094fbcbe170788486">rehash</a>();</div>
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+<div class="line"><span class="lineno">  132</span>    <span class="keywordtype">int</span> index = <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#ab431981b54c0bae1b2956f716aee1dcf">quadraticProbe</a>(key, <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  133</span>    <span class="keywordflow">if</span> (index == notPresent) {</div>
+<div class="line"><span class="lineno">  134</span>        <span class="keywordflow">return</span> <a class="code hl_struct" href="../../da/dd1/structquadratic__probing_1_1_entry.html">Entry</a>();</div>
+<div class="line"><span class="lineno">  135</span>    }</div>
+<div class="line"><span class="lineno">  136</span>    <span class="keywordflow">return</span> table[index];</div>
+<div class="line"><span class="lineno">  137</span>}</div>
 <div class="ttc" id="astructquadratic__probing_1_1_entry_html"><div class="ttname"><a href="../../da/dd1/structquadratic__probing_1_1_entry.html">quadratic_probing::Entry</a></div><div class="ttdef"><b>Definition:</b> quadratic_probing_hash_table.cpp:37</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -349,10 +349,10 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>hash of the key </dd></dl>
-<div class="fragment"><div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>                        {</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/hash.html">std::hash&lt;int&gt;</a> hash;</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <span class="keywordflow">return</span> hash(key);</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   46</span>                        {</div>
+<div class="line"><span class="lineno">   47</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/hash.html">std::hash&lt;int&gt;</a> hash;</div>
+<div class="line"><span class="lineno">   48</span>    <span class="keywordflow">return</span> hash(key);</div>
+<div class="line"><span class="lineno">   49</span>}</div>
 <div class="ttc" id="ahash_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/hash.html">std::hash</a></div></div>
 </div><!-- fragment -->
 </div>
@@ -392,12 +392,12 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if key is present </dd>
 <dd>
 <code>false</code> if key is absent </dd></dl>
-<div class="fragment"><div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>                                            {</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    <span class="keywordflow">if</span> (entry.<a class="code hl_variable" href="../../da/dd1/structquadratic__probing_1_1_entry.html#a75f72858f08a2fc8b94402de98db12d8">key</a> == notPresent || entry.<a class="code hl_variable" href="../../da/dd1/structquadratic__probing_1_1_entry.html#a75f72858f08a2fc8b94402de98db12d8">key</a> == tomb) {</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    }</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  106</span>                                            {</div>
+<div class="line"><span class="lineno">  107</span>    <span class="keywordflow">if</span> (entry.<a class="code hl_variable" href="../../da/dd1/structquadratic__probing_1_1_entry.html#a75f72858f08a2fc8b94402de98db12d8">key</a> == notPresent || entry.<a class="code hl_variable" href="../../da/dd1/structquadratic__probing_1_1_entry.html#a75f72858f08a2fc8b94402de98db12d8">key</a> == tomb) {</div>
+<div class="line"><span class="lineno">  108</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  109</span>    }</div>
+<div class="line"><span class="lineno">  110</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  111</span>}</div>
 <div class="ttc" id="astructquadratic__probing_1_1_entry_html_a75f72858f08a2fc8b94402de98db12d8"><div class="ttname"><a href="../../da/dd1/structquadratic__probing_1_1_entry.html#a75f72858f08a2fc8b94402de98db12d8">quadratic_probing::Entry::key</a></div><div class="ttdeci">int key</div><div class="ttdoc">key value</div><div class="ttdef"><b>Definition:</b> quadratic_probing_hash_table.cpp:39</div></div>
 </div><!-- fragment -->
 </div>
@@ -434,49 +434,49 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>                                            {</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    <span class="keywordtype">int</span> hash = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(<a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a2093d91dd3d377cf0a5c939e45dcefc7">hashFxn</a>(key));</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <span class="keywordtype">int</span> i = 0;</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <a class="code hl_struct" href="../../da/dd1/structquadratic__probing_1_1_entry.html">Entry</a> entry;</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <span class="keywordflow">do</span> {</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        <span class="keywordtype">size_t</span> index =</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>            (hash + <span class="keyword">static_cast&lt;</span><span class="keywordtype">size_t</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(i, 2)))) %</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>            totalSize;</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        entry = table[index];</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        <span class="keywordflow">if</span> (searching) {</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>            <span class="keywordflow">if</span> (entry.<a class="code hl_variable" href="../../da/dd1/structquadratic__probing_1_1_entry.html#a75f72858f08a2fc8b94402de98db12d8">key</a> == notPresent) {</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>                <span class="keywordflow">return</span> notPresent;</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>            }</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>            <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#aeb6bca8db4768226f8ea8291ea4f83f6">searchingProber</a>(entry, key)) {</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Found key!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>                <span class="keywordflow">return</span> index;</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>            }</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Found tombstone or equal hash, checking next&quot;</span></div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>                      &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>            i++;</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>            <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#adccc63a7e57cc6dba75bd62f40feb88b">putProber</a>(entry, key)) {</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>                <span class="keywordflow">if</span> (!rehashing) {</div>
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-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>                }</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>                <span class="keywordflow">return</span> index;</div>
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-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>            <span class="keywordflow">if</span> (!rehashing) {</div>
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-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>                          &lt;&lt; (<a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hash</a> + <span class="keyword">static_cast&lt;</span><span class="keywordtype">size_t</span><span class="keyword">&gt;</span>(</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>                                         <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(i + 1, 2)))) %</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>                                 totalSize</div>
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-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>            }</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>            i++;</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>        }</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>        <span class="keywordflow">if</span> (i == totalSize * 100) {</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Quadratic probe failed (infinite loop)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>            <span class="keywordflow">return</span> notPresent;</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>        }</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    } <span class="keywordflow">while</span> (entry.<a class="code hl_variable" href="../../da/dd1/structquadratic__probing_1_1_entry.html#a75f72858f08a2fc8b94402de98db12d8">key</a> != notPresent);</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    <span class="keywordflow">return</span> notPresent;</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   56</span>                                            {</div>
+<div class="line"><span class="lineno">   57</span>    <span class="keywordtype">int</span> hash = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(<a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a2093d91dd3d377cf0a5c939e45dcefc7">hashFxn</a>(key));</div>
+<div class="line"><span class="lineno">   58</span>    <span class="keywordtype">int</span> i = 0;</div>
+<div class="line"><span class="lineno">   59</span>    <a class="code hl_struct" href="../../da/dd1/structquadratic__probing_1_1_entry.html">Entry</a> entry;</div>
+<div class="line"><span class="lineno">   60</span>    <span class="keywordflow">do</span> {</div>
+<div class="line"><span class="lineno">   61</span>        <span class="keywordtype">size_t</span> index =</div>
+<div class="line"><span class="lineno">   62</span>            (hash + <span class="keyword">static_cast&lt;</span><span class="keywordtype">size_t</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(i, 2)))) %</div>
+<div class="line"><span class="lineno">   63</span>            totalSize;</div>
+<div class="line"><span class="lineno">   64</span>        entry = table[index];</div>
+<div class="line"><span class="lineno">   65</span>        <span class="keywordflow">if</span> (searching) {</div>
+<div class="line"><span class="lineno">   66</span>            <span class="keywordflow">if</span> (entry.<a class="code hl_variable" href="../../da/dd1/structquadratic__probing_1_1_entry.html#a75f72858f08a2fc8b94402de98db12d8">key</a> == notPresent) {</div>
+<div class="line"><span class="lineno">   67</span>                <span class="keywordflow">return</span> notPresent;</div>
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+<div class="line"><span class="lineno">   69</span>            <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#aeb6bca8db4768226f8ea8291ea4f83f6">searchingProber</a>(entry, key)) {</div>
+<div class="line"><span class="lineno">   70</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Found key!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   71</span>                <span class="keywordflow">return</span> index;</div>
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+<div class="line"><span class="lineno">   74</span>                      &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   75</span>            i++;</div>
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+<div class="line"><span class="lineno">   80</span>                }</div>
+<div class="line"><span class="lineno">   81</span>                <span class="keywordflow">return</span> index;</div>
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+<div class="line"><span class="lineno">   84</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Spot taken, looking at next (next index = &quot;</span></div>
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+<div class="line"><span class="lineno">   86</span>                                         <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(i + 1, 2)))) %</div>
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+<div class="line"><span class="lineno">   93</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Quadratic probe failed (infinite loop)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><span class="lineno">   98</span>}</div>
 <div class="ttc" id="amd5_8cpp_html_a88705fab5f92adf3427b4cf76ff33edb"><div class="ttname"><a href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hashing::md5::hash</a></div><div class="ttdeci">void * hash(const std::string &amp;message)</div><div class="ttdoc">Converts the string to bytestring and calls the main algorithm.</div><div class="ttdef"><b>Definition:</b> md5.cpp:287</div></div>
 <div class="ttc" id="anamespacequadratic__probing_html_adccc63a7e57cc6dba75bd62f40feb88b"><div class="ttname"><a href="../../d4/dd2/namespacequadratic__probing.html#adccc63a7e57cc6dba75bd62f40feb88b">quadratic_probing::putProber</a></div><div class="ttdeci">bool putProber(const Entry &amp;entry, int key)</div><div class="ttdef"><b>Definition:</b> quadratic_probing_hash_table.cpp:106</div></div>
 <div class="ttc" id="anamespacequadratic__probing_html_aeb6bca8db4768226f8ea8291ea4f83f6"><div class="ttname"><a href="../../d4/dd2/namespacequadratic__probing.html#aeb6bca8db4768226f8ea8291ea4f83f6">quadratic_probing::searchingProber</a></div><div class="ttdeci">bool searchingProber(const Entry &amp;entry, int key)</div><div class="ttdef"><b>Definition:</b> quadratic_probing_hash_table.cpp:119</div></div>
@@ -506,24 +506,24 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Rehashes the table into a bigger table </p><dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
-<div class="fragment"><div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>              {</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>    <span class="comment">// Necessary so wall of add info isn&#39;t printed all at once</span></div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>    rehashing = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>    <span class="keywordtype">int</span> oldSize = totalSize;</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Entry&gt;</a> oldTable(table);</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>    <span class="comment">// Really this should use the next prime number greater than totalSize * 2</span></div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    totalSize *= 2;</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>    table = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Entry&gt;</a>(totalSize);</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; oldSize; i++) {</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>        <span class="keywordflow">if</span> (oldTable[i].key != -1 &amp;&amp; oldTable[i].key != notPresent) {</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>            size--;  <span class="comment">// Size stays the same (add increments size)</span></div>
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-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>    <span class="comment">// delete[] oldTable;</span></div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>    rehashing = <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Table was rehashed, new size is: &quot;</span> &lt;&lt; totalSize &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  160</span>              {</div>
+<div class="line"><span class="lineno">  161</span>    <span class="comment">// Necessary so wall of add info isn&#39;t printed all at once</span></div>
+<div class="line"><span class="lineno">  162</span>    rehashing = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  163</span>    <span class="keywordtype">int</span> oldSize = totalSize;</div>
+<div class="line"><span class="lineno">  164</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Entry&gt;</a> oldTable(table);</div>
+<div class="line"><span class="lineno">  165</span>    <span class="comment">// Really this should use the next prime number greater than totalSize * 2</span></div>
+<div class="line"><span class="lineno">  166</span>    totalSize *= 2;</div>
+<div class="line"><span class="lineno">  167</span>    table = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Entry&gt;</a>(totalSize);</div>
+<div class="line"><span class="lineno">  168</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; oldSize; i++) {</div>
+<div class="line"><span class="lineno">  169</span>        <span class="keywordflow">if</span> (oldTable[i].key != -1 &amp;&amp; oldTable[i].key != notPresent) {</div>
+<div class="line"><span class="lineno">  170</span>            size--;  <span class="comment">// Size stays the same (add increments size)</span></div>
+<div class="line"><span class="lineno">  171</span>            <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a00ebcc6d39653eccc26f8432efbfc8d9">add</a>(oldTable[i].key);</div>
+<div class="line"><span class="lineno">  172</span>        }</div>
+<div class="line"><span class="lineno">  173</span>    }</div>
+<div class="line"><span class="lineno">  174</span>    <span class="comment">// delete[] oldTable;</span></div>
+<div class="line"><span class="lineno">  175</span>    rehashing = <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  176</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Table was rehashed, new size is: &quot;</span> &lt;&lt; totalSize &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  177</span>}</div>
 <div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
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 Here is the call graph for this function:</div>
@@ -555,17 +555,17 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>                          {</div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initial table: &quot;</span>;</div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a40d617ebf4d6ba21bcda8d8d1faa2357">display</a>();</div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;hash of &quot;</span> &lt;&lt; key &lt;&lt; <span class="stringliteral">&quot; is &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a2093d91dd3d377cf0a5c939e45dcefc7">hashFxn</a>(key) &lt;&lt; <span class="stringliteral">&quot; % &quot;</span></div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>              &lt;&lt; totalSize &lt;&lt; <span class="stringliteral">&quot; == &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a2093d91dd3d377cf0a5c939e45dcefc7">hashFxn</a>(key) % totalSize;</div>
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-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;New table: &quot;</span>;</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>    <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a40d617ebf4d6ba21bcda8d8d1faa2357">display</a>();</div>
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+<div class="fragment"><div class="line"><span class="lineno">  222</span>                          {</div>
+<div class="line"><span class="lineno">  223</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initial table: &quot;</span>;</div>
+<div class="line"><span class="lineno">  224</span>    <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a40d617ebf4d6ba21bcda8d8d1faa2357">display</a>();</div>
+<div class="line"><span class="lineno">  225</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  226</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;hash of &quot;</span> &lt;&lt; key &lt;&lt; <span class="stringliteral">&quot; is &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a2093d91dd3d377cf0a5c939e45dcefc7">hashFxn</a>(key) &lt;&lt; <span class="stringliteral">&quot; % &quot;</span></div>
+<div class="line"><span class="lineno">  227</span>              &lt;&lt; totalSize &lt;&lt; <span class="stringliteral">&quot; == &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a2093d91dd3d377cf0a5c939e45dcefc7">hashFxn</a>(key) % totalSize;</div>
+<div class="line"><span class="lineno">  228</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  229</span>    <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a07a0467b24102260fbb6b554c453c20a">remove</a>(key);</div>
+<div class="line"><span class="lineno">  230</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;New table: &quot;</span>;</div>
+<div class="line"><span class="lineno">  231</span>    <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a40d617ebf4d6ba21bcda8d8d1faa2357">display</a>();</div>
+<div class="line"><span class="lineno">  232</span>}</div>
 <div class="ttc" id="anamespacequadratic__probing_html_a07a0467b24102260fbb6b554c453c20a"><div class="ttname"><a href="../../d4/dd2/namespacequadratic__probing.html#a07a0467b24102260fbb6b554c453c20a">quadratic_probing::remove</a></div><div class="ttdeci">void remove(int key)</div><div class="ttdef"><b>Definition:</b> quadratic_probing_hash_table.cpp:194</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -597,15 +597,15 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>                     {</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>    <span class="keywordtype">int</span> index = <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#ab431981b54c0bae1b2956f716aee1dcf">quadraticProbe</a>(key, <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>    <span class="keywordflow">if</span> (index == notPresent) {</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;key not found&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>    table[index].key = tomb;</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Removal successful, leaving tombstone&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>    size--;</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  194</span>                     {</div>
+<div class="line"><span class="lineno">  195</span>    <span class="keywordtype">int</span> index = <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#ab431981b54c0bae1b2956f716aee1dcf">quadraticProbe</a>(key, <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  196</span>    <span class="keywordflow">if</span> (index == notPresent) {</div>
+<div class="line"><span class="lineno">  197</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;key not found&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  198</span>    }</div>
+<div class="line"><span class="lineno">  199</span>    table[index].key = tomb;</div>
+<div class="line"><span class="lineno">  200</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Removal successful, leaving tombstone&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  201</span>    size--;</div>
+<div class="line"><span class="lineno">  202</span>}</div>
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 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -650,12 +650,12 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if key matches the entry </dd>
 <dd>
 <code>false</code> if key does not match the entry </dd></dl>
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-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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+<div class="fragment"><div class="line"><span class="lineno">  119</span>                                                  {</div>
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+<div class="line"><span class="lineno">  121</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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+<div class="line"><span class="lineno">  123</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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 <p >Creates convex hull of a set of n points. There must be 3 points at least for the convex hull to exist</p>
 <dl class="section return"><dt>Returns</dt><dd>an vector array containing points in space which enclose all given points thus forming a hull </dd></dl>
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-<div class="line"><a id="l00592" name="l00592"></a><span class="lineno">  592</span>    <a class="code hl_function" href="../../d4/def/kohonen__som__topology_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
-<div class="line"><a id="l00593" name="l00593"></a><span class="lineno">  593</span>    <span class="keyword">auto</span> end_clk = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00594" name="l00594"></a><span class="lineno">  594</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 completed in &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d4/def/kohonen__som__topology_8cpp.html#a2256c10b16edba377b64a44b6c656908">get_clock_diff</a>(start_clk, end_clk)</div>
-<div class="line"><a id="l00595" name="l00595"></a><span class="lineno">  595</span>              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
-<div class="line"><a id="l00596" name="l00596"></a><span class="lineno">  596</span> </div>
-<div class="line"><a id="l00597" name="l00597"></a><span class="lineno">  597</span>    start_clk = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00598" name="l00598"></a><span class="lineno">  598</span>    <a class="code hl_function" href="../../d4/def/kohonen__som__topology_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
-<div class="line"><a id="l00599" name="l00599"></a><span class="lineno">  599</span>    end_clk = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00600" name="l00600"></a><span class="lineno">  600</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 completed in &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d4/def/kohonen__som__topology_8cpp.html#a2256c10b16edba377b64a44b6c656908">get_clock_diff</a>(start_clk, end_clk)</div>
-<div class="line"><a id="l00601" name="l00601"></a><span class="lineno">  601</span>              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
-<div class="line"><a id="l00602" name="l00602"></a><span class="lineno">  602</span> </div>
-<div class="line"><a id="l00603" name="l00603"></a><span class="lineno">  603</span>    start_clk = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00604" name="l00604"></a><span class="lineno">  604</span>    <a class="code hl_function" href="../../d4/def/kohonen__som__topology_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>();</div>
-<div class="line"><a id="l00605" name="l00605"></a><span class="lineno">  605</span>    end_clk = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00606" name="l00606"></a><span class="lineno">  606</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 completed in &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d4/def/kohonen__som__topology_8cpp.html#a2256c10b16edba377b64a44b6c656908">get_clock_diff</a>(start_clk, end_clk)</div>
-<div class="line"><a id="l00607" name="l00607"></a><span class="lineno">  607</span>              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
-<div class="line"><a id="l00608" name="l00608"></a><span class="lineno">  608</span> </div>
-<div class="line"><a id="l00609" name="l00609"></a><span class="lineno">  609</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
-<div class="line"><a id="l00610" name="l00610"></a><span class="lineno">  610</span>        &lt;&lt; <span class="stringliteral">&quot;(Note: Calculated times include: creating test sets, training &quot;</span></div>
-<div class="line"><a id="l00611" name="l00611"></a><span class="lineno">  611</span>           <span class="stringliteral">&quot;model and writing files to disk.)\n\n&quot;</span>;</div>
-<div class="line"><a id="l00612" name="l00612"></a><span class="lineno">  612</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00613" name="l00613"></a><span class="lineno">  613</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  582</span>                                {</div>
+<div class="line"><span class="lineno">  583</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  584</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Using OpenMP based parallelization\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  585</span><span class="preprocessor">#else</span></div>
+<div class="line"><span class="lineno">  586</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;NOT using OpenMP based parallelization\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  587</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  588</span> </div>
+<div class="line"><span class="lineno">  589</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
+<div class="line"><span class="lineno">  590</span> </div>
+<div class="line"><span class="lineno">  591</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start_clk = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  592</span>    <a class="code hl_function" href="../../d4/def/kohonen__som__topology_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
+<div class="line"><span class="lineno">  593</span>    <span class="keyword">auto</span> end_clk = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  594</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 completed in &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d4/def/kohonen__som__topology_8cpp.html#a2256c10b16edba377b64a44b6c656908">get_clock_diff</a>(start_clk, end_clk)</div>
+<div class="line"><span class="lineno">  595</span>              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  596</span> </div>
+<div class="line"><span class="lineno">  597</span>    start_clk = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  598</span>    <a class="code hl_function" href="../../d4/def/kohonen__som__topology_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
+<div class="line"><span class="lineno">  599</span>    end_clk = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  600</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 completed in &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d4/def/kohonen__som__topology_8cpp.html#a2256c10b16edba377b64a44b6c656908">get_clock_diff</a>(start_clk, end_clk)</div>
+<div class="line"><span class="lineno">  601</span>              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  602</span> </div>
+<div class="line"><span class="lineno">  603</span>    start_clk = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  604</span>    <a class="code hl_function" href="../../d4/def/kohonen__som__topology_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>();</div>
+<div class="line"><span class="lineno">  605</span>    end_clk = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  606</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 completed in &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d4/def/kohonen__som__topology_8cpp.html#a2256c10b16edba377b64a44b6c656908">get_clock_diff</a>(start_clk, end_clk)</div>
+<div class="line"><span class="lineno">  607</span>              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  608</span> </div>
+<div class="line"><span class="lineno">  609</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
+<div class="line"><span class="lineno">  610</span>        &lt;&lt; <span class="stringliteral">&quot;(Note: Calculated times include: creating test sets, training &quot;</span></div>
+<div class="line"><span class="lineno">  611</span>           <span class="stringliteral">&quot;model and writing files to disk.)\n\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  612</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  613</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aclock_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a></div><div class="ttdeci">T clock(T... args)</div></div>
 <div class="ttc" id="aclock_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a></div></div>
@@ -304,38 +304,38 @@ Here is the call graph for this function:</div>
 <li><code>w11.csv</code>: initial random map</li>
 <li><code>w12.csv</code>: trained SOM map </li>
 </ul>
-<div class="fragment"><div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span>             {</div>
-<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span>    <span class="keywordtype">int</span> j = 0, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 300;</div>
-<div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span>    <span class="keywordtype">int</span> features = 2;</div>
-<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span>    <span class="keywordtype">int</span> num_out = 30;</div>
-<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
-<div class="line"><a id="l00374" name="l00374"></a><span class="lineno">  374</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; W(num_out);</div>
-<div class="line"><a id="l00375" name="l00375"></a><span class="lineno">  375</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
-<div class="line"><a id="l00376" name="l00376"></a><span class="lineno">  376</span>        <span class="comment">// loop till max(N, num_out)</span></div>
-<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span>        <span class="keywordflow">if</span> (i &lt; N) {  <span class="comment">// only add new arrays if i &lt; N</span></div>
-<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span>            X[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
-<div class="line"><a id="l00379" name="l00379"></a><span class="lineno">  379</span>        }</div>
-<div class="line"><a id="l00380" name="l00380"></a><span class="lineno">  380</span>        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
-<div class="line"><a id="l00381" name="l00381"></a><span class="lineno">  381</span>            W[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt;(num_out);</div>
-<div class="line"><a id="l00382" name="l00382"></a><span class="lineno">  382</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt; num_out; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
-<div class="line"><a id="l00383" name="l00383"></a><span class="lineno">  383</span>                W[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
-<div class="line"><a id="l00384" name="l00384"></a><span class="lineno">  384</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00385" name="l00385"></a><span class="lineno">  385</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00386" name="l00386"></a><span class="lineno">  386</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00387" name="l00387"></a><span class="lineno">  387</span>                <span class="keywordflow">for</span> (j = 0; j &lt; features; j++) {</div>
-<div class="line"><a id="l00388" name="l00388"></a><span class="lineno">  388</span>                    <span class="comment">// preallocate with random initial weights</span></div>
-<div class="line"><a id="l00389" name="l00389"></a><span class="lineno">  389</span>                    W[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-10, 10);</div>
-<div class="line"><a id="l00390" name="l00390"></a><span class="lineno">  390</span>                }</div>
-<div class="line"><a id="l00391" name="l00391"></a><span class="lineno">  391</span>            }</div>
-<div class="line"><a id="l00392" name="l00392"></a><span class="lineno">  392</span>        }</div>
-<div class="line"><a id="l00393" name="l00393"></a><span class="lineno">  393</span>    }</div>
-<div class="line"><a id="l00394" name="l00394"></a><span class="lineno">  394</span> </div>
-<div class="line"><a id="l00395" name="l00395"></a><span class="lineno">  395</span>    <a class="code hl_function" href="../../d4/def/kohonen__som__topology_8cpp.html#a48efb079040c7aaa3a4917a0e486cba9">test_2d_classes</a>(&amp;X);  <span class="comment">// create test data around circumference of a circle</span></div>
-<div class="line"><a id="l00396" name="l00396"></a><span class="lineno">  396</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gabc90175770bf0d5853c466e14993a08c">save_2d_data</a>(<span class="stringliteral">&quot;test1.csv&quot;</span>, X);  <span class="comment">// save test data points</span></div>
-<div class="line"><a id="l00397" name="l00397"></a><span class="lineno">  397</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa72a53c88203fde278f1fe6c3afe5b07">save_u_matrix</a>(<span class="stringliteral">&quot;w11.csv&quot;</span>, W);   <span class="comment">// save initial random weights</span></div>
-<div class="line"><a id="l00398" name="l00398"></a><span class="lineno">  398</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ac43d294e21a0c4fa33c53757df054576">kohonen_som</a>(X, &amp;W, 1e-4);      <span class="comment">// train the SOM</span></div>
-<div class="line"><a id="l00399" name="l00399"></a><span class="lineno">  399</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa72a53c88203fde278f1fe6c3afe5b07">save_u_matrix</a>(<span class="stringliteral">&quot;w12.csv&quot;</span>, W);   <span class="comment">// save the resultant weights</span></div>
-<div class="line"><a id="l00400" name="l00400"></a><span class="lineno">  400</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  369</span>             {</div>
+<div class="line"><span class="lineno">  370</span>    <span class="keywordtype">int</span> j = 0, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 300;</div>
+<div class="line"><span class="lineno">  371</span>    <span class="keywordtype">int</span> features = 2;</div>
+<div class="line"><span class="lineno">  372</span>    <span class="keywordtype">int</span> num_out = 30;</div>
+<div class="line"><span class="lineno">  373</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
+<div class="line"><span class="lineno">  374</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; W(num_out);</div>
+<div class="line"><span class="lineno">  375</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
+<div class="line"><span class="lineno">  376</span>        <span class="comment">// loop till max(N, num_out)</span></div>
+<div class="line"><span class="lineno">  377</span>        <span class="keywordflow">if</span> (i &lt; N) {  <span class="comment">// only add new arrays if i &lt; N</span></div>
+<div class="line"><span class="lineno">  378</span>            X[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><span class="lineno">  379</span>        }</div>
+<div class="line"><span class="lineno">  380</span>        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
+<div class="line"><span class="lineno">  381</span>            W[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt;(num_out);</div>
+<div class="line"><span class="lineno">  382</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt; num_out; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
+<div class="line"><span class="lineno">  383</span>                W[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><span class="lineno">  384</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  385</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  386</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  387</span>                <span class="keywordflow">for</span> (j = 0; j &lt; features; j++) {</div>
+<div class="line"><span class="lineno">  388</span>                    <span class="comment">// preallocate with random initial weights</span></div>
+<div class="line"><span class="lineno">  389</span>                    W[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-10, 10);</div>
+<div class="line"><span class="lineno">  390</span>                }</div>
+<div class="line"><span class="lineno">  391</span>            }</div>
+<div class="line"><span class="lineno">  392</span>        }</div>
+<div class="line"><span class="lineno">  393</span>    }</div>
+<div class="line"><span class="lineno">  394</span> </div>
+<div class="line"><span class="lineno">  395</span>    <a class="code hl_function" href="../../d4/def/kohonen__som__topology_8cpp.html#a48efb079040c7aaa3a4917a0e486cba9">test_2d_classes</a>(&amp;X);  <span class="comment">// create test data around circumference of a circle</span></div>
+<div class="line"><span class="lineno">  396</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gabc90175770bf0d5853c466e14993a08c">save_2d_data</a>(<span class="stringliteral">&quot;test1.csv&quot;</span>, X);  <span class="comment">// save test data points</span></div>
+<div class="line"><span class="lineno">  397</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa72a53c88203fde278f1fe6c3afe5b07">save_u_matrix</a>(<span class="stringliteral">&quot;w11.csv&quot;</span>, W);   <span class="comment">// save initial random weights</span></div>
+<div class="line"><span class="lineno">  398</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ac43d294e21a0c4fa33c53757df054576">kohonen_som</a>(X, &amp;W, 1e-4);      <span class="comment">// train the SOM</span></div>
+<div class="line"><span class="lineno">  399</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa72a53c88203fde278f1fe6c3afe5b07">save_u_matrix</a>(<span class="stringliteral">&quot;w12.csv&quot;</span>, W);   <span class="comment">// save the resultant weights</span></div>
+<div class="line"><span class="lineno">  400</span>}</div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
 <div class="ttc" id="adata__structures_2sparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:47</div></div>
 <div class="ttc" id="agroup__machine__learning_html_gabc90175770bf0d5853c466e14993a08c"><div class="ttname"><a href="../../d9/d66/group__machine__learning.html#gabc90175770bf0d5853c466e14993a08c">save_2d_data</a></div><div class="ttdeci">int save_2d_data(const char *fname, const std::vector&lt; std::valarray&lt; double &gt; &gt; &amp;X)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:65</div></div>
@@ -344,7 +344,7 @@ Here is the call graph for this function:</div>
 <div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
 <div class="ttc" id="anamespacemachine__learning_html_aa72a53c88203fde278f1fe6c3afe5b07"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#aa72a53c88203fde278f1fe6c3afe5b07">machine_learning::save_u_matrix</a></div><div class="ttdeci">int save_u_matrix(const char *fname, const std::vector&lt; std::vector&lt; std::valarray&lt; double &gt; &gt; &gt; &amp;W)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:142</div></div>
 <div class="ttc" id="anamespacemachine__learning_html_ac43d294e21a0c4fa33c53757df054576"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#ac43d294e21a0c4fa33c53757df054576">machine_learning::kohonen_som</a></div><div class="ttdeci">void kohonen_som(const std::vector&lt; std::valarray&lt; double &gt; &gt; &amp;X, std::vector&lt; std::vector&lt; std::valarray&lt; double &gt; &gt; &gt; *W, double alpha_min)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:269</div></div>
-<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a></div></div>
+<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt; double &gt;</a></div></div>
 <div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -374,38 +374,38 @@ Here is the call graph for this function:</div>
 <li><code>w21.csv</code>: initial random map</li>
 <li><code>w22.csv</code>: trained SOM map </li>
 </ul>
-<div class="fragment"><div class="line"><a id="l00451" name="l00451"></a><span class="lineno">  451</span>             {</div>
-<div class="line"><a id="l00452" name="l00452"></a><span class="lineno">  452</span>    <span class="keywordtype">int</span> j = 0, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 300;</div>
-<div class="line"><a id="l00453" name="l00453"></a><span class="lineno">  453</span>    <span class="keywordtype">int</span> features = 3;</div>
-<div class="line"><a id="l00454" name="l00454"></a><span class="lineno">  454</span>    <span class="keywordtype">int</span> num_out = 30;</div>
-<div class="line"><a id="l00455" name="l00455"></a><span class="lineno">  455</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
-<div class="line"><a id="l00456" name="l00456"></a><span class="lineno">  456</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; W(num_out);</div>
-<div class="line"><a id="l00457" name="l00457"></a><span class="lineno">  457</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
-<div class="line"><a id="l00458" name="l00458"></a><span class="lineno">  458</span>        <span class="comment">// loop till max(N, num_out)</span></div>
-<div class="line"><a id="l00459" name="l00459"></a><span class="lineno">  459</span>        <span class="keywordflow">if</span> (i &lt; N) {  <span class="comment">// only add new arrays if i &lt; N</span></div>
-<div class="line"><a id="l00460" name="l00460"></a><span class="lineno">  460</span>            X[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
-<div class="line"><a id="l00461" name="l00461"></a><span class="lineno">  461</span>        }</div>
-<div class="line"><a id="l00462" name="l00462"></a><span class="lineno">  462</span>        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
-<div class="line"><a id="l00463" name="l00463"></a><span class="lineno">  463</span>            W[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt;(num_out);</div>
-<div class="line"><a id="l00464" name="l00464"></a><span class="lineno">  464</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt; num_out; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
-<div class="line"><a id="l00465" name="l00465"></a><span class="lineno">  465</span>                W[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
-<div class="line"><a id="l00466" name="l00466"></a><span class="lineno">  466</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00467" name="l00467"></a><span class="lineno">  467</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00468" name="l00468"></a><span class="lineno">  468</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00469" name="l00469"></a><span class="lineno">  469</span>                <span class="keywordflow">for</span> (j = 0; j &lt; features; j++) {</div>
-<div class="line"><a id="l00470" name="l00470"></a><span class="lineno">  470</span>                    <span class="comment">// preallocate with random initial weights</span></div>
-<div class="line"><a id="l00471" name="l00471"></a><span class="lineno">  471</span>                    W[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-10, 10);</div>
-<div class="line"><a id="l00472" name="l00472"></a><span class="lineno">  472</span>                }</div>
-<div class="line"><a id="l00473" name="l00473"></a><span class="lineno">  473</span>            }</div>
-<div class="line"><a id="l00474" name="l00474"></a><span class="lineno">  474</span>        }</div>
-<div class="line"><a id="l00475" name="l00475"></a><span class="lineno">  475</span>    }</div>
-<div class="line"><a id="l00476" name="l00476"></a><span class="lineno">  476</span> </div>
-<div class="line"><a id="l00477" name="l00477"></a><span class="lineno">  477</span>    <a class="code hl_function" href="../../d4/def/kohonen__som__topology_8cpp.html#a1302662a56ebf67a21249270b017297e">test_3d_classes1</a>(&amp;X);  <span class="comment">// create test data around circumference of a circle</span></div>
-<div class="line"><a id="l00478" name="l00478"></a><span class="lineno">  478</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gabc90175770bf0d5853c466e14993a08c">save_2d_data</a>(<span class="stringliteral">&quot;test2.csv&quot;</span>, X);  <span class="comment">// save test data points</span></div>
-<div class="line"><a id="l00479" name="l00479"></a><span class="lineno">  479</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa72a53c88203fde278f1fe6c3afe5b07">save_u_matrix</a>(<span class="stringliteral">&quot;w21.csv&quot;</span>, W);   <span class="comment">// save initial random weights</span></div>
-<div class="line"><a id="l00480" name="l00480"></a><span class="lineno">  480</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ac43d294e21a0c4fa33c53757df054576">kohonen_som</a>(X, &amp;W, 1e-4);      <span class="comment">// train the SOM</span></div>
-<div class="line"><a id="l00481" name="l00481"></a><span class="lineno">  481</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa72a53c88203fde278f1fe6c3afe5b07">save_u_matrix</a>(<span class="stringliteral">&quot;w22.csv&quot;</span>, W);   <span class="comment">// save the resultant weights</span></div>
-<div class="line"><a id="l00482" name="l00482"></a><span class="lineno">  482</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  451</span>             {</div>
+<div class="line"><span class="lineno">  452</span>    <span class="keywordtype">int</span> j = 0, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 300;</div>
+<div class="line"><span class="lineno">  453</span>    <span class="keywordtype">int</span> features = 3;</div>
+<div class="line"><span class="lineno">  454</span>    <span class="keywordtype">int</span> num_out = 30;</div>
+<div class="line"><span class="lineno">  455</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
+<div class="line"><span class="lineno">  456</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; W(num_out);</div>
+<div class="line"><span class="lineno">  457</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
+<div class="line"><span class="lineno">  458</span>        <span class="comment">// loop till max(N, num_out)</span></div>
+<div class="line"><span class="lineno">  459</span>        <span class="keywordflow">if</span> (i &lt; N) {  <span class="comment">// only add new arrays if i &lt; N</span></div>
+<div class="line"><span class="lineno">  460</span>            X[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><span class="lineno">  461</span>        }</div>
+<div class="line"><span class="lineno">  462</span>        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
+<div class="line"><span class="lineno">  463</span>            W[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt;(num_out);</div>
+<div class="line"><span class="lineno">  464</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt; num_out; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
+<div class="line"><span class="lineno">  465</span>                W[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><span class="lineno">  466</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  467</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  468</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  469</span>                <span class="keywordflow">for</span> (j = 0; j &lt; features; j++) {</div>
+<div class="line"><span class="lineno">  470</span>                    <span class="comment">// preallocate with random initial weights</span></div>
+<div class="line"><span class="lineno">  471</span>                    W[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-10, 10);</div>
+<div class="line"><span class="lineno">  472</span>                }</div>
+<div class="line"><span class="lineno">  473</span>            }</div>
+<div class="line"><span class="lineno">  474</span>        }</div>
+<div class="line"><span class="lineno">  475</span>    }</div>
+<div class="line"><span class="lineno">  476</span> </div>
+<div class="line"><span class="lineno">  477</span>    <a class="code hl_function" href="../../d4/def/kohonen__som__topology_8cpp.html#a1302662a56ebf67a21249270b017297e">test_3d_classes1</a>(&amp;X);  <span class="comment">// create test data around circumference of a circle</span></div>
+<div class="line"><span class="lineno">  478</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gabc90175770bf0d5853c466e14993a08c">save_2d_data</a>(<span class="stringliteral">&quot;test2.csv&quot;</span>, X);  <span class="comment">// save test data points</span></div>
+<div class="line"><span class="lineno">  479</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa72a53c88203fde278f1fe6c3afe5b07">save_u_matrix</a>(<span class="stringliteral">&quot;w21.csv&quot;</span>, W);   <span class="comment">// save initial random weights</span></div>
+<div class="line"><span class="lineno">  480</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ac43d294e21a0c4fa33c53757df054576">kohonen_som</a>(X, &amp;W, 1e-4);      <span class="comment">// train the SOM</span></div>
+<div class="line"><span class="lineno">  481</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa72a53c88203fde278f1fe6c3afe5b07">save_u_matrix</a>(<span class="stringliteral">&quot;w22.csv&quot;</span>, W);   <span class="comment">// save the resultant weights</span></div>
+<div class="line"><span class="lineno">  482</span>}</div>
 <div class="ttc" id="akohonen__som__topology_8cpp_html_a1302662a56ebf67a21249270b017297e"><div class="ttname"><a href="../../d4/def/kohonen__som__topology_8cpp.html#a1302662a56ebf67a21249270b017297e">test_3d_classes1</a></div><div class="ttdeci">void test_3d_classes1(std::vector&lt; std::valarray&lt; double &gt; &gt; *data)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:411</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -435,38 +435,38 @@ Here is the call graph for this function:</div>
 <li><code>w31.csv</code>: initial random map</li>
 <li><code>w32.csv</code>: trained SOM map </li>
 </ul>
-<div class="fragment"><div class="line"><a id="l00537" name="l00537"></a><span class="lineno">  537</span>             {</div>
-<div class="line"><a id="l00538" name="l00538"></a><span class="lineno">  538</span>    <span class="keywordtype">int</span> j = 0, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 500;</div>
-<div class="line"><a id="l00539" name="l00539"></a><span class="lineno">  539</span>    <span class="keywordtype">int</span> features = 3;</div>
-<div class="line"><a id="l00540" name="l00540"></a><span class="lineno">  540</span>    <span class="keywordtype">int</span> num_out = 30;</div>
-<div class="line"><a id="l00541" name="l00541"></a><span class="lineno">  541</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
-<div class="line"><a id="l00542" name="l00542"></a><span class="lineno">  542</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; W(num_out);</div>
-<div class="line"><a id="l00543" name="l00543"></a><span class="lineno">  543</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
-<div class="line"><a id="l00544" name="l00544"></a><span class="lineno">  544</span>        <span class="comment">// loop till max(N, num_out)</span></div>
-<div class="line"><a id="l00545" name="l00545"></a><span class="lineno">  545</span>        <span class="keywordflow">if</span> (i &lt; N) {  <span class="comment">// only add new arrays if i &lt; N</span></div>
-<div class="line"><a id="l00546" name="l00546"></a><span class="lineno">  546</span>            X[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
-<div class="line"><a id="l00547" name="l00547"></a><span class="lineno">  547</span>        }</div>
-<div class="line"><a id="l00548" name="l00548"></a><span class="lineno">  548</span>        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
-<div class="line"><a id="l00549" name="l00549"></a><span class="lineno">  549</span>            W[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt;(num_out);</div>
-<div class="line"><a id="l00550" name="l00550"></a><span class="lineno">  550</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt; num_out; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
-<div class="line"><a id="l00551" name="l00551"></a><span class="lineno">  551</span>                W[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
-<div class="line"><a id="l00552" name="l00552"></a><span class="lineno">  552</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00553" name="l00553"></a><span class="lineno">  553</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00554" name="l00554"></a><span class="lineno">  554</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00555" name="l00555"></a><span class="lineno">  555</span>                <span class="keywordflow">for</span> (j = 0; j &lt; features; j++) {</div>
-<div class="line"><a id="l00556" name="l00556"></a><span class="lineno">  556</span>                    <span class="comment">// preallocate with random initial weights</span></div>
-<div class="line"><a id="l00557" name="l00557"></a><span class="lineno">  557</span>                    W[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-10, 10);</div>
-<div class="line"><a id="l00558" name="l00558"></a><span class="lineno">  558</span>                }</div>
-<div class="line"><a id="l00559" name="l00559"></a><span class="lineno">  559</span>            }</div>
-<div class="line"><a id="l00560" name="l00560"></a><span class="lineno">  560</span>        }</div>
-<div class="line"><a id="l00561" name="l00561"></a><span class="lineno">  561</span>    }</div>
-<div class="line"><a id="l00562" name="l00562"></a><span class="lineno">  562</span> </div>
-<div class="line"><a id="l00563" name="l00563"></a><span class="lineno">  563</span>    <a class="code hl_function" href="../../d4/def/kohonen__som__topology_8cpp.html#a4b7ab643f6a5002f991837de46f70653">test_3d_classes2</a>(&amp;X);  <span class="comment">// create test data around circumference of a circle</span></div>
-<div class="line"><a id="l00564" name="l00564"></a><span class="lineno">  564</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gabc90175770bf0d5853c466e14993a08c">save_2d_data</a>(<span class="stringliteral">&quot;test3.csv&quot;</span>, X);  <span class="comment">// save test data points</span></div>
-<div class="line"><a id="l00565" name="l00565"></a><span class="lineno">  565</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa72a53c88203fde278f1fe6c3afe5b07">save_u_matrix</a>(<span class="stringliteral">&quot;w31.csv&quot;</span>, W);   <span class="comment">// save initial random weights</span></div>
-<div class="line"><a id="l00566" name="l00566"></a><span class="lineno">  566</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ac43d294e21a0c4fa33c53757df054576">kohonen_som</a>(X, &amp;W, 1e-4);      <span class="comment">// train the SOM</span></div>
-<div class="line"><a id="l00567" name="l00567"></a><span class="lineno">  567</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa72a53c88203fde278f1fe6c3afe5b07">save_u_matrix</a>(<span class="stringliteral">&quot;w32.csv&quot;</span>, W);   <span class="comment">// save the resultant weights</span></div>
-<div class="line"><a id="l00568" name="l00568"></a><span class="lineno">  568</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  537</span>             {</div>
+<div class="line"><span class="lineno">  538</span>    <span class="keywordtype">int</span> j = 0, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 500;</div>
+<div class="line"><span class="lineno">  539</span>    <span class="keywordtype">int</span> features = 3;</div>
+<div class="line"><span class="lineno">  540</span>    <span class="keywordtype">int</span> num_out = 30;</div>
+<div class="line"><span class="lineno">  541</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
+<div class="line"><span class="lineno">  542</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; W(num_out);</div>
+<div class="line"><span class="lineno">  543</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
+<div class="line"><span class="lineno">  544</span>        <span class="comment">// loop till max(N, num_out)</span></div>
+<div class="line"><span class="lineno">  545</span>        <span class="keywordflow">if</span> (i &lt; N) {  <span class="comment">// only add new arrays if i &lt; N</span></div>
+<div class="line"><span class="lineno">  546</span>            X[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><span class="lineno">  547</span>        }</div>
+<div class="line"><span class="lineno">  548</span>        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
+<div class="line"><span class="lineno">  549</span>            W[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt;(num_out);</div>
+<div class="line"><span class="lineno">  550</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt; num_out; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
+<div class="line"><span class="lineno">  551</span>                W[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><span class="lineno">  552</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  553</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  554</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  555</span>                <span class="keywordflow">for</span> (j = 0; j &lt; features; j++) {</div>
+<div class="line"><span class="lineno">  556</span>                    <span class="comment">// preallocate with random initial weights</span></div>
+<div class="line"><span class="lineno">  557</span>                    W[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-10, 10);</div>
+<div class="line"><span class="lineno">  558</span>                }</div>
+<div class="line"><span class="lineno">  559</span>            }</div>
+<div class="line"><span class="lineno">  560</span>        }</div>
+<div class="line"><span class="lineno">  561</span>    }</div>
+<div class="line"><span class="lineno">  562</span> </div>
+<div class="line"><span class="lineno">  563</span>    <a class="code hl_function" href="../../d4/def/kohonen__som__topology_8cpp.html#a4b7ab643f6a5002f991837de46f70653">test_3d_classes2</a>(&amp;X);  <span class="comment">// create test data around circumference of a circle</span></div>
+<div class="line"><span class="lineno">  564</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gabc90175770bf0d5853c466e14993a08c">save_2d_data</a>(<span class="stringliteral">&quot;test3.csv&quot;</span>, X);  <span class="comment">// save test data points</span></div>
+<div class="line"><span class="lineno">  565</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa72a53c88203fde278f1fe6c3afe5b07">save_u_matrix</a>(<span class="stringliteral">&quot;w31.csv&quot;</span>, W);   <span class="comment">// save initial random weights</span></div>
+<div class="line"><span class="lineno">  566</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ac43d294e21a0c4fa33c53757df054576">kohonen_som</a>(X, &amp;W, 1e-4);      <span class="comment">// train the SOM</span></div>
+<div class="line"><span class="lineno">  567</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa72a53c88203fde278f1fe6c3afe5b07">save_u_matrix</a>(<span class="stringliteral">&quot;w32.csv&quot;</span>, W);   <span class="comment">// save the resultant weights</span></div>
+<div class="line"><span class="lineno">  568</span>}</div>
 <div class="ttc" id="akohonen__som__topology_8cpp_html_a4b7ab643f6a5002f991837de46f70653"><div class="ttname"><a href="../../d4/def/kohonen__som__topology_8cpp.html#a4b7ab643f6a5002f991837de46f70653">test_3d_classes2</a></div><div class="ttdeci">void test_3d_classes2(std::vector&lt; std::valarray&lt; double &gt; &gt; *data)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:493</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -504,36 +504,36 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00330" name="l00330"></a><span class="lineno">  330</span>                                                           {</div>
-<div class="line"><a id="l00331" name="l00331"></a><span class="lineno">  331</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
-<div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span>    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.3;  <span class="comment">// radius of cluster</span></div>
-<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>    <span class="keywordtype">int</span> i = 0;</div>
-<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> num_classes = 4;</div>
-<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 2&gt;</a>, num_classes&gt; centres = {</div>
-<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span>        <span class="comment">// centres of each class cluster</span></div>
-<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 2&gt;</a>({.5, .5}),   <span class="comment">// centre of class 1</span></div>
-<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 2&gt;</a>({.5, -.5}),  <span class="comment">// centre of class 2</span></div>
-<div class="line"><a id="l00339" name="l00339"></a><span class="lineno">  339</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 2&gt;</a>({-.5, .5}),  <span class="comment">// centre of class 3</span></div>
-<div class="line"><a id="l00340" name="l00340"></a><span class="lineno">  340</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 2&gt;</a>({-.5, -.5})  <span class="comment">// centre of class 4</span></div>
-<div class="line"><a id="l00341" name="l00341"></a><span class="lineno">  341</span>    };</div>
-<div class="line"><a id="l00342" name="l00342"></a><span class="lineno">  342</span> </div>
-<div class="line"><a id="l00343" name="l00343"></a><span class="lineno">  343</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00344" name="l00344"></a><span class="lineno">  344</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00345" name="l00345"></a><span class="lineno">  345</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00346" name="l00346"></a><span class="lineno">  346</span>    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
-<div class="line"><a id="l00347" name="l00347"></a><span class="lineno">  347</span>        <span class="comment">// select a random class for the point</span></div>
-<div class="line"><a id="l00348" name="l00348"></a><span class="lineno">  348</span>        <span class="keywordtype">int</span> cls = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % num_classes;</div>
-<div class="line"><a id="l00349" name="l00349"></a><span class="lineno">  349</span> </div>
-<div class="line"><a id="l00350" name="l00350"></a><span class="lineno">  350</span>        <span class="comment">// create random coordinates (x,y,z) around the centre of the class</span></div>
-<div class="line"><a id="l00351" name="l00351"></a><span class="lineno">  351</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][0] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][0] - R, centres[cls][0] + R);</div>
-<div class="line"><a id="l00352" name="l00352"></a><span class="lineno">  352</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][1] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][1] - R, centres[cls][1] + R);</div>
-<div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span> </div>
-<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span>        <span class="comment">/* The follosing can also be used</span></div>
-<div class="line"><a id="l00355" name="l00355"></a><span class="lineno">  355</span><span class="comment">        for (int j = 0; j &lt; 2; j++)</span></div>
-<div class="line"><a id="l00356" name="l00356"></a><span class="lineno">  356</span><span class="comment">            data[i][j] = _random(centres[class][j] - R, centres[class][j] + R);</span></div>
-<div class="line"><a id="l00357" name="l00357"></a><span class="lineno">  357</span><span class="comment">        */</span></div>
-<div class="line"><a id="l00358" name="l00358"></a><span class="lineno">  358</span>    }</div>
-<div class="line"><a id="l00359" name="l00359"></a><span class="lineno">  359</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  330</span>                                                           {</div>
+<div class="line"><span class="lineno">  331</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
+<div class="line"><span class="lineno">  332</span>    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.3;  <span class="comment">// radius of cluster</span></div>
+<div class="line"><span class="lineno">  333</span>    <span class="keywordtype">int</span> i = 0;</div>
+<div class="line"><span class="lineno">  334</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> num_classes = 4;</div>
+<div class="line"><span class="lineno">  335</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 2&gt;</a>, num_classes&gt; centres = {</div>
+<div class="line"><span class="lineno">  336</span>        <span class="comment">// centres of each class cluster</span></div>
+<div class="line"><span class="lineno">  337</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 2&gt;</a>({.5, .5}),   <span class="comment">// centre of class 1</span></div>
+<div class="line"><span class="lineno">  338</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 2&gt;</a>({.5, -.5}),  <span class="comment">// centre of class 2</span></div>
+<div class="line"><span class="lineno">  339</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 2&gt;</a>({-.5, .5}),  <span class="comment">// centre of class 3</span></div>
+<div class="line"><span class="lineno">  340</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 2&gt;</a>({-.5, -.5})  <span class="comment">// centre of class 4</span></div>
+<div class="line"><span class="lineno">  341</span>    };</div>
+<div class="line"><span class="lineno">  342</span> </div>
+<div class="line"><span class="lineno">  343</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  344</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  345</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  346</span>    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
+<div class="line"><span class="lineno">  347</span>        <span class="comment">// select a random class for the point</span></div>
+<div class="line"><span class="lineno">  348</span>        <span class="keywordtype">int</span> cls = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % num_classes;</div>
+<div class="line"><span class="lineno">  349</span> </div>
+<div class="line"><span class="lineno">  350</span>        <span class="comment">// create random coordinates (x,y,z) around the centre of the class</span></div>
+<div class="line"><span class="lineno">  351</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][0] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][0] - R, centres[cls][0] + R);</div>
+<div class="line"><span class="lineno">  352</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][1] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][1] - R, centres[cls][1] + R);</div>
+<div class="line"><span class="lineno">  353</span> </div>
+<div class="line"><span class="lineno">  354</span>        <span class="comment">/* The follosing can also be used</span></div>
+<div class="line"><span class="lineno">  355</span><span class="comment">        for (int j = 0; j &lt; 2; j++)</span></div>
+<div class="line"><span class="lineno">  356</span><span class="comment">            data[i][j] = _random(centres[class][j] - R, centres[class][j] + R);</span></div>
+<div class="line"><span class="lineno">  357</span><span class="comment">        */</span></div>
+<div class="line"><span class="lineno">  358</span>    }</div>
+<div class="line"><span class="lineno">  359</span>}</div>
 <div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
 <div class="ttc" id="ahash__search_8cpp_html_a6e1a77282bc65ad359d753d25df23243"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a></div><div class="ttdeci">int data[MAX]</div><div class="ttdoc">test data</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:24</div></div>
 <div class="ttc" id="arand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a></div><div class="ttdeci">T rand(T... args)</div></div>
@@ -573,37 +573,37 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00411" name="l00411"></a><span class="lineno">  411</span>                                                            {</div>
-<div class="line"><a id="l00412" name="l00412"></a><span class="lineno">  412</span>    <span class="keyword">const</span> <span class="keywordtype">size_t</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
-<div class="line"><a id="l00413" name="l00413"></a><span class="lineno">  413</span>    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.3;  <span class="comment">// radius of cluster</span></div>
-<div class="line"><a id="l00414" name="l00414"></a><span class="lineno">  414</span>    <span class="keywordtype">int</span> i = 0;</div>
-<div class="line"><a id="l00415" name="l00415"></a><span class="lineno">  415</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> num_classes = 4;</div>
-<div class="line"><a id="l00416" name="l00416"></a><span class="lineno">  416</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 3&gt;</a>, num_classes&gt; centres = {</div>
-<div class="line"><a id="l00417" name="l00417"></a><span class="lineno">  417</span>        <span class="comment">// centres of each class cluster</span></div>
-<div class="line"><a id="l00418" name="l00418"></a><span class="lineno">  418</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, .5, .5}),    <span class="comment">// centre of class 1</span></div>
-<div class="line"><a id="l00419" name="l00419"></a><span class="lineno">  419</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, -.5, -.5}),  <span class="comment">// centre of class 2</span></div>
-<div class="line"><a id="l00420" name="l00420"></a><span class="lineno">  420</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({-.5, .5, .5}),   <span class="comment">// centre of class 3</span></div>
-<div class="line"><a id="l00421" name="l00421"></a><span class="lineno">  421</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({-.5, -.5 - .5})  <span class="comment">// centre of class 4</span></div>
-<div class="line"><a id="l00422" name="l00422"></a><span class="lineno">  422</span>    };</div>
-<div class="line"><a id="l00423" name="l00423"></a><span class="lineno">  423</span> </div>
-<div class="line"><a id="l00424" name="l00424"></a><span class="lineno">  424</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00425" name="l00425"></a><span class="lineno">  425</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00426" name="l00426"></a><span class="lineno">  426</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00427" name="l00427"></a><span class="lineno">  427</span>    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
-<div class="line"><a id="l00428" name="l00428"></a><span class="lineno">  428</span>        <span class="comment">// select a random class for the point</span></div>
-<div class="line"><a id="l00429" name="l00429"></a><span class="lineno">  429</span>        <span class="keywordtype">int</span> cls = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % num_classes;</div>
-<div class="line"><a id="l00430" name="l00430"></a><span class="lineno">  430</span> </div>
-<div class="line"><a id="l00431" name="l00431"></a><span class="lineno">  431</span>        <span class="comment">// create random coordinates (x,y,z) around the centre of the class</span></div>
-<div class="line"><a id="l00432" name="l00432"></a><span class="lineno">  432</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][0] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][0] - R, centres[cls][0] + R);</div>
-<div class="line"><a id="l00433" name="l00433"></a><span class="lineno">  433</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][1] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][1] - R, centres[cls][1] + R);</div>
-<div class="line"><a id="l00434" name="l00434"></a><span class="lineno">  434</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][2] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][2] - R, centres[cls][2] + R);</div>
-<div class="line"><a id="l00435" name="l00435"></a><span class="lineno">  435</span> </div>
-<div class="line"><a id="l00436" name="l00436"></a><span class="lineno">  436</span>        <span class="comment">/* The follosing can also be used</span></div>
-<div class="line"><a id="l00437" name="l00437"></a><span class="lineno">  437</span><span class="comment">        for (int j = 0; j &lt; 3; j++)</span></div>
-<div class="line"><a id="l00438" name="l00438"></a><span class="lineno">  438</span><span class="comment">            data[i][j] = _random(centres[class][j] - R, centres[class][j] + R);</span></div>
-<div class="line"><a id="l00439" name="l00439"></a><span class="lineno">  439</span><span class="comment">        */</span></div>
-<div class="line"><a id="l00440" name="l00440"></a><span class="lineno">  440</span>    }</div>
-<div class="line"><a id="l00441" name="l00441"></a><span class="lineno">  441</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  411</span>                                                            {</div>
+<div class="line"><span class="lineno">  412</span>    <span class="keyword">const</span> <span class="keywordtype">size_t</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
+<div class="line"><span class="lineno">  413</span>    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.3;  <span class="comment">// radius of cluster</span></div>
+<div class="line"><span class="lineno">  414</span>    <span class="keywordtype">int</span> i = 0;</div>
+<div class="line"><span class="lineno">  415</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> num_classes = 4;</div>
+<div class="line"><span class="lineno">  416</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 3&gt;</a>, num_classes&gt; centres = {</div>
+<div class="line"><span class="lineno">  417</span>        <span class="comment">// centres of each class cluster</span></div>
+<div class="line"><span class="lineno">  418</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, .5, .5}),    <span class="comment">// centre of class 1</span></div>
+<div class="line"><span class="lineno">  419</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, -.5, -.5}),  <span class="comment">// centre of class 2</span></div>
+<div class="line"><span class="lineno">  420</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({-.5, .5, .5}),   <span class="comment">// centre of class 3</span></div>
+<div class="line"><span class="lineno">  421</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({-.5, -.5 - .5})  <span class="comment">// centre of class 4</span></div>
+<div class="line"><span class="lineno">  422</span>    };</div>
+<div class="line"><span class="lineno">  423</span> </div>
+<div class="line"><span class="lineno">  424</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  425</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  426</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  427</span>    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
+<div class="line"><span class="lineno">  428</span>        <span class="comment">// select a random class for the point</span></div>
+<div class="line"><span class="lineno">  429</span>        <span class="keywordtype">int</span> cls = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % num_classes;</div>
+<div class="line"><span class="lineno">  430</span> </div>
+<div class="line"><span class="lineno">  431</span>        <span class="comment">// create random coordinates (x,y,z) around the centre of the class</span></div>
+<div class="line"><span class="lineno">  432</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][0] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][0] - R, centres[cls][0] + R);</div>
+<div class="line"><span class="lineno">  433</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][1] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][1] - R, centres[cls][1] + R);</div>
+<div class="line"><span class="lineno">  434</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][2] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][2] - R, centres[cls][2] + R);</div>
+<div class="line"><span class="lineno">  435</span> </div>
+<div class="line"><span class="lineno">  436</span>        <span class="comment">/* The follosing can also be used</span></div>
+<div class="line"><span class="lineno">  437</span><span class="comment">        for (int j = 0; j &lt; 3; j++)</span></div>
+<div class="line"><span class="lineno">  438</span><span class="comment">            data[i][j] = _random(centres[class][j] - R, centres[class][j] + R);</span></div>
+<div class="line"><span class="lineno">  439</span><span class="comment">        */</span></div>
+<div class="line"><span class="lineno">  440</span>    }</div>
+<div class="line"><span class="lineno">  441</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -640,41 +640,41 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00493" name="l00493"></a><span class="lineno">  493</span>                                                            {</div>
-<div class="line"><a id="l00494" name="l00494"></a><span class="lineno">  494</span>    <span class="keyword">const</span> <span class="keywordtype">size_t</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
-<div class="line"><a id="l00495" name="l00495"></a><span class="lineno">  495</span>    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.2;  <span class="comment">// radius of cluster</span></div>
-<div class="line"><a id="l00496" name="l00496"></a><span class="lineno">  496</span>    <span class="keywordtype">int</span> i = 0;</div>
-<div class="line"><a id="l00497" name="l00497"></a><span class="lineno">  497</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> num_classes = 8;</div>
-<div class="line"><a id="l00498" name="l00498"></a><span class="lineno">  498</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 3&gt;</a>, num_classes&gt; centres = {</div>
-<div class="line"><a id="l00499" name="l00499"></a><span class="lineno">  499</span>        <span class="comment">// centres of each class cluster</span></div>
-<div class="line"><a id="l00500" name="l00500"></a><span class="lineno">  500</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, .5, .5}),    <span class="comment">// centre of class 1</span></div>
-<div class="line"><a id="l00501" name="l00501"></a><span class="lineno">  501</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, .5, -.5}),   <span class="comment">// centre of class 2</span></div>
-<div class="line"><a id="l00502" name="l00502"></a><span class="lineno">  502</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, -.5, .5}),   <span class="comment">// centre of class 3</span></div>
-<div class="line"><a id="l00503" name="l00503"></a><span class="lineno">  503</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, -.5, -.5}),  <span class="comment">// centre of class 4</span></div>
-<div class="line"><a id="l00504" name="l00504"></a><span class="lineno">  504</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({-.5, .5, .5}),   <span class="comment">// centre of class 5</span></div>
-<div class="line"><a id="l00505" name="l00505"></a><span class="lineno">  505</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({-.5, .5, -.5}),  <span class="comment">// centre of class 6</span></div>
-<div class="line"><a id="l00506" name="l00506"></a><span class="lineno">  506</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({-.5, -.5, .5}),  <span class="comment">// centre of class 7</span></div>
-<div class="line"><a id="l00507" name="l00507"></a><span class="lineno">  507</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({-.5, -.5, -.5})  <span class="comment">// centre of class 8</span></div>
-<div class="line"><a id="l00508" name="l00508"></a><span class="lineno">  508</span>    };</div>
-<div class="line"><a id="l00509" name="l00509"></a><span class="lineno">  509</span> </div>
-<div class="line"><a id="l00510" name="l00510"></a><span class="lineno">  510</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00511" name="l00511"></a><span class="lineno">  511</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00512" name="l00512"></a><span class="lineno">  512</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00513" name="l00513"></a><span class="lineno">  513</span>    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
-<div class="line"><a id="l00514" name="l00514"></a><span class="lineno">  514</span>        <span class="comment">// select a random class for the point</span></div>
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-<div class="line"><a id="l00517" name="l00517"></a><span class="lineno">  517</span>        <span class="comment">// create random coordinates (x,y,z) around the centre of the class</span></div>
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-<div class="line"><a id="l00527" name="l00527"></a><span class="lineno">  527</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  493</span>                                                            {</div>
+<div class="line"><span class="lineno">  494</span>    <span class="keyword">const</span> <span class="keywordtype">size_t</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
+<div class="line"><span class="lineno">  495</span>    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.2;  <span class="comment">// radius of cluster</span></div>
+<div class="line"><span class="lineno">  496</span>    <span class="keywordtype">int</span> i = 0;</div>
+<div class="line"><span class="lineno">  497</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> num_classes = 8;</div>
+<div class="line"><span class="lineno">  498</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 3&gt;</a>, num_classes&gt; centres = {</div>
+<div class="line"><span class="lineno">  499</span>        <span class="comment">// centres of each class cluster</span></div>
+<div class="line"><span class="lineno">  500</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, .5, .5}),    <span class="comment">// centre of class 1</span></div>
+<div class="line"><span class="lineno">  501</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, .5, -.5}),   <span class="comment">// centre of class 2</span></div>
+<div class="line"><span class="lineno">  502</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, -.5, .5}),   <span class="comment">// centre of class 3</span></div>
+<div class="line"><span class="lineno">  503</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, -.5, -.5}),  <span class="comment">// centre of class 4</span></div>
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+<div class="line"><span class="lineno">  506</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({-.5, -.5, .5}),  <span class="comment">// centre of class 7</span></div>
+<div class="line"><span class="lineno">  507</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({-.5, -.5, -.5})  <span class="comment">// centre of class 8</span></div>
+<div class="line"><span class="lineno">  508</span>    };</div>
+<div class="line"><span class="lineno">  509</span> </div>
+<div class="line"><span class="lineno">  510</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  511</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  512</span><span class="preprocessor">#endif</span></div>
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+<div class="line"><span class="lineno">  514</span>        <span class="comment">// select a random class for the point</span></div>
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+<div class="line"><span class="lineno">  516</span> </div>
+<div class="line"><span class="lineno">  517</span>        <span class="comment">// create random coordinates (x,y,z) around the centre of the class</span></div>
+<div class="line"><span class="lineno">  518</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][0] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][0] - R, centres[cls][0] + R);</div>
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+<div class="line"><span class="lineno">  522</span>        <span class="comment">/* The follosing can also be used</span></div>
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 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
@@ -286,36 +292,36 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span>                                                          {</div>
-<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span>        <span class="comment">// First layer should not have activation</span></div>
-<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>        <span class="keywordflow">if</span> (config.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>()-&gt;second != <span class="stringliteral">&quot;none&quot;</span>) {</div>
-<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
-<div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div>
-<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>                &lt;&lt; <span class="stringliteral">&quot;First layer can&#39;t have activation other than none got &quot;</span></div>
-<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>                &lt;&lt; config.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>()-&gt;second;</div>
-<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
-<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>        }</div>
-<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>        <span class="comment">// Network should have atleast two layers</span></div>
-<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span>        <span class="keywordflow">if</span> (config.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;= 1) {</div>
-<div class="line"><a id="l00326" name="l00326"></a><span class="lineno">  326</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
-<div class="line"><a id="l00327" name="l00327"></a><span class="lineno">  327</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Invalid size of network, &quot;</span>;</div>
-<div class="line"><a id="l00328" name="l00328"></a><span class="lineno">  328</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Atleast two layers are required&quot;</span>;</div>
-<div class="line"><a id="l00329" name="l00329"></a><span class="lineno">  329</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
-<div class="line"><a id="l00330" name="l00330"></a><span class="lineno">  330</span>        }</div>
-<div class="line"><a id="l00331" name="l00331"></a><span class="lineno">  331</span>        <span class="comment">// Separately creating first layer so it can have unit matrix</span></div>
-<div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span>        <span class="comment">// as kernel.</span></div>
-<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>        <a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>.push_back(neural_network::layers::DenseLayer(</div>
-<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span>            config[0].first, config[0].second,</div>
-<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span>            {config[0].first, config[0].first}, <span class="keyword">false</span>));</div>
-<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span>        <span class="comment">// Creating remaining layers</span></div>
-<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 1; i &lt; config.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
-<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span>            <a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>.push_back(neural_network::layers::DenseLayer(</div>
-<div class="line"><a id="l00339" name="l00339"></a><span class="lineno">  339</span>                config[i].first, config[i].second,</div>
-<div class="line"><a id="l00340" name="l00340"></a><span class="lineno">  340</span>                {config[i - 1].first, config[i].first}, <span class="keyword">true</span>));</div>
-<div class="line"><a id="l00341" name="l00341"></a><span class="lineno">  341</span>        }</div>
-<div class="line"><a id="l00342" name="l00342"></a><span class="lineno">  342</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;INFO: Network constructed successfully&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00343" name="l00343"></a><span class="lineno">  343</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  314</span>                                                          {</div>
+<div class="line"><span class="lineno">  315</span>        <span class="comment">// First layer should not have activation</span></div>
+<div class="line"><span class="lineno">  316</span>        <span class="keywordflow">if</span> (config.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>()-&gt;second != <span class="stringliteral">&quot;none&quot;</span>) {</div>
+<div class="line"><span class="lineno">  317</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
+<div class="line"><span class="lineno">  318</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div>
+<div class="line"><span class="lineno">  319</span>                &lt;&lt; <span class="stringliteral">&quot;First layer can&#39;t have activation other than none got &quot;</span></div>
+<div class="line"><span class="lineno">  320</span>                &lt;&lt; config.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>()-&gt;second;</div>
+<div class="line"><span class="lineno">  321</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  322</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><span class="lineno">  323</span>        }</div>
+<div class="line"><span class="lineno">  324</span>        <span class="comment">// Network should have atleast two layers</span></div>
+<div class="line"><span class="lineno">  325</span>        <span class="keywordflow">if</span> (config.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;= 1) {</div>
+<div class="line"><span class="lineno">  326</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
+<div class="line"><span class="lineno">  327</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Invalid size of network, &quot;</span>;</div>
+<div class="line"><span class="lineno">  328</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Atleast two layers are required&quot;</span>;</div>
+<div class="line"><span class="lineno">  329</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><span class="lineno">  330</span>        }</div>
+<div class="line"><span class="lineno">  331</span>        <span class="comment">// Separately creating first layer so it can have unit matrix</span></div>
+<div class="line"><span class="lineno">  332</span>        <span class="comment">// as kernel.</span></div>
+<div class="line"><span class="lineno">  333</span>        <a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>.push_back(neural_network::layers::DenseLayer(</div>
+<div class="line"><span class="lineno">  334</span>            config[0].first, config[0].second,</div>
+<div class="line"><span class="lineno">  335</span>            {config[0].first, config[0].first}, <span class="keyword">false</span>));</div>
+<div class="line"><span class="lineno">  336</span>        <span class="comment">// Creating remaining layers</span></div>
+<div class="line"><span class="lineno">  337</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 1; i &lt; config.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
+<div class="line"><span class="lineno">  338</span>            <a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>.push_back(neural_network::layers::DenseLayer(</div>
+<div class="line"><span class="lineno">  339</span>                config[i].first, config[i].second,</div>
+<div class="line"><span class="lineno">  340</span>                {config[i - 1].first, config[i].first}, <span class="keyword">true</span>));</div>
+<div class="line"><span class="lineno">  341</span>        }</div>
+<div class="line"><span class="lineno">  342</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;INFO: Network constructed successfully&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  343</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -441,17 +447,17 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
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-<div class="fragment"><div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>                                                                          {</div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; details;</div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; current_pass = X;</div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>        details.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/emplace_back.html">emplace_back</a>(X);</div>
-<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>        <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;l : <a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>) {</div>
-<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>            current_pass = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a5342906d42b80fc6b6b3ad17bf00fcb9">multiply</a>(current_pass, <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a>.kernel);</div>
-<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span>            current_pass = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ad0bdc88e5f1be47c46c0f0c8ebf754bb">apply_function</a>(current_pass, <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a>.activation_function);</div>
-<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>            details.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/emplace_back.html">emplace_back</a>(current_pass);</div>
-<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>        }</div>
-<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>        <span class="keywordflow">return</span> details;</div>
-<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  289</span>                                                                          {</div>
+<div class="line"><span class="lineno">  290</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; details;</div>
+<div class="line"><span class="lineno">  291</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; current_pass = X;</div>
+<div class="line"><span class="lineno">  292</span>        details.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/emplace_back.html">emplace_back</a>(X);</div>
+<div class="line"><span class="lineno">  293</span>        <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;l : <a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>) {</div>
+<div class="line"><span class="lineno">  294</span>            current_pass = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a5342906d42b80fc6b6b3ad17bf00fcb9">multiply</a>(current_pass, <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a>.kernel);</div>
+<div class="line"><span class="lineno">  295</span>            current_pass = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ad0bdc88e5f1be47c46c0f0c8ebf754bb">apply_function</a>(current_pass, <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a>.activation_function);</div>
+<div class="line"><span class="lineno">  296</span>            details.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/emplace_back.html">emplace_back</a>(current_pass);</div>
+<div class="line"><span class="lineno">  297</span>        }</div>
+<div class="line"><span class="lineno">  298</span>        <span class="keywordflow">return</span> details;</div>
+<div class="line"><span class="lineno">  299</span>    }</div>
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 <div class="ttc" id="aemplace_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/emplace_back.html">std::vector::emplace_back</a></div><div class="ttdeci">T emplace_back(T... args)</div></div>
 <div class="ttc" id="anamespacemachine__learning_html_a5342906d42b80fc6b6b3ad17bf00fcb9"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a5342906d42b80fc6b6b3ad17bf00fcb9">machine_learning::multiply</a></div><div class="ttdeci">std::vector&lt; std::valarray&lt; T &gt; &gt; multiply(const std::vector&lt; std::valarray&lt; T &gt; &gt; &amp;A, const std::vector&lt; std::valarray&lt; T &gt; &gt; &amp;B)</div><div class="ttdef"><b>Definition:</b> vector_ops.hpp:460</div></div>
@@ -496,16 +502,16 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>returns predicted values as vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00465" name="l00465"></a><span class="lineno">  465</span>                                                            {</div>
-<div class="line"><a id="l00466" name="l00466"></a><span class="lineno">  466</span>        <span class="comment">// Store predicted values</span></div>
-<div class="line"><a id="l00467" name="l00467"></a><span class="lineno">  467</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; predicted_batch(</div>
-<div class="line"><a id="l00468" name="l00468"></a><span class="lineno">  468</span>            X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());</div>
-<div class="line"><a id="l00469" name="l00469"></a><span class="lineno">  469</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {  <span class="comment">// For every sample</span></div>
-<div class="line"><a id="l00470" name="l00470"></a><span class="lineno">  470</span>            <span class="comment">// Push predicted values</span></div>
-<div class="line"><a id="l00471" name="l00471"></a><span class="lineno">  471</span>            predicted_batch[i] = this-&gt;<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a3b9eac1824d365dce715fb17c33cb96f">single_predict</a>(X[i]);</div>
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-<div class="line"><a id="l00473" name="l00473"></a><span class="lineno">  473</span>        <span class="keywordflow">return</span> predicted_batch;  <span class="comment">// Return predicted values</span></div>
-<div class="line"><a id="l00474" name="l00474"></a><span class="lineno">  474</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  465</span>                                                            {</div>
+<div class="line"><span class="lineno">  466</span>        <span class="comment">// Store predicted values</span></div>
+<div class="line"><span class="lineno">  467</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; predicted_batch(</div>
+<div class="line"><span class="lineno">  468</span>            X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());</div>
+<div class="line"><span class="lineno">  469</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {  <span class="comment">// For every sample</span></div>
+<div class="line"><span class="lineno">  470</span>            <span class="comment">// Push predicted values</span></div>
+<div class="line"><span class="lineno">  471</span>            predicted_batch[i] = this-&gt;<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a3b9eac1824d365dce715fb17c33cb96f">single_predict</a>(X[i]);</div>
+<div class="line"><span class="lineno">  472</span>        }</div>
+<div class="line"><span class="lineno">  473</span>        <span class="keywordflow">return</span> predicted_batch;  <span class="comment">// Return predicted values</span></div>
+<div class="line"><span class="lineno">  474</span>    }</div>
 <div class="ttc" id="aclassmachine__learning_1_1neural__network_1_1_neural_network_html_a3b9eac1824d365dce715fb17c33cb96f"><div class="ttname"><a href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a3b9eac1824d365dce715fb17c33cb96f">machine_learning::neural_network::NeuralNetwork::single_predict</a></div><div class="ttdeci">std::vector&lt; std::valarray&lt; double &gt; &gt; single_predict(const std::vector&lt; std::valarray&lt; double &gt; &gt; &amp;X)</div><div class="ttdef"><b>Definition:</b> neural_network.cpp:451</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -556,29 +562,29 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00607" name="l00607"></a><span class="lineno">  607</span>                                                                      {</div>
-<div class="line"><a id="l00608" name="l00608"></a><span class="lineno">  608</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;INFO: Evaluation Started&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00609" name="l00609"></a><span class="lineno">  609</span>        <span class="keywordtype">double</span> acc = 0, loss = 0;  <span class="comment">// intialize performance metrics with zero</span></div>
-<div class="line"><a id="l00610" name="l00610"></a><span class="lineno">  610</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {  <span class="comment">// For every sample in input</span></div>
-<div class="line"><a id="l00611" name="l00611"></a><span class="lineno">  611</span>            <span class="comment">// Get predictions</span></div>
-<div class="line"><a id="l00612" name="l00612"></a><span class="lineno">  612</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; pred =</div>
-<div class="line"><a id="l00613" name="l00613"></a><span class="lineno">  613</span>                this-&gt;<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a3b9eac1824d365dce715fb17c33cb96f">single_predict</a>(X[i]);</div>
-<div class="line"><a id="l00614" name="l00614"></a><span class="lineno">  614</span>            <span class="comment">// If predicted class is correct</span></div>
-<div class="line"><a id="l00615" name="l00615"></a><span class="lineno">  615</span>            <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a50480fccfb39de20ca47f1bf51ecb6ec">argmax</a>(pred) == <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a50480fccfb39de20ca47f1bf51ecb6ec">argmax</a>(Y[i])) {</div>
-<div class="line"><a id="l00616" name="l00616"></a><span class="lineno">  616</span>                acc += 1;  <span class="comment">// Increment accuracy</span></div>
-<div class="line"><a id="l00617" name="l00617"></a><span class="lineno">  617</span>            }</div>
-<div class="line"><a id="l00618" name="l00618"></a><span class="lineno">  618</span>            <span class="comment">// Calculating loss - Mean Squared Error</span></div>
-<div class="line"><a id="l00619" name="l00619"></a><span class="lineno">  619</span>            loss += <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ad0bdc88e5f1be47c46c0f0c8ebf754bb">apply_function</a>((Y[i] - pred),</div>
-<div class="line"><a id="l00620" name="l00620"></a><span class="lineno">  620</span>                                       neural_network::util_functions::square) *</div>
-<div class="line"><a id="l00621" name="l00621"></a><span class="lineno">  621</span>                        0.5);</div>
-<div class="line"><a id="l00622" name="l00622"></a><span class="lineno">  622</span>        }</div>
-<div class="line"><a id="l00623" name="l00623"></a><span class="lineno">  623</span>        acc /= X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();   <span class="comment">// Averaging accuracy</span></div>
-<div class="line"><a id="l00624" name="l00624"></a><span class="lineno">  624</span>        loss /= X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();  <span class="comment">// Averaging loss</span></div>
-<div class="line"><a id="l00625" name="l00625"></a><span class="lineno">  625</span>        <span class="comment">// Prinitng performance of the model</span></div>
-<div class="line"><a id="l00626" name="l00626"></a><span class="lineno">  626</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Evaluation: Loss: &quot;</span> &lt;&lt; loss;</div>
-<div class="line"><a id="l00627" name="l00627"></a><span class="lineno">  627</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;, Accuracy: &quot;</span> &lt;&lt; acc &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00628" name="l00628"></a><span class="lineno">  628</span>        <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00629" name="l00629"></a><span class="lineno">  629</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  607</span>                                                                      {</div>
+<div class="line"><span class="lineno">  608</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;INFO: Evaluation Started&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  609</span>        <span class="keywordtype">double</span> acc = 0, loss = 0;  <span class="comment">// intialize performance metrics with zero</span></div>
+<div class="line"><span class="lineno">  610</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {  <span class="comment">// For every sample in input</span></div>
+<div class="line"><span class="lineno">  611</span>            <span class="comment">// Get predictions</span></div>
+<div class="line"><span class="lineno">  612</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; pred =</div>
+<div class="line"><span class="lineno">  613</span>                this-&gt;<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a3b9eac1824d365dce715fb17c33cb96f">single_predict</a>(X[i]);</div>
+<div class="line"><span class="lineno">  614</span>            <span class="comment">// If predicted class is correct</span></div>
+<div class="line"><span class="lineno">  615</span>            <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a50480fccfb39de20ca47f1bf51ecb6ec">argmax</a>(pred) == <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a50480fccfb39de20ca47f1bf51ecb6ec">argmax</a>(Y[i])) {</div>
+<div class="line"><span class="lineno">  616</span>                acc += 1;  <span class="comment">// Increment accuracy</span></div>
+<div class="line"><span class="lineno">  617</span>            }</div>
+<div class="line"><span class="lineno">  618</span>            <span class="comment">// Calculating loss - Mean Squared Error</span></div>
+<div class="line"><span class="lineno">  619</span>            loss += <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ad0bdc88e5f1be47c46c0f0c8ebf754bb">apply_function</a>((Y[i] - pred),</div>
+<div class="line"><span class="lineno">  620</span>                                       neural_network::util_functions::square) *</div>
+<div class="line"><span class="lineno">  621</span>                        0.5);</div>
+<div class="line"><span class="lineno">  622</span>        }</div>
+<div class="line"><span class="lineno">  623</span>        acc /= X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();   <span class="comment">// Averaging accuracy</span></div>
+<div class="line"><span class="lineno">  624</span>        loss /= X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();  <span class="comment">// Averaging loss</span></div>
+<div class="line"><span class="lineno">  625</span>        <span class="comment">// Prinitng performance of the model</span></div>
+<div class="line"><span class="lineno">  626</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Evaluation: Loss: &quot;</span> &lt;&lt; loss;</div>
+<div class="line"><span class="lineno">  627</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;, Accuracy: &quot;</span> &lt;&lt; acc &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  628</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  629</span>    }</div>
 <div class="ttc" id="anamespacemachine__learning_html_a50480fccfb39de20ca47f1bf51ecb6ec"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a50480fccfb39de20ca47f1bf51ecb6ec">machine_learning::argmax</a></div><div class="ttdeci">size_t argmax(const std::vector&lt; std::valarray&lt; T &gt; &gt; &amp;A)</div><div class="ttdef"><b>Definition:</b> vector_ops.hpp:307</div></div>
 <div class="ttc" id="anamespacemachine__learning_html_a6f1c98c016ad34ff3d9f39372161bd35"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">machine_learning::sum</a></div><div class="ttdeci">T sum(const std::vector&lt; std::valarray&lt; T &gt; &gt; &amp;A)</div><div class="ttdef"><b>Definition:</b> vector_ops.hpp:232</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -644,14 +650,14 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00639" name="l00639"></a><span class="lineno">  639</span>                                                                             {</div>
-<div class="line"><a id="l00640" name="l00640"></a><span class="lineno">  640</span>        <span class="comment">// Getting training data from csv file</span></div>
-<div class="line"><a id="l00641" name="l00641"></a><span class="lineno">  641</span>        <span class="keyword">auto</span> <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a> =</div>
-<div class="line"><a id="l00642" name="l00642"></a><span class="lineno">  642</span>            this-&gt;<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a650c677fd6512665741ddd9b7983275d">get_XY_from_csv</a>(file_name, last_label, normalize, slip_lines);</div>
-<div class="line"><a id="l00643" name="l00643"></a><span class="lineno">  643</span>        <span class="comment">// Evaluating model</span></div>
-<div class="line"><a id="l00644" name="l00644"></a><span class="lineno">  644</span>        this-&gt;<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#aec648ea4f40bd71123b5f907a681dd8e">evaluate</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>.first, <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>.second);</div>
-<div class="line"><a id="l00645" name="l00645"></a><span class="lineno">  645</span>        <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00646" name="l00646"></a><span class="lineno">  646</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  639</span>                                                                             {</div>
+<div class="line"><span class="lineno">  640</span>        <span class="comment">// Getting training data from csv file</span></div>
+<div class="line"><span class="lineno">  641</span>        <span class="keyword">auto</span> <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a> =</div>
+<div class="line"><span class="lineno">  642</span>            this-&gt;<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a650c677fd6512665741ddd9b7983275d">get_XY_from_csv</a>(file_name, last_label, normalize, slip_lines);</div>
+<div class="line"><span class="lineno">  643</span>        <span class="comment">// Evaluating model</span></div>
+<div class="line"><span class="lineno">  644</span>        this-&gt;<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#aec648ea4f40bd71123b5f907a681dd8e">evaluate</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>.first, <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>.second);</div>
+<div class="line"><span class="lineno">  645</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  646</span>    }</div>
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 <div class="ttc" id="ahash__search_8cpp_html_a6e1a77282bc65ad359d753d25df23243"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a></div><div class="ttdeci">int data[MAX]</div><div class="ttdoc">test data</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:24</div></div>
@@ -732,93 +738,93 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
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-<div class="fragment"><div class="line"><a id="l00488" name="l00488"></a><span class="lineno">  488</span>                                                                        {</div>
-<div class="line"><a id="l00489" name="l00489"></a><span class="lineno">  489</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; X = X_, Y = Y_;</div>
-<div class="line"><a id="l00490" name="l00490"></a><span class="lineno">  490</span>        <span class="comment">// Both label and input data should have same size</span></div>
-<div class="line"><a id="l00491" name="l00491"></a><span class="lineno">  491</span>        <span class="keywordflow">if</span> (X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() != Y.size()) {</div>
-<div class="line"><a id="l00492" name="l00492"></a><span class="lineno">  492</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
-<div class="line"><a id="l00493" name="l00493"></a><span class="lineno">  493</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;X and Y in fit have different sizes&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00494" name="l00494"></a><span class="lineno">  494</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
-<div class="line"><a id="l00495" name="l00495"></a><span class="lineno">  495</span>        }</div>
-<div class="line"><a id="l00496" name="l00496"></a><span class="lineno">  496</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;INFO: Training Started&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00497" name="l00497"></a><span class="lineno">  497</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> epoch = 1; epoch &lt;= epochs; epoch++) {  <span class="comment">// For every epoch</span></div>
-<div class="line"><a id="l00498" name="l00498"></a><span class="lineno">  498</span>            <span class="comment">// Shuffle X and Y if flag is set</span></div>
-<div class="line"><a id="l00499" name="l00499"></a><span class="lineno">  499</span>            <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d5/d91/namespacesorting.html#a7bfe11bd4703eacd1dab93f25ec639c5">shuffle</a>) {</div>
-<div class="line"><a id="l00500" name="l00500"></a><span class="lineno">  500</span>                <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#af801bf30591ca6b2c38ff4fed0ded23f">equal_shuffle</a>(X, Y);</div>
-<div class="line"><a id="l00501" name="l00501"></a><span class="lineno">  501</span>            }</div>
-<div class="line"><a id="l00502" name="l00502"></a><span class="lineno">  502</span>            <span class="keyword">auto</span> start =</div>
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-<div class="line"><a id="l00504" name="l00504"></a><span class="lineno">  504</span>            <span class="keywordtype">double</span> loss = 0,</div>
-<div class="line"><a id="l00505" name="l00505"></a><span class="lineno">  505</span>                   acc = 0;  <span class="comment">// Intialize performance metrics with zero</span></div>
-<div class="line"><a id="l00506" name="l00506"></a><span class="lineno">  506</span>            <span class="comment">// For each starting index of batch</span></div>
-<div class="line"><a id="l00507" name="l00507"></a><span class="lineno">  507</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> batch_start = 0; batch_start &lt; X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
-<div class="line"><a id="l00508" name="l00508"></a><span class="lineno">  508</span>                 batch_start += batch_size) {</div>
-<div class="line"><a id="l00509" name="l00509"></a><span class="lineno">  509</span>                <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = batch_start;</div>
-<div class="line"><a id="l00510" name="l00510"></a><span class="lineno">  510</span>                     i &lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(), batch_start + batch_size); i++) {</div>
-<div class="line"><a id="l00511" name="l00511"></a><span class="lineno">  511</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; grad, cur_error,</div>
-<div class="line"><a id="l00512" name="l00512"></a><span class="lineno">  512</span>                        predicted;</div>
-<div class="line"><a id="l00513" name="l00513"></a><span class="lineno">  513</span>                    <span class="keyword">auto</span> <a class="code hl_namespace" href="../../d5/d39/namespaceactivations.html">activations</a> = this-&gt;<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a361a45f3c3d8347d79103bf182d0570b">__detailed_single_prediction</a>(X[i]);</div>
-<div class="line"><a id="l00514" name="l00514"></a><span class="lineno">  514</span>                    <span class="comment">// Gradients vector to store gradients for all layers</span></div>
-<div class="line"><a id="l00515" name="l00515"></a><span class="lineno">  515</span>                    <span class="comment">// They will be averaged and applied to kernel</span></div>
-<div class="line"><a id="l00516" name="l00516"></a><span class="lineno">  516</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; gradients;</div>
-<div class="line"><a id="l00517" name="l00517"></a><span class="lineno">  517</span>                    gradients.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/resize.html">resize</a>(this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>.size());</div>
-<div class="line"><a id="l00518" name="l00518"></a><span class="lineno">  518</span>                    <span class="comment">// First intialize gradients to zero</span></div>
-<div class="line"><a id="l00519" name="l00519"></a><span class="lineno">  519</span>                    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; gradients.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
-<div class="line"><a id="l00520" name="l00520"></a><span class="lineno">  520</span>                        <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ac1bdaa2a724b4ce6a6bb371a5dbe2e7e">zeroes_initialization</a>(</div>
-<div class="line"><a id="l00521" name="l00521"></a><span class="lineno">  521</span>                            gradients[i], <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>[i].kernel));</div>
-<div class="line"><a id="l00522" name="l00522"></a><span class="lineno">  522</span>                    }</div>
-<div class="line"><a id="l00523" name="l00523"></a><span class="lineno">  523</span>                    predicted = <a class="code hl_namespace" href="../../d5/d39/namespaceactivations.html">activations</a>.back();  <span class="comment">// Predicted vector</span></div>
-<div class="line"><a id="l00524" name="l00524"></a><span class="lineno">  524</span>                    cur_error = predicted - Y[i];    <span class="comment">// Absoulute error</span></div>
-<div class="line"><a id="l00525" name="l00525"></a><span class="lineno">  525</span>                    <span class="comment">// Calculating loss with MSE</span></div>
-<div class="line"><a id="l00526" name="l00526"></a><span class="lineno">  526</span>                    loss += <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ad0bdc88e5f1be47c46c0f0c8ebf754bb">apply_function</a>(</div>
-<div class="line"><a id="l00527" name="l00527"></a><span class="lineno">  527</span>                        cur_error, neural_network::util_functions::square));</div>
-<div class="line"><a id="l00528" name="l00528"></a><span class="lineno">  528</span>                    <span class="comment">// If prediction is correct</span></div>
-<div class="line"><a id="l00529" name="l00529"></a><span class="lineno">  529</span>                    <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a50480fccfb39de20ca47f1bf51ecb6ec">argmax</a>(predicted) == <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a50480fccfb39de20ca47f1bf51ecb6ec">argmax</a>(Y[i])) {</div>
-<div class="line"><a id="l00530" name="l00530"></a><span class="lineno">  530</span>                        acc += 1;</div>
-<div class="line"><a id="l00531" name="l00531"></a><span class="lineno">  531</span>                    }</div>
-<div class="line"><a id="l00532" name="l00532"></a><span class="lineno">  532</span>                    <span class="comment">// For every layer (except first) starting from last one</span></div>
-<div class="line"><a id="l00533" name="l00533"></a><span class="lineno">  533</span>                    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>.size() - 1; j &gt;= 1; j--) {</div>
-<div class="line"><a id="l00534" name="l00534"></a><span class="lineno">  534</span>                        <span class="comment">// Backpropogating errors</span></div>
-<div class="line"><a id="l00535" name="l00535"></a><span class="lineno">  535</span>                        cur_error = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#acafa3e62b686aebdbad81c4f89913f43">hadamard_product</a>(</div>
-<div class="line"><a id="l00536" name="l00536"></a><span class="lineno">  536</span>                            cur_error,</div>
-<div class="line"><a id="l00537" name="l00537"></a><span class="lineno">  537</span>                            <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ad0bdc88e5f1be47c46c0f0c8ebf754bb">apply_function</a>(</div>
-<div class="line"><a id="l00538" name="l00538"></a><span class="lineno">  538</span>                                <a class="code hl_namespace" href="../../d5/d39/namespaceactivations.html">activations</a>[j + 1],</div>
-<div class="line"><a id="l00539" name="l00539"></a><span class="lineno">  539</span>                                this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>[j].dactivation_function));</div>
-<div class="line"><a id="l00540" name="l00540"></a><span class="lineno">  540</span>                        <span class="comment">// Calculating gradient for current layer</span></div>
-<div class="line"><a id="l00541" name="l00541"></a><span class="lineno">  541</span>                        grad = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a5342906d42b80fc6b6b3ad17bf00fcb9">multiply</a>(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a89fde571b38f9483576594f66572958a">transpose</a>(<a class="code hl_namespace" href="../../d5/d39/namespaceactivations.html">activations</a>[j]), cur_error);</div>
-<div class="line"><a id="l00542" name="l00542"></a><span class="lineno">  542</span>                        <span class="comment">// Change error according to current kernel values</span></div>
-<div class="line"><a id="l00543" name="l00543"></a><span class="lineno">  543</span>                        cur_error = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a5342906d42b80fc6b6b3ad17bf00fcb9">multiply</a>(cur_error,</div>
-<div class="line"><a id="l00544" name="l00544"></a><span class="lineno">  544</span>                                             <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a89fde571b38f9483576594f66572958a">transpose</a>(this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>[j].kernel));</div>
-<div class="line"><a id="l00545" name="l00545"></a><span class="lineno">  545</span>                        <span class="comment">// Adding gradient values to collection of gradients</span></div>
-<div class="line"><a id="l00546" name="l00546"></a><span class="lineno">  546</span>                        gradients[j] = gradients[j] + grad / double(batch_size);</div>
-<div class="line"><a id="l00547" name="l00547"></a><span class="lineno">  547</span>                    }</div>
-<div class="line"><a id="l00548" name="l00548"></a><span class="lineno">  548</span>                    <span class="comment">// Applying gradients</span></div>
-<div class="line"><a id="l00549" name="l00549"></a><span class="lineno">  549</span>                    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>.size() - 1; j &gt;= 1; j--) {</div>
-<div class="line"><a id="l00550" name="l00550"></a><span class="lineno">  550</span>                        <span class="comment">// Updating kernel (aka weights)</span></div>
-<div class="line"><a id="l00551" name="l00551"></a><span class="lineno">  551</span>                        this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>[j].kernel = this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>[j].kernel -</div>
-<div class="line"><a id="l00552" name="l00552"></a><span class="lineno">  552</span>                                                 gradients[j] * learning_rate;</div>
-<div class="line"><a id="l00553" name="l00553"></a><span class="lineno">  553</span>                    }</div>
-<div class="line"><a id="l00554" name="l00554"></a><span class="lineno">  554</span>                }</div>
-<div class="line"><a id="l00555" name="l00555"></a><span class="lineno">  555</span>            }</div>
-<div class="line"><a id="l00556" name="l00556"></a><span class="lineno">  556</span>            <span class="keyword">auto</span> stop =</div>
-<div class="line"><a id="l00557" name="l00557"></a><span class="lineno">  557</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/high_resolution_clock/now.html">std::chrono::high_resolution_clock::now</a>();  <span class="comment">// Stoping the clock</span></div>
-<div class="line"><a id="l00558" name="l00558"></a><span class="lineno">  558</span>            <span class="comment">// Calculate time taken by epoch</span></div>
-<div class="line"><a id="l00559" name="l00559"></a><span class="lineno">  559</span>            <span class="keyword">auto</span> duration =</div>
-<div class="line"><a id="l00560" name="l00560"></a><span class="lineno">  560</span>                std::chrono::duration_cast&lt;std::chrono::microseconds&gt;(stop -</div>
-<div class="line"><a id="l00561" name="l00561"></a><span class="lineno">  561</span>                                                                      start);</div>
-<div class="line"><a id="l00562" name="l00562"></a><span class="lineno">  562</span>            loss /= X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();        <span class="comment">// Averaging loss</span></div>
-<div class="line"><a id="l00563" name="l00563"></a><span class="lineno">  563</span>            acc /= X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();         <span class="comment">// Averaging accuracy</span></div>
-<div class="line"><a id="l00564" name="l00564"></a><span class="lineno">  564</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>.precision(4);  <span class="comment">// set output precision to 4</span></div>
-<div class="line"><a id="l00565" name="l00565"></a><span class="lineno">  565</span>            <span class="comment">// Printing training stats</span></div>
-<div class="line"><a id="l00566" name="l00566"></a><span class="lineno">  566</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Training: Epoch &quot;</span> &lt;&lt; epoch &lt;&lt; <span class="charliteral">&#39;/&#39;</span> &lt;&lt; epochs;</div>
-<div class="line"><a id="l00567" name="l00567"></a><span class="lineno">  567</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;, Loss: &quot;</span> &lt;&lt; loss;</div>
-<div class="line"><a id="l00568" name="l00568"></a><span class="lineno">  568</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;, Accuracy: &quot;</span> &lt;&lt; acc;</div>
-<div class="line"><a id="l00569" name="l00569"></a><span class="lineno">  569</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;, Taken time: &quot;</span> &lt;&lt; duration.count() / 1e6</div>
-<div class="line"><a id="l00570" name="l00570"></a><span class="lineno">  570</span>                      &lt;&lt; <span class="stringliteral">&quot; seconds&quot;</span>;</div>
-<div class="line"><a id="l00571" name="l00571"></a><span class="lineno">  571</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00572" name="l00572"></a><span class="lineno">  572</span>        }</div>
-<div class="line"><a id="l00573" name="l00573"></a><span class="lineno">  573</span>        <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00574" name="l00574"></a><span class="lineno">  574</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  488</span>                                                                        {</div>
+<div class="line"><span class="lineno">  489</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; X = X_, Y = Y_;</div>
+<div class="line"><span class="lineno">  490</span>        <span class="comment">// Both label and input data should have same size</span></div>
+<div class="line"><span class="lineno">  491</span>        <span class="keywordflow">if</span> (X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() != Y.size()) {</div>
+<div class="line"><span class="lineno">  492</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
+<div class="line"><span class="lineno">  493</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;X and Y in fit have different sizes&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  494</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><span class="lineno">  495</span>        }</div>
+<div class="line"><span class="lineno">  496</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;INFO: Training Started&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  497</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> epoch = 1; epoch &lt;= epochs; epoch++) {  <span class="comment">// For every epoch</span></div>
+<div class="line"><span class="lineno">  498</span>            <span class="comment">// Shuffle X and Y if flag is set</span></div>
+<div class="line"><span class="lineno">  499</span>            <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d5/d91/namespacesorting.html#a7bfe11bd4703eacd1dab93f25ec639c5">shuffle</a>) {</div>
+<div class="line"><span class="lineno">  500</span>                <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#af801bf30591ca6b2c38ff4fed0ded23f">equal_shuffle</a>(X, Y);</div>
+<div class="line"><span class="lineno">  501</span>            }</div>
+<div class="line"><span class="lineno">  502</span>            <span class="keyword">auto</span> start =</div>
+<div class="line"><span class="lineno">  503</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/high_resolution_clock/now.html">std::chrono::high_resolution_clock::now</a>();  <span class="comment">// Start clock</span></div>
+<div class="line"><span class="lineno">  504</span>            <span class="keywordtype">double</span> loss = 0,</div>
+<div class="line"><span class="lineno">  505</span>                   acc = 0;  <span class="comment">// Intialize performance metrics with zero</span></div>
+<div class="line"><span class="lineno">  506</span>            <span class="comment">// For each starting index of batch</span></div>
+<div class="line"><span class="lineno">  507</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> batch_start = 0; batch_start &lt; X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">  508</span>                 batch_start += batch_size) {</div>
+<div class="line"><span class="lineno">  509</span>                <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = batch_start;</div>
+<div class="line"><span class="lineno">  510</span>                     i &lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(), batch_start + batch_size); i++) {</div>
+<div class="line"><span class="lineno">  511</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; grad, cur_error,</div>
+<div class="line"><span class="lineno">  512</span>                        predicted;</div>
+<div class="line"><span class="lineno">  513</span>                    <span class="keyword">auto</span> <a class="code hl_namespace" href="../../d5/d39/namespaceactivations.html">activations</a> = this-&gt;<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a361a45f3c3d8347d79103bf182d0570b">__detailed_single_prediction</a>(X[i]);</div>
+<div class="line"><span class="lineno">  514</span>                    <span class="comment">// Gradients vector to store gradients for all layers</span></div>
+<div class="line"><span class="lineno">  515</span>                    <span class="comment">// They will be averaged and applied to kernel</span></div>
+<div class="line"><span class="lineno">  516</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; gradients;</div>
+<div class="line"><span class="lineno">  517</span>                    gradients.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/resize.html">resize</a>(this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>.size());</div>
+<div class="line"><span class="lineno">  518</span>                    <span class="comment">// First intialize gradients to zero</span></div>
+<div class="line"><span class="lineno">  519</span>                    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; gradients.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
+<div class="line"><span class="lineno">  520</span>                        <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ac1bdaa2a724b4ce6a6bb371a5dbe2e7e">zeroes_initialization</a>(</div>
+<div class="line"><span class="lineno">  521</span>                            gradients[i], <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>[i].kernel));</div>
+<div class="line"><span class="lineno">  522</span>                    }</div>
+<div class="line"><span class="lineno">  523</span>                    predicted = <a class="code hl_namespace" href="../../d5/d39/namespaceactivations.html">activations</a>.back();  <span class="comment">// Predicted vector</span></div>
+<div class="line"><span class="lineno">  524</span>                    cur_error = predicted - Y[i];    <span class="comment">// Absoulute error</span></div>
+<div class="line"><span class="lineno">  525</span>                    <span class="comment">// Calculating loss with MSE</span></div>
+<div class="line"><span class="lineno">  526</span>                    loss += <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ad0bdc88e5f1be47c46c0f0c8ebf754bb">apply_function</a>(</div>
+<div class="line"><span class="lineno">  527</span>                        cur_error, neural_network::util_functions::square));</div>
+<div class="line"><span class="lineno">  528</span>                    <span class="comment">// If prediction is correct</span></div>
+<div class="line"><span class="lineno">  529</span>                    <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a50480fccfb39de20ca47f1bf51ecb6ec">argmax</a>(predicted) == <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a50480fccfb39de20ca47f1bf51ecb6ec">argmax</a>(Y[i])) {</div>
+<div class="line"><span class="lineno">  530</span>                        acc += 1;</div>
+<div class="line"><span class="lineno">  531</span>                    }</div>
+<div class="line"><span class="lineno">  532</span>                    <span class="comment">// For every layer (except first) starting from last one</span></div>
+<div class="line"><span class="lineno">  533</span>                    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>.size() - 1; j &gt;= 1; j--) {</div>
+<div class="line"><span class="lineno">  534</span>                        <span class="comment">// Backpropogating errors</span></div>
+<div class="line"><span class="lineno">  535</span>                        cur_error = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#acafa3e62b686aebdbad81c4f89913f43">hadamard_product</a>(</div>
+<div class="line"><span class="lineno">  536</span>                            cur_error,</div>
+<div class="line"><span class="lineno">  537</span>                            <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ad0bdc88e5f1be47c46c0f0c8ebf754bb">apply_function</a>(</div>
+<div class="line"><span class="lineno">  538</span>                                <a class="code hl_namespace" href="../../d5/d39/namespaceactivations.html">activations</a>[j + 1],</div>
+<div class="line"><span class="lineno">  539</span>                                this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>[j].dactivation_function));</div>
+<div class="line"><span class="lineno">  540</span>                        <span class="comment">// Calculating gradient for current layer</span></div>
+<div class="line"><span class="lineno">  541</span>                        grad = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a5342906d42b80fc6b6b3ad17bf00fcb9">multiply</a>(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a89fde571b38f9483576594f66572958a">transpose</a>(<a class="code hl_namespace" href="../../d5/d39/namespaceactivations.html">activations</a>[j]), cur_error);</div>
+<div class="line"><span class="lineno">  542</span>                        <span class="comment">// Change error according to current kernel values</span></div>
+<div class="line"><span class="lineno">  543</span>                        cur_error = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a5342906d42b80fc6b6b3ad17bf00fcb9">multiply</a>(cur_error,</div>
+<div class="line"><span class="lineno">  544</span>                                             <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a89fde571b38f9483576594f66572958a">transpose</a>(this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>[j].kernel));</div>
+<div class="line"><span class="lineno">  545</span>                        <span class="comment">// Adding gradient values to collection of gradients</span></div>
+<div class="line"><span class="lineno">  546</span>                        gradients[j] = gradients[j] + grad / double(batch_size);</div>
+<div class="line"><span class="lineno">  547</span>                    }</div>
+<div class="line"><span class="lineno">  548</span>                    <span class="comment">// Applying gradients</span></div>
+<div class="line"><span class="lineno">  549</span>                    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>.size() - 1; j &gt;= 1; j--) {</div>
+<div class="line"><span class="lineno">  550</span>                        <span class="comment">// Updating kernel (aka weights)</span></div>
+<div class="line"><span class="lineno">  551</span>                        this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>[j].kernel = this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>[j].kernel -</div>
+<div class="line"><span class="lineno">  552</span>                                                 gradients[j] * learning_rate;</div>
+<div class="line"><span class="lineno">  553</span>                    }</div>
+<div class="line"><span class="lineno">  554</span>                }</div>
+<div class="line"><span class="lineno">  555</span>            }</div>
+<div class="line"><span class="lineno">  556</span>            <span class="keyword">auto</span> stop =</div>
+<div class="line"><span class="lineno">  557</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/high_resolution_clock/now.html">std::chrono::high_resolution_clock::now</a>();  <span class="comment">// Stoping the clock</span></div>
+<div class="line"><span class="lineno">  558</span>            <span class="comment">// Calculate time taken by epoch</span></div>
+<div class="line"><span class="lineno">  559</span>            <span class="keyword">auto</span> duration =</div>
+<div class="line"><span class="lineno">  560</span>                std::chrono::duration_cast&lt;std::chrono::microseconds&gt;(stop -</div>
+<div class="line"><span class="lineno">  561</span>                                                                      start);</div>
+<div class="line"><span class="lineno">  562</span>            loss /= X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();        <span class="comment">// Averaging loss</span></div>
+<div class="line"><span class="lineno">  563</span>            acc /= X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();         <span class="comment">// Averaging accuracy</span></div>
+<div class="line"><span class="lineno">  564</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>.precision(4);  <span class="comment">// set output precision to 4</span></div>
+<div class="line"><span class="lineno">  565</span>            <span class="comment">// Printing training stats</span></div>
+<div class="line"><span class="lineno">  566</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Training: Epoch &quot;</span> &lt;&lt; epoch &lt;&lt; <span class="charliteral">&#39;/&#39;</span> &lt;&lt; epochs;</div>
+<div class="line"><span class="lineno">  567</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;, Loss: &quot;</span> &lt;&lt; loss;</div>
+<div class="line"><span class="lineno">  568</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;, Accuracy: &quot;</span> &lt;&lt; acc;</div>
+<div class="line"><span class="lineno">  569</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;, Taken time: &quot;</span> &lt;&lt; duration.count() / 1e6</div>
+<div class="line"><span class="lineno">  570</span>                      &lt;&lt; <span class="stringliteral">&quot; seconds&quot;</span>;</div>
+<div class="line"><span class="lineno">  571</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  572</span>        }</div>
+<div class="line"><span class="lineno">  573</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  574</span>    }</div>
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 <div class="ttc" id="amin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a></div><div class="ttdeci">T min(T... args)</div></div>
 <div class="ttc" id="anamespaceactivations_html"><div class="ttname"><a href="../../d5/d39/namespaceactivations.html">activations</a></div><div class="ttdoc">Various activation functions used in Neural network.</div></div>
@@ -921,15 +927,15 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00591" name="l00591"></a><span class="lineno">  591</span>                                                  {</div>
-<div class="line"><a id="l00592" name="l00592"></a><span class="lineno">  592</span>        <span class="comment">// Getting training data from csv file</span></div>
-<div class="line"><a id="l00593" name="l00593"></a><span class="lineno">  593</span>        <span class="keyword">auto</span> <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a> =</div>
-<div class="line"><a id="l00594" name="l00594"></a><span class="lineno">  594</span>            this-&gt;<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a650c677fd6512665741ddd9b7983275d">get_XY_from_csv</a>(file_name, last_label, normalize, slip_lines);</div>
-<div class="line"><a id="l00595" name="l00595"></a><span class="lineno">  595</span>        <span class="comment">// Fit the model on training data</span></div>
-<div class="line"><a id="l00596" name="l00596"></a><span class="lineno">  596</span>        this-&gt;<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a2be1b52bb9f57486f9a436f35c9089c0">fit</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>.first, <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>.second, epochs, learning_rate, batch_size,</div>
-<div class="line"><a id="l00597" name="l00597"></a><span class="lineno">  597</span>                  <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a7bfe11bd4703eacd1dab93f25ec639c5">shuffle</a>);</div>
-<div class="line"><a id="l00598" name="l00598"></a><span class="lineno">  598</span>        <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00599" name="l00599"></a><span class="lineno">  599</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  591</span>                                                  {</div>
+<div class="line"><span class="lineno">  592</span>        <span class="comment">// Getting training data from csv file</span></div>
+<div class="line"><span class="lineno">  593</span>        <span class="keyword">auto</span> <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a> =</div>
+<div class="line"><span class="lineno">  594</span>            this-&gt;<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a650c677fd6512665741ddd9b7983275d">get_XY_from_csv</a>(file_name, last_label, normalize, slip_lines);</div>
+<div class="line"><span class="lineno">  595</span>        <span class="comment">// Fit the model on training data</span></div>
+<div class="line"><span class="lineno">  596</span>        this-&gt;<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a2be1b52bb9f57486f9a436f35c9089c0">fit</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>.first, <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>.second, epochs, learning_rate, batch_size,</div>
+<div class="line"><span class="lineno">  597</span>                  <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a7bfe11bd4703eacd1dab93f25ec639c5">shuffle</a>);</div>
+<div class="line"><span class="lineno">  598</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  599</span>    }</div>
 <div class="ttc" id="aclassmachine__learning_1_1neural__network_1_1_neural_network_html_a2be1b52bb9f57486f9a436f35c9089c0"><div class="ttname"><a href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a2be1b52bb9f57486f9a436f35c9089c0">machine_learning::neural_network::NeuralNetwork::fit</a></div><div class="ttdeci">void fit(const std::vector&lt; std::vector&lt; std::valarray&lt; double &gt; &gt; &gt; &amp;X_, const std::vector&lt; std::vector&lt; std::valarray&lt; double &gt; &gt; &gt; &amp;Y_, const int &amp;epochs=100, const double &amp;learning_rate=0.01, const size_t &amp;batch_size=32, const bool &amp;shuffle=true)</div><div class="ttdef"><b>Definition:</b> neural_network.cpp:485</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -995,68 +1001,68 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>returns pair of X and Y </dd></dl>
-<div class="fragment"><div class="line"><a id="l00383" name="l00383"></a><span class="lineno">  383</span>                                                                      {</div>
-<div class="line"><a id="l00384" name="l00384"></a><span class="lineno">  384</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ifstream.html">std::ifstream</a> in_file;                          <span class="comment">// Ifstream to read file</span></div>
-<div class="line"><a id="l00385" name="l00385"></a><span class="lineno">  385</span>        in_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ifstream/open.html">open</a>(file_name.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/c_str.html">c_str</a>(), std::ios::in);  <span class="comment">// Open file</span></div>
-<div class="line"><a id="l00386" name="l00386"></a><span class="lineno">  386</span>        <span class="comment">// If there is any problem in opening file</span></div>
-<div class="line"><a id="l00387" name="l00387"></a><span class="lineno">  387</span>        <span class="keywordflow">if</span> (!in_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ifstream/is_open.html">is_open</a>()) {</div>
-<div class="line"><a id="l00388" name="l00388"></a><span class="lineno">  388</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
-<div class="line"><a id="l00389" name="l00389"></a><span class="lineno">  389</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Unable to open file: &quot;</span> &lt;&lt; file_name &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00390" name="l00390"></a><span class="lineno">  390</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
-<div class="line"><a id="l00391" name="l00391"></a><span class="lineno">  391</span>        }</div>
-<div class="line"><a id="l00392" name="l00392"></a><span class="lineno">  392</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; X,</div>
-<div class="line"><a id="l00393" name="l00393"></a><span class="lineno">  393</span>            Y;             <span class="comment">// To store X and Y</span></div>
-<div class="line"><a id="l00394" name="l00394"></a><span class="lineno">  394</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> line;  <span class="comment">// To store each line</span></div>
-<div class="line"><a id="l00395" name="l00395"></a><span class="lineno">  395</span>        <span class="comment">// Skip lines</span></div>
-<div class="line"><a id="l00396" name="l00396"></a><span class="lineno">  396</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; slip_lines; i++) {</div>
-<div class="line"><a id="l00397" name="l00397"></a><span class="lineno">  397</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/getline.html">std::getline</a>(in_file, line, <span class="charliteral">&#39;\n&#39;</span>);  <span class="comment">// Ignore line</span></div>
-<div class="line"><a id="l00398" name="l00398"></a><span class="lineno">  398</span>        }</div>
-<div class="line"><a id="l00399" name="l00399"></a><span class="lineno">  399</span>        <span class="comment">// While file has information</span></div>
-<div class="line"><a id="l00400" name="l00400"></a><span class="lineno">  400</span>        <span class="keywordflow">while</span> (!in_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ios/eof.html">eof</a>() &amp;&amp; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/getline.html">std::getline</a>(in_file, line, <span class="charliteral">&#39;\n&#39;</span>)) {</div>
-<div class="line"><a id="l00401" name="l00401"></a><span class="lineno">  401</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> x_data,</div>
-<div class="line"><a id="l00402" name="l00402"></a><span class="lineno">  402</span>                y_data;                  <span class="comment">// To store single sample and label</span></div>
-<div class="line"><a id="l00403" name="l00403"></a><span class="lineno">  403</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_stringstream.html">std::stringstream</a> ss(line);  <span class="comment">// Constructing stringstream from line</span></div>
-<div class="line"><a id="l00404" name="l00404"></a><span class="lineno">  404</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> token;  <span class="comment">// To store each token in line (seprated by &#39;,&#39;)</span></div>
-<div class="line"><a id="l00405" name="l00405"></a><span class="lineno">  405</span>            <span class="keywordflow">while</span> (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/getline.html">std::getline</a>(ss, token, <span class="charliteral">&#39;,&#39;</span>)) {  <span class="comment">// For each token</span></div>
-<div class="line"><a id="l00406" name="l00406"></a><span class="lineno">  406</span>                <span class="comment">// Insert numerical value of token in x_data</span></div>
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-<div class="line"><a id="l00409" name="l00409"></a><span class="lineno">  409</span>            <span class="comment">// If label is in last column</span></div>
-<div class="line"><a id="l00410" name="l00410"></a><span class="lineno">  410</span>            <span class="keywordflow">if</span> (last_label) {</div>
-<div class="line"><a id="l00411" name="l00411"></a><span class="lineno">  411</span>                y_data.resize(this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>.back().neurons);</div>
-<div class="line"><a id="l00412" name="l00412"></a><span class="lineno">  412</span>                <span class="comment">// If task is classification</span></div>
-<div class="line"><a id="l00413" name="l00413"></a><span class="lineno">  413</span>                <span class="keywordflow">if</span> (y_data.size() &gt; 1) {</div>
-<div class="line"><a id="l00414" name="l00414"></a><span class="lineno">  414</span>                    y_data[x_data[x_data.size() - 1]] = 1;</div>
-<div class="line"><a id="l00415" name="l00415"></a><span class="lineno">  415</span>                }</div>
-<div class="line"><a id="l00416" name="l00416"></a><span class="lineno">  416</span>                <span class="comment">// If task is regrssion (of single value)</span></div>
-<div class="line"><a id="l00417" name="l00417"></a><span class="lineno">  417</span>                <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00418" name="l00418"></a><span class="lineno">  418</span>                    y_data[0] = x_data[x_data.size() - 1];</div>
-<div class="line"><a id="l00419" name="l00419"></a><span class="lineno">  419</span>                }</div>
-<div class="line"><a id="l00420" name="l00420"></a><span class="lineno">  420</span>                x_data = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ae10178b082f0205c326550877d998e5d">pop_back</a>(x_data);  <span class="comment">// Remove label from x_data</span></div>
-<div class="line"><a id="l00421" name="l00421"></a><span class="lineno">  421</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00422" name="l00422"></a><span class="lineno">  422</span>                y_data.resize(this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>.back().neurons);</div>
-<div class="line"><a id="l00423" name="l00423"></a><span class="lineno">  423</span>                <span class="comment">// If task is classification</span></div>
-<div class="line"><a id="l00424" name="l00424"></a><span class="lineno">  424</span>                <span class="keywordflow">if</span> (y_data.size() &gt; 1) {</div>
-<div class="line"><a id="l00425" name="l00425"></a><span class="lineno">  425</span>                    y_data[x_data[x_data.size() - 1]] = 1;</div>
-<div class="line"><a id="l00426" name="l00426"></a><span class="lineno">  426</span>                }</div>
-<div class="line"><a id="l00427" name="l00427"></a><span class="lineno">  427</span>                <span class="comment">// If task is regrssion (of single value)</span></div>
-<div class="line"><a id="l00428" name="l00428"></a><span class="lineno">  428</span>                <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00429" name="l00429"></a><span class="lineno">  429</span>                    y_data[0] = x_data[x_data.size() - 1];</div>
-<div class="line"><a id="l00430" name="l00430"></a><span class="lineno">  430</span>                }</div>
-<div class="line"><a id="l00431" name="l00431"></a><span class="lineno">  431</span>                x_data = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a912cf68863063a38d6e63545be5eb093">pop_front</a>(x_data);  <span class="comment">// Remove label from x_data</span></div>
-<div class="line"><a id="l00432" name="l00432"></a><span class="lineno">  432</span>            }</div>
-<div class="line"><a id="l00433" name="l00433"></a><span class="lineno">  433</span>            <span class="comment">// Push collected X_data and y_data in X and Y</span></div>
-<div class="line"><a id="l00434" name="l00434"></a><span class="lineno">  434</span>            X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>({x_data});</div>
-<div class="line"><a id="l00435" name="l00435"></a><span class="lineno">  435</span>            Y.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>({y_data});</div>
-<div class="line"><a id="l00436" name="l00436"></a><span class="lineno">  436</span>        }</div>
-<div class="line"><a id="l00437" name="l00437"></a><span class="lineno">  437</span>        <span class="comment">// Normalize training data if flag is set</span></div>
-<div class="line"><a id="l00438" name="l00438"></a><span class="lineno">  438</span>        <span class="keywordflow">if</span> (normalize) {</div>
-<div class="line"><a id="l00439" name="l00439"></a><span class="lineno">  439</span>            <span class="comment">// Scale data between 0 and 1 using min-max scaler</span></div>
-<div class="line"><a id="l00440" name="l00440"></a><span class="lineno">  440</span>            X = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ac332d152078e96311e43ac5e7183ea26">minmax_scaler</a>(X, 0.01, 1.0);</div>
-<div class="line"><a id="l00441" name="l00441"></a><span class="lineno">  441</span>        }</div>
-<div class="line"><a id="l00442" name="l00442"></a><span class="lineno">  442</span>        in_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ifstream/close.html">close</a>();         <span class="comment">// Closing file</span></div>
-<div class="line"><a id="l00443" name="l00443"></a><span class="lineno">  443</span>        <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">make_pair</a>(X, Y);  <span class="comment">// Return pair of X and Y</span></div>
-<div class="line"><a id="l00444" name="l00444"></a><span class="lineno">  444</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  383</span>                                                                      {</div>
+<div class="line"><span class="lineno">  384</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ifstream.html">std::ifstream</a> in_file;                          <span class="comment">// Ifstream to read file</span></div>
+<div class="line"><span class="lineno">  385</span>        in_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ifstream/open.html">open</a>(file_name.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/c_str.html">c_str</a>(), std::ios::in);  <span class="comment">// Open file</span></div>
+<div class="line"><span class="lineno">  386</span>        <span class="comment">// If there is any problem in opening file</span></div>
+<div class="line"><span class="lineno">  387</span>        <span class="keywordflow">if</span> (!in_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ifstream/is_open.html">is_open</a>()) {</div>
+<div class="line"><span class="lineno">  388</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
+<div class="line"><span class="lineno">  389</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Unable to open file: &quot;</span> &lt;&lt; file_name &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  390</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><span class="lineno">  391</span>        }</div>
+<div class="line"><span class="lineno">  392</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; X,</div>
+<div class="line"><span class="lineno">  393</span>            Y;             <span class="comment">// To store X and Y</span></div>
+<div class="line"><span class="lineno">  394</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> line;  <span class="comment">// To store each line</span></div>
+<div class="line"><span class="lineno">  395</span>        <span class="comment">// Skip lines</span></div>
+<div class="line"><span class="lineno">  396</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; slip_lines; i++) {</div>
+<div class="line"><span class="lineno">  397</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/getline.html">std::getline</a>(in_file, line, <span class="charliteral">&#39;\n&#39;</span>);  <span class="comment">// Ignore line</span></div>
+<div class="line"><span class="lineno">  398</span>        }</div>
+<div class="line"><span class="lineno">  399</span>        <span class="comment">// While file has information</span></div>
+<div class="line"><span class="lineno">  400</span>        <span class="keywordflow">while</span> (!in_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ios/eof.html">eof</a>() &amp;&amp; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/getline.html">std::getline</a>(in_file, line, <span class="charliteral">&#39;\n&#39;</span>)) {</div>
+<div class="line"><span class="lineno">  401</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> x_data,</div>
+<div class="line"><span class="lineno">  402</span>                y_data;                  <span class="comment">// To store single sample and label</span></div>
+<div class="line"><span class="lineno">  403</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_stringstream.html">std::stringstream</a> ss(line);  <span class="comment">// Constructing stringstream from line</span></div>
+<div class="line"><span class="lineno">  404</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> token;  <span class="comment">// To store each token in line (seprated by &#39;,&#39;)</span></div>
+<div class="line"><span class="lineno">  405</span>            <span class="keywordflow">while</span> (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/getline.html">std::getline</a>(ss, token, <span class="charliteral">&#39;,&#39;</span>)) {  <span class="comment">// For each token</span></div>
+<div class="line"><span class="lineno">  406</span>                <span class="comment">// Insert numerical value of token in x_data</span></div>
+<div class="line"><span class="lineno">  407</span>                x_data = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a496302e3371aa7b478cb7d5917904bdd">insert_element</a>(x_data, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/stof.html">std::stod</a>(token));</div>
+<div class="line"><span class="lineno">  408</span>            }</div>
+<div class="line"><span class="lineno">  409</span>            <span class="comment">// If label is in last column</span></div>
+<div class="line"><span class="lineno">  410</span>            <span class="keywordflow">if</span> (last_label) {</div>
+<div class="line"><span class="lineno">  411</span>                y_data.resize(this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>.back().neurons);</div>
+<div class="line"><span class="lineno">  412</span>                <span class="comment">// If task is classification</span></div>
+<div class="line"><span class="lineno">  413</span>                <span class="keywordflow">if</span> (y_data.size() &gt; 1) {</div>
+<div class="line"><span class="lineno">  414</span>                    y_data[x_data[x_data.size() - 1]] = 1;</div>
+<div class="line"><span class="lineno">  415</span>                }</div>
+<div class="line"><span class="lineno">  416</span>                <span class="comment">// If task is regrssion (of single value)</span></div>
+<div class="line"><span class="lineno">  417</span>                <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  418</span>                    y_data[0] = x_data[x_data.size() - 1];</div>
+<div class="line"><span class="lineno">  419</span>                }</div>
+<div class="line"><span class="lineno">  420</span>                x_data = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ae10178b082f0205c326550877d998e5d">pop_back</a>(x_data);  <span class="comment">// Remove label from x_data</span></div>
+<div class="line"><span class="lineno">  421</span>            } <span class="keywordflow">else</span> {</div>
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+<div class="line"><span class="lineno">  423</span>                <span class="comment">// If task is classification</span></div>
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+<div class="line"><span class="lineno">  425</span>                    y_data[x_data[x_data.size() - 1]] = 1;</div>
+<div class="line"><span class="lineno">  426</span>                }</div>
+<div class="line"><span class="lineno">  427</span>                <span class="comment">// If task is regrssion (of single value)</span></div>
+<div class="line"><span class="lineno">  428</span>                <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  429</span>                    y_data[0] = x_data[x_data.size() - 1];</div>
+<div class="line"><span class="lineno">  430</span>                }</div>
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+<div class="line"><span class="lineno">  432</span>            }</div>
+<div class="line"><span class="lineno">  433</span>            <span class="comment">// Push collected X_data and y_data in X and Y</span></div>
+<div class="line"><span class="lineno">  434</span>            X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>({x_data});</div>
+<div class="line"><span class="lineno">  435</span>            Y.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>({y_data});</div>
+<div class="line"><span class="lineno">  436</span>        }</div>
+<div class="line"><span class="lineno">  437</span>        <span class="comment">// Normalize training data if flag is set</span></div>
+<div class="line"><span class="lineno">  438</span>        <span class="keywordflow">if</span> (normalize) {</div>
+<div class="line"><span class="lineno">  439</span>            <span class="comment">// Scale data between 0 and 1 using min-max scaler</span></div>
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+<div class="line"><span class="lineno">  441</span>        }</div>
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+<div class="line"><span class="lineno">  443</span>        <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">make_pair</a>(X, Y);  <span class="comment">// Return pair of X and Y</span></div>
+<div class="line"><span class="lineno">  444</span>    }</div>
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 <div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
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 <div class="ttc" id="astof_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/stof.html">std::stod</a></div><div class="ttdeci">T stod(T... args)</div></div>
-<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a></div></div>
+<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt; double &gt;</a></div></div>
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 Here is the call graph for this function:</div>
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@@ -1113,43 +1119,43 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>instance of <a class="el" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html">NeuralNetwork</a> class with pretrained weights </dd></dl>
-<div class="fragment"><div class="line"><a id="l00732" name="l00732"></a><span class="lineno">  732</span>                                                         {</div>
-<div class="line"><a id="l00733" name="l00733"></a><span class="lineno">  733</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ifstream.html">std::ifstream</a> in_file;            <span class="comment">// Ifstream to read file</span></div>
-<div class="line"><a id="l00734" name="l00734"></a><span class="lineno">  734</span>        in_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ifstream/open.html">open</a>(file_name.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/c_str.html">c_str</a>());  <span class="comment">// Openinig file</span></div>
-<div class="line"><a id="l00735" name="l00735"></a><span class="lineno">  735</span>        <span class="comment">// If there is any problem in opening file</span></div>
-<div class="line"><a id="l00736" name="l00736"></a><span class="lineno">  736</span>        <span class="keywordflow">if</span> (!in_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ifstream/is_open.html">is_open</a>()) {</div>
-<div class="line"><a id="l00737" name="l00737"></a><span class="lineno">  737</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
-<div class="line"><a id="l00738" name="l00738"></a><span class="lineno">  738</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Unable to open file: &quot;</span> &lt;&lt; file_name &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00739" name="l00739"></a><span class="lineno">  739</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
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-<div class="line"><a id="l00742" name="l00742"></a><span class="lineno">  742</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt;</div>
-<div class="line"><a id="l00743" name="l00743"></a><span class="lineno">  743</span>            kernels;  <span class="comment">// To store pretrained kernels</span></div>
-<div class="line"><a id="l00744" name="l00744"></a><span class="lineno">  744</span>        <span class="comment">// Loading model from saved file format</span></div>
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-<div class="line"><a id="l00746" name="l00746"></a><span class="lineno">  746</span>        in_file &gt;&gt; total_layers;</div>
-<div class="line"><a id="l00747" name="l00747"></a><span class="lineno">  747</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; total_layers; i++) {</div>
-<div class="line"><a id="l00748" name="l00748"></a><span class="lineno">  748</span>            <span class="keywordtype">int</span> neurons = 0;</div>
-<div class="line"><a id="l00749" name="l00749"></a><span class="lineno">  749</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> activation;</div>
-<div class="line"><a id="l00750" name="l00750"></a><span class="lineno">  750</span>            <span class="keywordtype">size_t</span> shape_a = 0, shape_b = 0;</div>
-<div class="line"><a id="l00751" name="l00751"></a><span class="lineno">  751</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; kernel;</div>
-<div class="line"><a id="l00752" name="l00752"></a><span class="lineno">  752</span>            in_file &gt;&gt; neurons &gt;&gt; activation &gt;&gt; shape_a &gt;&gt; shape_b;</div>
-<div class="line"><a id="l00753" name="l00753"></a><span class="lineno">  753</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> r = 0; r &lt; shape_a; r++) {</div>
-<div class="line"><a id="l00754" name="l00754"></a><span class="lineno">  754</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> row(shape_b);</div>
-<div class="line"><a id="l00755" name="l00755"></a><span class="lineno">  755</span>                <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> c = 0; c &lt; shape_b; c++) {</div>
-<div class="line"><a id="l00756" name="l00756"></a><span class="lineno">  756</span>                    in_file &gt;&gt; row[c];</div>
-<div class="line"><a id="l00757" name="l00757"></a><span class="lineno">  757</span>                }</div>
-<div class="line"><a id="l00758" name="l00758"></a><span class="lineno">  758</span>                kernel.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(row);</div>
-<div class="line"><a id="l00759" name="l00759"></a><span class="lineno">  759</span>            }</div>
-<div class="line"><a id="l00760" name="l00760"></a><span class="lineno">  760</span>            config.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/emplace_back.html">emplace_back</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">make_pair</a>(neurons, activation));</div>
-<div class="line"><a id="l00761" name="l00761"></a><span class="lineno">  761</span>            ;</div>
-<div class="line"><a id="l00762" name="l00762"></a><span class="lineno">  762</span>            kernels.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/emplace_back.html">emplace_back</a>(kernel);</div>
-<div class="line"><a id="l00763" name="l00763"></a><span class="lineno">  763</span>        }</div>
-<div class="line"><a id="l00764" name="l00764"></a><span class="lineno">  764</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;INFO: Model loaded successfully&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00765" name="l00765"></a><span class="lineno">  765</span>        in_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ifstream/close.html">close</a>();  <span class="comment">// Closing file</span></div>
-<div class="line"><a id="l00766" name="l00766"></a><span class="lineno">  766</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#ae7cf126a3a8f9d20c81b21584d061a08">NeuralNetwork</a>(</div>
-<div class="line"><a id="l00767" name="l00767"></a><span class="lineno">  767</span>            config, kernels);  <span class="comment">// Return instance of NeuralNetwork class</span></div>
-<div class="line"><a id="l00768" name="l00768"></a><span class="lineno">  768</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  732</span>                                                         {</div>
+<div class="line"><span class="lineno">  733</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ifstream.html">std::ifstream</a> in_file;            <span class="comment">// Ifstream to read file</span></div>
+<div class="line"><span class="lineno">  734</span>        in_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ifstream/open.html">open</a>(file_name.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/c_str.html">c_str</a>());  <span class="comment">// Openinig file</span></div>
+<div class="line"><span class="lineno">  735</span>        <span class="comment">// If there is any problem in opening file</span></div>
+<div class="line"><span class="lineno">  736</span>        <span class="keywordflow">if</span> (!in_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ifstream/is_open.html">is_open</a>()) {</div>
+<div class="line"><span class="lineno">  737</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
+<div class="line"><span class="lineno">  738</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Unable to open file: &quot;</span> &lt;&lt; file_name &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  739</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><span class="lineno">  740</span>        }</div>
+<div class="line"><span class="lineno">  741</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::pair&lt;int, std::string&gt;</a>&gt; config;  <span class="comment">// To store config</span></div>
+<div class="line"><span class="lineno">  742</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt;</div>
+<div class="line"><span class="lineno">  743</span>            kernels;  <span class="comment">// To store pretrained kernels</span></div>
+<div class="line"><span class="lineno">  744</span>        <span class="comment">// Loading model from saved file format</span></div>
+<div class="line"><span class="lineno">  745</span>        <span class="keywordtype">size_t</span> total_layers = 0;</div>
+<div class="line"><span class="lineno">  746</span>        in_file &gt;&gt; total_layers;</div>
+<div class="line"><span class="lineno">  747</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; total_layers; i++) {</div>
+<div class="line"><span class="lineno">  748</span>            <span class="keywordtype">int</span> neurons = 0;</div>
+<div class="line"><span class="lineno">  749</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> activation;</div>
+<div class="line"><span class="lineno">  750</span>            <span class="keywordtype">size_t</span> shape_a = 0, shape_b = 0;</div>
+<div class="line"><span class="lineno">  751</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; kernel;</div>
+<div class="line"><span class="lineno">  752</span>            in_file &gt;&gt; neurons &gt;&gt; activation &gt;&gt; shape_a &gt;&gt; shape_b;</div>
+<div class="line"><span class="lineno">  753</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> r = 0; r &lt; shape_a; r++) {</div>
+<div class="line"><span class="lineno">  754</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> row(shape_b);</div>
+<div class="line"><span class="lineno">  755</span>                <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> c = 0; c &lt; shape_b; c++) {</div>
+<div class="line"><span class="lineno">  756</span>                    in_file &gt;&gt; row[c];</div>
+<div class="line"><span class="lineno">  757</span>                }</div>
+<div class="line"><span class="lineno">  758</span>                kernel.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(row);</div>
+<div class="line"><span class="lineno">  759</span>            }</div>
+<div class="line"><span class="lineno">  760</span>            config.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/emplace_back.html">emplace_back</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">make_pair</a>(neurons, activation));</div>
+<div class="line"><span class="lineno">  761</span>            ;</div>
+<div class="line"><span class="lineno">  762</span>            kernels.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/emplace_back.html">emplace_back</a>(kernel);</div>
+<div class="line"><span class="lineno">  763</span>        }</div>
+<div class="line"><span class="lineno">  764</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;INFO: Model loaded successfully&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  765</span>        in_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ifstream/close.html">close</a>();  <span class="comment">// Closing file</span></div>
+<div class="line"><span class="lineno">  766</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#ae7cf126a3a8f9d20c81b21584d061a08">NeuralNetwork</a>(</div>
+<div class="line"><span class="lineno">  767</span>            config, kernels);  <span class="comment">// Return instance of NeuralNetwork class</span></div>
+<div class="line"><span class="lineno">  768</span>    }</div>
 <div class="ttc" id="aclassmachine__learning_1_1neural__network_1_1_neural_network_html_ae7cf126a3a8f9d20c81b21584d061a08"><div class="ttname"><a href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#ae7cf126a3a8f9d20c81b21584d061a08">machine_learning::neural_network::NeuralNetwork::NeuralNetwork</a></div><div class="ttdeci">NeuralNetwork()=default</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -1244,7 +1250,11 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <p >Format in which model is saved:</p>
-<p >total_layers neurons(1st neural_network::layers::DenseLayer) activation_name(1st <a class="el" href="../../dc/d93/classmachine__learning_1_1neural__network_1_1layers_1_1_dense_layer.html">neural_network::layers::DenseLayer</a>) kernel_shape(1st <a class="el" href="../../dc/d93/classmachine__learning_1_1neural__network_1_1layers_1_1_dense_layer.html">neural_network::layers::DenseLayer</a>) kernel_values neurons(Nth neural_network::layers::DenseLayer) activation_name(Nth <a class="el" href="../../dc/d93/classmachine__learning_1_1neural__network_1_1layers_1_1_dense_layer.html">neural_network::layers::DenseLayer</a>) kernel_shape(Nth <a class="el" href="../../dc/d93/classmachine__learning_1_1neural__network_1_1layers_1_1_dense_layer.html">neural_network::layers::DenseLayer</a>) kernel_value</p>
+<p >total_layers neurons(1st neural_network::layers::DenseLayer) activation_name(1st
+neural_network::layers::DenseLayer) kernel_shape(1st
+neural_network::layers::DenseLayer) kernel_values neurons(Nth neural_network::layers::DenseLayer) activation_name(Nth
+neural_network::layers::DenseLayer) kernel_shape(Nth
+neural_network::layers::DenseLayer) kernel_value</p>
 <p >For Example, pretrained model with 3 layers: </p><pre>
  3
  4 none
@@ -1267,80 +1277,80 @@ Here is the call graph for this function:</div>
  -2.01336 -0.0219682 1.44145
  1.72853 -0.465264 -0.705373
  -0.908409 -0.740547 0.376416
- </pre><div class="fragment"><div class="line"><a id="l00652" name="l00652"></a><span class="lineno">  652</span>                                                 {</div>
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-<div class="line"><a id="l00654" name="l00654"></a><span class="lineno">  654</span>        <span class="comment">// Adding &quot;.model&quot; extension if it is not already there in name</span></div>
-<div class="line"><a id="l00655" name="l00655"></a><span class="lineno">  655</span>        <span class="keywordflow">if</span> (file_name.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/find.html">find</a>(<span class="stringliteral">&quot;.model&quot;</span>) == file_name.npos) {</div>
-<div class="line"><a id="l00656" name="l00656"></a><span class="lineno">  656</span>            file_name += <span class="stringliteral">&quot;.model&quot;</span>;</div>
-<div class="line"><a id="l00657" name="l00657"></a><span class="lineno">  657</span>        }</div>
-<div class="line"><a id="l00658" name="l00658"></a><span class="lineno">  658</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> out_file;  <span class="comment">// Ofstream to write in file</span></div>
-<div class="line"><a id="l00659" name="l00659"></a><span class="lineno">  659</span>        <span class="comment">// Open file in out|trunc mode</span></div>
-<div class="line"><a id="l00660" name="l00660"></a><span class="lineno">  660</span>        out_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">open</a>(file_name.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/c_str.html">c_str</a>(),</div>
-<div class="line"><a id="l00661" name="l00661"></a><span class="lineno">  661</span>                      std::ofstream::out | std::ofstream::trunc);</div>
-<div class="line"><a id="l00662" name="l00662"></a><span class="lineno">  662</span>        <span class="comment">// If there is any problem in opening file</span></div>
-<div class="line"><a id="l00663" name="l00663"></a><span class="lineno">  663</span>        <span class="keywordflow">if</span> (!out_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
-<div class="line"><a id="l00664" name="l00664"></a><span class="lineno">  664</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
-<div class="line"><a id="l00665" name="l00665"></a><span class="lineno">  665</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Unable to open file: &quot;</span> &lt;&lt; file_name &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00666" name="l00666"></a><span class="lineno">  666</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
-<div class="line"><a id="l00667" name="l00667"></a><span class="lineno">  667</span>        }<span class="comment"></span></div>
-<div class="line"><a id="l00668" name="l00668"></a><span class="lineno">  668</span><span class="comment">        /**</span></div>
-<div class="line"><a id="l00669" name="l00669"></a><span class="lineno">  669</span><span class="comment">            Format in which model is saved:</span></div>
-<div class="line"><a id="l00670" name="l00670"></a><span class="lineno">  670</span><span class="comment"></span> </div>
-<div class="line"><a id="l00671" name="l00671"></a><span class="lineno">  671</span><span class="comment">            total_layers</span></div>
-<div class="line"><a id="l00672" name="l00672"></a><span class="lineno">  672</span><span class="comment">            neurons(1st neural_network::layers::DenseLayer) activation_name(1st</span></div>
-<div class="line"><a id="l00673" name="l00673"></a><span class="lineno">  673</span><span class="comment">           neural_network::layers::DenseLayer) kernel_shape(1st</span></div>
-<div class="line"><a id="l00674" name="l00674"></a><span class="lineno">  674</span><span class="comment">           neural_network::layers::DenseLayer) kernel_values</span></div>
-<div class="line"><a id="l00675" name="l00675"></a><span class="lineno">  675</span><span class="comment">            .</span></div>
-<div class="line"><a id="l00676" name="l00676"></a><span class="lineno">  676</span><span class="comment">            .</span></div>
-<div class="line"><a id="l00677" name="l00677"></a><span class="lineno">  677</span><span class="comment">            .</span></div>
-<div class="line"><a id="l00678" name="l00678"></a><span class="lineno">  678</span><span class="comment">            neurons(Nth neural_network::layers::DenseLayer) activation_name(Nth</span></div>
-<div class="line"><a id="l00679" name="l00679"></a><span class="lineno">  679</span><span class="comment">           neural_network::layers::DenseLayer) kernel_shape(Nth</span></div>
-<div class="line"><a id="l00680" name="l00680"></a><span class="lineno">  680</span><span class="comment">           neural_network::layers::DenseLayer) kernel_value</span></div>
-<div class="line"><a id="l00681" name="l00681"></a><span class="lineno">  681</span><span class="comment"></span> </div>
-<div class="line"><a id="l00682" name="l00682"></a><span class="lineno">  682</span><span class="comment">            For Example, pretrained model with 3 layers:</span></div>
-<div class="line"><a id="l00683" name="l00683"></a><span class="lineno">  683</span><span class="comment">            &lt;pre&gt;</span></div>
-<div class="line"><a id="l00684" name="l00684"></a><span class="lineno">  684</span><span class="comment">            3</span></div>
-<div class="line"><a id="l00685" name="l00685"></a><span class="lineno">  685</span><span class="comment">            4 none</span></div>
-<div class="line"><a id="l00686" name="l00686"></a><span class="lineno">  686</span><span class="comment">            4 4</span></div>
-<div class="line"><a id="l00687" name="l00687"></a><span class="lineno">  687</span><span class="comment">            1 0 0 0</span></div>
-<div class="line"><a id="l00688" name="l00688"></a><span class="lineno">  688</span><span class="comment">            0 1 0 0</span></div>
-<div class="line"><a id="l00689" name="l00689"></a><span class="lineno">  689</span><span class="comment">            0 0 1 0</span></div>
-<div class="line"><a id="l00690" name="l00690"></a><span class="lineno">  690</span><span class="comment">            0 0 0 1</span></div>
-<div class="line"><a id="l00691" name="l00691"></a><span class="lineno">  691</span><span class="comment">            6 relu</span></div>
-<div class="line"><a id="l00692" name="l00692"></a><span class="lineno">  692</span><span class="comment">            4 6</span></div>
-<div class="line"><a id="l00693" name="l00693"></a><span class="lineno">  693</span><span class="comment">            -1.88963 -3.61165 1.30757 -0.443906 -2.41039 -2.69653</span></div>
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-<div class="line"><a id="l00695" name="l00695"></a><span class="lineno">  695</span><span class="comment">            -2.91451 -4.43249 -0.804187 2.51995 -6.97524 -1.07049</span></div>
-<div class="line"><a id="l00696" name="l00696"></a><span class="lineno">  696</span><span class="comment">            -0.571531 -1.81689 -1.24485 1.92264 -2.81322 1.01741</span></div>
-<div class="line"><a id="l00697" name="l00697"></a><span class="lineno">  697</span><span class="comment">            3 sigmoid</span></div>
-<div class="line"><a id="l00698" name="l00698"></a><span class="lineno">  698</span><span class="comment">            6 3</span></div>
-<div class="line"><a id="l00699" name="l00699"></a><span class="lineno">  699</span><span class="comment">            0.390267 -0.391703 -0.0989607</span></div>
-<div class="line"><a id="l00700" name="l00700"></a><span class="lineno">  700</span><span class="comment">            0.499234 -0.564539 -0.28097</span></div>
-<div class="line"><a id="l00701" name="l00701"></a><span class="lineno">  701</span><span class="comment">            0.553386 -0.153974 -1.92493</span></div>
-<div class="line"><a id="l00702" name="l00702"></a><span class="lineno">  702</span><span class="comment">            -2.01336 -0.0219682 1.44145</span></div>
-<div class="line"><a id="l00703" name="l00703"></a><span class="lineno">  703</span><span class="comment">            1.72853 -0.465264 -0.705373</span></div>
-<div class="line"><a id="l00704" name="l00704"></a><span class="lineno">  704</span><span class="comment">            -0.908409 -0.740547 0.376416</span></div>
-<div class="line"><a id="l00705" name="l00705"></a><span class="lineno">  705</span><span class="comment">            &lt;/pre&gt;</span></div>
-<div class="line"><a id="l00706" name="l00706"></a><span class="lineno">  706</span><span class="comment">        */</span></div>
-<div class="line"><a id="l00707" name="l00707"></a><span class="lineno">  707</span>        <span class="comment">// Saving model in the same format</span></div>
-<div class="line"><a id="l00708" name="l00708"></a><span class="lineno">  708</span>        out_file &lt;&lt; <a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>.size();</div>
-<div class="line"><a id="l00709" name="l00709"></a><span class="lineno">  709</span>        out_file &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00710" name="l00710"></a><span class="lineno">  710</span>        <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;layer : this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>) {</div>
-<div class="line"><a id="l00711" name="l00711"></a><span class="lineno">  711</span>            out_file &lt;&lt; layer.neurons &lt;&lt; <span class="charliteral">&#39; &#39;</span> &lt;&lt; layer.activation &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00712" name="l00712"></a><span class="lineno">  712</span>            <span class="keyword">const</span> <span class="keyword">auto</span> shape = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(layer.kernel);</div>
-<div class="line"><a id="l00713" name="l00713"></a><span class="lineno">  713</span>            out_file &lt;&lt; shape.first &lt;&lt; <span class="charliteral">&#39; &#39;</span> &lt;&lt; shape.second &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00714" name="l00714"></a><span class="lineno">  714</span>            <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;row : layer.kernel) {</div>
-<div class="line"><a id="l00715" name="l00715"></a><span class="lineno">  715</span>                <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;val : row) {</div>
-<div class="line"><a id="l00716" name="l00716"></a><span class="lineno">  716</span>                    out_file &lt;&lt; val &lt;&lt; <span class="charliteral">&#39; &#39;</span>;</div>
-<div class="line"><a id="l00717" name="l00717"></a><span class="lineno">  717</span>                }</div>
-<div class="line"><a id="l00718" name="l00718"></a><span class="lineno">  718</span>                out_file &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00719" name="l00719"></a><span class="lineno">  719</span>            }</div>
-<div class="line"><a id="l00720" name="l00720"></a><span class="lineno">  720</span>        }</div>
-<div class="line"><a id="l00721" name="l00721"></a><span class="lineno">  721</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;INFO: Model saved successfully with name : &quot;</span>;</div>
-<div class="line"><a id="l00722" name="l00722"></a><span class="lineno">  722</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; file_name &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00723" name="l00723"></a><span class="lineno">  723</span>        out_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/close.html">close</a>();  <span class="comment">// Closing file</span></div>
-<div class="line"><a id="l00724" name="l00724"></a><span class="lineno">  724</span>        <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00725" name="l00725"></a><span class="lineno">  725</span>    }</div>
+ </pre><div class="fragment"><div class="line"><span class="lineno">  652</span>                                                 {</div>
+<div class="line"><span class="lineno">  653</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> file_name = _file_name;</div>
+<div class="line"><span class="lineno">  654</span>        <span class="comment">// Adding &quot;.model&quot; extension if it is not already there in name</span></div>
+<div class="line"><span class="lineno">  655</span>        <span class="keywordflow">if</span> (file_name.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/find.html">find</a>(<span class="stringliteral">&quot;.model&quot;</span>) == file_name.npos) {</div>
+<div class="line"><span class="lineno">  656</span>            file_name += <span class="stringliteral">&quot;.model&quot;</span>;</div>
+<div class="line"><span class="lineno">  657</span>        }</div>
+<div class="line"><span class="lineno">  658</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> out_file;  <span class="comment">// Ofstream to write in file</span></div>
+<div class="line"><span class="lineno">  659</span>        <span class="comment">// Open file in out|trunc mode</span></div>
+<div class="line"><span class="lineno">  660</span>        out_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">open</a>(file_name.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/c_str.html">c_str</a>(),</div>
+<div class="line"><span class="lineno">  661</span>                      std::ofstream::out | std::ofstream::trunc);</div>
+<div class="line"><span class="lineno">  662</span>        <span class="comment">// If there is any problem in opening file</span></div>
+<div class="line"><span class="lineno">  663</span>        <span class="keywordflow">if</span> (!out_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
+<div class="line"><span class="lineno">  664</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
+<div class="line"><span class="lineno">  665</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Unable to open file: &quot;</span> &lt;&lt; file_name &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  666</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><span class="lineno">  667</span>        }<span class="comment"></span></div>
+<div class="line"><span class="lineno">  668</span><span class="comment">        /**</span></div>
+<div class="line"><span class="lineno">  669</span><span class="comment">            Format in which model is saved:</span></div>
+<div class="line"><span class="lineno">  670</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  671</span><span class="comment">            total_layers</span></div>
+<div class="line"><span class="lineno">  672</span><span class="comment">            neurons(1st neural_network::layers::DenseLayer) activation_name(1st</span></div>
+<div class="line"><span class="lineno">  673</span><span class="comment">           neural_network::layers::DenseLayer) kernel_shape(1st</span></div>
+<div class="line"><span class="lineno">  674</span><span class="comment">           neural_network::layers::DenseLayer) kernel_values</span></div>
+<div class="line"><span class="lineno">  675</span><span class="comment">            .</span></div>
+<div class="line"><span class="lineno">  676</span><span class="comment">            .</span></div>
+<div class="line"><span class="lineno">  677</span><span class="comment">            .</span></div>
+<div class="line"><span class="lineno">  678</span><span class="comment">            neurons(Nth neural_network::layers::DenseLayer) activation_name(Nth</span></div>
+<div class="line"><span class="lineno">  679</span><span class="comment">           neural_network::layers::DenseLayer) kernel_shape(Nth</span></div>
+<div class="line"><span class="lineno">  680</span><span class="comment">           neural_network::layers::DenseLayer) kernel_value</span></div>
+<div class="line"><span class="lineno">  681</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  682</span><span class="comment">            For Example, pretrained model with 3 layers:</span></div>
+<div class="line"><span class="lineno">  683</span><span class="comment">            &lt;pre&gt;</span></div>
+<div class="line"><span class="lineno">  684</span><span class="comment">            3</span></div>
+<div class="line"><span class="lineno">  685</span><span class="comment">            4 none</span></div>
+<div class="line"><span class="lineno">  686</span><span class="comment">            4 4</span></div>
+<div class="line"><span class="lineno">  687</span><span class="comment">            1 0 0 0</span></div>
+<div class="line"><span class="lineno">  688</span><span class="comment">            0 1 0 0</span></div>
+<div class="line"><span class="lineno">  689</span><span class="comment">            0 0 1 0</span></div>
+<div class="line"><span class="lineno">  690</span><span class="comment">            0 0 0 1</span></div>
+<div class="line"><span class="lineno">  691</span><span class="comment">            6 relu</span></div>
+<div class="line"><span class="lineno">  692</span><span class="comment">            4 6</span></div>
+<div class="line"><span class="lineno">  693</span><span class="comment">            -1.88963 -3.61165 1.30757 -0.443906 -2.41039 -2.69653</span></div>
+<div class="line"><span class="lineno">  694</span><span class="comment">            -0.684753 0.0891452 0.795294 -2.39619 2.73377 0.318202</span></div>
+<div class="line"><span class="lineno">  695</span><span class="comment">            -2.91451 -4.43249 -0.804187 2.51995 -6.97524 -1.07049</span></div>
+<div class="line"><span class="lineno">  696</span><span class="comment">            -0.571531 -1.81689 -1.24485 1.92264 -2.81322 1.01741</span></div>
+<div class="line"><span class="lineno">  697</span><span class="comment">            3 sigmoid</span></div>
+<div class="line"><span class="lineno">  698</span><span class="comment">            6 3</span></div>
+<div class="line"><span class="lineno">  699</span><span class="comment">            0.390267 -0.391703 -0.0989607</span></div>
+<div class="line"><span class="lineno">  700</span><span class="comment">            0.499234 -0.564539 -0.28097</span></div>
+<div class="line"><span class="lineno">  701</span><span class="comment">            0.553386 -0.153974 -1.92493</span></div>
+<div class="line"><span class="lineno">  702</span><span class="comment">            -2.01336 -0.0219682 1.44145</span></div>
+<div class="line"><span class="lineno">  703</span><span class="comment">            1.72853 -0.465264 -0.705373</span></div>
+<div class="line"><span class="lineno">  704</span><span class="comment">            -0.908409 -0.740547 0.376416</span></div>
+<div class="line"><span class="lineno">  705</span><span class="comment">            &lt;/pre&gt;</span></div>
+<div class="line"><span class="lineno">  706</span><span class="comment">        */</span></div>
+<div class="line"><span class="lineno">  707</span>        <span class="comment">// Saving model in the same format</span></div>
+<div class="line"><span class="lineno">  708</span>        out_file &lt;&lt; <a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>.size();</div>
+<div class="line"><span class="lineno">  709</span>        out_file &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  710</span>        <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;layer : this-&gt;<a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>) {</div>
+<div class="line"><span class="lineno">  711</span>            out_file &lt;&lt; layer.neurons &lt;&lt; <span class="charliteral">&#39; &#39;</span> &lt;&lt; layer.activation &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  712</span>            <span class="keyword">const</span> <span class="keyword">auto</span> shape = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(layer.kernel);</div>
+<div class="line"><span class="lineno">  713</span>            out_file &lt;&lt; shape.first &lt;&lt; <span class="charliteral">&#39; &#39;</span> &lt;&lt; shape.second &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  714</span>            <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;row : layer.kernel) {</div>
+<div class="line"><span class="lineno">  715</span>                <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;val : row) {</div>
+<div class="line"><span class="lineno">  716</span>                    out_file &lt;&lt; val &lt;&lt; <span class="charliteral">&#39; &#39;</span>;</div>
+<div class="line"><span class="lineno">  717</span>                }</div>
+<div class="line"><span class="lineno">  718</span>                out_file &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  719</span>            }</div>
+<div class="line"><span class="lineno">  720</span>        }</div>
+<div class="line"><span class="lineno">  721</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;INFO: Model saved successfully with name : &quot;</span>;</div>
+<div class="line"><span class="lineno">  722</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; file_name &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  723</span>        out_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/close.html">close</a>();  <span class="comment">// Closing file</span></div>
+<div class="line"><span class="lineno">  724</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  725</span>    }</div>
 <div class="ttc" id="abasic_ofstream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a></div></div>
 <div class="ttc" id="afind_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/find.html">std::string::find</a></div><div class="ttdeci">T find(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -1382,12 +1392,12 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>returns predictions as vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00452" name="l00452"></a><span class="lineno">  452</span>                                                 {</div>
-<div class="line"><a id="l00453" name="l00453"></a><span class="lineno">  453</span>        <span class="comment">// Get activations of all layers</span></div>
-<div class="line"><a id="l00454" name="l00454"></a><span class="lineno">  454</span>        <span class="keyword">auto</span> <a class="code hl_namespace" href="../../d5/d39/namespaceactivations.html">activations</a> = this-&gt;<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a361a45f3c3d8347d79103bf182d0570b">__detailed_single_prediction</a>(X);</div>
-<div class="line"><a id="l00455" name="l00455"></a><span class="lineno">  455</span>        <span class="comment">// Return activations of last layer (actual predicted values)</span></div>
-<div class="line"><a id="l00456" name="l00456"></a><span class="lineno">  456</span>        <span class="keywordflow">return</span> <a class="code hl_namespace" href="../../d5/d39/namespaceactivations.html">activations</a>.back();</div>
-<div class="line"><a id="l00457" name="l00457"></a><span class="lineno">  457</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  452</span>                                                 {</div>
+<div class="line"><span class="lineno">  453</span>        <span class="comment">// Get activations of all layers</span></div>
+<div class="line"><span class="lineno">  454</span>        <span class="keyword">auto</span> <a class="code hl_namespace" href="../../d5/d39/namespaceactivations.html">activations</a> = this-&gt;<a class="code hl_function" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a361a45f3c3d8347d79103bf182d0570b">__detailed_single_prediction</a>(X);</div>
+<div class="line"><span class="lineno">  455</span>        <span class="comment">// Return activations of last layer (actual predicted values)</span></div>
+<div class="line"><span class="lineno">  456</span>        <span class="keywordflow">return</span> <a class="code hl_namespace" href="../../d5/d39/namespaceactivations.html">activations</a>.back();</div>
+<div class="line"><span class="lineno">  457</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -1420,30 +1430,30 @@ Here is the call graph for this function:</div>
 </table>
 </div><div class="memdoc">
 <p >Function to print summary of the network. </p>
-<div class="fragment"><div class="line"><a id="l00773" name="l00773"></a><span class="lineno">  773</span>                   {</div>
-<div class="line"><a id="l00774" name="l00774"></a><span class="lineno">  774</span>        <span class="comment">// Printing Summary</span></div>
-<div class="line"><a id="l00775" name="l00775"></a><span class="lineno">  775</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
-<div class="line"><a id="l00776" name="l00776"></a><span class="lineno">  776</span>            &lt;&lt; <span class="stringliteral">&quot;===============================================================&quot;</span></div>
-<div class="line"><a id="l00777" name="l00777"></a><span class="lineno">  777</span>            &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00778" name="l00778"></a><span class="lineno">  778</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\t\t+ MODEL SUMMARY +\t\t\n&quot;</span>;</div>
-<div class="line"><a id="l00779" name="l00779"></a><span class="lineno">  779</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
-<div class="line"><a id="l00780" name="l00780"></a><span class="lineno">  780</span>            &lt;&lt; <span class="stringliteral">&quot;===============================================================&quot;</span></div>
-<div class="line"><a id="l00781" name="l00781"></a><span class="lineno">  781</span>            &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00782" name="l00782"></a><span class="lineno">  782</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 1; i &lt;= <a class="code hl_namespace" href="../../d5/d2c/namespacelayers.html">layers</a>.size(); i++) {  <span class="comment">// For every layer</span></div>
-<div class="line"><a id="l00783" name="l00783"></a><span class="lineno">  783</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;)&quot;</span>;</div>
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+<div class="line"><span class="lineno">   22</span>        <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *current = head;</div>
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+<div class="line"><span class="lineno">   28</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;Total element: &quot;</span> &lt;&lt; total &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
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-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span> </div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    <span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> = 1;</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span> </div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    <span class="keywordflow">while</span> (k &lt;= r) {</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>        <span class="keywordflow">if</span> (k == 1) {</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; c; j++)</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>                B[0][j] = A[0][j];  <span class="comment">/// First vector is copied as it is.</span></div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        }</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span> </div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 10&gt;</a></div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>                all_projection{};  <span class="comment">/// array to store projections</span></div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; c; ++i) {</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>                all_projection[i] = 0;  <span class="comment">/// First initialised to zero</span></div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>            }</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span> </div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>            <span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> = 1;</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>            <span class="keywordflow">while</span> (l &lt; k) {</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 10&gt;</a></div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>                    temp{};           <span class="comment">/// to store previous projected array</span></div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>                <span class="keywordtype">double</span> factor = NAN;  <span class="comment">/// to store the factor by which the</span><span class="comment"></span></div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span><span class="comment">                                      /// previous array will change</span></div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span><span class="comment"></span>                factor = <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#a46e459aff5eafffb5ad9ceb129b4d274">projection</a>(A[k - 1], B[l - 1], c);</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>                <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; c; ++i) {</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>                    temp[i] = B[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> - 1][i] * factor;  <span class="comment">/// projected array created</span></div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>                }</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>                <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; c; ++j) {</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>                    all_projection[j] =</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>                        all_projection[j] +</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>                        temp[j];  <span class="comment">/// we take the projection with all the</span><span class="comment"></span></div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span><span class="comment">                                  /// previous vector and add them.</span></div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span><span class="comment"></span>                }</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a>++;</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>            }</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; c; ++i) {</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>                B[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> - 1][i] =</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>                    A[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> - 1][i] -</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>                    all_projection[i];  <span class="comment">/// subtract total projection vector</span><span class="comment"></span></div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span><span class="comment">                                        /// from the input vector</span></div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span><span class="comment"></span>            }</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>        }</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>        <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++;</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>    }</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>    display(r, c, B);  <span class="comment">// for displaying orthogoanlised vectors</span></div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  123</span>                                                        {</div>
+<div class="line"><span class="lineno">  124</span>    <span class="keywordflow">if</span> (c &lt; r) {  <span class="comment">/// we check whether appropriate dimensions are given or not.</span></div>
+<div class="line"><span class="lineno">  125</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Dimension of vector is less than number of vector, hence &quot;</span></div>
+<div class="line"><span class="lineno">  126</span>                     <span class="stringliteral">&quot;\n first &quot;</span></div>
+<div class="line"><span class="lineno">  127</span>                  &lt;&lt; c &lt;&lt; <span class="stringliteral">&quot; vectors are orthogonalised\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  128</span>        r = c;</div>
+<div class="line"><span class="lineno">  129</span>    }</div>
+<div class="line"><span class="lineno">  130</span> </div>
+<div class="line"><span class="lineno">  131</span>    <span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> = 1;</div>
+<div class="line"><span class="lineno">  132</span> </div>
+<div class="line"><span class="lineno">  133</span>    <span class="keywordflow">while</span> (k &lt;= r) {</div>
+<div class="line"><span class="lineno">  134</span>        <span class="keywordflow">if</span> (k == 1) {</div>
+<div class="line"><span class="lineno">  135</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; c; j++)</div>
+<div class="line"><span class="lineno">  136</span>                B[0][j] = A[0][j];  <span class="comment">/// First vector is copied as it is.</span></div>
+<div class="line"><span class="lineno">  137</span>        }</div>
+<div class="line"><span class="lineno">  138</span> </div>
+<div class="line"><span class="lineno">  139</span>        <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  140</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 10&gt;</a></div>
+<div class="line"><span class="lineno">  141</span>                all_projection{};  <span class="comment">/// array to store projections</span></div>
+<div class="line"><span class="lineno">  142</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; c; ++i) {</div>
+<div class="line"><span class="lineno">  143</span>                all_projection[i] = 0;  <span class="comment">/// First initialised to zero</span></div>
+<div class="line"><span class="lineno">  144</span>            }</div>
+<div class="line"><span class="lineno">  145</span> </div>
+<div class="line"><span class="lineno">  146</span>            <span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> = 1;</div>
+<div class="line"><span class="lineno">  147</span>            <span class="keywordflow">while</span> (l &lt; k) {</div>
+<div class="line"><span class="lineno">  148</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 10&gt;</a></div>
+<div class="line"><span class="lineno">  149</span>                    temp{};           <span class="comment">/// to store previous projected array</span></div>
+<div class="line"><span class="lineno">  150</span>                <span class="keywordtype">double</span> factor = NAN;  <span class="comment">/// to store the factor by which the</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  151</span><span class="comment">                                      /// previous array will change</span></div>
+<div class="line"><span class="lineno">  152</span><span class="comment"></span>                factor = <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#a46e459aff5eafffb5ad9ceb129b4d274">projection</a>(A[k - 1], B[l - 1], c);</div>
+<div class="line"><span class="lineno">  153</span>                <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; c; ++i) {</div>
+<div class="line"><span class="lineno">  154</span>                    temp[i] = B[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> - 1][i] * factor;  <span class="comment">/// projected array created</span></div>
+<div class="line"><span class="lineno">  155</span>                }</div>
+<div class="line"><span class="lineno">  156</span>                <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; c; ++j) {</div>
+<div class="line"><span class="lineno">  157</span>                    all_projection[j] =</div>
+<div class="line"><span class="lineno">  158</span>                        all_projection[j] +</div>
+<div class="line"><span class="lineno">  159</span>                        temp[j];  <span class="comment">/// we take the projection with all the</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  160</span><span class="comment">                                  /// previous vector and add them.</span></div>
+<div class="line"><span class="lineno">  161</span><span class="comment"></span>                }</div>
+<div class="line"><span class="lineno">  162</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a>++;</div>
+<div class="line"><span class="lineno">  163</span>            }</div>
+<div class="line"><span class="lineno">  164</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; c; ++i) {</div>
+<div class="line"><span class="lineno">  165</span>                B[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> - 1][i] =</div>
+<div class="line"><span class="lineno">  166</span>                    A[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> - 1][i] -</div>
+<div class="line"><span class="lineno">  167</span>                    all_projection[i];  <span class="comment">/// subtract total projection vector</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  168</span><span class="comment">                                        /// from the input vector</span></div>
+<div class="line"><span class="lineno">  169</span><span class="comment"></span>            }</div>
+<div class="line"><span class="lineno">  170</span>        }</div>
+<div class="line"><span class="lineno">  171</span>        <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++;</div>
+<div class="line"><span class="lineno">  172</span>    }</div>
+<div class="line"><span class="lineno">  173</span>    display(r, c, B);  <span class="comment">// for displaying orthogoanlised vectors</span></div>
+<div class="line"><span class="lineno">  174</span>}</div>
 <div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a6d8df83a6f26ce24a75d3b358b7f5b8a"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">numerical_methods::simpson_method::l</a></div><div class="ttdeci">double l(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:119</div></div>
@@ -402,49 +402,49 @@ Here is the call graph for this function:</div>
 <p >Input of vectors is taken</p>
 <p >To check whether vectors are orthogonal or not</p>
 <p >take make the process numerically stable, upper bound for the dot product take 0.1</p>
-<div class="fragment"><div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>           {</div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>    <span class="keywordtype">int</span> r = 0, c = 0;</div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>    <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// perform self tests</span></div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the dimension of your vectors\n&quot;</span>;</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; c;</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number of vectors you will enter\n&quot;</span>;</div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; r;</div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span> </div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 10&gt;</a>, 20&gt;</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>        A{};  <span class="comment">/// a 2-D array for storing all vectors</span></div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 10&gt;</a>, 20&gt; B = {</div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>        {0}};  <span class="comment">/// a 2-D array for storing orthogonalised vectors</span><span class="comment"></span></div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span><span class="comment">    /// storing vectors in array A</span></div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span><span class="comment"></span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; r; ++i) {</div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter vector &quot;</span> &lt;&lt; i + 1</div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>                  &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;  <span class="comment">/// Input of vectors is taken</span></div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; c; ++j) {</div>
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-<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; A[i][j];</div>
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-<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span> </div>
-<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>    <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f">linear_algebra::gram_schmidt::gram_schmidt</a>(r, c, A, B);</div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span> </div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>    <span class="keywordtype">double</span> dot = 0;</div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>    <span class="keywordtype">int</span> flag = 1;  <span class="comment">/// To check whether vectors are orthogonal or  not</span></div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; r - 1; ++i) {</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j &lt; r; ++j) {</div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>            dot =</div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">fabs</a>(linear_algebra::gram_schmidt::dot_product(B[i], B[j], c));</div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>            <span class="keywordflow">if</span> (dot &gt; 0.1)  <span class="comment">/// take make the process numerically stable, upper</span><span class="comment"></span></div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span><span class="comment">                            /// bound for the dot product take 0.1</span></div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span><span class="comment"></span>            {</div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>                flag = 0;</div>
-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>            }</div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>        }</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>    }</div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>    <span class="keywordflow">if</span> (flag == 0)</div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Vectors are linearly dependent\n&quot;</span>;</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  248</span>           {</div>
+<div class="line"><span class="lineno">  249</span>    <span class="keywordtype">int</span> r = 0, c = 0;</div>
+<div class="line"><span class="lineno">  250</span>    <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// perform self tests</span></div>
+<div class="line"><span class="lineno">  251</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the dimension of your vectors\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  252</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; c;</div>
+<div class="line"><span class="lineno">  253</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number of vectors you will enter\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  254</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; r;</div>
+<div class="line"><span class="lineno">  255</span> </div>
+<div class="line"><span class="lineno">  256</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 10&gt;</a>, 20&gt;</div>
+<div class="line"><span class="lineno">  257</span>        A{};  <span class="comment">/// a 2-D array for storing all vectors</span></div>
+<div class="line"><span class="lineno">  258</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 10&gt;</a>, 20&gt; B = {</div>
+<div class="line"><span class="lineno">  259</span>        {0}};  <span class="comment">/// a 2-D array for storing orthogonalised vectors</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  260</span><span class="comment">    /// storing vectors in array A</span></div>
+<div class="line"><span class="lineno">  261</span><span class="comment"></span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; r; ++i) {</div>
+<div class="line"><span class="lineno">  262</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter vector &quot;</span> &lt;&lt; i + 1</div>
+<div class="line"><span class="lineno">  263</span>                  &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;  <span class="comment">/// Input of vectors is taken</span></div>
+<div class="line"><span class="lineno">  264</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; c; ++j) {</div>
+<div class="line"><span class="lineno">  265</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Value &quot;</span> &lt;&lt; j + 1 &lt;&lt; <span class="stringliteral">&quot;th of vector: &quot;</span>;</div>
+<div class="line"><span class="lineno">  266</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; A[i][j];</div>
+<div class="line"><span class="lineno">  267</span>        }</div>
+<div class="line"><span class="lineno">  268</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;</div>
+<div class="line"><span class="lineno">  269</span>    }</div>
+<div class="line"><span class="lineno">  270</span> </div>
+<div class="line"><span class="lineno">  271</span>    <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f">linear_algebra::gram_schmidt::gram_schmidt</a>(r, c, A, B);</div>
+<div class="line"><span class="lineno">  272</span> </div>
+<div class="line"><span class="lineno">  273</span>    <span class="keywordtype">double</span> dot = 0;</div>
+<div class="line"><span class="lineno">  274</span>    <span class="keywordtype">int</span> flag = 1;  <span class="comment">/// To check whether vectors are orthogonal or  not</span></div>
+<div class="line"><span class="lineno">  275</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; r - 1; ++i) {</div>
+<div class="line"><span class="lineno">  276</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j &lt; r; ++j) {</div>
+<div class="line"><span class="lineno">  277</span>            dot =</div>
+<div class="line"><span class="lineno">  278</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">fabs</a>(linear_algebra::gram_schmidt::dot_product(B[i], B[j], c));</div>
+<div class="line"><span class="lineno">  279</span>            <span class="keywordflow">if</span> (dot &gt; 0.1)  <span class="comment">/// take make the process numerically stable, upper</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  280</span><span class="comment">                            /// bound for the dot product take 0.1</span></div>
+<div class="line"><span class="lineno">  281</span><span class="comment"></span>            {</div>
+<div class="line"><span class="lineno">  282</span>                flag = 0;</div>
+<div class="line"><span class="lineno">  283</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  284</span>            }</div>
+<div class="line"><span class="lineno">  285</span>        }</div>
+<div class="line"><span class="lineno">  286</span>    }</div>
+<div class="line"><span class="lineno">  287</span>    <span class="keywordflow">if</span> (flag == 0)</div>
+<div class="line"><span class="lineno">  288</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Vectors are linearly dependent\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  289</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  290</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="afabs_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a></div><div class="ttdeci">T fabs(T... args)</div></div>
 <div class="ttc" id="agram__schmidt_8cpp_html_aa31ca28f60c880802462335eedc5d91f"><div class="ttname"><a href="../../d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f">linear_algebra::gram_schmidt::gram_schmidt</a></div><div class="ttdeci">void gram_schmidt(int r, const int &amp;c, const std::array&lt; std::array&lt; double, 10 &gt;, 20 &gt; &amp;A, std::array&lt; std::array&lt; double, 10 &gt;, 20 &gt; B)</div><div class="ttdef"><b>Definition:</b> gram_schmidt.cpp:121</div></div>
@@ -502,17 +502,17 @@ Here is the call graph for this function:</div>
 <p >The dot product of two vectors is taken</p>
 <p >The norm of the second vector is taken.</p>
 <p >multiply that factor with every element in a 3rd vector, whose initial values are same as the 2nd vector.</p>
-<div class="fragment"><div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>                                                               {</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    <span class="keywordtype">double</span> dot =</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aed4d308f46ca1d91e348ca260ec1d2fb">dot_product</a>(x, y, c);  <span class="comment">/// The dot product of two vectors is taken</span></div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    <span class="keywordtype">double</span> anorm =</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>        <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aed4d308f46ca1d91e348ca260ec1d2fb">dot_product</a>(y, y, c);  <span class="comment">/// The norm of the second vector is taken.</span></div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    <span class="keywordtype">double</span> factor =</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>        dot /</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>        anorm;  <span class="comment">/// multiply that factor with every element in a 3rd vector,</span><span class="comment"></span></div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span><span class="comment">                /// whose initial values are same as the 2nd vector.</span></div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span><span class="comment"></span>    <span class="keywordflow">return</span> factor;</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   80</span>                                                               {</div>
+<div class="line"><span class="lineno">   81</span>    <span class="keywordtype">double</span> dot =</div>
+<div class="line"><span class="lineno">   82</span>        <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aed4d308f46ca1d91e348ca260ec1d2fb">dot_product</a>(x, y, c);  <span class="comment">/// The dot product of two vectors is taken</span></div>
+<div class="line"><span class="lineno">   83</span>    <span class="keywordtype">double</span> anorm =</div>
+<div class="line"><span class="lineno">   84</span>        <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aed4d308f46ca1d91e348ca260ec1d2fb">dot_product</a>(y, y, c);  <span class="comment">/// The norm of the second vector is taken.</span></div>
+<div class="line"><span class="lineno">   85</span>    <span class="keywordtype">double</span> factor =</div>
+<div class="line"><span class="lineno">   86</span>        dot /</div>
+<div class="line"><span class="lineno">   87</span>        anorm;  <span class="comment">/// multiply that factor with every element in a 3rd vector,</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">   88</span><span class="comment">                /// whose initial values are same as the 2nd vector.</span></div>
+<div class="line"><span class="lineno">   89</span><span class="comment"></span>    <span class="keywordflow">return</span> factor;</div>
+<div class="line"><span class="lineno">   90</span>}</div>
 <div class="ttc" id="agram__schmidt_8cpp_html_aed4d308f46ca1d91e348ca260ec1d2fb"><div class="ttname"><a href="../../d5/d33/gram__schmidt_8cpp.html#aed4d308f46ca1d91e348ca260ec1d2fb">linear_algebra::gram_schmidt::dot_product</a></div><div class="ttdeci">double dot_product(const std::array&lt; double, 10 &gt; &amp;x, const std::array&lt; double, 10 &gt; &amp;y, const int &amp;c)</div><div class="ttdef"><b>Definition:</b> gram_schmidt.cpp:59</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -546,68 +546,68 @@ Here is the call graph for this function:</div>
 </table>
 </div><div class="memdoc">
 <p >Test Function. Process has been tested for 3 Sample Inputs </p><dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>                   {</div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 10&gt;</a>, 20&gt; a1 = {</div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>        {{1, 0, 1, 0}, {1, 1, 1, 1}, {0, 1, 2, 1}}};</div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 10&gt;</a>, 20&gt; b1 = {{0}};</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>    <span class="keywordtype">double</span> dot1 = 0;</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>    <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f">linear_algebra::gram_schmidt::gram_schmidt</a>(3, 4, a1, b1);</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>    <span class="keywordtype">int</span> flag = 1;</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 2; ++i) {</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j &lt; 3; ++j) {</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>            dot1 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">fabs</a>(</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>                linear_algebra::gram_schmidt::dot_product(b1[i], b1[j], 4));</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>            <span class="keywordflow">if</span> (dot1 &gt; 0.1) {</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>                flag = 0;</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>            }</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>        }</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>    }</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>    <span class="keywordflow">if</span> (flag == 0)</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Vectors are linearly dependent\n&quot;</span>;</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    assert(flag == 1);</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test Case 1\n &quot;</span>;</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span> </div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 10&gt;</a>, 20&gt; a2 = {{{3, 1}, {2, 2}}};</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 10&gt;</a>, 20&gt; b2 = {{0}};</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    <span class="keywordtype">double</span> dot2 = 0;</div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f">linear_algebra::gram_schmidt::gram_schmidt</a>(2, 2, a2, b2);</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>    flag = 1;</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 1; ++i) {</div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j &lt; 2; ++j) {</div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>            dot2 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">fabs</a>(</div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>                linear_algebra::gram_schmidt::dot_product(b2[i], b2[j], 2));</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>            <span class="keywordflow">if</span> (dot2 &gt; 0.1) {</div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>                flag = 0;</div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>            }</div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>        }</div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>    }</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>    <span class="keywordflow">if</span> (flag == 0)</div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Vectors are linearly dependent\n&quot;</span>;</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>    assert(flag == 1);</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test Case 2\n&quot;</span>;</div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span> </div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 10&gt;</a>, 20&gt; a3 = {{{1, 2, 2}, {-4, 3, 2}}};</div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 10&gt;</a>, 20&gt; b3 = {{0}};</div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>    <span class="keywordtype">double</span> dot3 = 0;</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>    <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f">linear_algebra::gram_schmidt::gram_schmidt</a>(2, 3, a3, b3);</div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>    flag = 1;</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 1; ++i) {</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j &lt; 2; ++j) {</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>            dot3 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">fabs</a>(</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>                linear_algebra::gram_schmidt::dot_product(b3[i], b3[j], 3));</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>            <span class="keywordflow">if</span> (dot3 &gt; 0.1) {</div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>                flag = 0;</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>                <span class="keywordflow">break</span>;</div>
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-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>    <span class="keywordflow">if</span> (flag == 0)</div>
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-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>    assert(flag == 1);</div>
-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test Case 3\n&quot;</span>;</div>
-<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  181</span>                   {</div>
+<div class="line"><span class="lineno">  182</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 10&gt;</a>, 20&gt; a1 = {</div>
+<div class="line"><span class="lineno">  183</span>        {{1, 0, 1, 0}, {1, 1, 1, 1}, {0, 1, 2, 1}}};</div>
+<div class="line"><span class="lineno">  184</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 10&gt;</a>, 20&gt; b1 = {{0}};</div>
+<div class="line"><span class="lineno">  185</span>    <span class="keywordtype">double</span> dot1 = 0;</div>
+<div class="line"><span class="lineno">  186</span>    <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f">linear_algebra::gram_schmidt::gram_schmidt</a>(3, 4, a1, b1);</div>
+<div class="line"><span class="lineno">  187</span>    <span class="keywordtype">int</span> flag = 1;</div>
+<div class="line"><span class="lineno">  188</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 2; ++i) {</div>
+<div class="line"><span class="lineno">  189</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j &lt; 3; ++j) {</div>
+<div class="line"><span class="lineno">  190</span>            dot1 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">fabs</a>(</div>
+<div class="line"><span class="lineno">  191</span>                linear_algebra::gram_schmidt::dot_product(b1[i], b1[j], 4));</div>
+<div class="line"><span class="lineno">  192</span>            <span class="keywordflow">if</span> (dot1 &gt; 0.1) {</div>
+<div class="line"><span class="lineno">  193</span>                flag = 0;</div>
+<div class="line"><span class="lineno">  194</span>                <span class="keywordflow">break</span>;</div>
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+<div class="line"><span class="lineno">  200</span>    assert(flag == 1);</div>
+<div class="line"><span class="lineno">  201</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test Case 1\n &quot;</span>;</div>
+<div class="line"><span class="lineno">  202</span> </div>
+<div class="line"><span class="lineno">  203</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 10&gt;</a>, 20&gt; a2 = {{{3, 1}, {2, 2}}};</div>
+<div class="line"><span class="lineno">  204</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 10&gt;</a>, 20&gt; b2 = {{0}};</div>
+<div class="line"><span class="lineno">  205</span>    <span class="keywordtype">double</span> dot2 = 0;</div>
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+<div class="line"><span class="lineno">  207</span>    flag = 1;</div>
+<div class="line"><span class="lineno">  208</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 1; ++i) {</div>
+<div class="line"><span class="lineno">  209</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j &lt; 2; ++j) {</div>
+<div class="line"><span class="lineno">  210</span>            dot2 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">fabs</a>(</div>
+<div class="line"><span class="lineno">  211</span>                linear_algebra::gram_schmidt::dot_product(b2[i], b2[j], 2));</div>
+<div class="line"><span class="lineno">  212</span>            <span class="keywordflow">if</span> (dot2 &gt; 0.1) {</div>
+<div class="line"><span class="lineno">  213</span>                flag = 0;</div>
+<div class="line"><span class="lineno">  214</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  215</span>            }</div>
+<div class="line"><span class="lineno">  216</span>        }</div>
+<div class="line"><span class="lineno">  217</span>    }</div>
+<div class="line"><span class="lineno">  218</span>    <span class="keywordflow">if</span> (flag == 0)</div>
+<div class="line"><span class="lineno">  219</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Vectors are linearly dependent\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  220</span>    assert(flag == 1);</div>
+<div class="line"><span class="lineno">  221</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test Case 2\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  222</span> </div>
+<div class="line"><span class="lineno">  223</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 10&gt;</a>, 20&gt; a3 = {{{1, 2, 2}, {-4, 3, 2}}};</div>
+<div class="line"><span class="lineno">  224</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;double, 10&gt;</a>, 20&gt; b3 = {{0}};</div>
+<div class="line"><span class="lineno">  225</span>    <span class="keywordtype">double</span> dot3 = 0;</div>
+<div class="line"><span class="lineno">  226</span>    <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f">linear_algebra::gram_schmidt::gram_schmidt</a>(2, 3, a3, b3);</div>
+<div class="line"><span class="lineno">  227</span>    flag = 1;</div>
+<div class="line"><span class="lineno">  228</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 1; ++i) {</div>
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+<div class="line"><span class="lineno">  231</span>                linear_algebra::gram_schmidt::dot_product(b3[i], b3[j], 3));</div>
+<div class="line"><span class="lineno">  232</span>            <span class="keywordflow">if</span> (dot3 &gt; 0.1) {</div>
+<div class="line"><span class="lineno">  233</span>                flag = 0;</div>
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+<div class="line"><span class="lineno">  237</span>    }</div>
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+<div class="line"><span class="lineno">  240</span>    assert(flag == 1);</div>
+<div class="line"><span class="lineno">  241</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test Case 3\n&quot;</span>;</div>
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-<div class="line"><a id="l00345" name="l00345"></a><span class="lineno">  345</span> </div>
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-<div class="line"><a id="l00347" name="l00347"></a><span class="lineno">  347</span>        <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a70ca8d0267008e09cfa50b4e2ddfbe53">search::sublist_search::makeLinkedList</a>(mainlistData);</div>
-<div class="line"><a id="l00348" name="l00348"></a><span class="lineno">  348</span>    <a class="code hl_struct" href="../../da/d61/structsearch_1_1sublist__search_1_1_node.html">search::sublist_search::Node</a> *sublistLL =</div>
-<div class="line"><a id="l00349" name="l00349"></a><span class="lineno">  349</span>        <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a70ca8d0267008e09cfa50b4e2ddfbe53">search::sublist_search::makeLinkedList</a>(</div>
-<div class="line"><a id="l00350" name="l00350"></a><span class="lineno">  350</span>            sublistData);  <span class="comment">///&lt; Main list in which sublist is to be</span><span class="comment"></span></div>
-<div class="line"><a id="l00351" name="l00351"></a><span class="lineno">  351</span><span class="comment">                           ///&lt; searched</span></div>
-<div class="line"><a id="l00352" name="l00352"></a><span class="lineno">  352</span><span class="comment"></span> </div>
-<div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span>    <span class="keywordtype">bool</span> <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a1cc9dd6e6190d10a010fdcdfe7a21a81">exists</a> = <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a4faee403e2758aaab682ed6622ae218c">search::sublist_search::sublistSearch</a>(</div>
-<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span>        sublistLL,</div>
-<div class="line"><a id="l00355" name="l00355"></a><span class="lineno">  355</span>        mainlistLL);  <span class="comment">///&lt; boolean to check if the sublist exists or not</span></div>
-<div class="line"><a id="l00356" name="l00356"></a><span class="lineno">  356</span> </div>
-<div class="line"><a id="l00357" name="l00357"></a><span class="lineno">  357</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Sublist: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00358" name="l00358"></a><span class="lineno">  358</span>    <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#ad1028bc215281d62e344af99da57fab2">search::sublist_search::printLinkedList</a>(sublistLL);</div>
-<div class="line"><a id="l00359" name="l00359"></a><span class="lineno">  359</span> </div>
-<div class="line"><a id="l00360" name="l00360"></a><span class="lineno">  360</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Main list: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00361" name="l00361"></a><span class="lineno">  361</span>    <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#ad1028bc215281d62e344af99da57fab2">search::sublist_search::printLinkedList</a>(mainlistLL);</div>
-<div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00363" name="l00363"></a><span class="lineno">  363</span> </div>
-<div class="line"><a id="l00364" name="l00364"></a><span class="lineno">  364</span>    <span class="keywordflow">if</span> (exists) {</div>
-<div class="line"><a id="l00365" name="l00365"></a><span class="lineno">  365</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;[TRUE] - sublist found in main list\n&quot;</span>;</div>
-<div class="line"><a id="l00366" name="l00366"></a><span class="lineno">  366</span>    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00367" name="l00367"></a><span class="lineno">  367</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;[FALSE] - sublist NOT found in main list\n&quot;</span>;</div>
-<div class="line"><a id="l00368" name="l00368"></a><span class="lineno">  368</span>    }</div>
-<div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  339</span>                                 {</div>
+<div class="line"><span class="lineno">  340</span>    <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
+<div class="line"><span class="lineno">  341</span> </div>
+<div class="line"><span class="lineno">  342</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> mainlistData = {</div>
+<div class="line"><span class="lineno">  343</span>        2, 5, 6, 7, 8};  <span class="comment">///&lt; Main list in which sublist is to be searched</span></div>
+<div class="line"><span class="lineno">  344</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> sublistData = {6, 8};  <span class="comment">///&lt; Sublist to be searched</span></div>
+<div class="line"><span class="lineno">  345</span> </div>
+<div class="line"><span class="lineno">  346</span>    <a class="code hl_struct" href="../../da/d61/structsearch_1_1sublist__search_1_1_node.html">search::sublist_search::Node</a> *mainlistLL =</div>
+<div class="line"><span class="lineno">  347</span>        <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a70ca8d0267008e09cfa50b4e2ddfbe53">search::sublist_search::makeLinkedList</a>(mainlistData);</div>
+<div class="line"><span class="lineno">  348</span>    <a class="code hl_struct" href="../../da/d61/structsearch_1_1sublist__search_1_1_node.html">search::sublist_search::Node</a> *sublistLL =</div>
+<div class="line"><span class="lineno">  349</span>        <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a70ca8d0267008e09cfa50b4e2ddfbe53">search::sublist_search::makeLinkedList</a>(</div>
+<div class="line"><span class="lineno">  350</span>            sublistData);  <span class="comment">///&lt; Main list in which sublist is to be</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  351</span><span class="comment">                           ///&lt; searched</span></div>
+<div class="line"><span class="lineno">  352</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  353</span>    <span class="keywordtype">bool</span> <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a1cc9dd6e6190d10a010fdcdfe7a21a81">exists</a> = <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a4faee403e2758aaab682ed6622ae218c">search::sublist_search::sublistSearch</a>(</div>
+<div class="line"><span class="lineno">  354</span>        sublistLL,</div>
+<div class="line"><span class="lineno">  355</span>        mainlistLL);  <span class="comment">///&lt; boolean to check if the sublist exists or not</span></div>
+<div class="line"><span class="lineno">  356</span> </div>
+<div class="line"><span class="lineno">  357</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Sublist: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  358</span>    <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#ad1028bc215281d62e344af99da57fab2">search::sublist_search::printLinkedList</a>(sublistLL);</div>
+<div class="line"><span class="lineno">  359</span> </div>
+<div class="line"><span class="lineno">  360</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Main list: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  361</span>    <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#ad1028bc215281d62e344af99da57fab2">search::sublist_search::printLinkedList</a>(mainlistLL);</div>
+<div class="line"><span class="lineno">  362</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  363</span> </div>
+<div class="line"><span class="lineno">  364</span>    <span class="keywordflow">if</span> (exists) {</div>
+<div class="line"><span class="lineno">  365</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;[TRUE] - sublist found in main list\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  366</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  367</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;[FALSE] - sublist NOT found in main list\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  368</span>    }</div>
+<div class="line"><span class="lineno">  369</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  370</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
 <div class="ttc" id="astructsearch_1_1sublist__search_1_1_node_html"><div class="ttname"><a href="../../da/d61/structsearch_1_1sublist__search_1_1_node.html">search::sublist_search::Node</a></div><div class="ttdoc">A Node structure representing a single link Node in a linked list.</div><div class="ttdef"><b>Definition:</b> sublist_search.cpp:47</div></div>
@@ -241,7 +241,7 @@ Working</h3>
 <div class="ttc" id="asublist__search_8cpp_html_a70ca8d0267008e09cfa50b4e2ddfbe53"><div class="ttname"><a href="../../d5/d45/sublist__search_8cpp.html#a70ca8d0267008e09cfa50b4e2ddfbe53">search::sublist_search::makeLinkedList</a></div><div class="ttdeci">Node * makeLinkedList(const std::vector&lt; uint64_t &gt; &amp;data)</div><div class="ttdoc">Give a vector of data, it adds each element of vector in the linked list and return the address of he...</div><div class="ttdef"><b>Definition:</b> sublist_search.cpp:73</div></div>
 <div class="ttc" id="asublist__search_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d5/d45/sublist__search_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition:</b> sublist_search.cpp:328</div></div>
 <div class="ttc" id="asublist__search_8cpp_html_ad1028bc215281d62e344af99da57fab2"><div class="ttname"><a href="../../d5/d45/sublist__search_8cpp.html#ad1028bc215281d62e344af99da57fab2">search::sublist_search::printLinkedList</a></div><div class="ttdeci">void printLinkedList(Node *start)</div><div class="ttdoc">A simple function to print the linked list.</div><div class="ttdef"><b>Definition:</b> sublist_search.cpp:57</div></div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; uint64_t &gt;</a></div></div>
 <div class="ttc" id="aword__break_8cpp_html_a1cc9dd6e6190d10a010fdcdfe7a21a81"><div class="ttname"><a href="../../d3/d84/word__break_8cpp.html#a1cc9dd6e6190d10a010fdcdfe7a21a81">dynamic_programming::word_break::exists</a></div><div class="ttdeci">bool exists(const std::string &amp;str, const std::unordered_set&lt; std::string &gt; &amp;strSet)</div><div class="ttdoc">Function that checks if the string passed in param is present in the the unordered_set passed.</div><div class="ttdef"><b>Definition:</b> word_break.cpp:60</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -277,25 +277,25 @@ Here is the call graph for this function:</div>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>Node* A head pointer to the linked list. </dd></dl>
 <p >This is used in test cases for rapidly creating linked list with 100+ elements, instead of hard-coding 100 elements in test cases.</p>
-<div class="fragment"><div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>                                                      {<span class="comment"></span></div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span><span class="comment">    /// This is used in test cases for rapidly creating linked list with 100+</span></div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span><span class="comment">    /// elements, instead of hard-coding 100 elements in test cases.</span></div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span><span class="comment"></span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *head = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *tail = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i : <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>) {</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>;</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>        <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;data = i;</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>        <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;next = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        <span class="keywordflow">if</span> (head == <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>            head = <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>            tail = <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>        } <span class="keywordflow">else</span> {</div>
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-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>            tail = tail-&gt;next;</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        }</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    }</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    <span class="keywordflow">return</span> head;</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   73</span>                                                      {<span class="comment"></span></div>
+<div class="line"><span class="lineno">   74</span><span class="comment">    /// This is used in test cases for rapidly creating linked list with 100+</span></div>
+<div class="line"><span class="lineno">   75</span><span class="comment">    /// elements, instead of hard-coding 100 elements in test cases.</span></div>
+<div class="line"><span class="lineno">   76</span><span class="comment"></span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *head = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">   77</span>    <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *tail = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">   78</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i : <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>) {</div>
+<div class="line"><span class="lineno">   79</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *<a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>;</div>
+<div class="line"><span class="lineno">   80</span>        <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;data = i;</div>
+<div class="line"><span class="lineno">   81</span>        <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;next = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">   82</span>        <span class="keywordflow">if</span> (head == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">   83</span>            head = <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
+<div class="line"><span class="lineno">   84</span>            tail = <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
+<div class="line"><span class="lineno">   85</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   86</span>            tail-&gt;next = <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
+<div class="line"><span class="lineno">   87</span>            tail = tail-&gt;next;</div>
+<div class="line"><span class="lineno">   88</span>        }</div>
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+<div class="line"><span class="lineno">   90</span>    <span class="keywordflow">return</span> head;</div>
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 <div class="ttc" id="ahash__search_8cpp_html_a6e1a77282bc65ad359d753d25df23243"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a></div><div class="ttdeci">int data[MAX]</div><div class="ttdoc">test data</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:24</div></div>
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 <div class="ttc" id="astruct_node_html"><div class="ttname"><a href="../../db/d8b/struct_node.html">Node</a></div><div class="ttdef"><b>Definition:</b> linkedlist_implentation_usingarray.cpp:14</div></div>
@@ -333,13 +333,13 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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 Here is the call graph for this function:</div>
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@@ -393,52 +393,52 @@ false if the sublist is NOT found </dd></dl>
 <p >set the target pointer again to stating point of target list.</p>
 <p >set the main pointer to the next element of the main list and repeat the algo.</p>
 <p >If the main list is exhausted, means sublist does not found, return false</p>
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 <p>Self-test implementations. </p>
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-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        heapify(arr, n, largest);</div>
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+<div class="fragment"><div class="line"><span class="lineno">   58</span>                                   {</div>
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+<div class="line"><span class="lineno">   60</span>    <span class="keywordtype">int</span> l = 2 * i + 1;</div>
+<div class="line"><span class="lineno">   61</span>    <span class="keywordtype">int</span> r = 2 * i + 2;</div>
+<div class="line"><span class="lineno">   62</span> </div>
+<div class="line"><span class="lineno">   63</span>    <span class="keywordflow">if</span> (l &lt; n &amp;&amp; arr[l] &gt; arr[largest])</div>
+<div class="line"><span class="lineno">   64</span>        largest = l;</div>
+<div class="line"><span class="lineno">   65</span> </div>
+<div class="line"><span class="lineno">   66</span>    <span class="keywordflow">if</span> (r &lt; n &amp;&amp; arr[r] &gt; arr[largest])</div>
+<div class="line"><span class="lineno">   67</span>        largest = r;</div>
+<div class="line"><span class="lineno">   68</span> </div>
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+<div class="line"><span class="lineno">   70</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[i], arr[largest]);</div>
+<div class="line"><span class="lineno">   71</span>        heapify(arr, n, largest);</div>
+<div class="line"><span class="lineno">   72</span>    }</div>
+<div class="line"><span class="lineno">   73</span>}</div>
 <div class="ttc" id="aswap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a></div><div class="ttdeci">T swap(T... args)</div></div>
 </div><!-- fragment -->
 </div>
@@ -292,14 +292,14 @@ template&lt;typename T &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>                             {</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = n - 1; i &gt;= 0; i--) heapify(arr, n, i);</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span> </div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = n - 1; i &gt;= 0; i--) {</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[0], arr[i]);</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        heapify(arr, i, 0);</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    }</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   84</span>                             {</div>
+<div class="line"><span class="lineno">   85</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = n - 1; i &gt;= 0; i--) heapify(arr, n, i);</div>
+<div class="line"><span class="lineno">   86</span> </div>
+<div class="line"><span class="lineno">   87</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = n - 1; i &gt;= 0; i--) {</div>
+<div class="line"><span class="lineno">   88</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[0], arr[i]);</div>
+<div class="line"><span class="lineno">   89</span>        heapify(arr, i, 0);</div>
+<div class="line"><span class="lineno">   90</span>    }</div>
+<div class="line"><span class="lineno">   91</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -320,21 +320,21 @@ template&lt;typename T &gt; </div>
 </div><div class="memdoc">
 <p >Main function</p>
 <p >Driver Code </p>
-<div class="fragment"><div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>           {</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    <span class="keywordtype">int</span> size;</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number of elements : &quot;</span>;</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; size;</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>    <span class="keywordtype">int</span> *arr = <span class="keyword">new</span> <span class="keywordtype">int</span>[size];</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the unsorted elements : &quot;</span>;</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; size; ++i) {</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; arr[i];</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    }</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>    <a class="code hl_function" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a>(arr, 0, size - 1);</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Sorted array : &quot;</span>;</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <a class="code hl_function" href="../../d5/d4c/group__sorting.html#ga0a9a57a1f1bbba3d4822531d002b7e07">show</a>(arr, size);</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <span class="keyword">delete</span>[] arr;</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   90</span>           {</div>
+<div class="line"><span class="lineno">   91</span>    <span class="keywordtype">int</span> size;</div>
+<div class="line"><span class="lineno">   92</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number of elements : &quot;</span>;</div>
+<div class="line"><span class="lineno">   93</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; size;</div>
+<div class="line"><span class="lineno">   94</span>    <span class="keywordtype">int</span> *arr = <span class="keyword">new</span> <span class="keywordtype">int</span>[size];</div>
+<div class="line"><span class="lineno">   95</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the unsorted elements : &quot;</span>;</div>
+<div class="line"><span class="lineno">   96</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; size; ++i) {</div>
+<div class="line"><span class="lineno">   97</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; arr[i];</div>
+<div class="line"><span class="lineno">   98</span>    }</div>
+<div class="line"><span class="lineno">   99</span>    <a class="code hl_function" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a>(arr, 0, size - 1);</div>
+<div class="line"><span class="lineno">  100</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Sorted array : &quot;</span>;</div>
+<div class="line"><span class="lineno">  101</span>    <a class="code hl_function" href="../../d5/d4c/group__sorting.html#ga0a9a57a1f1bbba3d4822531d002b7e07">show</a>(arr, size);</div>
+<div class="line"><span class="lineno">  102</span>    <span class="keyword">delete</span>[] arr;</div>
+<div class="line"><span class="lineno">  103</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  104</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="agroup__sorting_html_ga0a9a57a1f1bbba3d4822531d002b7e07"><div class="ttname"><a href="../../d5/d4c/group__sorting.html#ga0a9a57a1f1bbba3d4822531d002b7e07">show</a></div><div class="ttdeci">void show(int *arr, int size)</div><div class="ttdef"><b>Definition:</b> merge_sort.cpp:84</div></div>
 <div class="ttc" id="agroup__sorting_html_gab6b14fea48d9841e29b9fc26be6e05d7"><div class="ttname"><a href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a></div><div class="ttdeci">void mergeSort(int *arr, int l, int r)</div><div class="ttdef"><b>Definition:</b> merge_sort.cpp:71</div></div>
@@ -394,33 +394,33 @@ template&lt;typename T &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>                                          {</div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>    <span class="keywordtype">int</span> i, j, k;</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    <span class="keywordtype">int</span> n1 = m - l + 1;</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>    <span class="keywordtype">int</span> n2 = r - m;</div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span> </div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    <span class="keywordtype">int</span> *L = <span class="keyword">new</span> <span class="keywordtype">int</span>[n1], *R = <span class="keyword">new</span> <span class="keywordtype">int</span>[n2];</div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span> </div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    <span class="keywordflow">for</span> (i = 0; i &lt; n1; i++) L[i] = arr[l + i];</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    <span class="keywordflow">for</span> (j = 0; j &lt; n2; j++) R[j] = arr[m + 1 + j];</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span> </div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>    i = 0;</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    j = 0;</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>    k = l;</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>    <span class="keywordflow">while</span> (i &lt; n1 || j &lt; n2) {</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>        <span class="keywordflow">if</span> (j &gt;= n2 || (i &lt; n1 &amp;&amp; L[i] &lt;= R[j])) {</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>            arr[k] = L[i];</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>            i++;</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>            arr[k] = R[j];</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>            j++;</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>        }</div>
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-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    }</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span> </div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    <span class="keyword">delete</span>[] L;</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <span class="keyword">delete</span>[] R;</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   33</span>                                          {</div>
+<div class="line"><span class="lineno">   34</span>    <span class="keywordtype">int</span> i, j, k;</div>
+<div class="line"><span class="lineno">   35</span>    <span class="keywordtype">int</span> n1 = m - l + 1;</div>
+<div class="line"><span class="lineno">   36</span>    <span class="keywordtype">int</span> n2 = r - m;</div>
+<div class="line"><span class="lineno">   37</span> </div>
+<div class="line"><span class="lineno">   38</span>    <span class="keywordtype">int</span> *L = <span class="keyword">new</span> <span class="keywordtype">int</span>[n1], *R = <span class="keyword">new</span> <span class="keywordtype">int</span>[n2];</div>
+<div class="line"><span class="lineno">   39</span> </div>
+<div class="line"><span class="lineno">   40</span>    <span class="keywordflow">for</span> (i = 0; i &lt; n1; i++) L[i] = arr[l + i];</div>
+<div class="line"><span class="lineno">   41</span>    <span class="keywordflow">for</span> (j = 0; j &lt; n2; j++) R[j] = arr[m + 1 + j];</div>
+<div class="line"><span class="lineno">   42</span> </div>
+<div class="line"><span class="lineno">   43</span>    i = 0;</div>
+<div class="line"><span class="lineno">   44</span>    j = 0;</div>
+<div class="line"><span class="lineno">   45</span>    k = l;</div>
+<div class="line"><span class="lineno">   46</span>    <span class="keywordflow">while</span> (i &lt; n1 || j &lt; n2) {</div>
+<div class="line"><span class="lineno">   47</span>        <span class="keywordflow">if</span> (j &gt;= n2 || (i &lt; n1 &amp;&amp; L[i] &lt;= R[j])) {</div>
+<div class="line"><span class="lineno">   48</span>            arr[k] = L[i];</div>
+<div class="line"><span class="lineno">   49</span>            i++;</div>
+<div class="line"><span class="lineno">   50</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   51</span>            arr[k] = R[j];</div>
+<div class="line"><span class="lineno">   52</span>            j++;</div>
+<div class="line"><span class="lineno">   53</span>        }</div>
+<div class="line"><span class="lineno">   54</span>        <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++;</div>
+<div class="line"><span class="lineno">   55</span>    }</div>
+<div class="line"><span class="lineno">   56</span> </div>
+<div class="line"><span class="lineno">   57</span>    <span class="keyword">delete</span>[] L;</div>
+<div class="line"><span class="lineno">   58</span>    <span class="keyword">delete</span>[] R;</div>
+<div class="line"><span class="lineno">   59</span>}</div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
 </div><!-- fragment -->
 </div>
@@ -465,14 +465,14 @@ template&lt;typename T &gt; </div>
   </table>
   </dd>
 </dl>
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-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>        <a class="code hl_function" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a>(arr, m + 1, r);</div>
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-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   71</span>                                       {</div>
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+<div class="line"><span class="lineno">   73</span>        <span class="keywordtype">int</span> m = l + (r - l) / 2;</div>
+<div class="line"><span class="lineno">   74</span>        <a class="code hl_function" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a>(arr, l, m);</div>
+<div class="line"><span class="lineno">   75</span>        <a class="code hl_function" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a>(arr, m + 1, r);</div>
+<div class="line"><span class="lineno">   76</span>        <a class="code hl_function" href="../../d5/d4c/group__sorting.html#ga460c61cd948203b4816bef2accb3fc73">merge</a>(arr, l, m, r);</div>
+<div class="line"><span class="lineno">   77</span>    }</div>
+<div class="line"><span class="lineno">   78</span>}</div>
 <div class="ttc" id="agroup__sorting_html_ga460c61cd948203b4816bef2accb3fc73"><div class="ttname"><a href="../../d5/d4c/group__sorting.html#ga460c61cd948203b4816bef2accb3fc73">merge</a></div><div class="ttdeci">void merge(int *arr, int l, int m, int r)</div><div class="ttdef"><b>Definition:</b> merge_sort.cpp:33</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -509,10 +509,10 @@ Here is the call graph for this function:</div>
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@@ -193,10 +193,10 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>                    {</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>        <span class="comment">// It&#39;s just to avoid writing cout and endl</span></div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;[TESTS] : ---&gt; &quot;</span> &lt;&lt; msg &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  233</span>                    {</div>
+<div class="line"><span class="lineno">  234</span>        <span class="comment">// It&#39;s just to avoid writing cout and endl</span></div>
+<div class="line"><span class="lineno">  235</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;[TESTS] : ---&gt; &quot;</span> &lt;&lt; msg &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  236</span>    }</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -242,10 +242,10 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>                    {</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>        <span class="comment">// It&#39;s just to avoid writing cout and endl</span></div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;[TESTS] : ---&gt; &quot;</span> &lt;&lt; msg &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  161</span>                    {</div>
+<div class="line"><span class="lineno">  162</span>        <span class="comment">// It&#39;s just to avoid writing cout and endl</span></div>
+<div class="line"><span class="lineno">  163</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;[TESTS] : ---&gt; &quot;</span> &lt;&lt; msg &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  164</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -289,10 +289,10 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>                    {</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>        <span class="comment">// It&#39;s just to avoid writing cout and endl</span></div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;[TESTS] : ---&gt; &quot;</span> &lt;&lt; msg &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  189</span>                    {</div>
+<div class="line"><span class="lineno">  190</span>        <span class="comment">// It&#39;s just to avoid writing cout and endl</span></div>
+<div class="line"><span class="lineno">  191</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;[TESTS] : ---&gt; &quot;</span> &lt;&lt; msg &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  192</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -327,16 +327,16 @@ Here is the call graph for this function:</div>
 
 <p>Executes test cases. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>                    {</div>
-<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Running Tests...&quot;</span>);</div>
-<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span> </div>
-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#ac2636e8b5b9e053374c45bfcf0603008">testCase_1</a>();</div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#abae0148985f159b582a385cf399254e3">testCase_2</a>();</div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#ad9f95c09931625b41e3be1f88d1e28c5">testCase_3</a>();</div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span> </div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Test Cases over!&quot;</span>);</div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  243</span>                    {</div>
+<div class="line"><span class="lineno">  244</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Running Tests...&quot;</span>);</div>
+<div class="line"><span class="lineno">  245</span> </div>
+<div class="line"><span class="lineno">  246</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#ac2636e8b5b9e053374c45bfcf0603008">testCase_1</a>();</div>
+<div class="line"><span class="lineno">  247</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#abae0148985f159b582a385cf399254e3">testCase_2</a>();</div>
+<div class="line"><span class="lineno">  248</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#ad9f95c09931625b41e3be1f88d1e28c5">testCase_3</a>();</div>
+<div class="line"><span class="lineno">  249</span> </div>
+<div class="line"><span class="lineno">  250</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Test Cases over!&quot;</span>);</div>
+<div class="line"><span class="lineno">  251</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  252</span>    }</div>
 <div class="ttc" id="aclass_test_cases_html_aa3aa3d5bf666f327ee8e2d11d397b06e"><div class="ttname"><a href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">TestCases::log</a></div><div class="ttdeci">void log(T msg)</div><div class="ttdoc">A function to print given message on console.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:233</div></div>
 <div class="ttc" id="aclass_test_cases_html_abae0148985f159b582a385cf399254e3"><div class="ttname"><a href="../../d5/d58/class_test_cases.html#abae0148985f159b582a385cf399254e3">TestCases::testCase_2</a></div><div class="ttdeci">void testCase_2()</div><div class="ttdoc">A test case which contains main list of 100 elements and sublist of 20.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:304</div></div>
 <div class="ttc" id="aclass_test_cases_html_ac2636e8b5b9e053374c45bfcf0603008"><div class="ttname"><a href="../../d5/d58/class_test_cases.html#ac2636e8b5b9e053374c45bfcf0603008">TestCases::testCase_1</a></div><div class="ttdeci">void testCase_1()</div><div class="ttdoc">A test case contains edge case, printing inorder successor of last node.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:259</div></div>
@@ -375,16 +375,16 @@ Here is the call graph for this function:</div>
 
 <p>Executes test cases. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>                    {</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Running Tests...&quot;</span>);</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span> </div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#ac2636e8b5b9e053374c45bfcf0603008">testCase_1</a>();</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#abae0148985f159b582a385cf399254e3">testCase_2</a>();</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#ad9f95c09931625b41e3be1f88d1e28c5">testCase_3</a>();</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span> </div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Test Cases over!&quot;</span>);</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  171</span>                    {</div>
+<div class="line"><span class="lineno">  172</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Running Tests...&quot;</span>);</div>
+<div class="line"><span class="lineno">  173</span> </div>
+<div class="line"><span class="lineno">  174</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#ac2636e8b5b9e053374c45bfcf0603008">testCase_1</a>();</div>
+<div class="line"><span class="lineno">  175</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#abae0148985f159b582a385cf399254e3">testCase_2</a>();</div>
+<div class="line"><span class="lineno">  176</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#ad9f95c09931625b41e3be1f88d1e28c5">testCase_3</a>();</div>
+<div class="line"><span class="lineno">  177</span> </div>
+<div class="line"><span class="lineno">  178</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Test Cases over!&quot;</span>);</div>
+<div class="line"><span class="lineno">  179</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  180</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -419,16 +419,16 @@ Here is the call graph for this function:</div>
 
 <p>Executes test cases. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>                    {</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Running Tests...&quot;</span>);</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span> </div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#ac2636e8b5b9e053374c45bfcf0603008">testCase_1</a>();</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#abae0148985f159b582a385cf399254e3">testCase_2</a>();</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#ad9f95c09931625b41e3be1f88d1e28c5">testCase_3</a>();</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span> </div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Test Cases over!&quot;</span>);</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  199</span>                    {</div>
+<div class="line"><span class="lineno">  200</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Running Tests...&quot;</span>);</div>
+<div class="line"><span class="lineno">  201</span> </div>
+<div class="line"><span class="lineno">  202</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#ac2636e8b5b9e053374c45bfcf0603008">testCase_1</a>();</div>
+<div class="line"><span class="lineno">  203</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#abae0148985f159b582a385cf399254e3">testCase_2</a>();</div>
+<div class="line"><span class="lineno">  204</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#ad9f95c09931625b41e3be1f88d1e28c5">testCase_3</a>();</div>
+<div class="line"><span class="lineno">  205</span> </div>
+<div class="line"><span class="lineno">  206</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Test Cases over!&quot;</span>);</div>
+<div class="line"><span class="lineno">  207</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  208</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -469,50 +469,50 @@ Here is the call graph for this function:</div>
 <p >&lt; Printing inorder to cross-verify.</p>
 <p >&lt; The inorder successor node for given data</p>
 <p >memory cleanup!</p>
-<div class="fragment"><div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>                      {</div>
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-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span> </div>
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-<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Description:&quot;</span>);</div>
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-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>            <span class="stringliteral">&quot;BST, Output will be nullptr.&quot;</span>);</div>
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-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>        <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a> *root =</div>
-<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>            <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> node_data{</div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>            20, 3, 5, 6, 2, 23, 45, 78, 21};  <span class="comment">///&lt; Data to make nodes in BST</span></div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span> </div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>        root = <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a05fe8a029e155c43e4efa598d4d089d9">operations_on_datastructures::inorder_traversal_of_bst::makeBST</a>(</div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>            root,</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>            node_data);  <span class="comment">///&lt; Adding nodes to BST</span></div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span> </div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Inorder sequence is : &quot;</span>;</div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>        <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">operations_on_datastructures::inorder_traversal_of_bst::printInorder</a>(</div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>            root);  <span class="comment">///&lt; Printing inorder to cross-verify.</span></div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span> </div>
-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>        <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a></div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>            *inorderSuccessor = operations_on_datastructures::</div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>                inorder_traversal_of_bst::getInorderSuccessor(</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>                    root, 78);  <span class="comment">///&lt; The inorder successor node for given data</span></div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span> </div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Checking assert expression...&quot;</span>);</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>        assert(inorderSuccessor == expectedOutput);</div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Assertion check passed!&quot;</span>);</div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span> </div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>        <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7b20eb99272665c1777949e26ab59589">operations_on_datastructures::inorder_traversal_of_bst::deallocate</a>(</div>
-<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>            root);  <span class="comment">/// memory cleanup!</span></div>
-<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span> </div>
-<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;[PASS] : TEST CASE 1 PASS!&quot;</span>);</div>
-<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span>);</div>
-<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  259</span>                      {</div>
+<div class="line"><span class="lineno">  260</span>        <span class="keyword">const</span> <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a></div>
+<div class="line"><span class="lineno">  261</span>            *expectedOutput = <span class="keyword">nullptr</span>;  <span class="comment">///&lt; Expected output of this test</span></div>
+<div class="line"><span class="lineno">  262</span> </div>
+<div class="line"><span class="lineno">  263</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span>);</div>
+<div class="line"><span class="lineno">  264</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;This is test case 1 : &quot;</span>);</div>
+<div class="line"><span class="lineno">  265</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Description:&quot;</span>);</div>
+<div class="line"><span class="lineno">  266</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;   EDGE CASE : Printing inorder successor for last node in the &quot;</span></div>
+<div class="line"><span class="lineno">  267</span>            <span class="stringliteral">&quot;BST, Output will be nullptr.&quot;</span>);</div>
+<div class="line"><span class="lineno">  268</span> </div>
+<div class="line"><span class="lineno">  269</span>        <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a> *root =</div>
+<div class="line"><span class="lineno">  270</span>            <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  271</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> node_data{</div>
+<div class="line"><span class="lineno">  272</span>            20, 3, 5, 6, 2, 23, 45, 78, 21};  <span class="comment">///&lt; Data to make nodes in BST</span></div>
+<div class="line"><span class="lineno">  273</span> </div>
+<div class="line"><span class="lineno">  274</span>        root = <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a05fe8a029e155c43e4efa598d4d089d9">operations_on_datastructures::inorder_traversal_of_bst::makeBST</a>(</div>
+<div class="line"><span class="lineno">  275</span>            root,</div>
+<div class="line"><span class="lineno">  276</span>            node_data);  <span class="comment">///&lt; Adding nodes to BST</span></div>
+<div class="line"><span class="lineno">  277</span> </div>
+<div class="line"><span class="lineno">  278</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Inorder sequence is : &quot;</span>;</div>
+<div class="line"><span class="lineno">  279</span>        <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">operations_on_datastructures::inorder_traversal_of_bst::printInorder</a>(</div>
+<div class="line"><span class="lineno">  280</span>            root);  <span class="comment">///&lt; Printing inorder to cross-verify.</span></div>
+<div class="line"><span class="lineno">  281</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  282</span> </div>
+<div class="line"><span class="lineno">  283</span>        <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a></div>
+<div class="line"><span class="lineno">  284</span>            *inorderSuccessor = operations_on_datastructures::</div>
+<div class="line"><span class="lineno">  285</span>                inorder_traversal_of_bst::getInorderSuccessor(</div>
+<div class="line"><span class="lineno">  286</span>                    root, 78);  <span class="comment">///&lt; The inorder successor node for given data</span></div>
+<div class="line"><span class="lineno">  287</span> </div>
+<div class="line"><span class="lineno">  288</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Checking assert expression...&quot;</span>);</div>
+<div class="line"><span class="lineno">  289</span>        assert(inorderSuccessor == expectedOutput);</div>
+<div class="line"><span class="lineno">  290</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Assertion check passed!&quot;</span>);</div>
+<div class="line"><span class="lineno">  291</span> </div>
+<div class="line"><span class="lineno">  292</span>        <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7b20eb99272665c1777949e26ab59589">operations_on_datastructures::inorder_traversal_of_bst::deallocate</a>(</div>
+<div class="line"><span class="lineno">  293</span>            root);  <span class="comment">/// memory cleanup!</span></div>
+<div class="line"><span class="lineno">  294</span> </div>
+<div class="line"><span class="lineno">  295</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;[PASS] : TEST CASE 1 PASS!&quot;</span>);</div>
+<div class="line"><span class="lineno">  296</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span>);</div>
+<div class="line"><span class="lineno">  297</span>    }</div>
 <div class="ttc" id="aclassoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node_html"><div class="ttname"><a href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a></div><div class="ttdoc">A Node structure representing a single node in BST.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:56</div></div>
 <div class="ttc" id="ainorder__successor__of__bst_8cpp_html_a05fe8a029e155c43e4efa598d4d089d9"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a05fe8a029e155c43e4efa598d4d089d9">operations_on_datastructures::inorder_traversal_of_bst::makeBST</a></div><div class="ttdeci">Node * makeBST(Node *root, const std::vector&lt; int64_t &gt; &amp;data)</div><div class="ttdoc">This function is used in test cases to quickly create BST containing large data instead of hard codin...</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:155</div></div>
 <div class="ttc" id="ainorder__successor__of__bst_8cpp_html_a5d7266b934ca50c4f53e4f1e725d89a4"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">operations_on_datastructures::inorder_traversal_of_bst::printInorder</a></div><div class="ttdeci">void printInorder(Node *root)</div><div class="ttdoc">Prints the BST in inorder traversal using recursion.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:136</div></div>
 <div class="ttc" id="ainorder__successor__of__bst_8cpp_html_a7b20eb99272665c1777949e26ab59589"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7b20eb99272665c1777949e26ab59589">operations_on_datastructures::inorder_traversal_of_bst::deallocate</a></div><div class="ttdeci">void deallocate(Node *rootNode)</div><div class="ttdoc">This function clears the memory allocated to entire tree recursively. Its just for clean up the memor...</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:210</div></div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int64_t &gt;</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -553,43 +553,43 @@ Here is the call graph for this function:</div>
 <p >&lt; Sublist to be searched</p>
 <p >&lt; Main list in which sublist is to be searched</p>
 <p >&lt; boolean, if sublist exist or not</p>
-<div class="fragment"><div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>                      {</div>
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-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span> </div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;This is test case 1 for sublist search Algorithm : &quot;</span>);</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Description:&quot;</span>);</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;   EDGE CASE : Only contains one element&quot;</span>);</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span> </div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> sublistData = {</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>            6};  <span class="comment">///&lt; Data to make linked list which will be the sublist</span></div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> mainlistData = {</div>
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-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span> </div>
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-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>                sublistData);  <span class="comment">///&lt; Sublist to be searched</span></div>
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-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>                mainlistData);  <span class="comment">///&lt; Main list in which sublist is to be</span><span class="comment"></span></div>
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-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>            sublistLL, mainlistLL);  <span class="comment">///&lt; boolean, if sublist exist or not</span></div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span> </div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Checking assert expression...&quot;</span>);</div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>        assert(exists == expectedOutput);</div>
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-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span> </div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;[PASS] : TEST CASE 1 PASS!&quot;</span>);</div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span> </div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>        <span class="keyword">delete</span> (sublistLL);</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>        <span class="keyword">delete</span> (mainlistLL);</div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  186</span>                      {</div>
+<div class="line"><span class="lineno">  187</span>        <span class="keyword">const</span> <span class="keywordtype">bool</span> expectedOutput = <span class="keyword">true</span>;  <span class="comment">///&lt; Expected output of this test</span></div>
+<div class="line"><span class="lineno">  188</span> </div>
+<div class="line"><span class="lineno">  189</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
+<div class="line"><span class="lineno">  190</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
+<div class="line"><span class="lineno">  191</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;This is test case 1 for sublist search Algorithm : &quot;</span>);</div>
+<div class="line"><span class="lineno">  192</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Description:&quot;</span>);</div>
+<div class="line"><span class="lineno">  193</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;   EDGE CASE : Only contains one element&quot;</span>);</div>
+<div class="line"><span class="lineno">  194</span> </div>
+<div class="line"><span class="lineno">  195</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> sublistData = {</div>
+<div class="line"><span class="lineno">  196</span>            6};  <span class="comment">///&lt; Data to make linked list which will be the sublist</span></div>
+<div class="line"><span class="lineno">  197</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> mainlistData = {</div>
+<div class="line"><span class="lineno">  198</span>            2, 5, 6, 7,</div>
+<div class="line"><span class="lineno">  199</span>            8};  <span class="comment">///&lt; Data to make linked list which will be the main list</span></div>
+<div class="line"><span class="lineno">  200</span> </div>
+<div class="line"><span class="lineno">  201</span>        <a class="code hl_struct" href="../../da/d61/structsearch_1_1sublist__search_1_1_node.html">search::sublist_search::Node</a> *sublistLL =</div>
+<div class="line"><span class="lineno">  202</span>            <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a70ca8d0267008e09cfa50b4e2ddfbe53">search::sublist_search::makeLinkedList</a>(</div>
+<div class="line"><span class="lineno">  203</span>                sublistData);  <span class="comment">///&lt; Sublist to be searched</span></div>
+<div class="line"><span class="lineno">  204</span>        <a class="code hl_struct" href="../../da/d61/structsearch_1_1sublist__search_1_1_node.html">search::sublist_search::Node</a> *mainlistLL =</div>
+<div class="line"><span class="lineno">  205</span>            <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a70ca8d0267008e09cfa50b4e2ddfbe53">search::sublist_search::makeLinkedList</a>(</div>
+<div class="line"><span class="lineno">  206</span>                mainlistData);  <span class="comment">///&lt; Main list in which sublist is to be</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  207</span><span class="comment">                                ///&lt; searched</span></div>
+<div class="line"><span class="lineno">  208</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  209</span>        <span class="keywordtype">bool</span> <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a1cc9dd6e6190d10a010fdcdfe7a21a81">exists</a> = <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a4faee403e2758aaab682ed6622ae218c">search::sublist_search::sublistSearch</a>(</div>
+<div class="line"><span class="lineno">  210</span>            sublistLL, mainlistLL);  <span class="comment">///&lt; boolean, if sublist exist or not</span></div>
+<div class="line"><span class="lineno">  211</span> </div>
+<div class="line"><span class="lineno">  212</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Checking assert expression...&quot;</span>);</div>
+<div class="line"><span class="lineno">  213</span>        assert(exists == expectedOutput);</div>
+<div class="line"><span class="lineno">  214</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Assertion check passed!&quot;</span>);</div>
+<div class="line"><span class="lineno">  215</span> </div>
+<div class="line"><span class="lineno">  216</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;[PASS] : TEST CASE 1 PASS!&quot;</span>);</div>
+<div class="line"><span class="lineno">  217</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
+<div class="line"><span class="lineno">  218</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
+<div class="line"><span class="lineno">  219</span> </div>
+<div class="line"><span class="lineno">  220</span>        <span class="keyword">delete</span> (sublistLL);</div>
+<div class="line"><span class="lineno">  221</span>        <span class="keyword">delete</span> (mainlistLL);</div>
+<div class="line"><span class="lineno">  222</span>    }</div>
 <div class="ttc" id="astructsearch_1_1sublist__search_1_1_node_html"><div class="ttname"><a href="../../da/d61/structsearch_1_1sublist__search_1_1_node.html">search::sublist_search::Node</a></div><div class="ttdoc">A Node structure representing a single link Node in a linked list.</div><div class="ttdef"><b>Definition:</b> sublist_search.cpp:47</div></div>
 <div class="ttc" id="asublist__search_8cpp_html_a4faee403e2758aaab682ed6622ae218c"><div class="ttname"><a href="../../d5/d45/sublist__search_8cpp.html#a4faee403e2758aaab682ed6622ae218c">search::sublist_search::sublistSearch</a></div><div class="ttdeci">bool sublistSearch(Node *sublist, Node *mainList)</div><div class="ttdoc">Main searching function.</div><div class="ttdef"><b>Definition:</b> sublist_search.cpp:100</div></div>
 <div class="ttc" id="asublist__search_8cpp_html_a70ca8d0267008e09cfa50b4e2ddfbe53"><div class="ttname"><a href="../../d5/d45/sublist__search_8cpp.html#a70ca8d0267008e09cfa50b4e2ddfbe53">search::sublist_search::makeLinkedList</a></div><div class="ttdeci">Node * makeLinkedList(const std::vector&lt; uint64_t &gt; &amp;data)</div><div class="ttdoc">Give a vector of data, it adds each element of vector in the linked list and return the address of he...</div><div class="ttdef"><b>Definition:</b> sublist_search.cpp:73</div></div>
@@ -628,32 +628,32 @@ Here is the call graph for this function:</div>
 
 <p>A test case with single input. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>                      {</div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>        <span class="keyword">const</span> int64_t inputSize = 1;</div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;This is test case 1 for Random Pivot Quick Sort Algorithm : &quot;</span>);</div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Description:&quot;</span>);</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;   EDGE CASE : Only contains one element&quot;</span>);</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int64_t, inputSize&gt;</a> unsorted_arr{2};</div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span> </div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>        int64_t start = 0;</div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>        int64_t <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = unsorted_arr.size() - 1;  <span class="comment">// length - 1</span></div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span> </div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Running algorithm of data of length 50 ...&quot;</span>);</div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt;int64_t, unsorted_arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/size.html">size</a>()&gt; sorted_arr =</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>            <a class="code hl_function" href="../../d1/daa/random__pivot__quick__sort_8cpp.html#a7d2e7465e7b5d54c2de6d5e9db1ea6a5">sorting::random_pivot_quick_sort::quickSortRP</a>(unsorted_arr, start,</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>                                                          end);</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Algorithm finished!&quot;</span>);</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span> </div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Checking assert expression...&quot;</span>);</div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>        assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(sorted_arr.begin(), sorted_arr.end()));</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Assertion check passed!&quot;</span>);</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span> </div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;[PASS] : TEST CASE 1 PASS!&quot;</span>);</div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  214</span>                      {</div>
+<div class="line"><span class="lineno">  215</span>        <span class="keyword">const</span> int64_t inputSize = 1;</div>
+<div class="line"><span class="lineno">  216</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
+<div class="line"><span class="lineno">  217</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
+<div class="line"><span class="lineno">  218</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;This is test case 1 for Random Pivot Quick Sort Algorithm : &quot;</span>);</div>
+<div class="line"><span class="lineno">  219</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Description:&quot;</span>);</div>
+<div class="line"><span class="lineno">  220</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;   EDGE CASE : Only contains one element&quot;</span>);</div>
+<div class="line"><span class="lineno">  221</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int64_t, inputSize&gt;</a> unsorted_arr{2};</div>
+<div class="line"><span class="lineno">  222</span> </div>
+<div class="line"><span class="lineno">  223</span>        int64_t start = 0;</div>
+<div class="line"><span class="lineno">  224</span>        int64_t <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = unsorted_arr.size() - 1;  <span class="comment">// length - 1</span></div>
+<div class="line"><span class="lineno">  225</span> </div>
+<div class="line"><span class="lineno">  226</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Running algorithm of data of length 50 ...&quot;</span>);</div>
+<div class="line"><span class="lineno">  227</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt;int64_t, unsorted_arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/size.html">size</a>()&gt; sorted_arr =</div>
+<div class="line"><span class="lineno">  228</span>            <a class="code hl_function" href="../../d1/daa/random__pivot__quick__sort_8cpp.html#a7d2e7465e7b5d54c2de6d5e9db1ea6a5">sorting::random_pivot_quick_sort::quickSortRP</a>(unsorted_arr, start,</div>
+<div class="line"><span class="lineno">  229</span>                                                          end);</div>
+<div class="line"><span class="lineno">  230</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Algorithm finished!&quot;</span>);</div>
+<div class="line"><span class="lineno">  231</span> </div>
+<div class="line"><span class="lineno">  232</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Checking assert expression...&quot;</span>);</div>
+<div class="line"><span class="lineno">  233</span>        assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(sorted_arr.begin(), sorted_arr.end()));</div>
+<div class="line"><span class="lineno">  234</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Assertion check passed!&quot;</span>);</div>
+<div class="line"><span class="lineno">  235</span> </div>
+<div class="line"><span class="lineno">  236</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;[PASS] : TEST CASE 1 PASS!&quot;</span>);</div>
+<div class="line"><span class="lineno">  237</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
+<div class="line"><span class="lineno">  238</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
+<div class="line"><span class="lineno">  239</span>    }</div>
 <div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
 <div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a></div><div class="ttdeci">T end(T... args)</div></div>
 <div class="ttc" id="ais_sorted_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a></div><div class="ttdeci">T is_sorted(T... args)</div></div>
@@ -699,41 +699,41 @@ Here is the call graph for this function:</div>
 <p >&lt; Printing inorder to cross-verify.</p>
 <p >&lt; The inorder successor node for given data</p>
 <p >memory cleanup!</p>
-<div class="fragment"><div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span>                      {</div>
-<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span>        <span class="keyword">const</span> <span class="keywordtype">int</span> expectedOutput = 21;  <span class="comment">///&lt; Expected output of this test</span></div>
-<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span> </div>
-<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span>);</div>
-<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;This is test case 2 : &quot;</span>);</div>
-<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span> </div>
-<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span>        <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a> *root =</div>
-<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>            <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> node_data{</div>
-<div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span>            20, 3, 5, 6, 2, 23, 45, 78, 21};  <span class="comment">///&lt; Data to make nodes in BST</span></div>
-<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span> </div>
-<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span>        root = <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a05fe8a029e155c43e4efa598d4d089d9">operations_on_datastructures::inorder_traversal_of_bst::makeBST</a>(</div>
-<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>            root,</div>
-<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span>            node_data);  <span class="comment">///&lt; Adding nodes to BST</span></div>
-<div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span> </div>
-<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Inorder sequence is : &quot;</span>;</div>
-<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>        <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">operations_on_datastructures::inorder_traversal_of_bst::printInorder</a>(</div>
-<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>            root);  <span class="comment">///&lt; Printing inorder to cross-verify.</span></div>
-<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span> </div>
-<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>        <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a></div>
-<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span>            *inorderSuccessor = operations_on_datastructures::</div>
-<div class="line"><a id="l00326" name="l00326"></a><span class="lineno">  326</span>                inorder_traversal_of_bst::getInorderSuccessor(</div>
-<div class="line"><a id="l00327" name="l00327"></a><span class="lineno">  327</span>                    root, 20);  <span class="comment">///&lt; The inorder successor node for given data</span></div>
-<div class="line"><a id="l00328" name="l00328"></a><span class="lineno">  328</span> </div>
-<div class="line"><a id="l00329" name="l00329"></a><span class="lineno">  329</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Checking assert expression...&quot;</span>);</div>
-<div class="line"><a id="l00330" name="l00330"></a><span class="lineno">  330</span>        assert(inorderSuccessor-&gt;<a class="code hl_variable" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html#ae161f3e5ef33ade73429cab9291612e2">data</a> == expectedOutput);</div>
-<div class="line"><a id="l00331" name="l00331"></a><span class="lineno">  331</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Assertion check passed!&quot;</span>);</div>
-<div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span> </div>
-<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>        <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7b20eb99272665c1777949e26ab59589">operations_on_datastructures::inorder_traversal_of_bst::deallocate</a>(</div>
-<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span>            root);  <span class="comment">/// memory cleanup!</span></div>
-<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span> </div>
-<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;[PASS] : TEST CASE 2 PASS!&quot;</span>);</div>
-<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span>);</div>
-<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  304</span>                      {</div>
+<div class="line"><span class="lineno">  305</span>        <span class="keyword">const</span> <span class="keywordtype">int</span> expectedOutput = 21;  <span class="comment">///&lt; Expected output of this test</span></div>
+<div class="line"><span class="lineno">  306</span> </div>
+<div class="line"><span class="lineno">  307</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span>);</div>
+<div class="line"><span class="lineno">  308</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;This is test case 2 : &quot;</span>);</div>
+<div class="line"><span class="lineno">  309</span> </div>
+<div class="line"><span class="lineno">  310</span>        <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a> *root =</div>
+<div class="line"><span class="lineno">  311</span>            <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  312</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> node_data{</div>
+<div class="line"><span class="lineno">  313</span>            20, 3, 5, 6, 2, 23, 45, 78, 21};  <span class="comment">///&lt; Data to make nodes in BST</span></div>
+<div class="line"><span class="lineno">  314</span> </div>
+<div class="line"><span class="lineno">  315</span>        root = <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a05fe8a029e155c43e4efa598d4d089d9">operations_on_datastructures::inorder_traversal_of_bst::makeBST</a>(</div>
+<div class="line"><span class="lineno">  316</span>            root,</div>
+<div class="line"><span class="lineno">  317</span>            node_data);  <span class="comment">///&lt; Adding nodes to BST</span></div>
+<div class="line"><span class="lineno">  318</span> </div>
+<div class="line"><span class="lineno">  319</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Inorder sequence is : &quot;</span>;</div>
+<div class="line"><span class="lineno">  320</span>        <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">operations_on_datastructures::inorder_traversal_of_bst::printInorder</a>(</div>
+<div class="line"><span class="lineno">  321</span>            root);  <span class="comment">///&lt; Printing inorder to cross-verify.</span></div>
+<div class="line"><span class="lineno">  322</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  323</span> </div>
+<div class="line"><span class="lineno">  324</span>        <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a></div>
+<div class="line"><span class="lineno">  325</span>            *inorderSuccessor = operations_on_datastructures::</div>
+<div class="line"><span class="lineno">  326</span>                inorder_traversal_of_bst::getInorderSuccessor(</div>
+<div class="line"><span class="lineno">  327</span>                    root, 20);  <span class="comment">///&lt; The inorder successor node for given data</span></div>
+<div class="line"><span class="lineno">  328</span> </div>
+<div class="line"><span class="lineno">  329</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Checking assert expression...&quot;</span>);</div>
+<div class="line"><span class="lineno">  330</span>        assert(inorderSuccessor-&gt;<a class="code hl_variable" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html#ae161f3e5ef33ade73429cab9291612e2">data</a> == expectedOutput);</div>
+<div class="line"><span class="lineno">  331</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Assertion check passed!&quot;</span>);</div>
+<div class="line"><span class="lineno">  332</span> </div>
+<div class="line"><span class="lineno">  333</span>        <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7b20eb99272665c1777949e26ab59589">operations_on_datastructures::inorder_traversal_of_bst::deallocate</a>(</div>
+<div class="line"><span class="lineno">  334</span>            root);  <span class="comment">/// memory cleanup!</span></div>
+<div class="line"><span class="lineno">  335</span> </div>
+<div class="line"><span class="lineno">  336</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;[PASS] : TEST CASE 2 PASS!&quot;</span>);</div>
+<div class="line"><span class="lineno">  337</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span>);</div>
+<div class="line"><span class="lineno">  338</span>    }</div>
 <div class="ttc" id="aclassoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node_html_ae161f3e5ef33ade73429cab9291612e2"><div class="ttname"><a href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html#ae161f3e5ef33ade73429cab9291612e2">operations_on_datastructures::inorder_traversal_of_bst::Node::data</a></div><div class="ttdeci">int64_t data</div><div class="ttdoc">The key/value of the node.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:58</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -777,51 +777,51 @@ Here is the call graph for this function:</div>
 <p >&lt; Sublist to be searched</p>
 <p >&lt; Main list in which sublist is to be searched</p>
 <p >&lt; boolean, if sublist exist or not</p>
-<div class="fragment"><div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>                      {</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>        <span class="keyword">const</span> <span class="keywordtype">bool</span> expectedOutput = <span class="keyword">true</span>;  <span class="comment">/// Expected output of this test</span></div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span> </div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;This is test case 2 for sublist search Algorithm : &quot;</span>);</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Description:&quot;</span>);</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;   contains main list of 100 elements and sublist of 20&quot;</span>);</div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span> </div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> sublistData(</div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>            20);  <span class="comment">///&lt; Data to make linked list which will be the sublist</span></div>
-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> mainlistData(</div>
-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>            100);  <span class="comment">///&lt; Main list in which sublist is to be searched</span></div>
-<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span> </div>
-<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 100; i++) {<span class="comment"></span></div>
-<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span><span class="comment">            /// Inserts 100 elements in main list</span></div>
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-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>        <span class="keywordtype">int</span> temp = 0;</div>
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-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span><span class="comment">            /// Inserts 20 elements in sublist</span></div>
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-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>            temp++;</div>
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-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>            <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a70ca8d0267008e09cfa50b4e2ddfbe53">search::sublist_search::makeLinkedList</a>(</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>                sublistData);  <span class="comment">///&lt; Sublist to be searched</span></div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>        <a class="code hl_struct" href="../../da/d61/structsearch_1_1sublist__search_1_1_node.html">search::sublist_search::Node</a> *mainlistLL =</div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>            <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a70ca8d0267008e09cfa50b4e2ddfbe53">search::sublist_search::makeLinkedList</a>(</div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>                mainlistData);  <span class="comment">///&lt; Main list in which sublist is to be</span><span class="comment"></span></div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span><span class="comment">                                ///&lt; searched</span></div>
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-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>            sublistLL, mainlistLL);  <span class="comment">///&lt; boolean, if sublist exist or not</span></div>
-<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span> </div>
-<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Checking assert expression...&quot;</span>);</div>
-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>        assert(exists == expectedOutput);</div>
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-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span> </div>
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-<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
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+<div class="fragment"><div class="line"><span class="lineno">  229</span>                      {</div>
+<div class="line"><span class="lineno">  230</span>        <span class="keyword">const</span> <span class="keywordtype">bool</span> expectedOutput = <span class="keyword">true</span>;  <span class="comment">/// Expected output of this test</span></div>
+<div class="line"><span class="lineno">  231</span> </div>
+<div class="line"><span class="lineno">  232</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
+<div class="line"><span class="lineno">  233</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
+<div class="line"><span class="lineno">  234</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;This is test case 2 for sublist search Algorithm : &quot;</span>);</div>
+<div class="line"><span class="lineno">  235</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Description:&quot;</span>);</div>
+<div class="line"><span class="lineno">  236</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;   contains main list of 100 elements and sublist of 20&quot;</span>);</div>
+<div class="line"><span class="lineno">  237</span> </div>
+<div class="line"><span class="lineno">  238</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> sublistData(</div>
+<div class="line"><span class="lineno">  239</span>            20);  <span class="comment">///&lt; Data to make linked list which will be the sublist</span></div>
+<div class="line"><span class="lineno">  240</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> mainlistData(</div>
+<div class="line"><span class="lineno">  241</span>            100);  <span class="comment">///&lt; Main list in which sublist is to be searched</span></div>
+<div class="line"><span class="lineno">  242</span> </div>
+<div class="line"><span class="lineno">  243</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 100; i++) {<span class="comment"></span></div>
+<div class="line"><span class="lineno">  244</span><span class="comment">            /// Inserts 100 elements in main list</span></div>
+<div class="line"><span class="lineno">  245</span><span class="comment"></span>            mainlistData[i] = i + 1;</div>
+<div class="line"><span class="lineno">  246</span>        }</div>
+<div class="line"><span class="lineno">  247</span> </div>
+<div class="line"><span class="lineno">  248</span>        <span class="keywordtype">int</span> temp = 0;</div>
+<div class="line"><span class="lineno">  249</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 45; i &lt; 65; i++) {<span class="comment"></span></div>
+<div class="line"><span class="lineno">  250</span><span class="comment">            /// Inserts 20 elements in sublist</span></div>
+<div class="line"><span class="lineno">  251</span><span class="comment"></span>            sublistData[temp] = i + 1;</div>
+<div class="line"><span class="lineno">  252</span>            temp++;</div>
+<div class="line"><span class="lineno">  253</span>        }</div>
+<div class="line"><span class="lineno">  254</span> </div>
+<div class="line"><span class="lineno">  255</span>        <a class="code hl_struct" href="../../da/d61/structsearch_1_1sublist__search_1_1_node.html">search::sublist_search::Node</a> *sublistLL =</div>
+<div class="line"><span class="lineno">  256</span>            <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a70ca8d0267008e09cfa50b4e2ddfbe53">search::sublist_search::makeLinkedList</a>(</div>
+<div class="line"><span class="lineno">  257</span>                sublistData);  <span class="comment">///&lt; Sublist to be searched</span></div>
+<div class="line"><span class="lineno">  258</span>        <a class="code hl_struct" href="../../da/d61/structsearch_1_1sublist__search_1_1_node.html">search::sublist_search::Node</a> *mainlistLL =</div>
+<div class="line"><span class="lineno">  259</span>            <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a70ca8d0267008e09cfa50b4e2ddfbe53">search::sublist_search::makeLinkedList</a>(</div>
+<div class="line"><span class="lineno">  260</span>                mainlistData);  <span class="comment">///&lt; Main list in which sublist is to be</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  261</span><span class="comment">                                ///&lt; searched</span></div>
+<div class="line"><span class="lineno">  262</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  263</span>        <span class="keywordtype">bool</span> <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a1cc9dd6e6190d10a010fdcdfe7a21a81">exists</a> = <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a4faee403e2758aaab682ed6622ae218c">search::sublist_search::sublistSearch</a>(</div>
+<div class="line"><span class="lineno">  264</span>            sublistLL, mainlistLL);  <span class="comment">///&lt; boolean, if sublist exist or not</span></div>
+<div class="line"><span class="lineno">  265</span> </div>
+<div class="line"><span class="lineno">  266</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Checking assert expression...&quot;</span>);</div>
+<div class="line"><span class="lineno">  267</span>        assert(exists == expectedOutput);</div>
+<div class="line"><span class="lineno">  268</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Assertion check passed!&quot;</span>);</div>
+<div class="line"><span class="lineno">  269</span> </div>
+<div class="line"><span class="lineno">  270</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;[PASS] : TEST CASE 2 PASS!&quot;</span>);</div>
+<div class="line"><span class="lineno">  271</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
+<div class="line"><span class="lineno">  272</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
+<div class="line"><span class="lineno">  273</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -856,34 +856,34 @@ Here is the call graph for this function:</div>
 
 <p>A test case with input array of length 500. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>                      {</div>
-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>        <span class="keyword">const</span> int64_t inputSize = 500;</div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Description:&quot;</span>);</div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;   BIG INPUT : Contains 500 elements and repeated elements&quot;</span>);</div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;This is test case 2 for Random Pivot Quick Sort Algorithm : &quot;</span>);</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int64_t, inputSize&gt;</a> unsorted_arr =</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>            sorting::random_pivot_quick_sort::generateUnsortedArray&lt;inputSize&gt;(</div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>                1, 10000);</div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span> </div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>        int64_t start = 0;</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>        int64_t <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = unsorted_arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/size.html">size</a>() - 1;  <span class="comment">// length - 1</span></div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span> </div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Running algorithm of data of length 500 ...&quot;</span>);</div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt;int64_t, unsorted_arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/size.html">size</a>()&gt; sorted_arr =</div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>            <a class="code hl_function" href="../../d1/daa/random__pivot__quick__sort_8cpp.html#a7d2e7465e7b5d54c2de6d5e9db1ea6a5">sorting::random_pivot_quick_sort::quickSortRP</a>(unsorted_arr, start,</div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>                                                          end);</div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Algorithm finished!&quot;</span>);</div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span> </div>
-<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Checking assert expression...&quot;</span>);</div>
-<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>        assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(sorted_arr.begin(), sorted_arr.end()));</div>
-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Assertion check passed!&quot;</span>);</div>
-<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span> </div>
-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;[PASS] : TEST CASE 2 PASS!&quot;</span>);</div>
-<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
-<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  245</span>                      {</div>
+<div class="line"><span class="lineno">  246</span>        <span class="keyword">const</span> int64_t inputSize = 500;</div>
+<div class="line"><span class="lineno">  247</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
+<div class="line"><span class="lineno">  248</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
+<div class="line"><span class="lineno">  249</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Description:&quot;</span>);</div>
+<div class="line"><span class="lineno">  250</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;   BIG INPUT : Contains 500 elements and repeated elements&quot;</span>);</div>
+<div class="line"><span class="lineno">  251</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;This is test case 2 for Random Pivot Quick Sort Algorithm : &quot;</span>);</div>
+<div class="line"><span class="lineno">  252</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int64_t, inputSize&gt;</a> unsorted_arr =</div>
+<div class="line"><span class="lineno">  253</span>            sorting::random_pivot_quick_sort::generateUnsortedArray&lt;inputSize&gt;(</div>
+<div class="line"><span class="lineno">  254</span>                1, 10000);</div>
+<div class="line"><span class="lineno">  255</span> </div>
+<div class="line"><span class="lineno">  256</span>        int64_t start = 0;</div>
+<div class="line"><span class="lineno">  257</span>        int64_t <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = unsorted_arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/size.html">size</a>() - 1;  <span class="comment">// length - 1</span></div>
+<div class="line"><span class="lineno">  258</span> </div>
+<div class="line"><span class="lineno">  259</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Running algorithm of data of length 500 ...&quot;</span>);</div>
+<div class="line"><span class="lineno">  260</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt;int64_t, unsorted_arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/size.html">size</a>()&gt; sorted_arr =</div>
+<div class="line"><span class="lineno">  261</span>            <a class="code hl_function" href="../../d1/daa/random__pivot__quick__sort_8cpp.html#a7d2e7465e7b5d54c2de6d5e9db1ea6a5">sorting::random_pivot_quick_sort::quickSortRP</a>(unsorted_arr, start,</div>
+<div class="line"><span class="lineno">  262</span>                                                          end);</div>
+<div class="line"><span class="lineno">  263</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Algorithm finished!&quot;</span>);</div>
+<div class="line"><span class="lineno">  264</span> </div>
+<div class="line"><span class="lineno">  265</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Checking assert expression...&quot;</span>);</div>
+<div class="line"><span class="lineno">  266</span>        assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(sorted_arr.begin(), sorted_arr.end()));</div>
+<div class="line"><span class="lineno">  267</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Assertion check passed!&quot;</span>);</div>
+<div class="line"><span class="lineno">  268</span> </div>
+<div class="line"><span class="lineno">  269</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;[PASS] : TEST CASE 2 PASS!&quot;</span>);</div>
+<div class="line"><span class="lineno">  270</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
+<div class="line"><span class="lineno">  271</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
+<div class="line"><span class="lineno">  272</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
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 <div class="dyncontent">
@@ -924,42 +924,42 @@ Here is the call graph for this function:</div>
 <p >&lt; Printing inorder to cross-verify.</p>
 <p >&lt; The inorder successor node for given data</p>
 <p >memory cleanup!</p>
-<div class="fragment"><div class="line"><a id="l00345" name="l00345"></a><span class="lineno">  345</span>                      {</div>
-<div class="line"><a id="l00346" name="l00346"></a><span class="lineno">  346</span>        <span class="keyword">const</span> <span class="keywordtype">int</span> expectedOutput = 110;  <span class="comment">///&lt; Expected output of this test</span></div>
-<div class="line"><a id="l00347" name="l00347"></a><span class="lineno">  347</span> </div>
-<div class="line"><a id="l00348" name="l00348"></a><span class="lineno">  348</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span>);</div>
-<div class="line"><a id="l00349" name="l00349"></a><span class="lineno">  349</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;This is test case 3 : &quot;</span>);</div>
-<div class="line"><a id="l00350" name="l00350"></a><span class="lineno">  350</span> </div>
-<div class="line"><a id="l00351" name="l00351"></a><span class="lineno">  351</span>        <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a> *root =</div>
-<div class="line"><a id="l00352" name="l00352"></a><span class="lineno">  352</span>            <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> node_data{</div>
-<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span>            89,  67,  32, 56, 90, 123, 120,</div>
-<div class="line"><a id="l00355" name="l00355"></a><span class="lineno">  355</span>            110, 115, 6,  78, 7,  10};  <span class="comment">///&lt; Data to make nodes in BST</span></div>
-<div class="line"><a id="l00356" name="l00356"></a><span class="lineno">  356</span> </div>
-<div class="line"><a id="l00357" name="l00357"></a><span class="lineno">  357</span>        root = <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a05fe8a029e155c43e4efa598d4d089d9">operations_on_datastructures::inorder_traversal_of_bst::makeBST</a>(</div>
-<div class="line"><a id="l00358" name="l00358"></a><span class="lineno">  358</span>            root,</div>
-<div class="line"><a id="l00359" name="l00359"></a><span class="lineno">  359</span>            node_data);  <span class="comment">///&lt; Adding nodes to BST</span></div>
-<div class="line"><a id="l00360" name="l00360"></a><span class="lineno">  360</span> </div>
-<div class="line"><a id="l00361" name="l00361"></a><span class="lineno">  361</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Inorder sequence is : &quot;</span>;</div>
-<div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span>        <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">operations_on_datastructures::inorder_traversal_of_bst::printInorder</a>(</div>
-<div class="line"><a id="l00363" name="l00363"></a><span class="lineno">  363</span>            root);  <span class="comment">///&lt; Printing inorder to cross-verify.</span></div>
-<div class="line"><a id="l00364" name="l00364"></a><span class="lineno">  364</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00365" name="l00365"></a><span class="lineno">  365</span> </div>
-<div class="line"><a id="l00366" name="l00366"></a><span class="lineno">  366</span>        <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a></div>
-<div class="line"><a id="l00367" name="l00367"></a><span class="lineno">  367</span>            *inorderSuccessor = operations_on_datastructures::</div>
-<div class="line"><a id="l00368" name="l00368"></a><span class="lineno">  368</span>                inorder_traversal_of_bst::getInorderSuccessor(</div>
-<div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span>                    root, 90);  <span class="comment">///&lt; The inorder successor node for given data</span></div>
-<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span> </div>
-<div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Checking assert expression...&quot;</span>);</div>
-<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span>        assert(inorderSuccessor-&gt;<a class="code hl_variable" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html#ae161f3e5ef33ade73429cab9291612e2">data</a> == expectedOutput);</div>
-<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Assertion check passed!&quot;</span>);</div>
-<div class="line"><a id="l00374" name="l00374"></a><span class="lineno">  374</span> </div>
-<div class="line"><a id="l00375" name="l00375"></a><span class="lineno">  375</span>        <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7b20eb99272665c1777949e26ab59589">operations_on_datastructures::inorder_traversal_of_bst::deallocate</a>(</div>
-<div class="line"><a id="l00376" name="l00376"></a><span class="lineno">  376</span>            root);  <span class="comment">/// memory cleanup!</span></div>
-<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span> </div>
-<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;[PASS] : TEST CASE 3 PASS!&quot;</span>);</div>
-<div class="line"><a id="l00379" name="l00379"></a><span class="lineno">  379</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span>);</div>
-<div class="line"><a id="l00380" name="l00380"></a><span class="lineno">  380</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  345</span>                      {</div>
+<div class="line"><span class="lineno">  346</span>        <span class="keyword">const</span> <span class="keywordtype">int</span> expectedOutput = 110;  <span class="comment">///&lt; Expected output of this test</span></div>
+<div class="line"><span class="lineno">  347</span> </div>
+<div class="line"><span class="lineno">  348</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span>);</div>
+<div class="line"><span class="lineno">  349</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;This is test case 3 : &quot;</span>);</div>
+<div class="line"><span class="lineno">  350</span> </div>
+<div class="line"><span class="lineno">  351</span>        <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a> *root =</div>
+<div class="line"><span class="lineno">  352</span>            <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  353</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> node_data{</div>
+<div class="line"><span class="lineno">  354</span>            89,  67,  32, 56, 90, 123, 120,</div>
+<div class="line"><span class="lineno">  355</span>            110, 115, 6,  78, 7,  10};  <span class="comment">///&lt; Data to make nodes in BST</span></div>
+<div class="line"><span class="lineno">  356</span> </div>
+<div class="line"><span class="lineno">  357</span>        root = <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a05fe8a029e155c43e4efa598d4d089d9">operations_on_datastructures::inorder_traversal_of_bst::makeBST</a>(</div>
+<div class="line"><span class="lineno">  358</span>            root,</div>
+<div class="line"><span class="lineno">  359</span>            node_data);  <span class="comment">///&lt; Adding nodes to BST</span></div>
+<div class="line"><span class="lineno">  360</span> </div>
+<div class="line"><span class="lineno">  361</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Inorder sequence is : &quot;</span>;</div>
+<div class="line"><span class="lineno">  362</span>        <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">operations_on_datastructures::inorder_traversal_of_bst::printInorder</a>(</div>
+<div class="line"><span class="lineno">  363</span>            root);  <span class="comment">///&lt; Printing inorder to cross-verify.</span></div>
+<div class="line"><span class="lineno">  364</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  365</span> </div>
+<div class="line"><span class="lineno">  366</span>        <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a></div>
+<div class="line"><span class="lineno">  367</span>            *inorderSuccessor = operations_on_datastructures::</div>
+<div class="line"><span class="lineno">  368</span>                inorder_traversal_of_bst::getInorderSuccessor(</div>
+<div class="line"><span class="lineno">  369</span>                    root, 90);  <span class="comment">///&lt; The inorder successor node for given data</span></div>
+<div class="line"><span class="lineno">  370</span> </div>
+<div class="line"><span class="lineno">  371</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Checking assert expression...&quot;</span>);</div>
+<div class="line"><span class="lineno">  372</span>        assert(inorderSuccessor-&gt;<a class="code hl_variable" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html#ae161f3e5ef33ade73429cab9291612e2">data</a> == expectedOutput);</div>
+<div class="line"><span class="lineno">  373</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Assertion check passed!&quot;</span>);</div>
+<div class="line"><span class="lineno">  374</span> </div>
+<div class="line"><span class="lineno">  375</span>        <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7b20eb99272665c1777949e26ab59589">operations_on_datastructures::inorder_traversal_of_bst::deallocate</a>(</div>
+<div class="line"><span class="lineno">  376</span>            root);  <span class="comment">/// memory cleanup!</span></div>
+<div class="line"><span class="lineno">  377</span> </div>
+<div class="line"><span class="lineno">  378</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;[PASS] : TEST CASE 3 PASS!&quot;</span>);</div>
+<div class="line"><span class="lineno">  379</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span>);</div>
+<div class="line"><span class="lineno">  380</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -1002,48 +1002,48 @@ Here is the call graph for this function:</div>
 <p >&lt; Sublist to be searched</p>
 <p >&lt; Main list in which sublist is to be searched</p>
 <p >&lt; boolean, if sublist exist or not</p>
-<div class="fragment"><div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>                      {</div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>        <span class="keyword">const</span> <span class="keywordtype">bool</span> expectedOutput = <span class="keyword">false</span>;  <span class="comment">///&lt; Expected output of this test</span></div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span> </div>
-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;This is test case 3 for sublist search Algorithm : &quot;</span>);</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Description:&quot;</span>);</div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;   contains main list of 50 elements and sublist of 20&quot;</span>);</div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span> </div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> sublistData(20);  <span class="comment">///&lt; Sublist to be searched</span></div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> mainlistData(</div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>            50);  <span class="comment">///&lt; Main list in which sublist is to be searched</span></div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span> </div>
-<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 50; i++) {<span class="comment"></span></div>
-<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span><span class="comment">            /// Inserts 100 elements in main list</span></div>
-<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span><span class="comment"></span>            mainlistData.push_back(i + 1);</div>
-<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>        }</div>
-<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span> </div>
-<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 45; i &lt; 65; i++) {<span class="comment"></span></div>
-<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span><span class="comment">            /// Inserts 20 elements in sublist</span></div>
-<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span><span class="comment"></span>            sublistData.push_back(i + 1);</div>
-<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span>        }</div>
-<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span> </div>
-<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span>        <a class="code hl_struct" href="../../da/d61/structsearch_1_1sublist__search_1_1_node.html">search::sublist_search::Node</a> *sublistLL =</div>
-<div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span>            <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a70ca8d0267008e09cfa50b4e2ddfbe53">search::sublist_search::makeLinkedList</a>(</div>
-<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span>                sublistData);  <span class="comment">///&lt; Sublist to be searched</span></div>
-<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>        <a class="code hl_struct" href="../../da/d61/structsearch_1_1sublist__search_1_1_node.html">search::sublist_search::Node</a> *mainlistLL =</div>
-<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>            <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a70ca8d0267008e09cfa50b4e2ddfbe53">search::sublist_search::makeLinkedList</a>(</div>
-<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>                mainlistData);  <span class="comment">///&lt; Main list in which sublist is to be</span><span class="comment"></span></div>
-<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span><span class="comment">                                ///&lt; searched</span></div>
-<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span><span class="comment"></span> </div>
-<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>        <span class="keywordtype">bool</span> <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a1cc9dd6e6190d10a010fdcdfe7a21a81">exists</a> = <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a4faee403e2758aaab682ed6622ae218c">search::sublist_search::sublistSearch</a>(</div>
-<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>            sublistLL, mainlistLL);  <span class="comment">///&lt; boolean, if sublist exist or not</span></div>
-<div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span> </div>
-<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Checking assert expression...&quot;</span>);</div>
-<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span>        assert(exists == expectedOutput);</div>
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-<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span> </div>
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-<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
-<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
-<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  280</span>                      {</div>
+<div class="line"><span class="lineno">  281</span>        <span class="keyword">const</span> <span class="keywordtype">bool</span> expectedOutput = <span class="keyword">false</span>;  <span class="comment">///&lt; Expected output of this test</span></div>
+<div class="line"><span class="lineno">  282</span> </div>
+<div class="line"><span class="lineno">  283</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
+<div class="line"><span class="lineno">  284</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
+<div class="line"><span class="lineno">  285</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;This is test case 3 for sublist search Algorithm : &quot;</span>);</div>
+<div class="line"><span class="lineno">  286</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Description:&quot;</span>);</div>
+<div class="line"><span class="lineno">  287</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;   contains main list of 50 elements and sublist of 20&quot;</span>);</div>
+<div class="line"><span class="lineno">  288</span> </div>
+<div class="line"><span class="lineno">  289</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> sublistData(20);  <span class="comment">///&lt; Sublist to be searched</span></div>
+<div class="line"><span class="lineno">  290</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> mainlistData(</div>
+<div class="line"><span class="lineno">  291</span>            50);  <span class="comment">///&lt; Main list in which sublist is to be searched</span></div>
+<div class="line"><span class="lineno">  292</span> </div>
+<div class="line"><span class="lineno">  293</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 50; i++) {<span class="comment"></span></div>
+<div class="line"><span class="lineno">  294</span><span class="comment">            /// Inserts 100 elements in main list</span></div>
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+<div class="line"><span class="lineno">  296</span>        }</div>
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+<div class="line"><span class="lineno">  299</span><span class="comment">            /// Inserts 20 elements in sublist</span></div>
+<div class="line"><span class="lineno">  300</span><span class="comment"></span>            sublistData.push_back(i + 1);</div>
+<div class="line"><span class="lineno">  301</span>        }</div>
+<div class="line"><span class="lineno">  302</span> </div>
+<div class="line"><span class="lineno">  303</span>        <a class="code hl_struct" href="../../da/d61/structsearch_1_1sublist__search_1_1_node.html">search::sublist_search::Node</a> *sublistLL =</div>
+<div class="line"><span class="lineno">  304</span>            <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a70ca8d0267008e09cfa50b4e2ddfbe53">search::sublist_search::makeLinkedList</a>(</div>
+<div class="line"><span class="lineno">  305</span>                sublistData);  <span class="comment">///&lt; Sublist to be searched</span></div>
+<div class="line"><span class="lineno">  306</span>        <a class="code hl_struct" href="../../da/d61/structsearch_1_1sublist__search_1_1_node.html">search::sublist_search::Node</a> *mainlistLL =</div>
+<div class="line"><span class="lineno">  307</span>            <a class="code hl_function" href="../../d5/d45/sublist__search_8cpp.html#a70ca8d0267008e09cfa50b4e2ddfbe53">search::sublist_search::makeLinkedList</a>(</div>
+<div class="line"><span class="lineno">  308</span>                mainlistData);  <span class="comment">///&lt; Main list in which sublist is to be</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  309</span><span class="comment">                                ///&lt; searched</span></div>
+<div class="line"><span class="lineno">  310</span><span class="comment"></span> </div>
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+<div class="line"><span class="lineno">  312</span>            sublistLL, mainlistLL);  <span class="comment">///&lt; boolean, if sublist exist or not</span></div>
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@@ -1078,34 +1078,34 @@ Here is the call graph for this function:</div>
 
 <p>A test case with array of length 1000. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>                      {</div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>        <span class="keyword">const</span> int64_t inputSize = 1000;</div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
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-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Description:&quot;</span>);</div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;   LARGE INPUT : Contains 1000 elements and repeated elements&quot;</span>);</div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int64_t, inputSize&gt;</a> unsorted_arr =</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>            sorting::random_pivot_quick_sort::generateUnsortedArray&lt;inputSize&gt;(</div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>                1, 10000);</div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span> </div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>        int64_t start = 0;</div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>        int64_t <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = unsorted_arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/size.html">size</a>() - 1;  <span class="comment">// length - 1</span></div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span> </div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Running algorithm...&quot;</span>);</div>
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+<div class="line"><span class="lineno">  280</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~&quot;</span></div>
+<div class="line"><span class="lineno">  281</span>            <span class="stringliteral">&quot;~&quot;</span>);</div>
+<div class="line"><span class="lineno">  282</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;This is test case 3 for Random Pivot Quick Sort Algorithm : &quot;</span>);</div>
+<div class="line"><span class="lineno">  283</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Description:&quot;</span>);</div>
+<div class="line"><span class="lineno">  284</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;   LARGE INPUT : Contains 1000 elements and repeated elements&quot;</span>);</div>
+<div class="line"><span class="lineno">  285</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int64_t, inputSize&gt;</a> unsorted_arr =</div>
+<div class="line"><span class="lineno">  286</span>            sorting::random_pivot_quick_sort::generateUnsortedArray&lt;inputSize&gt;(</div>
+<div class="line"><span class="lineno">  287</span>                1, 10000);</div>
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+<div class="line"><span class="lineno">  289</span>        int64_t start = 0;</div>
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+<div class="line"><span class="lineno">  291</span> </div>
+<div class="line"><span class="lineno">  292</span>        <a class="code hl_function" href="../../d5/d58/class_test_cases.html#aa3aa3d5bf666f327ee8e2d11d397b06e">log</a>(<span class="stringliteral">&quot;Running algorithm...&quot;</span>);</div>
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-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>              &lt;&lt; tree.<a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ae8ae4b1835e5e8aec32f68c5059ed4d4">query</a>(2, 4, 0) &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;</div>
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+<div class="line"><span class="lineno">  280</span>        arr);  <span class="comment">// constructing the original segment tree (version = 0)</span></div>
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+<div class="line"><span class="lineno">  297</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Elements of the segment tree whose version = 2 (after 2 &quot;</span></div>
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+<div class="line"><span class="lineno">  187</span>    os &lt;&lt; <span class="stringliteral">&quot;(&quot;</span> &lt;&lt; num.<a class="code hl_function" href="../../da/d5a/class_complex.html#a312e4b19146128408fb06e0150b0faf6">real</a>();</div>
+<div class="line"><span class="lineno">  188</span>    <span class="keywordflow">if</span> (num.<a class="code hl_function" href="../../da/d5a/class_complex.html#af8aacf982e2e6c142921bc850f6dc974">imag</a>() &lt; 0) {</div>
+<div class="line"><span class="lineno">  189</span>        os &lt;&lt; <span class="stringliteral">&quot; - &quot;</span> &lt;&lt; -num.<a class="code hl_function" href="../../da/d5a/class_complex.html#af8aacf982e2e6c142921bc850f6dc974">imag</a>();</div>
+<div class="line"><span class="lineno">  190</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  191</span>        os &lt;&lt; <span class="stringliteral">&quot; + &quot;</span> &lt;&lt; num.<a class="code hl_function" href="../../da/d5a/class_complex.html#af8aacf982e2e6c142921bc850f6dc974">imag</a>();</div>
+<div class="line"><span class="lineno">  192</span>    }</div>
+<div class="line"><span class="lineno">  193</span>    os &lt;&lt; <span class="stringliteral">&quot;i)&quot;</span>;</div>
+<div class="line"><span class="lineno">  194</span>    <span class="keywordflow">return</span> os;</div>
+<div class="line"><span class="lineno">  195</span>}</div>
 <div class="ttc" id="aclass_complex_html_a312e4b19146128408fb06e0150b0faf6"><div class="ttname"><a href="../../da/d5a/class_complex.html#a312e4b19146128408fb06e0150b0faf6">Complex::real</a></div><div class="ttdeci">double real() const</div><div class="ttdoc">Member function to get real value of our complex number. Member function (getter) to access the class...</div><div class="ttdef"><b>Definition:</b> complex_numbers.cpp:64</div></div>
 <div class="ttc" id="aclass_complex_html_af8aacf982e2e6c142921bc850f6dc974"><div class="ttname"><a href="../../da/d5a/class_complex.html#af8aacf982e2e6c142921bc850f6dc974">Complex::imag</a></div><div class="ttdeci">double imag() const</div><div class="ttdoc">Member function to get imaginary value of our complex number. Member function (getter) to access the ...</div><div class="ttdef"><b>Definition:</b> complex_numbers.cpp:70</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -288,9 +288,9 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd>'True' If real and imaginary parts of a and b are same </dd>
 <dd>
 'False' Otherwise. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>                                                    {</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>    <span class="keywordflow">return</span> a.real() == b.<a class="code hl_function" href="../../da/d5a/class_complex.html#a312e4b19146128408fb06e0150b0faf6">real</a>() &amp;&amp; a.imag() == b.<a class="code hl_function" href="../../da/d5a/class_complex.html#af8aacf982e2e6c142921bc850f6dc974">imag</a>();</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  175</span>                                                    {</div>
+<div class="line"><span class="lineno">  176</span>    <span class="keywordflow">return</span> a.real() == b.<a class="code hl_function" href="../../da/d5a/class_complex.html#a312e4b19146128408fb06e0150b0faf6">real</a>() &amp;&amp; a.imag() == b.<a class="code hl_function" href="../../da/d5a/class_complex.html#af8aacf982e2e6c142921bc850f6dc974">imag</a>();</div>
+<div class="line"><span class="lineno">  177</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -315,64 +315,64 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Tests Function </p>
-<div class="fragment"><div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>             {</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    <span class="keywordtype">double</span> x1 = <a class="code hl_function" href="../../d5/d67/complex__numbers_8cpp.html#a5d4d5b8250b50703de888514c8e7a7a0">get_rand</a>(), y1 = <a class="code hl_function" href="../../d5/d67/complex__numbers_8cpp.html#a5d4d5b8250b50703de888514c8e7a7a0">get_rand</a>(), x2 = <a class="code hl_function" href="../../d5/d67/complex__numbers_8cpp.html#a5d4d5b8250b50703de888514c8e7a7a0">get_rand</a>(), y2 = <a class="code hl_function" href="../../d5/d67/complex__numbers_8cpp.html#a5d4d5b8250b50703de888514c8e7a7a0">get_rand</a>();</div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>    <a class="code hl_class" href="../../da/d5a/class_complex.html">Complex</a> num1(x1, y1), num2(x2, y2);</div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> cnum1(x1, y1), cnum2(x2, y2);</div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>    <a class="code hl_class" href="../../da/d5a/class_complex.html">Complex</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> expected;</div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>    <span class="comment">// Test for addition</span></div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = num1 + num2;</div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>    expected = cnum1 + cnum2;</div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>    assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;1 + 1i + 1 + 1i is equal to 2 + 2i but the addition doesn&#39;t &quot;</span></div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>                  <span class="stringliteral">&quot;add up \n&quot;</span>,</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>            (<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.real() == expected.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>() &amp;&amp;</div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>             <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.imag() == expected.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>())));</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;First test passes.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>    <span class="comment">// Test for subtraction</span></div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = num1 - num2;</div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>    expected = cnum1 - cnum2;</div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;1 + 1i - 1 - 1i is equal to 0 but the program says &quot;</span></div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>                  <span class="stringliteral">&quot;otherwise. \n&quot;</span>,</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>            (<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.real() == expected.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>() &amp;&amp;</div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>             <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.imag() == expected.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>())));</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Second test passes.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>    <span class="comment">// Test for multiplication</span></div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = num1 * num2;</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>    expected = cnum1 * cnum2;</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>    assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;(1 + 1i) * (1 + 1i) is equal to 2i but the program says &quot;</span></div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>                  <span class="stringliteral">&quot;otherwise. \n&quot;</span>,</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>            (<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.real() == expected.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>() &amp;&amp;</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>             <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.imag() == expected.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>())));</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Third test passes.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>    <span class="comment">// Test for division</span></div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = num1 / num2;</div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>    expected = cnum1 / cnum2;</div>
-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>    assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;(1 + 1i) / (1 + 1i) is equal to 1 but the program says &quot;</span></div>
-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>                  <span class="stringliteral">&quot;otherwise.\n&quot;</span>,</div>
-<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>            (<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.real() == expected.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>() &amp;&amp;</div>
-<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>             <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.imag() == expected.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>())));</div>
-<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Fourth test passes.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>    <span class="comment">// Test for conjugates</span></div>
-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = ~num1;</div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>    expected = std::conj(cnum1);</div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>    assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;(1 + 1i) has a conjugate which is equal to (1 - 1i) but the &quot;</span></div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>                  <span class="stringliteral">&quot;program says otherwise.\n&quot;</span>,</div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>            (<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.real() == expected.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>() &amp;&amp;</div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>             <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.imag() == expected.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>())));</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Fifth test passes.\n&quot;</span>;</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>    <span class="comment">// Test for Argument of our complex number</span></div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>    assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;(1 + 1i) has argument PI / 4 but the program differs from &quot;</span></div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>                  <span class="stringliteral">&quot;the std::complex result.\n&quot;</span>,</div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>            (num1.arg() == std::arg(cnum1))));</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Sixth test passes.\n&quot;</span>;</div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>    <span class="comment">// Test for absolute value of our complex number</span></div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>    assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;(1 + 1i) has absolute value sqrt(2) but the program differs &quot;</span></div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>                  <span class="stringliteral">&quot;from the std::complex result. \n&quot;</span>,</div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>            (num1.abs() == std::abs(cnum1))));</div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Seventh test passes.\n&quot;</span>;</div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  206</span>             {</div>
+<div class="line"><span class="lineno">  207</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
+<div class="line"><span class="lineno">  208</span>    <span class="keywordtype">double</span> x1 = <a class="code hl_function" href="../../d5/d67/complex__numbers_8cpp.html#a5d4d5b8250b50703de888514c8e7a7a0">get_rand</a>(), y1 = <a class="code hl_function" href="../../d5/d67/complex__numbers_8cpp.html#a5d4d5b8250b50703de888514c8e7a7a0">get_rand</a>(), x2 = <a class="code hl_function" href="../../d5/d67/complex__numbers_8cpp.html#a5d4d5b8250b50703de888514c8e7a7a0">get_rand</a>(), y2 = <a class="code hl_function" href="../../d5/d67/complex__numbers_8cpp.html#a5d4d5b8250b50703de888514c8e7a7a0">get_rand</a>();</div>
+<div class="line"><span class="lineno">  209</span>    <a class="code hl_class" href="../../da/d5a/class_complex.html">Complex</a> num1(x1, y1), num2(x2, y2);</div>
+<div class="line"><span class="lineno">  210</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> cnum1(x1, y1), cnum2(x2, y2);</div>
+<div class="line"><span class="lineno">  211</span>    <a class="code hl_class" href="../../da/d5a/class_complex.html">Complex</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  212</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> expected;</div>
+<div class="line"><span class="lineno">  213</span>    <span class="comment">// Test for addition</span></div>
+<div class="line"><span class="lineno">  214</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = num1 + num2;</div>
+<div class="line"><span class="lineno">  215</span>    expected = cnum1 + cnum2;</div>
+<div class="line"><span class="lineno">  216</span>    assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;1 + 1i + 1 + 1i is equal to 2 + 2i but the addition doesn&#39;t &quot;</span></div>
+<div class="line"><span class="lineno">  217</span>                  <span class="stringliteral">&quot;add up \n&quot;</span>,</div>
+<div class="line"><span class="lineno">  218</span>            (<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.real() == expected.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>() &amp;&amp;</div>
+<div class="line"><span class="lineno">  219</span>             <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.imag() == expected.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>())));</div>
+<div class="line"><span class="lineno">  220</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;First test passes.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  221</span>    <span class="comment">// Test for subtraction</span></div>
+<div class="line"><span class="lineno">  222</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = num1 - num2;</div>
+<div class="line"><span class="lineno">  223</span>    expected = cnum1 - cnum2;</div>
+<div class="line"><span class="lineno">  224</span>    assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;1 + 1i - 1 - 1i is equal to 0 but the program says &quot;</span></div>
+<div class="line"><span class="lineno">  225</span>                  <span class="stringliteral">&quot;otherwise. \n&quot;</span>,</div>
+<div class="line"><span class="lineno">  226</span>            (<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.real() == expected.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>() &amp;&amp;</div>
+<div class="line"><span class="lineno">  227</span>             <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.imag() == expected.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>())));</div>
+<div class="line"><span class="lineno">  228</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Second test passes.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  229</span>    <span class="comment">// Test for multiplication</span></div>
+<div class="line"><span class="lineno">  230</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = num1 * num2;</div>
+<div class="line"><span class="lineno">  231</span>    expected = cnum1 * cnum2;</div>
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+<div class="line"><span class="lineno">  233</span>                  <span class="stringliteral">&quot;otherwise. \n&quot;</span>,</div>
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+<div class="line"><span class="lineno">  236</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Third test passes.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  237</span>    <span class="comment">// Test for division</span></div>
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+<div class="line"><span class="lineno">  239</span>    expected = cnum1 / cnum2;</div>
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+<div class="line"><span class="lineno">  241</span>                  <span class="stringliteral">&quot;otherwise.\n&quot;</span>,</div>
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+<div class="line"><span class="lineno">  244</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Fourth test passes.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  245</span>    <span class="comment">// Test for conjugates</span></div>
+<div class="line"><span class="lineno">  246</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = ~num1;</div>
+<div class="line"><span class="lineno">  247</span>    expected = std::conj(cnum1);</div>
+<div class="line"><span class="lineno">  248</span>    assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;(1 + 1i) has a conjugate which is equal to (1 - 1i) but the &quot;</span></div>
+<div class="line"><span class="lineno">  249</span>                  <span class="stringliteral">&quot;program says otherwise.\n&quot;</span>,</div>
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+<div class="line"><span class="lineno">  253</span>    <span class="comment">// Test for Argument of our complex number</span></div>
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+<div class="line"><span class="lineno">  255</span>                  <span class="stringliteral">&quot;the std::complex result.\n&quot;</span>,</div>
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+<div class="line"><span class="lineno">  258</span>    <span class="comment">// Test for absolute value of our complex number</span></div>
+<div class="line"><span class="lineno">  259</span>    assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;(1 + 1i) has absolute value sqrt(2) but the program differs &quot;</span></div>
+<div class="line"><span class="lineno">  260</span>                  <span class="stringliteral">&quot;from the std::complex result. \n&quot;</span>,</div>
+<div class="line"><span class="lineno">  261</span>            (num1.abs() == std::abs(cnum1))));</div>
+<div class="line"><span class="lineno">  262</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Seventh test passes.\n&quot;</span>;</div>
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 <p>Function for testing largestPower function. test cases and assert statement. </p>
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-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;app&quot;</span>);</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;abscond&quot;</span>);</div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;about&quot;</span>);</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;apps&quot;</span>);</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;apen&quot;</span>);</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;apples&quot;</span>);</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;apple&quot;</span>);</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;approach&quot;</span>);</div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;bus&quot;</span>);</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;buses&quot;</span>);</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;Apple&quot;</span>);</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;Bounce&quot;</span>);</div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span> </div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>    assert(!obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;appy&quot;</span>));</div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;appy is not a word in trie&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span> </div>
-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>    assert(!obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;car&quot;</span>));</div>
-<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;car is not a word in trie&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;app&quot;</span>));</div>
-<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;apple&quot;</span>));</div>
-<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;apples&quot;</span>));</div>
-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;apps&quot;</span>));</div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;apen&quot;</span>));</div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;approach&quot;</span>));</div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;about&quot;</span>));</div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;abscond&quot;</span>));</div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;bus&quot;</span>));</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;buses&quot;</span>));</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;Bounce&quot;</span>));</div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;Apple&quot;</span>));</div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span> </div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All the Inserted words are present in the trie&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span> </div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>    <span class="comment">// test for startwith prefix method</span></div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>    assert(!obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;approachs&quot;</span>));</div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;approach&quot;</span>));</div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;about&quot;</span>));</div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>    assert(!obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;appy&quot;</span>));</div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;abscond&quot;</span>));</div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;bus&quot;</span>));</div>
-<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;buses&quot;</span>));</div>
-<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;Bounce&quot;</span>));</div>
-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;Apple&quot;</span>));</div>
-<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;abs&quot;</span>));</div>
-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;b&quot;</span>));</div>
-<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;bus&quot;</span>));</div>
-<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;Bo&quot;</span>));</div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;A&quot;</span>));</div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>    assert(!obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;Ca&quot;</span>));</div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span> </div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>    assert(!obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;C&quot;</span>));</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span> </div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All the tests passed for startwith method&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span> </div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>    <span class="comment">// test for predict_words/recommendation of words based on a given prefix</span></div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span> </div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::string&gt;</a> pred_words = obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ae15fdc7f2b5023992d87a711d78566c4">predict_words</a>(<span class="stringliteral">&quot;a&quot;</span>);</div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span> </div>
-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&amp; str : obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ae15fdc7f2b5023992d87a711d78566c4">predict_words</a>(<span class="stringliteral">&quot;a&quot;</span>)) {</div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; str &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>    }</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>    assert(pred_words.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() == 8);</div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Returned all words that start with prefix a &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>    pred_words = obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ae15fdc7f2b5023992d87a711d78566c4">predict_words</a>(<span class="stringliteral">&quot;app&quot;</span>);</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span> </div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&amp; str : pred_words) {</div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; str &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>    }</div>
-<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span> </div>
-<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>    assert(pred_words.size() == 5);</div>
-<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Returned all words that start with prefix app &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>    pred_words = obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ae15fdc7f2b5023992d87a711d78566c4">predict_words</a>(<span class="stringliteral">&quot;A&quot;</span>);</div>
-<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span> </div>
-<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&amp; str : pred_words) {</div>
-<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; str &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span>    }</div>
-<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span> </div>
-<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span>    assert(pred_words.size() == 1);</div>
-<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Returned all words that start with prefix A &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span>    pred_words = obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ae15fdc7f2b5023992d87a711d78566c4">predict_words</a>(<span class="stringliteral">&quot;bu&quot;</span>);</div>
-<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span> </div>
-<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&amp; str : pred_words) {</div>
-<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; str &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>    }</div>
-<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span> </div>
-<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span>    assert(pred_words.size() == 2);</div>
-<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Returned all words that start with prefix bu &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span> </div>
-<div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span>    <span class="comment">// tests for delete method</span></div>
-<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span> </div>
-<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ac0bf3d6791cba144b3f539835d835e75">delete_word</a>(<span class="stringliteral">&quot;app&quot;</span>);</div>
-<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>    assert(!obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;app&quot;</span>));</div>
-<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;word app is deleted sucessful&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span> </div>
-<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>    pred_words = obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ae15fdc7f2b5023992d87a711d78566c4">predict_words</a>(<span class="stringliteral">&quot;app&quot;</span>);</div>
-<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&amp; str : pred_words) {</div>
-<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; str &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>    }</div>
-<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>    assert(pred_words.size() == 4);</div>
-<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;app is deleted sucessful&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span> </div>
-<div class="line"><a id="l00326" name="l00326"></a><span class="lineno">  326</span>    <span class="comment">// test case for Chinese language</span></div>
-<div class="line"><a id="l00327" name="l00327"></a><span class="lineno">  327</span> </div>
-<div class="line"><a id="l00328" name="l00328"></a><span class="lineno">  328</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;苹果&quot;</span>);</div>
-<div class="line"><a id="l00329" name="l00329"></a><span class="lineno">  329</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;苹&quot;</span>));</div>
-<div class="line"><a id="l00330" name="l00330"></a><span class="lineno">  330</span>    pred_words = obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ae15fdc7f2b5023992d87a711d78566c4">predict_words</a>(<span class="stringliteral">&quot;h&quot;</span>);</div>
-<div class="line"><a id="l00331" name="l00331"></a><span class="lineno">  331</span> </div>
-<div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span>    assert(pred_words.size() == 0);</div>
-<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;No word starts with prefix h in trie&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span> </div>
-<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All tests passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  221</span>                   {</div>
+<div class="line"><span class="lineno">  222</span>    <a class="code hl_class" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html">data_structures::trie_using_hashmap::Trie</a> obj;</div>
+<div class="line"><span class="lineno">  223</span>    <span class="comment">// Inserting data into trie using the insert</span></div>
+<div class="line"><span class="lineno">  224</span>    <span class="comment">// method and testing it with search method</span></div>
+<div class="line"><span class="lineno">  225</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;app&quot;</span>);</div>
+<div class="line"><span class="lineno">  226</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;abscond&quot;</span>);</div>
+<div class="line"><span class="lineno">  227</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;about&quot;</span>);</div>
+<div class="line"><span class="lineno">  228</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;apps&quot;</span>);</div>
+<div class="line"><span class="lineno">  229</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;apen&quot;</span>);</div>
+<div class="line"><span class="lineno">  230</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;apples&quot;</span>);</div>
+<div class="line"><span class="lineno">  231</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;apple&quot;</span>);</div>
+<div class="line"><span class="lineno">  232</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;approach&quot;</span>);</div>
+<div class="line"><span class="lineno">  233</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;bus&quot;</span>);</div>
+<div class="line"><span class="lineno">  234</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;buses&quot;</span>);</div>
+<div class="line"><span class="lineno">  235</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;Apple&quot;</span>);</div>
+<div class="line"><span class="lineno">  236</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;Bounce&quot;</span>);</div>
+<div class="line"><span class="lineno">  237</span> </div>
+<div class="line"><span class="lineno">  238</span>    assert(!obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;appy&quot;</span>));</div>
+<div class="line"><span class="lineno">  239</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;appy is not a word in trie&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  240</span> </div>
+<div class="line"><span class="lineno">  241</span>    assert(!obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;car&quot;</span>));</div>
+<div class="line"><span class="lineno">  242</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;car is not a word in trie&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  243</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;app&quot;</span>));</div>
+<div class="line"><span class="lineno">  244</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;apple&quot;</span>));</div>
+<div class="line"><span class="lineno">  245</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;apples&quot;</span>));</div>
+<div class="line"><span class="lineno">  246</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;apps&quot;</span>));</div>
+<div class="line"><span class="lineno">  247</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;apen&quot;</span>));</div>
+<div class="line"><span class="lineno">  248</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;approach&quot;</span>));</div>
+<div class="line"><span class="lineno">  249</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;about&quot;</span>));</div>
+<div class="line"><span class="lineno">  250</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;abscond&quot;</span>));</div>
+<div class="line"><span class="lineno">  251</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;bus&quot;</span>));</div>
+<div class="line"><span class="lineno">  252</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;buses&quot;</span>));</div>
+<div class="line"><span class="lineno">  253</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;Bounce&quot;</span>));</div>
+<div class="line"><span class="lineno">  254</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;Apple&quot;</span>));</div>
+<div class="line"><span class="lineno">  255</span> </div>
+<div class="line"><span class="lineno">  256</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All the Inserted words are present in the trie&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  257</span> </div>
+<div class="line"><span class="lineno">  258</span>    <span class="comment">// test for startwith prefix method</span></div>
+<div class="line"><span class="lineno">  259</span>    assert(!obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;approachs&quot;</span>));</div>
+<div class="line"><span class="lineno">  260</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;approach&quot;</span>));</div>
+<div class="line"><span class="lineno">  261</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;about&quot;</span>));</div>
+<div class="line"><span class="lineno">  262</span>    assert(!obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;appy&quot;</span>));</div>
+<div class="line"><span class="lineno">  263</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;abscond&quot;</span>));</div>
+<div class="line"><span class="lineno">  264</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;bus&quot;</span>));</div>
+<div class="line"><span class="lineno">  265</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;buses&quot;</span>));</div>
+<div class="line"><span class="lineno">  266</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;Bounce&quot;</span>));</div>
+<div class="line"><span class="lineno">  267</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;Apple&quot;</span>));</div>
+<div class="line"><span class="lineno">  268</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;abs&quot;</span>));</div>
+<div class="line"><span class="lineno">  269</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;b&quot;</span>));</div>
+<div class="line"><span class="lineno">  270</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;bus&quot;</span>));</div>
+<div class="line"><span class="lineno">  271</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;Bo&quot;</span>));</div>
+<div class="line"><span class="lineno">  272</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;A&quot;</span>));</div>
+<div class="line"><span class="lineno">  273</span>    assert(!obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;Ca&quot;</span>));</div>
+<div class="line"><span class="lineno">  274</span> </div>
+<div class="line"><span class="lineno">  275</span>    assert(!obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;C&quot;</span>));</div>
+<div class="line"><span class="lineno">  276</span> </div>
+<div class="line"><span class="lineno">  277</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All the tests passed for startwith method&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  278</span> </div>
+<div class="line"><span class="lineno">  279</span>    <span class="comment">// test for predict_words/recommendation of words based on a given prefix</span></div>
+<div class="line"><span class="lineno">  280</span> </div>
+<div class="line"><span class="lineno">  281</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::string&gt;</a> pred_words = obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ae15fdc7f2b5023992d87a711d78566c4">predict_words</a>(<span class="stringliteral">&quot;a&quot;</span>);</div>
+<div class="line"><span class="lineno">  282</span> </div>
+<div class="line"><span class="lineno">  283</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&amp; str : obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ae15fdc7f2b5023992d87a711d78566c4">predict_words</a>(<span class="stringliteral">&quot;a&quot;</span>)) {</div>
+<div class="line"><span class="lineno">  284</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; str &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  285</span>    }</div>
+<div class="line"><span class="lineno">  286</span>    assert(pred_words.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() == 8);</div>
+<div class="line"><span class="lineno">  287</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Returned all words that start with prefix a &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  288</span>    pred_words = obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ae15fdc7f2b5023992d87a711d78566c4">predict_words</a>(<span class="stringliteral">&quot;app&quot;</span>);</div>
+<div class="line"><span class="lineno">  289</span> </div>
+<div class="line"><span class="lineno">  290</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&amp; str : pred_words) {</div>
+<div class="line"><span class="lineno">  291</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; str &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  292</span>    }</div>
+<div class="line"><span class="lineno">  293</span> </div>
+<div class="line"><span class="lineno">  294</span>    assert(pred_words.size() == 5);</div>
+<div class="line"><span class="lineno">  295</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Returned all words that start with prefix app &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  296</span>    pred_words = obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ae15fdc7f2b5023992d87a711d78566c4">predict_words</a>(<span class="stringliteral">&quot;A&quot;</span>);</div>
+<div class="line"><span class="lineno">  297</span> </div>
+<div class="line"><span class="lineno">  298</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&amp; str : pred_words) {</div>
+<div class="line"><span class="lineno">  299</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; str &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  300</span>    }</div>
+<div class="line"><span class="lineno">  301</span> </div>
+<div class="line"><span class="lineno">  302</span>    assert(pred_words.size() == 1);</div>
+<div class="line"><span class="lineno">  303</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Returned all words that start with prefix A &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  304</span>    pred_words = obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ae15fdc7f2b5023992d87a711d78566c4">predict_words</a>(<span class="stringliteral">&quot;bu&quot;</span>);</div>
+<div class="line"><span class="lineno">  305</span> </div>
+<div class="line"><span class="lineno">  306</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&amp; str : pred_words) {</div>
+<div class="line"><span class="lineno">  307</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; str &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  308</span>    }</div>
+<div class="line"><span class="lineno">  309</span> </div>
+<div class="line"><span class="lineno">  310</span>    assert(pred_words.size() == 2);</div>
+<div class="line"><span class="lineno">  311</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Returned all words that start with prefix bu &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  312</span> </div>
+<div class="line"><span class="lineno">  313</span>    <span class="comment">// tests for delete method</span></div>
+<div class="line"><span class="lineno">  314</span> </div>
+<div class="line"><span class="lineno">  315</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ac0bf3d6791cba144b3f539835d835e75">delete_word</a>(<span class="stringliteral">&quot;app&quot;</span>);</div>
+<div class="line"><span class="lineno">  316</span>    assert(!obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ad71eb24207c28b546631802dba97310f">search</a>(<span class="stringliteral">&quot;app&quot;</span>));</div>
+<div class="line"><span class="lineno">  317</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;word app is deleted sucessful&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  318</span> </div>
+<div class="line"><span class="lineno">  319</span>    pred_words = obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ae15fdc7f2b5023992d87a711d78566c4">predict_words</a>(<span class="stringliteral">&quot;app&quot;</span>);</div>
+<div class="line"><span class="lineno">  320</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&amp; str : pred_words) {</div>
+<div class="line"><span class="lineno">  321</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; str &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  322</span>    }</div>
+<div class="line"><span class="lineno">  323</span>    assert(pred_words.size() == 4);</div>
+<div class="line"><span class="lineno">  324</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;app is deleted sucessful&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  325</span> </div>
+<div class="line"><span class="lineno">  326</span>    <span class="comment">// test case for Chinese language</span></div>
+<div class="line"><span class="lineno">  327</span> </div>
+<div class="line"><span class="lineno">  328</span>    obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#abcae0a4456e7f583ce716e3ef466dfd2">insert</a>(<span class="stringliteral">&quot;苹果&quot;</span>);</div>
+<div class="line"><span class="lineno">  329</span>    assert(obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#af3aee573fbabd2c1510c0f74f842dd17">startwith</a>(<span class="stringliteral">&quot;苹&quot;</span>));</div>
+<div class="line"><span class="lineno">  330</span>    pred_words = obj.<a class="code hl_function" href="../../d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html#ae15fdc7f2b5023992d87a711d78566c4">predict_words</a>(<span class="stringliteral">&quot;h&quot;</span>);</div>
+<div class="line"><span class="lineno">  331</span> </div>
+<div class="line"><span class="lineno">  332</span>    assert(pred_words.size() == 0);</div>
+<div class="line"><span class="lineno">  333</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;No word starts with prefix h in trie&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  334</span> </div>
+<div class="line"><span class="lineno">  335</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All tests passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  336</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
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@@ -344,7 +344,7 @@ Here is the call graph for this function:</div>
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diff --git a/d5/d8a/trie__using__hashmap_8cpp_aa8dca7b867074164d5f45b0f3851269d_cgraph.map b/d5/d8a/trie__using__hashmap_8cpp_aa8dca7b867074164d5f45b0f3851269d_cgraph.map
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 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
 <div class="textblock"><p >Implements <a href="https://leetcode.com/problems/palindrome-partitioning-ii/" target="_blank">Palindrome Partitioning</a> algorithm, giving you the minimum number of partitions you need to make. </p>
-<p >palindrome partitioning uses dynamic programming and goes to all the possible partitions to find the minimum you are given a string and you need to give minimum number of partitions needed to divide it into a number of palindromes <a href="https://www.geeksforgeeks.org/palindrome-partitioning-dp-17/" target="_blank">Palindrome Partitioning</a> overall time complexity O(n^2) For example: example 1:- String : "nitik" Output : 2 =&gt; "n
-| iti | k" For example: example 2:- String : "ababbbabbababa" Output : 3 =&gt; "aba | b | bbabb | ababa" </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/sujaykaushik008" target="_blank">Sujay Kaushik</a> </dd></dl>
+<p >palindrome partitioning uses dynamic programming and goes to all the possible partitions to find the minimum you are given a string and you need to give minimum number of partitions needed to divide it into a number of palindromes [Palindrome Partitioning] (<a href="https://www.geeksforgeeks.org/palindrome-partitioning-dp-17/">https://www.geeksforgeeks.org/palindrome-partitioning-dp-17/</a>) overall time complexity O(n^2) For example: example 1:- String : "nitik" Output : 2 =&gt; "n
+| iti | k" For example: example 2:- String : "ababbbabbababa" Output : 3 =&gt; "aba | b | bbabb | ababa" </p><dl class="section author"><dt>Author</dt><dd>[Sujay Kaushik] (<a href="https://github.com/sujaykaushik008">https://github.com/sujaykaushik008</a>) </dd></dl>
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+<div class="line"><span class="lineno">   70</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (arr[mid] &lt; val) {</div>
+<div class="line"><span class="lineno">   71</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a034d8b276518a902962e87d3158b64fd">binary_search</a>(arr, val, mid + 1, high);</div>
+<div class="line"><span class="lineno">   72</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   73</span>        <span class="keywordflow">return</span> mid + 1;</div>
+<div class="line"><span class="lineno">   74</span>    }</div>
+<div class="line"><span class="lineno">   75</span>}</div>
 <div class="ttc" id="anamespacesorting_html_a034d8b276518a902962e87d3158b64fd"><div class="ttname"><a href="../../d5/d91/namespacesorting.html#a034d8b276518a902962e87d3158b64fd">sorting::binary_search</a></div><div class="ttdeci">int64_t binary_search(std::vector&lt; T &gt; &amp;arr, T val, int64_t low, int64_t high)</div><div class="ttdoc">Binary search function to find the most suitable pace for an element.</div><div class="ttdef"><b>Definition:</b> binary_insertion_sort.cpp:63</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -313,24 +313,24 @@ template&lt;typename T , size_t size&gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>array with elements sorted </dd></dl>
-<div class="fragment"><div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>                                                   {</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    <span class="comment">// few easy cases</span></div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    <span class="keywordflow">if</span> (size &lt;= 1) {</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        <span class="keywordflow">return</span> arr;</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    }</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span> </div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <span class="keywordtype">int</span> index = 0;  <span class="comment">// initialize loop index</span></div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    <span class="keywordflow">while</span> (index &lt; size) {</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        <span class="comment">// check for swap</span></div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        <span class="keywordflow">if</span> ((index == 0) || (arr[index] &gt;= arr[index - 1])) {</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>            index++;</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[index], arr[index - 1]);  <span class="comment">// swap</span></div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>            index--;</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        }</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    }</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    <span class="keywordflow">return</span> arr;</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   62</span>                                                   {</div>
+<div class="line"><span class="lineno">   63</span>    <span class="comment">// few easy cases</span></div>
+<div class="line"><span class="lineno">   64</span>    <span class="keywordflow">if</span> (size &lt;= 1) {</div>
+<div class="line"><span class="lineno">   65</span>        <span class="keywordflow">return</span> arr;</div>
+<div class="line"><span class="lineno">   66</span>    }</div>
+<div class="line"><span class="lineno">   67</span> </div>
+<div class="line"><span class="lineno">   68</span>    <span class="keywordtype">int</span> index = 0;  <span class="comment">// initialize loop index</span></div>
+<div class="line"><span class="lineno">   69</span>    <span class="keywordflow">while</span> (index &lt; size) {</div>
+<div class="line"><span class="lineno">   70</span>        <span class="comment">// check for swap</span></div>
+<div class="line"><span class="lineno">   71</span>        <span class="keywordflow">if</span> ((index == 0) || (arr[index] &gt;= arr[index - 1])) {</div>
+<div class="line"><span class="lineno">   72</span>            index++;</div>
+<div class="line"><span class="lineno">   73</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   74</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[index], arr[index - 1]);  <span class="comment">// swap</span></div>
+<div class="line"><span class="lineno">   75</span>            index--;</div>
+<div class="line"><span class="lineno">   76</span>        }</div>
+<div class="line"><span class="lineno">   77</span>    }</div>
+<div class="line"><span class="lineno">   78</span>    <span class="keywordflow">return</span> arr;</div>
+<div class="line"><span class="lineno">   79</span>}</div>
 <div class="ttc" id="aswap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a></div><div class="ttdeci">T swap(T... args)</div></div>
 </div><!-- fragment -->
 </div>
@@ -369,23 +369,23 @@ template&lt;typename T &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>                                 {</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    <span class="comment">// few easy cases</span></div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>    <span class="keywordflow">if</span> (size &lt;= 1) {</div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>        <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    }</div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span> </div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    <span class="keywordtype">int</span> index = 0;  <span class="comment">// initialize some variables.</span></div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    <span class="keywordflow">while</span> (index &lt; size) {</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>        <span class="comment">// check for swap</span></div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>        <span class="keywordflow">if</span> ((index == 0) || (arr[index] &gt;= arr[index - 1])) {</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>            index++;</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[index], arr[index - 1]);  <span class="comment">// swap</span></div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>            index--;</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>        }</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    }</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   34</span>                                 {</div>
+<div class="line"><span class="lineno">   35</span>    <span class="comment">// few easy cases</span></div>
+<div class="line"><span class="lineno">   36</span>    <span class="keywordflow">if</span> (size &lt;= 1) {</div>
+<div class="line"><span class="lineno">   37</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">   38</span>    }</div>
+<div class="line"><span class="lineno">   39</span> </div>
+<div class="line"><span class="lineno">   40</span>    <span class="keywordtype">int</span> index = 0;  <span class="comment">// initialize some variables.</span></div>
+<div class="line"><span class="lineno">   41</span>    <span class="keywordflow">while</span> (index &lt; size) {</div>
+<div class="line"><span class="lineno">   42</span>        <span class="comment">// check for swap</span></div>
+<div class="line"><span class="lineno">   43</span>        <span class="keywordflow">if</span> ((index == 0) || (arr[index] &gt;= arr[index - 1])) {</div>
+<div class="line"><span class="lineno">   44</span>            index++;</div>
+<div class="line"><span class="lineno">   45</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   46</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[index], arr[index - 1]);  <span class="comment">// swap</span></div>
+<div class="line"><span class="lineno">   47</span>            index--;</div>
+<div class="line"><span class="lineno">   48</span>        }</div>
+<div class="line"><span class="lineno">   49</span>    }</div>
+<div class="line"><span class="lineno">   50</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -419,19 +419,19 @@ template&lt;typename T &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>                                      {</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    <span class="keywordtype">size_t</span> n = arr-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span> </div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 1; i &lt; n; i++) {</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>        T temp = arr[0][i];</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        int32_t j = i - 1;</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>        <span class="keywordflow">while</span> (j &gt;= 0 &amp;&amp; temp &lt; arr[0][j]) {</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>            arr[0][j + 1] = arr[0][j];</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>            j--;</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>        }</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>        arr[0][j + 1] = temp;</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    }</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   77</span>                                      {</div>
+<div class="line"><span class="lineno">   78</span>    <span class="keywordtype">size_t</span> n = arr-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   79</span> </div>
+<div class="line"><span class="lineno">   80</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 1; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">   81</span>        T temp = arr[0][i];</div>
+<div class="line"><span class="lineno">   82</span>        int32_t j = i - 1;</div>
+<div class="line"><span class="lineno">   83</span>        <span class="keywordflow">while</span> (j &gt;= 0 &amp;&amp; temp &lt; arr[0][j]) {</div>
+<div class="line"><span class="lineno">   84</span>            arr[0][j + 1] = arr[0][j];</div>
+<div class="line"><span class="lineno">   85</span>            j--;</div>
+<div class="line"><span class="lineno">   86</span>        }</div>
+<div class="line"><span class="lineno">   87</span>        arr[0][j + 1] = temp;</div>
+<div class="line"><span class="lineno">   88</span>    }</div>
+<div class="line"><span class="lineno">   89</span>}</div>
 <div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -484,17 +484,17 @@ template&lt;typename T &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>                                  {</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt; n; i++) {</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        T temp = arr[i];</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        <span class="keywordtype">int</span> j = i - 1;</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        <span class="keywordflow">while</span> (j &gt;= 0 &amp;&amp; temp &lt; arr[j]) {</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>            arr[j + 1] = arr[j];</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>            j--;</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        }</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        arr[j + 1] = temp;</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    }</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   59</span>                                  {</div>
+<div class="line"><span class="lineno">   60</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">   61</span>        T temp = arr[i];</div>
+<div class="line"><span class="lineno">   62</span>        <span class="keywordtype">int</span> j = i - 1;</div>
+<div class="line"><span class="lineno">   63</span>        <span class="keywordflow">while</span> (j &gt;= 0 &amp;&amp; temp &lt; arr[j]) {</div>
+<div class="line"><span class="lineno">   64</span>            arr[j + 1] = arr[j];</div>
+<div class="line"><span class="lineno">   65</span>            j--;</div>
+<div class="line"><span class="lineno">   66</span>        }</div>
+<div class="line"><span class="lineno">   67</span>        arr[j + 1] = temp;</div>
+<div class="line"><span class="lineno">   68</span>    }</div>
+<div class="line"><span class="lineno">   69</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -530,20 +530,20 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>Void. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>                                              {</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    int64_t n = arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span> </div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    <span class="keywordflow">for</span> (int64_t i = 1; i &lt; n; i++) {</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        T key = arr[i];</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        int64_t j = i - 1;</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>        int64_t loc = <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a034d8b276518a902962e87d3158b64fd">sorting::binary_search</a>(arr, key, 0, j);</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>        <span class="keywordflow">while</span> (j &gt;= loc) {</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>            arr[j + 1] = arr[j];</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>            j--;</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>        }</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>        arr[j + 1] = key;</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    }</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   84</span>                                              {</div>
+<div class="line"><span class="lineno">   85</span>    int64_t n = arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   86</span> </div>
+<div class="line"><span class="lineno">   87</span>    <span class="keywordflow">for</span> (int64_t i = 1; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">   88</span>        T key = arr[i];</div>
+<div class="line"><span class="lineno">   89</span>        int64_t j = i - 1;</div>
+<div class="line"><span class="lineno">   90</span>        int64_t loc = <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a034d8b276518a902962e87d3158b64fd">sorting::binary_search</a>(arr, key, 0, j);</div>
+<div class="line"><span class="lineno">   91</span>        <span class="keywordflow">while</span> (j &gt;= loc) {</div>
+<div class="line"><span class="lineno">   92</span>            arr[j + 1] = arr[j];</div>
+<div class="line"><span class="lineno">   93</span>            j--;</div>
+<div class="line"><span class="lineno">   94</span>        }</div>
+<div class="line"><span class="lineno">   95</span>        arr[j + 1] = key;</div>
+<div class="line"><span class="lineno">   96</span>    }</div>
+<div class="line"><span class="lineno">   97</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -603,20 +603,20 @@ template&lt;class Iterator &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>                                                               {</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <span class="comment">// create 2 pointers to point at the buffer</span></div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <span class="keyword">auto</span> p(<span class="keyword">reinterpret_cast&lt;</span>std::remove_reference_t&lt;decltype(*l)<span class="keyword">&gt;</span>*&gt;(b)), c(p);</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <span class="comment">// move the left part of the segment</span></div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    <span class="keywordflow">for</span> (Iterator t(l); r != t; ++t) *p++ = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(*t);</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>    <span class="comment">// while neither the buffer nor the right part has been exhausted</span></div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    <span class="comment">// move the smallest element of the two back to the container</span></div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    <span class="keywordflow">while</span> (e != r &amp;&amp; c != p) *l++ = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(*r &lt; *c ? *r++ : *c++);</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <span class="comment">// notice only one of the two following loops will be executed</span></div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <span class="comment">// while the right part hasn&#39;t bee exhausted, move it back</span></div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <span class="keywordflow">while</span> (e != r) *l++ = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(*r++);</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <span class="comment">// while the buffer hasn&#39;t bee exhausted, move it back</span></div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    <span class="keywordflow">while</span> (c != p) *l++ = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(*c++);</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   57</span>                                                               {</div>
+<div class="line"><span class="lineno">   58</span>    <span class="comment">// create 2 pointers to point at the buffer</span></div>
+<div class="line"><span class="lineno">   59</span>    <span class="keyword">auto</span> p(<span class="keyword">reinterpret_cast&lt;</span>std::remove_reference_t&lt;decltype(*l)<span class="keyword">&gt;</span>*&gt;(b)), c(p);</div>
+<div class="line"><span class="lineno">   60</span>    <span class="comment">// move the left part of the segment</span></div>
+<div class="line"><span class="lineno">   61</span>    <span class="keywordflow">for</span> (Iterator t(l); r != t; ++t) *p++ = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(*t);</div>
+<div class="line"><span class="lineno">   62</span>    <span class="comment">// while neither the buffer nor the right part has been exhausted</span></div>
+<div class="line"><span class="lineno">   63</span>    <span class="comment">// move the smallest element of the two back to the container</span></div>
+<div class="line"><span class="lineno">   64</span>    <span class="keywordflow">while</span> (e != r &amp;&amp; c != p) *l++ = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(*r &lt; *c ? *r++ : *c++);</div>
+<div class="line"><span class="lineno">   65</span>    <span class="comment">// notice only one of the two following loops will be executed</span></div>
+<div class="line"><span class="lineno">   66</span>    <span class="comment">// while the right part hasn&#39;t bee exhausted, move it back</span></div>
+<div class="line"><span class="lineno">   67</span>    <span class="keywordflow">while</span> (e != r) *l++ = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(*r++);</div>
+<div class="line"><span class="lineno">   68</span>    <span class="comment">// while the buffer hasn&#39;t bee exhausted, move it back</span></div>
+<div class="line"><span class="lineno">   69</span>    <span class="keywordflow">while</span> (c != p) *l++ = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(*c++);</div>
+<div class="line"><span class="lineno">   70</span>}</div>
 <div class="ttc" id="amove_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a></div><div class="ttdeci">T move(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -663,9 +663,9 @@ template&lt;class Iterator &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>                                                                         {</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#ae97f4dd815654c4682f564afd718e824">non_recursive_merge_sort</a>(first, last, last - first);</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   86</span>                                                                         {</div>
+<div class="line"><span class="lineno">   87</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#ae97f4dd815654c4682f564afd718e824">non_recursive_merge_sort</a>(first, last, last - first);</div>
+<div class="line"><span class="lineno">   88</span>}</div>
 <div class="ttc" id="anamespacesorting_html_ae97f4dd815654c4682f564afd718e824"><div class="ttname"><a href="../../d5/d91/namespacesorting.html#ae97f4dd815654c4682f564afd718e824">sorting::non_recursive_merge_sort</a></div><div class="ttdeci">void non_recursive_merge_sort(const Iterator first, const Iterator last)</div><div class="ttdoc">bottom-up merge sort which sorts elements in a non-decreasing order</div><div class="ttdef"><b>Definition:</b> non_recursive_merge_sort.cpp:86</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -719,28 +719,28 @@ template&lt;class Iterator &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>                                              {</div>
-<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>    <span class="comment">// create a buffer large enough to store all elements</span></div>
-<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>    <span class="comment">// dynamically allocated to comply with cpplint</span></div>
-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>    <span class="keywordtype">char</span>* buffer = <span class="keyword">new</span> <span class="keywordtype">char</span>[n * <span class="keyword">sizeof</span>(*first)];</div>
-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>    <span class="comment">// buffer size can be optimized to largest power of 2 less than n</span></div>
-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>    <span class="comment">// elements divide the container into equally-sized segments whose</span></div>
-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>    <span class="comment">// length start at 1 and keeps increasing by factors of 2</span></div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> length(1); length &lt; n; length &lt;&lt;= 1) {</div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>        <span class="comment">// merge adjacent segments whose number is n / (length * 2)</span></div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>        Iterator left(first);</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> counter(n / (length &lt;&lt; 1)); counter; --counter) {</div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>            Iterator right(left + length), end(right + length);</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>            <a class="code hl_function" href="../../d5/d4c/group__sorting.html#ga460c61cd948203b4816bef2accb3fc73">merge</a>(left, right, end, buffer);</div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>            left = end;</div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>        }</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>        <span class="comment">// if the number of remaining elements (n * 2 % length) is longer</span></div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>        <span class="comment">// than a segment, merge the remaining elements</span></div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>        <span class="keywordflow">if</span> ((n &amp; ((length &lt;&lt; 1) - 1)) &gt; length)</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>            <a class="code hl_function" href="../../d5/d4c/group__sorting.html#ga460c61cd948203b4816bef2accb3fc73">merge</a>(left, left + length, last, buffer);</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>    }</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>    <span class="keyword">delete</span>[] buffer;</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   26</span>                                              {</div>
+<div class="line"><span class="lineno">   27</span>    <span class="comment">// create a buffer large enough to store all elements</span></div>
+<div class="line"><span class="lineno">   28</span>    <span class="comment">// dynamically allocated to comply with cpplint</span></div>
+<div class="line"><span class="lineno">   29</span>    <span class="keywordtype">char</span>* buffer = <span class="keyword">new</span> <span class="keywordtype">char</span>[n * <span class="keyword">sizeof</span>(*first)];</div>
+<div class="line"><span class="lineno">   30</span>    <span class="comment">// buffer size can be optimized to largest power of 2 less than n</span></div>
+<div class="line"><span class="lineno">   31</span>    <span class="comment">// elements divide the container into equally-sized segments whose</span></div>
+<div class="line"><span class="lineno">   32</span>    <span class="comment">// length start at 1 and keeps increasing by factors of 2</span></div>
+<div class="line"><span class="lineno">   33</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> length(1); length &lt; n; length &lt;&lt;= 1) {</div>
+<div class="line"><span class="lineno">   34</span>        <span class="comment">// merge adjacent segments whose number is n / (length * 2)</span></div>
+<div class="line"><span class="lineno">   35</span>        Iterator left(first);</div>
+<div class="line"><span class="lineno">   36</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> counter(n / (length &lt;&lt; 1)); counter; --counter) {</div>
+<div class="line"><span class="lineno">   37</span>            Iterator right(left + length), end(right + length);</div>
+<div class="line"><span class="lineno">   38</span>            <a class="code hl_function" href="../../d5/d4c/group__sorting.html#ga460c61cd948203b4816bef2accb3fc73">merge</a>(left, right, end, buffer);</div>
+<div class="line"><span class="lineno">   39</span>            left = end;</div>
+<div class="line"><span class="lineno">   40</span>        }</div>
+<div class="line"><span class="lineno">   41</span>        <span class="comment">// if the number of remaining elements (n * 2 % length) is longer</span></div>
+<div class="line"><span class="lineno">   42</span>        <span class="comment">// than a segment, merge the remaining elements</span></div>
+<div class="line"><span class="lineno">   43</span>        <span class="keywordflow">if</span> ((n &amp; ((length &lt;&lt; 1) - 1)) &gt; length)</div>
+<div class="line"><span class="lineno">   44</span>            <a class="code hl_function" href="../../d5/d4c/group__sorting.html#ga460c61cd948203b4816bef2accb3fc73">merge</a>(left, left + length, last, buffer);</div>
+<div class="line"><span class="lineno">   45</span>    }</div>
+<div class="line"><span class="lineno">   46</span>    <span class="keyword">delete</span>[] buffer;</div>
+<div class="line"><span class="lineno">   47</span>}</div>
 <div class="ttc" id="agroup__sorting_html_ga460c61cd948203b4816bef2accb3fc73"><div class="ttname"><a href="../../d5/d4c/group__sorting.html#ga460c61cd948203b4816bef2accb3fc73">merge</a></div><div class="ttdeci">void merge(int *arr, int l, int m, int r)</div><div class="ttdef"><b>Definition:</b> merge_sort.cpp:33</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -787,9 +787,9 @@ template&lt;class Iterator &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>                                                                    {</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#ae97f4dd815654c4682f564afd718e824">non_recursive_merge_sort</a>(first, first + n, n);</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   77</span>                                                                    {</div>
+<div class="line"><span class="lineno">   78</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#ae97f4dd815654c4682f564afd718e824">non_recursive_merge_sort</a>(first, first + n, n);</div>
+<div class="line"><span class="lineno">   79</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -831,25 +831,25 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >This function takes last element as pivot, places the pivot element at its correct position in sorted array, and places all smaller (smaller than pivot) to left of pivot and all greater elements to right of pivot </p>
-<div class="fragment"><div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>                                            {</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    <span class="keywordtype">int</span> pivot = arr[high];  <span class="comment">// taking the last element as pivot</span></div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>    <span class="keywordtype">int</span> i = (low - 1);      <span class="comment">// Index of smaller element</span></div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span> </div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = low; j &lt; high; j++) {</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>        <span class="comment">// If current element is smaller than or</span></div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>        <span class="comment">// equal to pivot</span></div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>        <span class="keywordflow">if</span> (arr[j] &lt;= pivot) {</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>            i++;  <span class="comment">// increment index of smaller element</span></div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>            <span class="keywordtype">int</span> temp = arr[i];</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>            arr[i] = arr[j];</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>            arr[j] = temp;</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        }</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    }</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    <span class="keywordtype">int</span> temp = arr[i + 1];</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    arr[i + 1] = arr[high];</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    arr[high] = temp;</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>    <span class="keywordflow">return</span> (i + 1);</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   37</span>                                            {</div>
+<div class="line"><span class="lineno">   38</span>    <span class="keywordtype">int</span> pivot = arr[high];  <span class="comment">// taking the last element as pivot</span></div>
+<div class="line"><span class="lineno">   39</span>    <span class="keywordtype">int</span> i = (low - 1);      <span class="comment">// Index of smaller element</span></div>
+<div class="line"><span class="lineno">   40</span> </div>
+<div class="line"><span class="lineno">   41</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = low; j &lt; high; j++) {</div>
+<div class="line"><span class="lineno">   42</span>        <span class="comment">// If current element is smaller than or</span></div>
+<div class="line"><span class="lineno">   43</span>        <span class="comment">// equal to pivot</span></div>
+<div class="line"><span class="lineno">   44</span>        <span class="keywordflow">if</span> (arr[j] &lt;= pivot) {</div>
+<div class="line"><span class="lineno">   45</span>            i++;  <span class="comment">// increment index of smaller element</span></div>
+<div class="line"><span class="lineno">   46</span>            <span class="keywordtype">int</span> temp = arr[i];</div>
+<div class="line"><span class="lineno">   47</span>            arr[i] = arr[j];</div>
+<div class="line"><span class="lineno">   48</span>            arr[j] = temp;</div>
+<div class="line"><span class="lineno">   49</span>        }</div>
+<div class="line"><span class="lineno">   50</span>    }</div>
+<div class="line"><span class="lineno">   51</span>    <span class="keywordtype">int</span> temp = arr[i + 1];</div>
+<div class="line"><span class="lineno">   52</span>    arr[i + 1] = arr[high];</div>
+<div class="line"><span class="lineno">   53</span>    arr[high] = temp;</div>
+<div class="line"><span class="lineno">   54</span>    <span class="keywordflow">return</span> (i + 1);</div>
+<div class="line"><span class="lineno">   55</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -877,33 +877,33 @@ template&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>sorted array of elements </dd></dl>
-<div class="fragment"><div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>                                                  {</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    <span class="comment">// Finding min and max*</span></div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>    <span class="keyword">auto</span> min = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min_element.html">std::min_element</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr));</div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    <span class="keyword">auto</span> max = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max_element.html">std::max_element</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr));</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span> </div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>    <span class="comment">// Range refers to the number of holes required</span></div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    <span class="keywordtype">int</span> range = *max - *min + 1;</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    <span class="keywordtype">int</span> *hole = <span class="keyword">new</span> <span class="keywordtype">int</span>[range]();</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span> </div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>    <span class="comment">// Copying all array values to pigeonhole</span></div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; i++) {</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>        hole[arr[i] - *min] = arr[i];</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>    }</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span> </div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <span class="comment">// Deleting elements from list and storing to original array</span></div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    <span class="keywordtype">int</span> count = 0;</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; range; i++) {</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>        <span class="keywordflow">while</span> (hole[i] != <span class="charliteral">&#39;\0&#39;</span>) {</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>            arr[count] = hole[i];</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>            hole[i] = {};</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>            count++;</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>        }</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    }</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    <span class="keyword">delete</span>[] hole;</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span> </div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <span class="keywordflow">return</span> arr;</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   34</span>                                                  {</div>
+<div class="line"><span class="lineno">   35</span>    <span class="comment">// Finding min and max*</span></div>
+<div class="line"><span class="lineno">   36</span>    <span class="keyword">auto</span> min = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min_element.html">std::min_element</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr));</div>
+<div class="line"><span class="lineno">   37</span>    <span class="keyword">auto</span> max = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max_element.html">std::max_element</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr));</div>
+<div class="line"><span class="lineno">   38</span> </div>
+<div class="line"><span class="lineno">   39</span>    <span class="comment">// Range refers to the number of holes required</span></div>
+<div class="line"><span class="lineno">   40</span>    <span class="keywordtype">int</span> range = *max - *min + 1;</div>
+<div class="line"><span class="lineno">   41</span>    <span class="keywordtype">int</span> *hole = <span class="keyword">new</span> <span class="keywordtype">int</span>[range]();</div>
+<div class="line"><span class="lineno">   42</span> </div>
+<div class="line"><span class="lineno">   43</span>    <span class="comment">// Copying all array values to pigeonhole</span></div>
+<div class="line"><span class="lineno">   44</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; i++) {</div>
+<div class="line"><span class="lineno">   45</span>        hole[arr[i] - *min] = arr[i];</div>
+<div class="line"><span class="lineno">   46</span>    }</div>
+<div class="line"><span class="lineno">   47</span> </div>
+<div class="line"><span class="lineno">   48</span>    <span class="comment">// Deleting elements from list and storing to original array</span></div>
+<div class="line"><span class="lineno">   49</span>    <span class="keywordtype">int</span> count = 0;</div>
+<div class="line"><span class="lineno">   50</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; range; i++) {</div>
+<div class="line"><span class="lineno">   51</span>        <span class="keywordflow">while</span> (hole[i] != <span class="charliteral">&#39;\0&#39;</span>) {</div>
+<div class="line"><span class="lineno">   52</span>            arr[count] = hole[i];</div>
+<div class="line"><span class="lineno">   53</span>            hole[i] = {};</div>
+<div class="line"><span class="lineno">   54</span>            count++;</div>
+<div class="line"><span class="lineno">   55</span>        }</div>
+<div class="line"><span class="lineno">   56</span>    }</div>
+<div class="line"><span class="lineno">   57</span>    <span class="keyword">delete</span>[] hole;</div>
+<div class="line"><span class="lineno">   58</span> </div>
+<div class="line"><span class="lineno">   59</span>    <span class="keywordflow">return</span> arr;</div>
+<div class="line"><span class="lineno">   60</span>}</div>
 <div class="ttc" id="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a></div><div class="ttdeci">T begin(T... args)</div></div>
 <div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a></div><div class="ttdeci">T end(T... args)</div></div>
 <div class="ttc" id="amax_element_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max_element.html">std::max_element</a></div><div class="ttdeci">T max_element(T... args)</div></div>
@@ -949,13 +949,13 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >The main function that implements QuickSort arr[] --&gt; Array to be sorted, low --&gt; Starting index, high --&gt; Ending index </p>
-<div class="fragment"><div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>                                             {</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    <span class="keywordflow">if</span> (low &lt; high) {</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        <span class="keywordtype">int</span> p = <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a7e7f25f31c50523990437abf2ac3907e">partition</a>(arr, low, high);</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a50b66a1c652291b9a346ec7342967178">quickSort</a>(arr, low, p - 1);</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a50b66a1c652291b9a346ec7342967178">quickSort</a>(arr, p + 1, high);</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    }</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   63</span>                                             {</div>
+<div class="line"><span class="lineno">   64</span>    <span class="keywordflow">if</span> (low &lt; high) {</div>
+<div class="line"><span class="lineno">   65</span>        <span class="keywordtype">int</span> p = <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a7e7f25f31c50523990437abf2ac3907e">partition</a>(arr, low, high);</div>
+<div class="line"><span class="lineno">   66</span>        <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a50b66a1c652291b9a346ec7342967178">quickSort</a>(arr, low, p - 1);</div>
+<div class="line"><span class="lineno">   67</span>        <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a50b66a1c652291b9a346ec7342967178">quickSort</a>(arr, p + 1, high);</div>
+<div class="line"><span class="lineno">   68</span>    }</div>
+<div class="line"><span class="lineno">   69</span>}</div>
 <div class="ttc" id="anamespacesorting_html_a50b66a1c652291b9a346ec7342967178"><div class="ttname"><a href="../../d5/d91/namespacesorting.html#a50b66a1c652291b9a346ec7342967178">sorting::quickSort</a></div><div class="ttdeci">void quickSort(int arr[], int low, int high)</div><div class="ttdef"><b>Definition:</b> quick_sort.cpp:63</div></div>
 <div class="ttc" id="anamespacesorting_html_a7e7f25f31c50523990437abf2ac3907e"><div class="ttname"><a href="../../d5/d91/namespacesorting.html#a7e7f25f31c50523990437abf2ac3907e">sorting::partition</a></div><div class="ttdeci">int partition(int arr[], int low, int high)</div><div class="ttdef"><b>Definition:</b> quick_sort.cpp:37</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -1014,20 +1014,20 @@ template&lt;typename T &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>                                                             {</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>    <span class="keywordflow">if</span> (low &gt;= high) {  <span class="comment">// 1 or 0 elements</span></div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>        <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    }</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span> </div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>    int32_t i = 0, j = 0;</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span> </div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <span class="comment">// i and j are passed as reference</span></div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    partition3(arr, low, high, &amp;i, &amp;j);</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span> </div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <span class="comment">// Recur two halves</span></div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a6eb67c2f91c98cf4464f75b5882022de">quicksort</a>(arr, low, i);</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a6eb67c2f91c98cf4464f75b5882022de">quicksort</a>(arr, j, high);</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   94</span>                                                             {</div>
+<div class="line"><span class="lineno">   95</span>    <span class="keywordflow">if</span> (low &gt;= high) {  <span class="comment">// 1 or 0 elements</span></div>
+<div class="line"><span class="lineno">   96</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">   97</span>    }</div>
+<div class="line"><span class="lineno">   98</span> </div>
+<div class="line"><span class="lineno">   99</span>    int32_t i = 0, j = 0;</div>
+<div class="line"><span class="lineno">  100</span> </div>
+<div class="line"><span class="lineno">  101</span>    <span class="comment">// i and j are passed as reference</span></div>
+<div class="line"><span class="lineno">  102</span>    partition3(arr, low, high, &amp;i, &amp;j);</div>
+<div class="line"><span class="lineno">  103</span> </div>
+<div class="line"><span class="lineno">  104</span>    <span class="comment">// Recur two halves</span></div>
+<div class="line"><span class="lineno">  105</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a6eb67c2f91c98cf4464f75b5882022de">quicksort</a>(arr, low, i);</div>
+<div class="line"><span class="lineno">  106</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a6eb67c2f91c98cf4464f75b5882022de">quicksort</a>(arr, j, high);</div>
+<div class="line"><span class="lineno">  107</span>}</div>
 <div class="ttc" id="anamespacesorting_html_a6eb67c2f91c98cf4464f75b5882022de"><div class="ttname"><a href="../../d5/d91/namespacesorting.html#a6eb67c2f91c98cf4464f75b5882022de">sorting::quicksort</a></div><div class="ttdeci">std::vector&lt; T &gt; quicksort(std::vector&lt; T &gt; arr, int32_t low, int32_t high)</div><div class="ttdef"><b>Definition:</b> quick_sort_3.cpp:119</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -1086,22 +1086,22 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>sorted array vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>                                                                    {</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <span class="keywordflow">if</span> (low &gt;= high) {  <span class="comment">// 1 or 0 elements</span></div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>        <span class="keywordflow">return</span> arr;</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    }</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span> </div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    int32_t i = 0, j = 0;</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span> </div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    <span class="comment">// i and j are passed as reference</span></div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    partition3(&amp;arr, low, high, &amp;i, &amp;j);</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span> </div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    <span class="comment">// Recur two halves</span></div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a6eb67c2f91c98cf4464f75b5882022de">quicksort</a>(&amp;arr, low, i);</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a6eb67c2f91c98cf4464f75b5882022de">quicksort</a>(&amp;arr, j, high);</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span> </div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    <span class="keywordflow">return</span> arr;</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  119</span>                                                                    {</div>
+<div class="line"><span class="lineno">  120</span>    <span class="keywordflow">if</span> (low &gt;= high) {  <span class="comment">// 1 or 0 elements</span></div>
+<div class="line"><span class="lineno">  121</span>        <span class="keywordflow">return</span> arr;</div>
+<div class="line"><span class="lineno">  122</span>    }</div>
+<div class="line"><span class="lineno">  123</span> </div>
+<div class="line"><span class="lineno">  124</span>    int32_t i = 0, j = 0;</div>
+<div class="line"><span class="lineno">  125</span> </div>
+<div class="line"><span class="lineno">  126</span>    <span class="comment">// i and j are passed as reference</span></div>
+<div class="line"><span class="lineno">  127</span>    partition3(&amp;arr, low, high, &amp;i, &amp;j);</div>
+<div class="line"><span class="lineno">  128</span> </div>
+<div class="line"><span class="lineno">  129</span>    <span class="comment">// Recur two halves</span></div>
+<div class="line"><span class="lineno">  130</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a6eb67c2f91c98cf4464f75b5882022de">quicksort</a>(&amp;arr, low, i);</div>
+<div class="line"><span class="lineno">  131</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a6eb67c2f91c98cf4464f75b5882022de">quicksort</a>(&amp;arr, j, high);</div>
+<div class="line"><span class="lineno">  132</span> </div>
+<div class="line"><span class="lineno">  133</span>    <span class="keywordflow">return</span> arr;</div>
+<div class="line"><span class="lineno">  134</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -1142,13 +1142,13 @@ template&lt;typename T , size_t N&gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>new array with elements sorted from a given array </dd></dl>
-<div class="fragment"><div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>                                                          {</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    <span class="comment">// Untill array is not sorted</span></div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    <span class="keywordflow">while</span> (!<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/begin.html">begin</a>(), arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/end.html">end</a>())) {</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/random_shuffle.html">std::random_shuffle</a>(arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/begin.html">begin</a>(), arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/end.html">end</a>());<span class="comment">// Shuffle the array</span></div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    }</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    <span class="keywordflow">return</span> arr;</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   51</span>                                                          {</div>
+<div class="line"><span class="lineno">   52</span>    <span class="comment">// Untill array is not sorted</span></div>
+<div class="line"><span class="lineno">   53</span>    <span class="keywordflow">while</span> (!<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/begin.html">begin</a>(), arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/end.html">end</a>())) {</div>
+<div class="line"><span class="lineno">   54</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/random_shuffle.html">std::random_shuffle</a>(arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/begin.html">begin</a>(), arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/end.html">end</a>());<span class="comment">// Shuffle the array</span></div>
+<div class="line"><span class="lineno">   55</span>    }</div>
+<div class="line"><span class="lineno">   56</span>    <span class="keywordflow">return</span> arr;</div>
+<div class="line"><span class="lineno">   57</span>}</div>
 <div class="ttc" id="ais_sorted_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a></div><div class="ttdeci">T is_sorted(T... args)</div></div>
 <div class="ttc" id="arandom_shuffle_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/random_shuffle.html">std::random_shuffle</a></div><div class="ttdeci">T random_shuffle(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -1205,21 +1205,21 @@ template&lt;typename T &gt; </div>
 <p >&lt; base case; when size of the array is 1</p>
 <p >&lt; iterating over the entire array</p>
 <p >&lt; if a larger number appears before the smaller one, swap them.</p>
-<div class="fragment"><div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>                                                           {</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    <span class="keywordflow">if</span> (n == 1) {  <span class="comment">//!&lt; base case; when size of the array is 1</span></div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    }</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span> </div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; n - 1; i++) {  <span class="comment">//!&lt; iterating over the entire array</span><span class="comment"></span></div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span><span class="comment">        //!&lt; if a larger number appears before the smaller one, swap them.</span></div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span><span class="comment"></span>        <span class="keywordflow">if</span> ((*nums)[i] &gt; (*nums)[i + 1]) {</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>((*nums)[i], (*nums)[i + 1]);</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>        }</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    }</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span><span class="comment"></span> </div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span><span class="comment">    //!&lt; calling the function after we have fixed the last element</span></div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span><span class="comment"></span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#ae3a775d99dbbb94c130a973df0cfddcf">recursive_bubble_sort</a>(nums, n - 1);</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   74</span>                                                           {</div>
+<div class="line"><span class="lineno">   75</span>    <span class="keywordflow">if</span> (n == 1) {  <span class="comment">//!&lt; base case; when size of the array is 1</span></div>
+<div class="line"><span class="lineno">   76</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">   77</span>    }</div>
+<div class="line"><span class="lineno">   78</span> </div>
+<div class="line"><span class="lineno">   79</span>    <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; n - 1; i++) {  <span class="comment">//!&lt; iterating over the entire array</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">   80</span><span class="comment">        //!&lt; if a larger number appears before the smaller one, swap them.</span></div>
+<div class="line"><span class="lineno">   81</span><span class="comment"></span>        <span class="keywordflow">if</span> ((*nums)[i] &gt; (*nums)[i + 1]) {</div>
+<div class="line"><span class="lineno">   82</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>((*nums)[i], (*nums)[i + 1]);</div>
+<div class="line"><span class="lineno">   83</span>        }</div>
+<div class="line"><span class="lineno">   84</span>    }</div>
+<div class="line"><span class="lineno">   85</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   86</span><span class="comment">    //!&lt; calling the function after we have fixed the last element</span></div>
+<div class="line"><span class="lineno">   87</span><span class="comment"></span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#ae3a775d99dbbb94c130a973df0cfddcf">recursive_bubble_sort</a>(nums, n - 1);</div>
+<div class="line"><span class="lineno">   88</span>}</div>
 <div class="ttc" id="anamespacesorting_html_ae3a775d99dbbb94c130a973df0cfddcf"><div class="ttname"><a href="../../d5/d91/namespacesorting.html#ae3a775d99dbbb94c130a973df0cfddcf">sorting::recursive_bubble_sort</a></div><div class="ttdeci">void recursive_bubble_sort(std::vector&lt; T &gt; *nums, uint64_t n)</div><div class="ttdoc">This is an implementation of the recursive_bubble_sort. A vector is passed to the function which is t...</div><div class="ttdef"><b>Definition:</b> recursive_bubble_sort.cpp:74</div></div>
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@@ -1255,29 +1255,29 @@ Here is the call graph for this function:</div>
         </tr>
       </table>
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-<div class="fragment"><div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>                                                  {</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> array(</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>        arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(),</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>        arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>());  <span class="comment">// declare a vector in which result will be stored</span></div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    <span class="keywordflow">for</span> (uint64_t it = 0; it &lt; len; ++it) {</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>        uint64_t min = it;  <span class="comment">// set min value</span></div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>        <span class="keywordflow">for</span> (uint64_t it2 = it + 1; it2 &lt; len; ++it2) {</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>            <span class="keywordflow">if</span> (array[it2] &lt; array[min]) {  <span class="comment">// check which element is smaller</span></div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>                min = it2;  <span class="comment">// store index of smallest element to min</span></div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>            }</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>        }</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span> </div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        <span class="keywordflow">if</span> (min != it) {  <span class="comment">// swap if min does not match to i</span></div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>            uint64_t tmp = array[<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a>];</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>            array[<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a>] = array[it];</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>            array[it] = tmp;</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        }</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    }</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span> </div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <span class="keywordflow">return</span> array;  <span class="comment">// return sorted vector</span></div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   48</span>                                                  {</div>
+<div class="line"><span class="lineno">   49</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> array(</div>
+<div class="line"><span class="lineno">   50</span>        arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(),</div>
+<div class="line"><span class="lineno">   51</span>        arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>());  <span class="comment">// declare a vector in which result will be stored</span></div>
+<div class="line"><span class="lineno">   52</span>    <span class="keywordflow">for</span> (uint64_t it = 0; it &lt; len; ++it) {</div>
+<div class="line"><span class="lineno">   53</span>        uint64_t min = it;  <span class="comment">// set min value</span></div>
+<div class="line"><span class="lineno">   54</span>        <span class="keywordflow">for</span> (uint64_t it2 = it + 1; it2 &lt; len; ++it2) {</div>
+<div class="line"><span class="lineno">   55</span>            <span class="keywordflow">if</span> (array[it2] &lt; array[min]) {  <span class="comment">// check which element is smaller</span></div>
+<div class="line"><span class="lineno">   56</span>                min = it2;  <span class="comment">// store index of smallest element to min</span></div>
+<div class="line"><span class="lineno">   57</span>            }</div>
+<div class="line"><span class="lineno">   58</span>        }</div>
+<div class="line"><span class="lineno">   59</span> </div>
+<div class="line"><span class="lineno">   60</span>        <span class="keywordflow">if</span> (min != it) {  <span class="comment">// swap if min does not match to i</span></div>
+<div class="line"><span class="lineno">   61</span>            uint64_t tmp = array[<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a>];</div>
+<div class="line"><span class="lineno">   62</span>            array[<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a>] = array[it];</div>
+<div class="line"><span class="lineno">   63</span>            array[it] = tmp;</div>
+<div class="line"><span class="lineno">   64</span>        }</div>
+<div class="line"><span class="lineno">   65</span>    }</div>
+<div class="line"><span class="lineno">   66</span> </div>
+<div class="line"><span class="lineno">   67</span>    <span class="keywordflow">return</span> array;  <span class="comment">// return sorted vector</span></div>
+<div class="line"><span class="lineno">   68</span>}</div>
 <div class="ttc" id="amin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a></div><div class="ttdeci">T min(T... args)</div></div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; uint64_t &gt;</a></div></div>
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@@ -1299,9 +1299,9 @@ template&lt;typename T &gt; </div>
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 <p >function overload - when input array is of type <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>, simply send the data content and the data length to the above function. </p>
-<div class="fragment"><div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>                                   {</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">shell_sort</a>(arr-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a>(), arr-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   75</span>                                   {</div>
+<div class="line"><span class="lineno">   76</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">shell_sort</a>(arr-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a>(), arr-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());</div>
+<div class="line"><span class="lineno">   77</span>}</div>
 <div class="ttc" id="adata_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/data.html">std::vector::data</a></div><div class="ttdeci">T data(T... args)</div></div>
 <div class="ttc" id="anamespacesorting_html_af2c5b92cbfe73f63f6074c61b0a45331"><div class="ttname"><a href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">sorting::shell_sort</a></div><div class="ttdeci">void shell_sort(std::vector&lt; T &gt; *arr)</div><div class="ttdef"><b>Definition:</b> shell_sort2.cpp:75</div></div>
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@@ -1341,24 +1341,24 @@ template&lt;typename T &gt; </div>
       </table>
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 <p >Optimized algorithm - takes half the time by utilizing Mar </p>
-<div class="fragment"><div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>                                    {</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>    <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> gaps[] = {701, 301, 132, 57, 23, 10, 4, 1};</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>    <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> gap_len = 8;</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <span class="keywordtype">size_t</span> i, j, g;</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span> </div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    <span class="keywordflow">for</span> (g = 0; g &lt; gap_len; g++) {</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>        <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> gap = gaps[g];</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>        <span class="keywordflow">for</span> (i = gap; i &lt; LEN; i++) {</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>            T tmp = arr[i];</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span> </div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>            <span class="keywordflow">for</span> (j = i; j &gt;= gap &amp;&amp; (arr[j - gap] - tmp) &gt; 0; j -= gap) {</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>                arr[j] = arr[j - gap];</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>            }</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span> </div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>            arr[j] = tmp;</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        }</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    }</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   45</span>                                    {</div>
+<div class="line"><span class="lineno">   46</span>    <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> gaps[] = {701, 301, 132, 57, 23, 10, 4, 1};</div>
+<div class="line"><span class="lineno">   47</span>    <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> gap_len = 8;</div>
+<div class="line"><span class="lineno">   48</span>    <span class="keywordtype">size_t</span> i, j, g;</div>
+<div class="line"><span class="lineno">   49</span> </div>
+<div class="line"><span class="lineno">   50</span>    <span class="keywordflow">for</span> (g = 0; g &lt; gap_len; g++) {</div>
+<div class="line"><span class="lineno">   51</span>        <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> gap = gaps[g];</div>
+<div class="line"><span class="lineno">   52</span>        <span class="keywordflow">for</span> (i = gap; i &lt; LEN; i++) {</div>
+<div class="line"><span class="lineno">   53</span>            T tmp = arr[i];</div>
+<div class="line"><span class="lineno">   54</span> </div>
+<div class="line"><span class="lineno">   55</span>            <span class="keywordflow">for</span> (j = i; j &gt;= gap &amp;&amp; (arr[j - gap] - tmp) &gt; 0; j -= gap) {</div>
+<div class="line"><span class="lineno">   56</span>                arr[j] = arr[j - gap];</div>
+<div class="line"><span class="lineno">   57</span>            }</div>
+<div class="line"><span class="lineno">   58</span> </div>
+<div class="line"><span class="lineno">   59</span>            arr[j] = tmp;</div>
+<div class="line"><span class="lineno">   60</span>        }</div>
+<div class="line"><span class="lineno">   61</span>    }</div>
+<div class="line"><span class="lineno">   62</span>}</div>
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@@ -1380,9 +1380,9 @@ template&lt;typename T , size_t N&gt; </div>
       </table>
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 <p >function overload - when input array is of a known length array type </p>
-<div class="fragment"><div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>                             {</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">shell_sort</a>(arr, N);</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   67</span>                             {</div>
+<div class="line"><span class="lineno">   68</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">shell_sort</a>(arr, N);</div>
+<div class="line"><span class="lineno">   69</span>}</div>
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@@ -1423,13 +1423,13 @@ template&lt;typename T , size_t N&gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>new array with elements shuffled from a given array </dd></dl>
-<div class="fragment"><div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>                                              {</div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; i++) {</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>        <span class="comment">// Swaps i&#39;th  index with random index (less than array size)</span></div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[i], arr[<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % N]);</div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    }</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    <span class="keywordflow">return</span> arr;</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   36</span>                                              {</div>
+<div class="line"><span class="lineno">   37</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; i++) {</div>
+<div class="line"><span class="lineno">   38</span>        <span class="comment">// Swaps i&#39;th  index with random index (less than array size)</span></div>
+<div class="line"><span class="lineno">   39</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[i], arr[<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % N]);</div>
+<div class="line"><span class="lineno">   40</span>    }</div>
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@@ -166,7 +166,7 @@ Functions</h2></td></tr>
 <p >However <a class="el" href="../../dd/d43/namespace_m_d5.html" title="Functions for the MD5 algorithm implementation.">MD5</a> has be know to be cryptographically weak for quite some time, yet it is still widely used. This weakness was exploited by the <a href="https://en.wikipedia.org/wiki/Flame_(malware)" target="_blank">Flame Malware</a> in 2012</p>
 <h3><a class="anchor" id="autotoc_md81"></a>
 Algorithm</h3>
-<p >First of all, all values are expected to be in <a href="https://en.wikipedia.org/wiki/Endianness" target="_blank">little endian</a>. This is especially important when using part of the bytestring as an integer.</p>
+<p >First of all, all values are expected to be in [little endian] (<a href="https://en.wikipedia.org/wiki/Endianness">https://en.wikipedia.org/wiki/Endianness</a>). This is especially important when using part of the bytestring as an integer.</p>
 <p >The first step of the algorithm is to pad the message for its length to be a multiple of 64 (bytes). This is done by first adding 0x80 (10000000) and then only zeroes until the last 8 bytes must be filled, where then the 64 bit size of the input will be added</p>
 <p >Once this is done, the algo breaks down this padded message into 64 bytes chunks. Each chunk is used for one <em>round</em>, a round breaks the chunk into 16 blocks of 4 bytes. During these rounds the algorithm will update its 128 bit state (represented by 4 ints: A,B,C,D) For more precisions on these operations please see the <a href="https://en.wikipedia.org/wiki/MD5#Algorithm" target="_blank">Wikipedia aritcle</a>. The signature given by <a class="el" href="../../dd/d43/namespace_m_d5.html" title="Functions for the MD5 algorithm implementation.">MD5</a> is its 128 bit state once all rounds are done. </p><dl class="section note"><dt>Note</dt><dd>This is a simple implementation for a byte string but some implmenetations can work on bytestream, messages of unknown length. </dd></dl>
 </div><h2 class="groupheader">Function Documentation</h2>
@@ -194,9 +194,9 @@ Algorithm</h3>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void* Pointer to the <a class="el" href="../../dd/d43/namespace_m_d5.html" title="Functions for the MD5 algorithm implementation.">MD5</a> signature </dd></dl>
-<div class="fragment"><div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>                                     {</div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a5341431cef7fcfc33794326e1deb2425">hash_bs</a>(&amp;message[0], message.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>());</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  287</span>                                     {</div>
+<div class="line"><span class="lineno">  288</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a5341431cef7fcfc33794326e1deb2425">hash_bs</a>(&amp;message[0], message.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>());</div>
+<div class="line"><span class="lineno">  289</span>}</div>
 <div class="ttc" id="amd5_8cpp_html_a5341431cef7fcfc33794326e1deb2425"><div class="ttname"><a href="../../d5/d96/md5_8cpp.html#a5341431cef7fcfc33794326e1deb2425">hashing::md5::hash_bs</a></div><div class="ttdeci">void * hash_bs(const void *input_bs, uint64_t input_size)</div><div class="ttdoc">The MD5 algorithm itself, taking in a bytestring.</div><div class="ttdef"><b>Definition:</b> md5.cpp:138</div></div>
 <div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">std::string::size</a></div><div class="ttdeci">T size(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -248,150 +248,150 @@ Here is the call graph for this function:</div>
 <div class="line"><span class="keywordflow">for</span> i <span class="keywordflow">in</span> range(64):</div>
 <div class="line">    <a class="code hl_function" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a235843bdf82d2a6cc8596ae8fd3b8df9">print</a>(floor(2**32 * abs(sin(i+1))))</div>
 <div class="ttc" id="asieve__of__eratosthenes_8cpp_html_a235843bdf82d2a6cc8596ae8fd3b8df9"><div class="ttname"><a href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a235843bdf82d2a6cc8596ae8fd3b8df9">print</a></div><div class="ttdeci">void print(uint32_t N, const std::vector&lt; bool &gt; &amp;is_prime)</div><div class="ttdef"><b>Definition:</b> sieve_of_eratosthenes.cpp:44</div></div>
-</div><!-- fragment --><div class="fragment"><div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>                                                         {</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>    <span class="keyword">auto</span>* input = <span class="keyword">static_cast&lt;</span><span class="keyword">const </span>uint8_t*<span class="keyword">&gt;</span>(input_bs);</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span> </div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    <span class="comment">// Step 0: Initial Data (Those are decided in the MD5 protocol)</span></div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    <span class="comment">// s is the shift used in the leftrotate each round</span></div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;uint32_t, 64&gt;</a> s = {</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>        7, 12, 17, 22, 7, 12, 17, 22, 7, 12, 17, 22, 7, 12, 17, 22,</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>        5, 9,  14, 20, 5, 9,  14, 20, 5, 9,  14, 20, 5, 9,  14, 20,</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>        4, 11, 16, 23, 4, 11, 16, 23, 4, 11, 16, 23, 4, 11, 16, 23,</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>        6, 10, 15, 21, 6, 10, 15, 21, 6, 10, 15, 21, 6, 10, 15, 21};</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>    <span class="comment">// K is pseudo-random values used each round</span></div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>    <span class="comment">// The values can be obtained by the following python code:</span></div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span><span class="comment"></span> </div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span><span class="comment">    /**</span></div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span><span class="comment">     * @brief Values of K are pseudo-random and used to &quot;salt&quot; each round</span></div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span><span class="comment">     * The values can be obtained by the following python code</span></div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span><span class="comment">     * @code{.py}</span></div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span><span class="comment">     * from math import floor, sin</span></div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span><span class="comment">     *</span></div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span><span class="comment">     * for i in range(64):</span></div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span><span class="comment">     *     print(floor(2**32 * abs(sin(i+1))))</span></div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span><span class="comment">     * @endcode</span></div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span><span class="comment">     */</span></div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;uint32_t, 64&gt;</a> K = {</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>        3614090360, 3905402710, 606105819,  3250441966, 4118548399, 1200080426,</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>        2821735955, 4249261313, 1770035416, 2336552879, 4294925233, 2304563134,</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>        1804603682, 4254626195, 2792965006, 1236535329, 4129170786, 3225465664,</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>        643717713,  3921069994, 3593408605, 38016083,   3634488961, 3889429448,</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>        568446438,  3275163606, 4107603335, 1163531501, 2850285829, 4243563512,</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>        1735328473, 2368359562, 4294588738, 2272392833, 1839030562, 4259657740,</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>        2763975236, 1272893353, 4139469664, 3200236656, 681279174,  3936430074,</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>        3572445317, 76029189,   3654602809, 3873151461, 530742520,  3299628645,</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>        4096336452, 1126891415, 2878612391, 4237533241, 1700485571, 2399980690,</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>        4293915773, 2240044497, 1873313359, 4264355552, 2734768916, 1309151649,</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>        4149444226, 3174756917, 718787259,  3951481745};</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span> </div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>    <span class="comment">// The initial 128-bit state</span></div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>    uint32_t a0 = 0x67452301, A = 0;</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>    uint32_t b0 = 0xefcdab89, B = 0;</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>    uint32_t c0 = 0x98badcfe, C = 0;</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>    uint32_t d0 = 0x10325476, D = 0;</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span> </div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>    <span class="comment">// Step 1: Processing the bytestring</span></div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span> </div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>    <span class="comment">// First compute the size the padded message will have</span></div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>    <span class="comment">// so it is possible to allocate the right amount of memory</span></div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>    uint64_t padded_message_size = 0;</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>    <span class="keywordflow">if</span> (input_size % 64 &lt; 56) {</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>        padded_message_size = input_size + 64 - (input_size % 64);</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>        padded_message_size = input_size + 128 - (input_size % 64);</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>    }</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span> </div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint8_t&gt;</a> padded_message(padded_message_size);</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span> </div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>    <span class="comment">// Beginning of the padded message is the original message</span></div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/copy.html">std::copy</a>(input, input + input_size, padded_message.begin());</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span> </div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>    <span class="comment">// Afterwards comes a single 1 bit and then only zeroes</span></div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>    padded_message[input_size] = 1 &lt;&lt; 7;  <span class="comment">// 10000000</span></div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>    <span class="keywordflow">for</span> (uint64_t i = input_size; i % 64 != 56; i++) {</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>        <span class="keywordflow">if</span> (i == input_size) {</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>            <span class="keywordflow">continue</span>;  <span class="comment">// pass first iteration</span></div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>        }</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>        padded_message[i] = 0;</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>    }</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span> </div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    <span class="comment">// We then have to add the 64-bit size of the message at the end</span></div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    <span class="comment">// When there is a conversion from int to bytestring or vice-versa</span></div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>    <span class="comment">// We always need to make sure it is little endian</span></div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    uint64_t input_bitsize_le = <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a6be48c1e6e742f9bd329f501d61dcaef">toLittleEndian64</a>(input_size * 8);</div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>    <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; 8; i++) {</div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>        padded_message[padded_message_size - 8 + i] =</div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>            (input_bitsize_le &gt;&gt; (56 - 8 * i)) &amp; 0xFF;</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>    }</div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span> </div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>    <span class="comment">// Already allocate memory for blocks</span></div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;uint32_t, 16&gt;</a> blocks{};</div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span> </div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>    <span class="comment">// Rounds</span></div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>    <span class="keywordflow">for</span> (uint64_t chunk = 0; chunk * 64 &lt; padded_message_size; chunk++) {</div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>        <span class="comment">// First, build the 16 32-bits blocks from the chunk</span></div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>        <span class="keywordflow">for</span> (uint8_t bid = 0; bid &lt; 16; bid++) {</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>            blocks[bid] = 0;</div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span> </div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>            <span class="comment">// Having to build a 32-bit word from 4-bit words</span></div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>            <span class="comment">// Add each and shift them to the left</span></div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>            <span class="keywordflow">for</span> (uint8_t cid = 0; cid &lt; 4; cid++) {</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>                blocks[bid] = (blocks[bid] &lt;&lt; 8) +</div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>                              padded_message[chunk * 64 + bid * 4 + cid];</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>            }</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>        }</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span> </div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>        A = a0;</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>        B = b0;</div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>        C = c0;</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>        D = d0;</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span> </div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>        <span class="comment">// Main &quot;hashing&quot; loop</span></div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>        <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; 64; i++) {</div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>            uint32_t F = 0, <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = 0;</div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>            <span class="keywordflow">if</span> (i &lt; 16) {</div>
-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>                F = (B &amp; C) | ((~B) &amp; D);</div>
-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = i;</div>
-<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (i &lt; 32) {</div>
-<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>                F = (D &amp; B) | ((~D) &amp; C);</div>
-<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = (5 * i + 1) % 16;</div>
-<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (i &lt; 48) {</div>
-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>                F = B ^ C ^ D;</div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = (3 * i + 5) % 16;</div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>                F = C ^ (B | (~D));</div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = (7 * i) % 16;</div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>            }</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span> </div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>            <span class="comment">// Update the accumulators</span></div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>            F += A + K[i] + <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a694712c9665051ba52b686387b87a689">toLittleEndian32</a>(blocks[g]);</div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span> </div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>            A = D;</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>            D = C;</div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>            C = B;</div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>            B += <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#add2bf982d5dd64a45d13cba52c2b371d">leftRotate32bits</a>(F, s[i]);</div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>        }</div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>        <span class="comment">// Update the state with this chunk&#39;s hash</span></div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>        a0 += A;</div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>        b0 += B;</div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>        c0 += C;</div>
-<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>        d0 += D;</div>
-<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>    }</div>
-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span> </div>
-<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>    <span class="comment">// Build signature from state</span></div>
-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>    <span class="comment">// Note, any type could be used for the signature</span></div>
-<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>    <span class="comment">// uint8_t was used to make the 16 bytes obvious</span></div>
-<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>    <span class="comment">// The sig needs to be little endian</span></div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>    <span class="keyword">auto</span>* sig = <span class="keyword">new</span> uint8_t[16];</div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>    <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; 4; i++) {</div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>        sig[i] = (a0 &gt;&gt; (8 * i)) &amp; 0xFF;</div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>        sig[i + 4] = (b0 &gt;&gt; (8 * i)) &amp; 0xFF;</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>        sig[i + 8] = (c0 &gt;&gt; (8 * i)) &amp; 0xFF;</div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>        sig[i + 12] = (d0 &gt;&gt; (8 * i)) &amp; 0xFF;</div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>    }</div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span> </div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>    <span class="keywordflow">return</span> sig;</div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>}</div>
+</div><!-- fragment --><div class="fragment"><div class="line"><span class="lineno">  138</span>                                                         {</div>
+<div class="line"><span class="lineno">  139</span>    <span class="keyword">auto</span>* input = <span class="keyword">static_cast&lt;</span><span class="keyword">const </span>uint8_t*<span class="keyword">&gt;</span>(input_bs);</div>
+<div class="line"><span class="lineno">  140</span> </div>
+<div class="line"><span class="lineno">  141</span>    <span class="comment">// Step 0: Initial Data (Those are decided in the MD5 protocol)</span></div>
+<div class="line"><span class="lineno">  142</span>    <span class="comment">// s is the shift used in the leftrotate each round</span></div>
+<div class="line"><span class="lineno">  143</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;uint32_t, 64&gt;</a> s = {</div>
+<div class="line"><span class="lineno">  144</span>        7, 12, 17, 22, 7, 12, 17, 22, 7, 12, 17, 22, 7, 12, 17, 22,</div>
+<div class="line"><span class="lineno">  145</span>        5, 9,  14, 20, 5, 9,  14, 20, 5, 9,  14, 20, 5, 9,  14, 20,</div>
+<div class="line"><span class="lineno">  146</span>        4, 11, 16, 23, 4, 11, 16, 23, 4, 11, 16, 23, 4, 11, 16, 23,</div>
+<div class="line"><span class="lineno">  147</span>        6, 10, 15, 21, 6, 10, 15, 21, 6, 10, 15, 21, 6, 10, 15, 21};</div>
+<div class="line"><span class="lineno">  148</span>    <span class="comment">// K is pseudo-random values used each round</span></div>
+<div class="line"><span class="lineno">  149</span>    <span class="comment">// The values can be obtained by the following python code:</span></div>
+<div class="line"><span class="lineno">  150</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  151</span><span class="comment">    /**</span></div>
+<div class="line"><span class="lineno">  152</span><span class="comment">     * @brief Values of K are pseudo-random and used to &quot;salt&quot; each round</span></div>
+<div class="line"><span class="lineno">  153</span><span class="comment">     * The values can be obtained by the following python code</span></div>
+<div class="line"><span class="lineno">  154</span><span class="comment">     * @code{.py}</span></div>
+<div class="line"><span class="lineno">  155</span><span class="comment">     * from math import floor, sin</span></div>
+<div class="line"><span class="lineno">  156</span><span class="comment">     *</span></div>
+<div class="line"><span class="lineno">  157</span><span class="comment">     * for i in range(64):</span></div>
+<div class="line"><span class="lineno">  158</span><span class="comment">     *     print(floor(2**32 * abs(sin(i+1))))</span></div>
+<div class="line"><span class="lineno">  159</span><span class="comment">     * @endcode</span></div>
+<div class="line"><span class="lineno">  160</span><span class="comment">     */</span></div>
+<div class="line"><span class="lineno">  161</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;uint32_t, 64&gt;</a> K = {</div>
+<div class="line"><span class="lineno">  162</span>        3614090360, 3905402710, 606105819,  3250441966, 4118548399, 1200080426,</div>
+<div class="line"><span class="lineno">  163</span>        2821735955, 4249261313, 1770035416, 2336552879, 4294925233, 2304563134,</div>
+<div class="line"><span class="lineno">  164</span>        1804603682, 4254626195, 2792965006, 1236535329, 4129170786, 3225465664,</div>
+<div class="line"><span class="lineno">  165</span>        643717713,  3921069994, 3593408605, 38016083,   3634488961, 3889429448,</div>
+<div class="line"><span class="lineno">  166</span>        568446438,  3275163606, 4107603335, 1163531501, 2850285829, 4243563512,</div>
+<div class="line"><span class="lineno">  167</span>        1735328473, 2368359562, 4294588738, 2272392833, 1839030562, 4259657740,</div>
+<div class="line"><span class="lineno">  168</span>        2763975236, 1272893353, 4139469664, 3200236656, 681279174,  3936430074,</div>
+<div class="line"><span class="lineno">  169</span>        3572445317, 76029189,   3654602809, 3873151461, 530742520,  3299628645,</div>
+<div class="line"><span class="lineno">  170</span>        4096336452, 1126891415, 2878612391, 4237533241, 1700485571, 2399980690,</div>
+<div class="line"><span class="lineno">  171</span>        4293915773, 2240044497, 1873313359, 4264355552, 2734768916, 1309151649,</div>
+<div class="line"><span class="lineno">  172</span>        4149444226, 3174756917, 718787259,  3951481745};</div>
+<div class="line"><span class="lineno">  173</span> </div>
+<div class="line"><span class="lineno">  174</span>    <span class="comment">// The initial 128-bit state</span></div>
+<div class="line"><span class="lineno">  175</span>    uint32_t a0 = 0x67452301, A = 0;</div>
+<div class="line"><span class="lineno">  176</span>    uint32_t b0 = 0xefcdab89, B = 0;</div>
+<div class="line"><span class="lineno">  177</span>    uint32_t c0 = 0x98badcfe, C = 0;</div>
+<div class="line"><span class="lineno">  178</span>    uint32_t d0 = 0x10325476, D = 0;</div>
+<div class="line"><span class="lineno">  179</span> </div>
+<div class="line"><span class="lineno">  180</span>    <span class="comment">// Step 1: Processing the bytestring</span></div>
+<div class="line"><span class="lineno">  181</span> </div>
+<div class="line"><span class="lineno">  182</span>    <span class="comment">// First compute the size the padded message will have</span></div>
+<div class="line"><span class="lineno">  183</span>    <span class="comment">// so it is possible to allocate the right amount of memory</span></div>
+<div class="line"><span class="lineno">  184</span>    uint64_t padded_message_size = 0;</div>
+<div class="line"><span class="lineno">  185</span>    <span class="keywordflow">if</span> (input_size % 64 &lt; 56) {</div>
+<div class="line"><span class="lineno">  186</span>        padded_message_size = input_size + 64 - (input_size % 64);</div>
+<div class="line"><span class="lineno">  187</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  188</span>        padded_message_size = input_size + 128 - (input_size % 64);</div>
+<div class="line"><span class="lineno">  189</span>    }</div>
+<div class="line"><span class="lineno">  190</span> </div>
+<div class="line"><span class="lineno">  191</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint8_t&gt;</a> padded_message(padded_message_size);</div>
+<div class="line"><span class="lineno">  192</span> </div>
+<div class="line"><span class="lineno">  193</span>    <span class="comment">// Beginning of the padded message is the original message</span></div>
+<div class="line"><span class="lineno">  194</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/copy.html">std::copy</a>(input, input + input_size, padded_message.begin());</div>
+<div class="line"><span class="lineno">  195</span> </div>
+<div class="line"><span class="lineno">  196</span>    <span class="comment">// Afterwards comes a single 1 bit and then only zeroes</span></div>
+<div class="line"><span class="lineno">  197</span>    padded_message[input_size] = 1 &lt;&lt; 7;  <span class="comment">// 10000000</span></div>
+<div class="line"><span class="lineno">  198</span>    <span class="keywordflow">for</span> (uint64_t i = input_size; i % 64 != 56; i++) {</div>
+<div class="line"><span class="lineno">  199</span>        <span class="keywordflow">if</span> (i == input_size) {</div>
+<div class="line"><span class="lineno">  200</span>            <span class="keywordflow">continue</span>;  <span class="comment">// pass first iteration</span></div>
+<div class="line"><span class="lineno">  201</span>        }</div>
+<div class="line"><span class="lineno">  202</span>        padded_message[i] = 0;</div>
+<div class="line"><span class="lineno">  203</span>    }</div>
+<div class="line"><span class="lineno">  204</span> </div>
+<div class="line"><span class="lineno">  205</span>    <span class="comment">// We then have to add the 64-bit size of the message at the end</span></div>
+<div class="line"><span class="lineno">  206</span>    <span class="comment">// When there is a conversion from int to bytestring or vice-versa</span></div>
+<div class="line"><span class="lineno">  207</span>    <span class="comment">// We always need to make sure it is little endian</span></div>
+<div class="line"><span class="lineno">  208</span>    uint64_t input_bitsize_le = <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a6be48c1e6e742f9bd329f501d61dcaef">toLittleEndian64</a>(input_size * 8);</div>
+<div class="line"><span class="lineno">  209</span>    <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; 8; i++) {</div>
+<div class="line"><span class="lineno">  210</span>        padded_message[padded_message_size - 8 + i] =</div>
+<div class="line"><span class="lineno">  211</span>            (input_bitsize_le &gt;&gt; (56 - 8 * i)) &amp; 0xFF;</div>
+<div class="line"><span class="lineno">  212</span>    }</div>
+<div class="line"><span class="lineno">  213</span> </div>
+<div class="line"><span class="lineno">  214</span>    <span class="comment">// Already allocate memory for blocks</span></div>
+<div class="line"><span class="lineno">  215</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;uint32_t, 16&gt;</a> blocks{};</div>
+<div class="line"><span class="lineno">  216</span> </div>
+<div class="line"><span class="lineno">  217</span>    <span class="comment">// Rounds</span></div>
+<div class="line"><span class="lineno">  218</span>    <span class="keywordflow">for</span> (uint64_t chunk = 0; chunk * 64 &lt; padded_message_size; chunk++) {</div>
+<div class="line"><span class="lineno">  219</span>        <span class="comment">// First, build the 16 32-bits blocks from the chunk</span></div>
+<div class="line"><span class="lineno">  220</span>        <span class="keywordflow">for</span> (uint8_t bid = 0; bid &lt; 16; bid++) {</div>
+<div class="line"><span class="lineno">  221</span>            blocks[bid] = 0;</div>
+<div class="line"><span class="lineno">  222</span> </div>
+<div class="line"><span class="lineno">  223</span>            <span class="comment">// Having to build a 32-bit word from 4-bit words</span></div>
+<div class="line"><span class="lineno">  224</span>            <span class="comment">// Add each and shift them to the left</span></div>
+<div class="line"><span class="lineno">  225</span>            <span class="keywordflow">for</span> (uint8_t cid = 0; cid &lt; 4; cid++) {</div>
+<div class="line"><span class="lineno">  226</span>                blocks[bid] = (blocks[bid] &lt;&lt; 8) +</div>
+<div class="line"><span class="lineno">  227</span>                              padded_message[chunk * 64 + bid * 4 + cid];</div>
+<div class="line"><span class="lineno">  228</span>            }</div>
+<div class="line"><span class="lineno">  229</span>        }</div>
+<div class="line"><span class="lineno">  230</span> </div>
+<div class="line"><span class="lineno">  231</span>        A = a0;</div>
+<div class="line"><span class="lineno">  232</span>        B = b0;</div>
+<div class="line"><span class="lineno">  233</span>        C = c0;</div>
+<div class="line"><span class="lineno">  234</span>        D = d0;</div>
+<div class="line"><span class="lineno">  235</span> </div>
+<div class="line"><span class="lineno">  236</span>        <span class="comment">// Main &quot;hashing&quot; loop</span></div>
+<div class="line"><span class="lineno">  237</span>        <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; 64; i++) {</div>
+<div class="line"><span class="lineno">  238</span>            uint32_t F = 0, <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = 0;</div>
+<div class="line"><span class="lineno">  239</span>            <span class="keywordflow">if</span> (i &lt; 16) {</div>
+<div class="line"><span class="lineno">  240</span>                F = (B &amp; C) | ((~B) &amp; D);</div>
+<div class="line"><span class="lineno">  241</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = i;</div>
+<div class="line"><span class="lineno">  242</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (i &lt; 32) {</div>
+<div class="line"><span class="lineno">  243</span>                F = (D &amp; B) | ((~D) &amp; C);</div>
+<div class="line"><span class="lineno">  244</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = (5 * i + 1) % 16;</div>
+<div class="line"><span class="lineno">  245</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (i &lt; 48) {</div>
+<div class="line"><span class="lineno">  246</span>                F = B ^ C ^ D;</div>
+<div class="line"><span class="lineno">  247</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = (3 * i + 5) % 16;</div>
+<div class="line"><span class="lineno">  248</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  249</span>                F = C ^ (B | (~D));</div>
+<div class="line"><span class="lineno">  250</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = (7 * i) % 16;</div>
+<div class="line"><span class="lineno">  251</span>            }</div>
+<div class="line"><span class="lineno">  252</span> </div>
+<div class="line"><span class="lineno">  253</span>            <span class="comment">// Update the accumulators</span></div>
+<div class="line"><span class="lineno">  254</span>            F += A + K[i] + <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a694712c9665051ba52b686387b87a689">toLittleEndian32</a>(blocks[g]);</div>
+<div class="line"><span class="lineno">  255</span> </div>
+<div class="line"><span class="lineno">  256</span>            A = D;</div>
+<div class="line"><span class="lineno">  257</span>            D = C;</div>
+<div class="line"><span class="lineno">  258</span>            C = B;</div>
+<div class="line"><span class="lineno">  259</span>            B += <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#add2bf982d5dd64a45d13cba52c2b371d">leftRotate32bits</a>(F, s[i]);</div>
+<div class="line"><span class="lineno">  260</span>        }</div>
+<div class="line"><span class="lineno">  261</span>        <span class="comment">// Update the state with this chunk&#39;s hash</span></div>
+<div class="line"><span class="lineno">  262</span>        a0 += A;</div>
+<div class="line"><span class="lineno">  263</span>        b0 += B;</div>
+<div class="line"><span class="lineno">  264</span>        c0 += C;</div>
+<div class="line"><span class="lineno">  265</span>        d0 += D;</div>
+<div class="line"><span class="lineno">  266</span>    }</div>
+<div class="line"><span class="lineno">  267</span> </div>
+<div class="line"><span class="lineno">  268</span>    <span class="comment">// Build signature from state</span></div>
+<div class="line"><span class="lineno">  269</span>    <span class="comment">// Note, any type could be used for the signature</span></div>
+<div class="line"><span class="lineno">  270</span>    <span class="comment">// uint8_t was used to make the 16 bytes obvious</span></div>
+<div class="line"><span class="lineno">  271</span>    <span class="comment">// The sig needs to be little endian</span></div>
+<div class="line"><span class="lineno">  272</span>    <span class="keyword">auto</span>* sig = <span class="keyword">new</span> uint8_t[16];</div>
+<div class="line"><span class="lineno">  273</span>    <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; 4; i++) {</div>
+<div class="line"><span class="lineno">  274</span>        sig[i] = (a0 &gt;&gt; (8 * i)) &amp; 0xFF;</div>
+<div class="line"><span class="lineno">  275</span>        sig[i + 4] = (b0 &gt;&gt; (8 * i)) &amp; 0xFF;</div>
+<div class="line"><span class="lineno">  276</span>        sig[i + 8] = (c0 &gt;&gt; (8 * i)) &amp; 0xFF;</div>
+<div class="line"><span class="lineno">  277</span>        sig[i + 12] = (d0 &gt;&gt; (8 * i)) &amp; 0xFF;</div>
+<div class="line"><span class="lineno">  278</span>    }</div>
+<div class="line"><span class="lineno">  279</span> </div>
+<div class="line"><span class="lineno">  280</span>    <span class="keywordflow">return</span> sig;</div>
+<div class="line"><span class="lineno">  281</span>}</div>
 <div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a2f67508d5f392b0321772169342c98ad"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">numerical_methods::simpson_method::g</a></div><div class="ttdeci">double g(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:115</div></div>
 <div class="ttc" id="acopy_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/copy.html">std::copy</a></div><div class="ttdeci">T copy(T... args)</div></div>
@@ -433,26 +433,26 @@ Here is the call graph for this function:</div>
 
 <p>Puts user in a loop where inputs can be given and <a class="el" href="../../dd/d43/namespace_m_d5.html" title="Functions for the MD5 algorithm implementation.">MD5</a> hash will be computed and printed. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00351" name="l00351"></a><span class="lineno">  351</span>                          {</div>
-<div class="line"><a id="l00352" name="l00352"></a><span class="lineno">  352</span>    <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
-<div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> input;</div>
-<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter a message to be hashed (Ctrl-C to exit): &quot;</span></div>
-<div class="line"><a id="l00355" name="l00355"></a><span class="lineno">  355</span>                  &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00356" name="l00356"></a><span class="lineno">  356</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/getline.html">std::getline</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>, input);</div>
-<div class="line"><a id="l00357" name="l00357"></a><span class="lineno">  357</span>        <span class="keywordtype">void</span>* sig = <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hashing::md5::hash</a>(input);</div>
-<div class="line"><a id="l00358" name="l00358"></a><span class="lineno">  358</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hash is: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#aaee69c6136a841043f956de32116e348">hashing::md5::sig2hex</a>(sig) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00359" name="l00359"></a><span class="lineno">  359</span> </div>
-<div class="line"><a id="l00360" name="l00360"></a><span class="lineno">  360</span>        <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
-<div class="line"><a id="l00361" name="l00361"></a><span class="lineno">  361</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Want to enter another message? (y/n) &quot;</span>;</div>
-<div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/getline.html">std::getline</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>, input);</div>
-<div class="line"><a id="l00363" name="l00363"></a><span class="lineno">  363</span>            <span class="keywordflow">if</span> (input.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/compare.html">compare</a>(<span class="stringliteral">&quot;y&quot;</span>) == 0) {</div>
-<div class="line"><a id="l00364" name="l00364"></a><span class="lineno">  364</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00365" name="l00365"></a><span class="lineno">  365</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (input.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/compare.html">compare</a>(<span class="stringliteral">&quot;n&quot;</span>) == 0) {</div>
-<div class="line"><a id="l00366" name="l00366"></a><span class="lineno">  366</span>                <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00367" name="l00367"></a><span class="lineno">  367</span>            }</div>
-<div class="line"><a id="l00368" name="l00368"></a><span class="lineno">  368</span>        }</div>
-<div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span>    }</div>
-<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  351</span>                          {</div>
+<div class="line"><span class="lineno">  352</span>    <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
+<div class="line"><span class="lineno">  353</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> input;</div>
+<div class="line"><span class="lineno">  354</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter a message to be hashed (Ctrl-C to exit): &quot;</span></div>
+<div class="line"><span class="lineno">  355</span>                  &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  356</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/getline.html">std::getline</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>, input);</div>
+<div class="line"><span class="lineno">  357</span>        <span class="keywordtype">void</span>* sig = <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hashing::md5::hash</a>(input);</div>
+<div class="line"><span class="lineno">  358</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hash is: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#aaee69c6136a841043f956de32116e348">hashing::md5::sig2hex</a>(sig) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  359</span> </div>
+<div class="line"><span class="lineno">  360</span>        <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
+<div class="line"><span class="lineno">  361</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Want to enter another message? (y/n) &quot;</span>;</div>
+<div class="line"><span class="lineno">  362</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/getline.html">std::getline</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>, input);</div>
+<div class="line"><span class="lineno">  363</span>            <span class="keywordflow">if</span> (input.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/compare.html">compare</a>(<span class="stringliteral">&quot;y&quot;</span>) == 0) {</div>
+<div class="line"><span class="lineno">  364</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  365</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (input.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/compare.html">compare</a>(<span class="stringliteral">&quot;n&quot;</span>) == 0) {</div>
+<div class="line"><span class="lineno">  366</span>                <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  367</span>            }</div>
+<div class="line"><span class="lineno">  368</span>        }</div>
+<div class="line"><span class="lineno">  369</span>    }</div>
+<div class="line"><span class="lineno">  370</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
@@ -490,14 +490,14 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd>true IF integers are detected to work as big-endian </dd>
 <dd>
 false IF integers are detected to work as little-endian </dd></dl>
-<div class="fragment"><div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>                   {</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <span class="keyword">union </span>{</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        uint32_t i;</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;char, 4&gt;</a> c;</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    } bint = {0x01020304};</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span> </div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <span class="keywordflow">return</span> bint.c[0] == 1;</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   76</span>                   {</div>
+<div class="line"><span class="lineno">   77</span>    <span class="keyword">union </span>{</div>
+<div class="line"><span class="lineno">   78</span>        uint32_t i;</div>
+<div class="line"><span class="lineno">   79</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;char, 4&gt;</a> c;</div>
+<div class="line"><span class="lineno">   80</span>    } bint = {0x01020304};</div>
+<div class="line"><span class="lineno">   81</span> </div>
+<div class="line"><span class="lineno">   82</span>    <span class="keywordflow">return</span> bint.c[0] == 1;</div>
+<div class="line"><span class="lineno">   83</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -542,9 +542,9 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>uint32_t The rotated integer </dd></dl>
-<div class="fragment"><div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>                                                        {</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <span class="keywordflow">return</span> (n &lt;&lt; rotate) | (n &gt;&gt; (32 - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/rotate.html">rotate</a>));</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   66</span>                                                        {</div>
+<div class="line"><span class="lineno">   67</span>    <span class="keywordflow">return</span> (n &lt;&lt; rotate) | (n &gt;&gt; (32 - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/rotate.html">rotate</a>));</div>
+<div class="line"><span class="lineno">   68</span>}</div>
 <div class="ttc" id="arotate_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/rotate.html">std::rotate</a></div><div class="ttdeci">T rotate(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -573,14 +573,14 @@ Here is the call graph for this function:</div>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00376" name="l00376"></a><span class="lineno">  376</span>           {</div>
-<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span>    <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
-<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span> </div>
-<div class="line"><a id="l00379" name="l00379"></a><span class="lineno">  379</span>    <span class="comment">// Launch interactive mode where user can input messages and see</span></div>
-<div class="line"><a id="l00380" name="l00380"></a><span class="lineno">  380</span>    <span class="comment">// their hash</span></div>
-<div class="line"><a id="l00381" name="l00381"></a><span class="lineno">  381</span>    <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#ac9e1a11f44135b890dd10a00e73b5661">interactive</a>();</div>
-<div class="line"><a id="l00382" name="l00382"></a><span class="lineno">  382</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00383" name="l00383"></a><span class="lineno">  383</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  376</span>           {</div>
+<div class="line"><span class="lineno">  377</span>    <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
+<div class="line"><span class="lineno">  378</span> </div>
+<div class="line"><span class="lineno">  379</span>    <span class="comment">// Launch interactive mode where user can input messages and see</span></div>
+<div class="line"><span class="lineno">  380</span>    <span class="comment">// their hash</span></div>
+<div class="line"><span class="lineno">  381</span>    <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#ac9e1a11f44135b890dd10a00e73b5661">interactive</a>();</div>
+<div class="line"><span class="lineno">  382</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  383</span>}</div>
 <div class="ttc" id="amd5_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d5/d96/md5_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations of well-known MD5 hashes.</div><div class="ttdef"><b>Definition:</b> md5.cpp:297</div></div>
 <div class="ttc" id="amd5_8cpp_html_ac9e1a11f44135b890dd10a00e73b5661"><div class="ttname"><a href="../../d5/d96/md5_8cpp.html#ac9e1a11f44135b890dd10a00e73b5661">interactive</a></div><div class="ttdeci">static void interactive()</div><div class="ttdoc">Puts user in a loop where inputs can be given and MD5 hash will be computed and printed.</div><div class="ttdef"><b>Definition:</b> md5.cpp:351</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -616,16 +616,16 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> The hex signature </dd></dl>
-<div class="fragment"><div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>                             {</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <span class="keyword">const</span> <span class="keywordtype">char</span>* hexChars = <span class="stringliteral">&quot;0123456789abcdef&quot;</span>;</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    <span class="keyword">auto</span>* intsig = <span class="keyword">static_cast&lt;</span>uint8_t*<span class="keyword">&gt;</span>(sig);</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/hex.html">hex</a> = <span class="stringliteral">&quot;&quot;</span>;</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; 16; i++) {</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/hex.html">hex</a>.push_back(hexChars[(intsig[i] &gt;&gt; 4) &amp; 0xF]);</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/hex.html">hex</a>.push_back(hexChars[(intsig[i]) &amp; 0xF]);</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    }</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/hex.html">hex</a>;</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  122</span>                             {</div>
+<div class="line"><span class="lineno">  123</span>    <span class="keyword">const</span> <span class="keywordtype">char</span>* hexChars = <span class="stringliteral">&quot;0123456789abcdef&quot;</span>;</div>
+<div class="line"><span class="lineno">  124</span>    <span class="keyword">auto</span>* intsig = <span class="keyword">static_cast&lt;</span>uint8_t*<span class="keyword">&gt;</span>(sig);</div>
+<div class="line"><span class="lineno">  125</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/hex.html">hex</a> = <span class="stringliteral">&quot;&quot;</span>;</div>
+<div class="line"><span class="lineno">  126</span>    <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; 16; i++) {</div>
+<div class="line"><span class="lineno">  127</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/hex.html">hex</a>.push_back(hexChars[(intsig[i] &gt;&gt; 4) &amp; 0xF]);</div>
+<div class="line"><span class="lineno">  128</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/hex.html">hex</a>.push_back(hexChars[(intsig[i]) &amp; 0xF]);</div>
+<div class="line"><span class="lineno">  129</span>    }</div>
+<div class="line"><span class="lineno">  130</span>    <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/hex.html">hex</a>;</div>
+<div class="line"><span class="lineno">  131</span>}</div>
 <div class="ttc" id="ahex_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/hex.html">std::hex</a></div><div class="ttdeci">T hex(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -661,54 +661,54 @@ Here is the call graph for this function:</div>
 
 <p>Self-test implementations of well-known <a class="el" href="../../dd/d43/namespace_m_d5.html" title="Functions for the MD5 algorithm implementation.">MD5</a> hashes. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>                   {</div>
-<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>    <span class="comment">// Hashes empty string and stores signature</span></div>
-<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>    <span class="keywordtype">void</span>* sig = <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hashing::md5::hash</a>(<span class="stringliteral">&quot;&quot;</span>);</div>
-<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hashing empty string&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span>    <span class="comment">// Prints signature hex representation</span></div>
-<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#aaee69c6136a841043f956de32116e348">hashing::md5::sig2hex</a>(sig) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span>    <span class="comment">// Test with cassert whether sig is correct from the expected value</span></div>
-<div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span>    assert(hashing::md5::sig2hex(sig).<a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a>(</div>
-<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span>               <span class="stringliteral">&quot;d41d8cd98f00b204e9800998ecf8427e&quot;</span>) == 0);</div>
-<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span> </div>
-<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>    <span class="comment">// Hashes &quot;The quick brown fox jumps over the lazy dog&quot; and stores signature</span></div>
-<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>    <span class="keywordtype">void</span>* sig2 =</div>
-<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span>        <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hashing::md5::hash</a>(<span class="stringliteral">&quot;The quick brown fox jumps over the lazy dog&quot;</span>);</div>
-<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hashing The quick brown fox jumps over the lazy dog&quot;</span></div>
-<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>    <span class="comment">// Prints signature hex representation</span></div>
-<div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#aaee69c6136a841043f956de32116e348">hashing::md5::sig2hex</a>(sig2) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span>    <span class="comment">// Test with cassert whether sig is correct from the expected value</span></div>
-<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span>    assert(hashing::md5::sig2hex(sig2).<a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a>(</div>
-<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>               <span class="stringliteral">&quot;9e107d9d372bb6826bd81d3542a419d6&quot;</span>) == 0);</div>
-<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span> </div>
-<div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span>    <span class="comment">// Hashes &quot;The quick brown fox jumps over the lazy dog.&quot; (notice the</span></div>
-<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>    <span class="comment">// additional period) and stores signature</span></div>
-<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>    <span class="keywordtype">void</span>* sig3 =</div>
-<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>        <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hashing::md5::hash</a>(<span class="stringliteral">&quot;The quick brown fox jumps over the lazy dog.&quot;</span>);</div>
-<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hashing &quot;</span></div>
-<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>                 <span class="stringliteral">&quot;The quick brown fox jumps over the lazy dog.&quot;</span></div>
-<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span>    <span class="comment">// Prints signature hex representation</span></div>
-<div class="line"><a id="l00326" name="l00326"></a><span class="lineno">  326</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#aaee69c6136a841043f956de32116e348">hashing::md5::sig2hex</a>(sig3) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00327" name="l00327"></a><span class="lineno">  327</span>    <span class="comment">// Test with cassert whether sig is correct from the expected value</span></div>
-<div class="line"><a id="l00328" name="l00328"></a><span class="lineno">  328</span>    assert(hashing::md5::sig2hex(sig3).<a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a>(</div>
-<div class="line"><a id="l00329" name="l00329"></a><span class="lineno">  329</span>               <span class="stringliteral">&quot;e4d909c290d0fb1ca068ffaddf22cbd0&quot;</span>) == 0);</div>
-<div class="line"><a id="l00330" name="l00330"></a><span class="lineno">  330</span> </div>
-<div class="line"><a id="l00331" name="l00331"></a><span class="lineno">  331</span>    <span class="comment">// Hashes &quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789&quot;</span></div>
-<div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span>    <span class="comment">// and stores signature</span></div>
-<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>    <span class="keywordtype">void</span>* sig4 = <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hashing::md5::hash</a>(</div>
-<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span>        <span class="stringliteral">&quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789&quot;</span>);</div>
-<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
-<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span>        &lt;&lt; <span class="stringliteral">&quot;Hashing &quot;</span></div>
-<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span>           <span class="stringliteral">&quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789&quot;</span></div>
-<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span>        &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00339" name="l00339"></a><span class="lineno">  339</span>    <span class="comment">// Prints signature hex representation</span></div>
-<div class="line"><a id="l00340" name="l00340"></a><span class="lineno">  340</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#aaee69c6136a841043f956de32116e348">hashing::md5::sig2hex</a>(sig4) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00341" name="l00341"></a><span class="lineno">  341</span>    <span class="comment">// Test with cassert whether sig is correct from the expected value</span></div>
-<div class="line"><a id="l00342" name="l00342"></a><span class="lineno">  342</span>    assert(hashing::md5::sig2hex(sig4).<a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a>(</div>
-<div class="line"><a id="l00343" name="l00343"></a><span class="lineno">  343</span>               <span class="stringliteral">&quot;d174ab98d277d9f5a5611c2c9f419d9f&quot;</span>) == 0);</div>
-<div class="line"><a id="l00344" name="l00344"></a><span class="lineno">  344</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  297</span>                   {</div>
+<div class="line"><span class="lineno">  298</span>    <span class="comment">// Hashes empty string and stores signature</span></div>
+<div class="line"><span class="lineno">  299</span>    <span class="keywordtype">void</span>* sig = <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hashing::md5::hash</a>(<span class="stringliteral">&quot;&quot;</span>);</div>
+<div class="line"><span class="lineno">  300</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hashing empty string&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  301</span>    <span class="comment">// Prints signature hex representation</span></div>
+<div class="line"><span class="lineno">  302</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#aaee69c6136a841043f956de32116e348">hashing::md5::sig2hex</a>(sig) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  303</span>    <span class="comment">// Test with cassert whether sig is correct from the expected value</span></div>
+<div class="line"><span class="lineno">  304</span>    assert(hashing::md5::sig2hex(sig).<a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a>(</div>
+<div class="line"><span class="lineno">  305</span>               <span class="stringliteral">&quot;d41d8cd98f00b204e9800998ecf8427e&quot;</span>) == 0);</div>
+<div class="line"><span class="lineno">  306</span> </div>
+<div class="line"><span class="lineno">  307</span>    <span class="comment">// Hashes &quot;The quick brown fox jumps over the lazy dog&quot; and stores signature</span></div>
+<div class="line"><span class="lineno">  308</span>    <span class="keywordtype">void</span>* sig2 =</div>
+<div class="line"><span class="lineno">  309</span>        <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hashing::md5::hash</a>(<span class="stringliteral">&quot;The quick brown fox jumps over the lazy dog&quot;</span>);</div>
+<div class="line"><span class="lineno">  310</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hashing The quick brown fox jumps over the lazy dog&quot;</span></div>
+<div class="line"><span class="lineno">  311</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  312</span>    <span class="comment">// Prints signature hex representation</span></div>
+<div class="line"><span class="lineno">  313</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#aaee69c6136a841043f956de32116e348">hashing::md5::sig2hex</a>(sig2) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  314</span>    <span class="comment">// Test with cassert whether sig is correct from the expected value</span></div>
+<div class="line"><span class="lineno">  315</span>    assert(hashing::md5::sig2hex(sig2).<a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a>(</div>
+<div class="line"><span class="lineno">  316</span>               <span class="stringliteral">&quot;9e107d9d372bb6826bd81d3542a419d6&quot;</span>) == 0);</div>
+<div class="line"><span class="lineno">  317</span> </div>
+<div class="line"><span class="lineno">  318</span>    <span class="comment">// Hashes &quot;The quick brown fox jumps over the lazy dog.&quot; (notice the</span></div>
+<div class="line"><span class="lineno">  319</span>    <span class="comment">// additional period) and stores signature</span></div>
+<div class="line"><span class="lineno">  320</span>    <span class="keywordtype">void</span>* sig3 =</div>
+<div class="line"><span class="lineno">  321</span>        <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hashing::md5::hash</a>(<span class="stringliteral">&quot;The quick brown fox jumps over the lazy dog.&quot;</span>);</div>
+<div class="line"><span class="lineno">  322</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hashing &quot;</span></div>
+<div class="line"><span class="lineno">  323</span>                 <span class="stringliteral">&quot;The quick brown fox jumps over the lazy dog.&quot;</span></div>
+<div class="line"><span class="lineno">  324</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  325</span>    <span class="comment">// Prints signature hex representation</span></div>
+<div class="line"><span class="lineno">  326</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#aaee69c6136a841043f956de32116e348">hashing::md5::sig2hex</a>(sig3) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  327</span>    <span class="comment">// Test with cassert whether sig is correct from the expected value</span></div>
+<div class="line"><span class="lineno">  328</span>    assert(hashing::md5::sig2hex(sig3).<a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a>(</div>
+<div class="line"><span class="lineno">  329</span>               <span class="stringliteral">&quot;e4d909c290d0fb1ca068ffaddf22cbd0&quot;</span>) == 0);</div>
+<div class="line"><span class="lineno">  330</span> </div>
+<div class="line"><span class="lineno">  331</span>    <span class="comment">// Hashes &quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789&quot;</span></div>
+<div class="line"><span class="lineno">  332</span>    <span class="comment">// and stores signature</span></div>
+<div class="line"><span class="lineno">  333</span>    <span class="keywordtype">void</span>* sig4 = <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hashing::md5::hash</a>(</div>
+<div class="line"><span class="lineno">  334</span>        <span class="stringliteral">&quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789&quot;</span>);</div>
+<div class="line"><span class="lineno">  335</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
+<div class="line"><span class="lineno">  336</span>        &lt;&lt; <span class="stringliteral">&quot;Hashing &quot;</span></div>
+<div class="line"><span class="lineno">  337</span>           <span class="stringliteral">&quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789&quot;</span></div>
+<div class="line"><span class="lineno">  338</span>        &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  339</span>    <span class="comment">// Prints signature hex representation</span></div>
+<div class="line"><span class="lineno">  340</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#aaee69c6136a841043f956de32116e348">hashing::md5::sig2hex</a>(sig4) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  341</span>    <span class="comment">// Test with cassert whether sig is correct from the expected value</span></div>
+<div class="line"><span class="lineno">  342</span>    assert(hashing::md5::sig2hex(sig4).<a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a>(</div>
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@@ -41,7 +41,7 @@ MathJax.Hub.Config({
 </table>
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-<!-- Generated by Doxygen 1.9.2 -->
+<!-- Generated by Doxygen 1.9.3 -->
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@@ -100,6 +100,12 @@ $(document).ready(function(){initNavTree('d5/dab/structdata__structures_1_1list_
 
 <p>Structure of List with supporting methods.  
  <a href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#details">More...</a></p>
+<div class="dynheader">
+Collaboration diagram for data_structures::list_array::list:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dd/d9d/structdata__structures_1_1list__array_1_1list__coll__graph.svg" width="148" height="246"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+<center><span class="legend">[<a target="top" href="../../graph_legend.html">legend</a>]</span></center></div>
 <table class="memberdecls">
 <tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
 Public Member Functions</h2></td></tr>
@@ -196,25 +202,25 @@ bool&#160;</td><td class="memItemRight" valign="bottom"><b>isSorted</b> = false<
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>index of element in the list if present else -1 </dd></dl>
-<div class="fragment"><div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>                                                   {</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>            <span class="comment">// If both pointer cross each other means no element present in the list which is equal to the val</span></div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>            <span class="keywordflow">if</span> (last &lt; first) {</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>                <span class="keywordflow">return</span> -1;</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>            }</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>            uint64_t mid = (first + last) / 2;</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>            <span class="comment">// check whether current mid pointer value is equal to element or not</span></div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>            <span class="keywordflow">if</span> (dataArr[mid] == val)</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>                <span class="keywordflow">return</span> mid;</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>                <span class="comment">// if current mid value is greater than  element we have to search in first half</span></div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (val &lt; dataArr[mid])</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>                <span class="keywordflow">return</span> (<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a3b4abfffc730e07fcbd5844e09add8cd">BinarySearch</a>(dataArr, first, mid - 1, val));</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>                <span class="comment">// if current mid value is greater than  element we have to search in second half</span></div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (val &gt; dataArr[mid])</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>                <span class="keywordflow">return</span> (<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a3b4abfffc730e07fcbd5844e09add8cd">BinarySearch</a>(dataArr, mid + 1, last, val));</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span> </div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;:&quot;</span> &lt;&lt; __LINE__ &lt;&lt; <span class="stringliteral">&quot;: Undefined condition\n&quot;</span>;</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>            <span class="keywordflow">return</span> -1;</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        }</div>
+<div class="fragment"><div class="line"><span class="lineno">   45</span>                                                   {</div>
+<div class="line"><span class="lineno">   46</span>            <span class="comment">// If both pointer cross each other means no element present in the list which is equal to the val</span></div>
+<div class="line"><span class="lineno">   47</span>            <span class="keywordflow">if</span> (last &lt; first) {</div>
+<div class="line"><span class="lineno">   48</span>                <span class="keywordflow">return</span> -1;</div>
+<div class="line"><span class="lineno">   49</span>            }</div>
+<div class="line"><span class="lineno">   50</span>            uint64_t mid = (first + last) / 2;</div>
+<div class="line"><span class="lineno">   51</span>            <span class="comment">// check whether current mid pointer value is equal to element or not</span></div>
+<div class="line"><span class="lineno">   52</span>            <span class="keywordflow">if</span> (dataArr[mid] == val)</div>
+<div class="line"><span class="lineno">   53</span>                <span class="keywordflow">return</span> mid;</div>
+<div class="line"><span class="lineno">   54</span>                <span class="comment">// if current mid value is greater than  element we have to search in first half</span></div>
+<div class="line"><span class="lineno">   55</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (val &lt; dataArr[mid])</div>
+<div class="line"><span class="lineno">   56</span>                <span class="keywordflow">return</span> (<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a3b4abfffc730e07fcbd5844e09add8cd">BinarySearch</a>(dataArr, first, mid - 1, val));</div>
+<div class="line"><span class="lineno">   57</span>                <span class="comment">// if current mid value is greater than  element we have to search in second half</span></div>
+<div class="line"><span class="lineno">   58</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (val &gt; dataArr[mid])</div>
+<div class="line"><span class="lineno">   59</span>                <span class="keywordflow">return</span> (<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a3b4abfffc730e07fcbd5844e09add8cd">BinarySearch</a>(dataArr, mid + 1, last, val));</div>
+<div class="line"><span class="lineno">   60</span> </div>
+<div class="line"><span class="lineno">   61</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;:&quot;</span> &lt;&lt; __LINE__ &lt;&lt; <span class="stringliteral">&quot;: Undefined condition\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   62</span>            <span class="keywordflow">return</span> -1;</div>
+<div class="line"><span class="lineno">   63</span>        }</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div></div>
 <div class="ttc" id="astructdata__structures_1_1list__array_1_1list_html_a3b4abfffc730e07fcbd5844e09add8cd"><div class="ttname"><a href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a3b4abfffc730e07fcbd5844e09add8cd">data_structures::list_array::list::BinarySearch</a></div><div class="ttdeci">uint64_t BinarySearch(const std::array&lt; uint64_t, 50 &gt; &amp;dataArr, const uint64_t &amp;first, const uint64_t &amp;last, const uint64_t &amp;val)</div><div class="ttdoc">Search an element in the list using binarySearch.</div><div class="ttdef"><b>Definition:</b> list_array.cpp:44</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -258,39 +264,39 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>                                         {</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>            <span class="comment">// overflow check</span></div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>            <span class="keywordflow">if</span> (top == 49) {</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nOverflow&quot;</span>;</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>                <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>            }</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>            <span class="comment">// if list is not sorted, insert at the last</span></div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>            <span class="comment">// otherwise place it to correct position</span></div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>            <span class="keywordflow">if</span> (!isSorted) {</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>                data[top] = val;</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>                top++;</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>                uint64_t pos = 0; <span class="comment">// Initialize the index variable</span></div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>                <span class="comment">// Going through each element and find correct position for element</span></div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>                <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; top - 1; i++) {</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>                    <span class="comment">// check for the correct position</span></div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>                    <span class="keywordflow">if</span> (data[i] &lt;= val &amp;&amp; val &lt;= data[i + 1]) {</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>                        pos = i + 1; <span class="comment">// assign correct pos to the index var</span></div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>                        <span class="keywordflow">break</span>; <span class="comment">// to get out from the loop</span></div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>                    }</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>                }</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>                <span class="comment">// if all elements are smaller than the element</span></div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>                <span class="keywordflow">if</span> (pos == 0) {</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>                    pos = top - 1;</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>                }</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>                <span class="comment">// shift all element to make a room for new element</span></div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>                <span class="keywordflow">for</span> (uint64_t i = top; i &gt; pos; i--) {</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>                    data[i] = data[i - 1];</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>                }</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>                top++; <span class="comment">// Increment the value of top.</span></div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>                data[pos] = val; <span class="comment">// Assign the value to the correct index in the array</span></div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>            }</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>        }</div>
+<div class="fragment"><div class="line"><span class="lineno">  132</span>                                         {</div>
+<div class="line"><span class="lineno">  133</span>            <span class="comment">// overflow check</span></div>
+<div class="line"><span class="lineno">  134</span>            <span class="keywordflow">if</span> (top == 49) {</div>
+<div class="line"><span class="lineno">  135</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nOverflow&quot;</span>;</div>
+<div class="line"><span class="lineno">  136</span>                <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  137</span>            }</div>
+<div class="line"><span class="lineno">  138</span>            <span class="comment">// if list is not sorted, insert at the last</span></div>
+<div class="line"><span class="lineno">  139</span>            <span class="comment">// otherwise place it to correct position</span></div>
+<div class="line"><span class="lineno">  140</span>            <span class="keywordflow">if</span> (!isSorted) {</div>
+<div class="line"><span class="lineno">  141</span>                data[top] = val;</div>
+<div class="line"><span class="lineno">  142</span>                top++;</div>
+<div class="line"><span class="lineno">  143</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  144</span>                uint64_t pos = 0; <span class="comment">// Initialize the index variable</span></div>
+<div class="line"><span class="lineno">  145</span>                <span class="comment">// Going through each element and find correct position for element</span></div>
+<div class="line"><span class="lineno">  146</span>                <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; top - 1; i++) {</div>
+<div class="line"><span class="lineno">  147</span>                    <span class="comment">// check for the correct position</span></div>
+<div class="line"><span class="lineno">  148</span>                    <span class="keywordflow">if</span> (data[i] &lt;= val &amp;&amp; val &lt;= data[i + 1]) {</div>
+<div class="line"><span class="lineno">  149</span>                        pos = i + 1; <span class="comment">// assign correct pos to the index var</span></div>
+<div class="line"><span class="lineno">  150</span>                        <span class="keywordflow">break</span>; <span class="comment">// to get out from the loop</span></div>
+<div class="line"><span class="lineno">  151</span>                    }</div>
+<div class="line"><span class="lineno">  152</span>                }</div>
+<div class="line"><span class="lineno">  153</span>                <span class="comment">// if all elements are smaller than the element</span></div>
+<div class="line"><span class="lineno">  154</span>                <span class="keywordflow">if</span> (pos == 0) {</div>
+<div class="line"><span class="lineno">  155</span>                    pos = top - 1;</div>
+<div class="line"><span class="lineno">  156</span>                }</div>
+<div class="line"><span class="lineno">  157</span>                <span class="comment">// shift all element to make a room for new element</span></div>
+<div class="line"><span class="lineno">  158</span>                <span class="keywordflow">for</span> (uint64_t i = top; i &gt; pos; i--) {</div>
+<div class="line"><span class="lineno">  159</span>                    data[i] = data[i - 1];</div>
+<div class="line"><span class="lineno">  160</span>                }</div>
+<div class="line"><span class="lineno">  161</span>                top++; <span class="comment">// Increment the value of top.</span></div>
+<div class="line"><span class="lineno">  162</span>                data[pos] = val; <span class="comment">// Assign the value to the correct index in the array</span></div>
+<div class="line"><span class="lineno">  163</span>            }</div>
+<div class="line"><span class="lineno">  164</span>        }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -337,16 +343,16 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>index of element in the list if present else -1 </dd></dl>
-<div class="fragment"><div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>                                                                                                {</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>            <span class="comment">// Going through each element in the list</span></div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>            <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; top; i++) {</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>                <span class="keywordflow">if</span> (dataArr[i] == val) {</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>                    <span class="keywordflow">return</span> i; <span class="comment">// element found at ith index</span></div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>                }</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>            }</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>            <span class="comment">// element is not present in the list</span></div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>            <span class="keywordflow">return</span> -1;</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>        }</div>
+<div class="fragment"><div class="line"><span class="lineno">   71</span>                                                                                                {</div>
+<div class="line"><span class="lineno">   72</span>            <span class="comment">// Going through each element in the list</span></div>
+<div class="line"><span class="lineno">   73</span>            <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; top; i++) {</div>
+<div class="line"><span class="lineno">   74</span>                <span class="keywordflow">if</span> (dataArr[i] == val) {</div>
+<div class="line"><span class="lineno">   75</span>                    <span class="keywordflow">return</span> i; <span class="comment">// element found at ith index</span></div>
+<div class="line"><span class="lineno">   76</span>                }</div>
+<div class="line"><span class="lineno">   77</span>            }</div>
+<div class="line"><span class="lineno">   78</span>            <span class="comment">// element is not present in the list</span></div>
+<div class="line"><span class="lineno">   79</span>            <span class="keywordflow">return</span> -1;</div>
+<div class="line"><span class="lineno">   80</span>        }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -382,20 +388,20 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>                                         {</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>            uint64_t pos = <a class="code hl_namespace" href="../../d9/dca/namespacesearch.html">search</a>(val); <span class="comment">// search the index of the value</span></div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>            <span class="comment">// if search returns -1, element does not present in the list</span></div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>            <span class="keywordflow">if</span> (pos == -1) {</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n Element does not present in the list &quot;</span>;</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>                <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>            }</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span> &lt;&lt; data[pos] &lt;&lt; <span class="stringliteral">&quot; deleted&quot;</span>; <span class="comment">// print the appropriate message</span></div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>            <span class="comment">// shift all the element 1 left to fill vacant space</span></div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>            <span class="keywordflow">for</span> (uint64_t i = pos; i &lt; top; i++) {</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>                <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i + 1];</div>
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-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>            top--; <span class="comment">// decrement the top variable to maintain last index</span></div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>        }</div>
+<div class="fragment"><div class="line"><span class="lineno">  171</span>                                         {</div>
+<div class="line"><span class="lineno">  172</span>            uint64_t pos = <a class="code hl_namespace" href="../../d9/dca/namespacesearch.html">search</a>(val); <span class="comment">// search the index of the value</span></div>
+<div class="line"><span class="lineno">  173</span>            <span class="comment">// if search returns -1, element does not present in the list</span></div>
+<div class="line"><span class="lineno">  174</span>            <span class="keywordflow">if</span> (pos == -1) {</div>
+<div class="line"><span class="lineno">  175</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n Element does not present in the list &quot;</span>;</div>
+<div class="line"><span class="lineno">  176</span>                <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  177</span>            }</div>
+<div class="line"><span class="lineno">  178</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span> &lt;&lt; data[pos] &lt;&lt; <span class="stringliteral">&quot; deleted&quot;</span>; <span class="comment">// print the appropriate message</span></div>
+<div class="line"><span class="lineno">  179</span>            <span class="comment">// shift all the element 1 left to fill vacant space</span></div>
+<div class="line"><span class="lineno">  180</span>            <span class="keywordflow">for</span> (uint64_t i = pos; i &lt; top; i++) {</div>
+<div class="line"><span class="lineno">  181</span>                <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i + 1];</div>
+<div class="line"><span class="lineno">  182</span>            }</div>
+<div class="line"><span class="lineno">  183</span>            top--; <span class="comment">// decrement the top variable to maintain last index</span></div>
+<div class="line"><span class="lineno">  184</span>        }</div>
 <div class="ttc" id="ahash__search_8cpp_html_a6e1a77282bc65ad359d753d25df23243"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a></div><div class="ttdeci">int data[MAX]</div><div class="ttdoc">test data</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:24</div></div>
 <div class="ttc" id="anamespacesearch_html"><div class="ttname"><a href="../../d9/dca/namespacesearch.html">search</a></div><div class="ttdoc">for std::vector</div><div class="ttdef"><b>Definition:</b> binary_search.cpp:45</div></div>
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-<div class="fragment"><div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>                                             {</div>
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-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>            <span class="comment">// if list is sorted, binary search works efficiently else linear search is the only option</span></div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>            <span class="keywordflow">if</span> (isSorted) {</div>
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-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>            <span class="comment">// if index is equal to -1 means element does not present</span></div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>            <span class="comment">// else print the index of that element</span></div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>            <span class="keywordflow">if</span> (pos != -1) {</div>
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-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>            } <span class="keywordflow">else</span> {</div>
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-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>            }</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>            <span class="comment">// return the index of element or -1.</span></div>
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-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>        }</div>
+<div class="fragment"><div class="line"><span class="lineno">   87</span>                                             {</div>
+<div class="line"><span class="lineno">   88</span>            uint64_t pos; <span class="comment">// pos variable to store index value of element.</span></div>
+<div class="line"><span class="lineno">   89</span>            <span class="comment">// if list is sorted, binary search works efficiently else linear search is the only option</span></div>
+<div class="line"><span class="lineno">   90</span>            <span class="keywordflow">if</span> (isSorted) {</div>
+<div class="line"><span class="lineno">   91</span>                pos = <a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a3b4abfffc730e07fcbd5844e09add8cd">BinarySearch</a>(data, 0, top - 1, val);</div>
+<div class="line"><span class="lineno">   92</span>            } <span class="keywordflow">else</span> {</div>
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+<div class="line"><span class="lineno">   94</span>            }</div>
+<div class="line"><span class="lineno">   95</span>            <span class="comment">// if index is equal to -1 means element does not present</span></div>
+<div class="line"><span class="lineno">   96</span>            <span class="comment">// else print the index of that element</span></div>
+<div class="line"><span class="lineno">   97</span>            <span class="keywordflow">if</span> (pos != -1) {</div>
+<div class="line"><span class="lineno">   98</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nElement found at position : &quot;</span> &lt;&lt; pos;</div>
+<div class="line"><span class="lineno">   99</span>            } <span class="keywordflow">else</span> {</div>
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+<div class="line"><span class="lineno">  102</span>            <span class="comment">// return the index of element or -1.</span></div>
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    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
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    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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@@ -179,28 +179,28 @@ Variables</h2></td></tr>
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 <p >Main function </p>
-<div class="fragment"><div class="line"><a id="l00357" name="l00357"></a><span class="lineno">  357</span>                                {</div>
-<div class="line"><a id="l00358" name="l00358"></a><span class="lineno">  358</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));  <span class="comment">// initialize random number generator</span></div>
-<div class="line"><a id="l00359" name="l00359"></a><span class="lineno">  359</span> </div>
-<div class="line"><a id="l00360" name="l00360"></a><span class="lineno">  360</span>    <span class="keywordtype">double</span> eta = 0.1;  <span class="comment">// default value of eta</span></div>
-<div class="line"><a id="l00361" name="l00361"></a><span class="lineno">  361</span>    <span class="keywordflow">if</span> (argc == 2) {   <span class="comment">// read eta value from commandline argument if present</span></div>
-<div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span>        eta = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/strtof.html">strtof</a>(argv[1], <span class="keyword">nullptr</span>);</div>
-<div class="line"><a id="l00363" name="l00363"></a><span class="lineno">  363</span>    }</div>
-<div class="line"><a id="l00364" name="l00364"></a><span class="lineno">  364</span> </div>
-<div class="line"><a id="l00365" name="l00365"></a><span class="lineno">  365</span>    <a class="code hl_function" href="../../d5/db0/adaline__learning_8cpp.html#a52053d88ea1bcbbed9aca67ab4eeb499">test1</a>(eta);</div>
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-<div class="line"><a id="l00367" name="l00367"></a><span class="lineno">  367</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Press ENTER to continue...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00368" name="l00368"></a><span class="lineno">  368</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>.get();</div>
-<div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span> </div>
-<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span>    <a class="code hl_function" href="../../d5/db0/adaline__learning_8cpp.html#a379f7488a305f2571f2932b319931f82">test2</a>(eta);</div>
-<div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span> </div>
-<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Press ENTER to continue...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>.get();</div>
-<div class="line"><a id="l00374" name="l00374"></a><span class="lineno">  374</span> </div>
-<div class="line"><a id="l00375" name="l00375"></a><span class="lineno">  375</span>    <a class="code hl_function" href="../../d5/db0/adaline__learning_8cpp.html#a992bdf1fdb0b9d414bcf7981d2d87aa9">test3</a>(eta);</div>
-<div class="line"><a id="l00376" name="l00376"></a><span class="lineno">  376</span> </div>
-<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span>    <span class="keywordflow">return</span> 0;</div>
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+<div class="fragment"><div class="line"><span class="lineno">  357</span>                                {</div>
+<div class="line"><span class="lineno">  358</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));  <span class="comment">// initialize random number generator</span></div>
+<div class="line"><span class="lineno">  359</span> </div>
+<div class="line"><span class="lineno">  360</span>    <span class="keywordtype">double</span> eta = 0.1;  <span class="comment">// default value of eta</span></div>
+<div class="line"><span class="lineno">  361</span>    <span class="keywordflow">if</span> (argc == 2) {   <span class="comment">// read eta value from commandline argument if present</span></div>
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+<div class="line"><span class="lineno">  363</span>    }</div>
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+<div class="line"><span class="lineno">  365</span>    <a class="code hl_function" href="../../d5/db0/adaline__learning_8cpp.html#a52053d88ea1bcbbed9aca67ab4eeb499">test1</a>(eta);</div>
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+<div class="line"><span class="lineno">  367</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Press ENTER to continue...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  368</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>.get();</div>
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+<div class="line"><span class="lineno">  370</span>    <a class="code hl_function" href="../../d5/db0/adaline__learning_8cpp.html#a379f7488a305f2571f2932b319931f82">test2</a>(eta);</div>
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+<div class="line"><span class="lineno">  372</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Press ENTER to continue...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  373</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>.get();</div>
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+<div class="line"><span class="lineno">  375</span>    <a class="code hl_function" href="../../d5/db0/adaline__learning_8cpp.html#a992bdf1fdb0b9d414bcf7981d2d87aa9">test3</a>(eta);</div>
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+<div class="line"><span class="lineno">  377</span>    <span class="keywordflow">return</span> 0;</div>
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-<div class="fragment"><div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>                              {</div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>    <a class="code hl_class" href="../../d6/d30/classmachine__learning_1_1adaline.html">adaline</a> ada(2, eta);  <span class="comment">// 2 features</span></div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span> </div>
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-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span> </div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::vector&lt;double&gt;</a>, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>&gt; X = {</div>
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-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a>({2, 3}),   <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a>({3, -1}),</div>
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-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, N&gt;</a> y = {1,  -1, 1, -1, -1,</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>                            -1, 1,  1, 1,  -1};  <span class="comment">// corresponding y-values</span></div>
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+<div class="line"><span class="lineno">  237</span> </div>
+<div class="line"><span class="lineno">  238</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------- Test 1 -------&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  239</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model before fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  240</span> </div>
+<div class="line"><span class="lineno">  241</span>    ada.fit&lt;<a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>&gt;(X, y);</div>
+<div class="line"><span class="lineno">  242</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model after fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  243</span> </div>
+<div class="line"><span class="lineno">  244</span>    <span class="keywordtype">int</span> predict = ada.predict({5, -3});</div>
+<div class="line"><span class="lineno">  245</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Predict for x=(5,-3): &quot;</span> &lt;&lt; predict;</div>
+<div class="line"><span class="lineno">  246</span>    assert(predict == -1);</div>
+<div class="line"><span class="lineno">  247</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; ...passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  248</span> </div>
+<div class="line"><span class="lineno">  249</span>    predict = ada.predict({5, 8});</div>
+<div class="line"><span class="lineno">  250</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Predict for x=(5,8): &quot;</span> &lt;&lt; predict;</div>
+<div class="line"><span class="lineno">  251</span>    assert(predict == 1);</div>
+<div class="line"><span class="lineno">  252</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; ...passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  253</span>}</div>
 <div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
 <div class="ttc" id="aclassmachine__learning_1_1adaline_html"><div class="ttname"><a href="../../d6/d30/classmachine__learning_1_1adaline.html">machine_learning::adaline</a></div><div class="ttdef"><b>Definition:</b> adaline_learning.cpp:46</div></div>
 <div class="ttc" id="adata__structures_2sparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:47</div></div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; double &gt;</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d5/db0/adaline__learning_8cpp_a52053d88ea1bcbbed9aca67ab4eeb499_cgraph.svg" width="100%" height="556"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d5/db0/adaline__learning_8cpp_a52053d88ea1bcbbed9aca67ab4eeb499_cgraph.svg" width="100%" height="594"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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@@ -304,50 +304,50 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>                              {</div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>    <a class="code hl_class" href="../../d6/d30/classmachine__learning_1_1adaline.html">adaline</a> ada(2, eta);  <span class="comment">// 2 features</span></div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span> </div>
-<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 50;  <span class="comment">// number of sample points</span></div>
-<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span> </div>
-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::vector&lt;double&gt;</a>, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>&gt; X;</div>
-<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, N&gt;</a> Y{};  <span class="comment">// corresponding y-values</span></div>
-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span> </div>
-<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>    <span class="comment">// generate sample points in the interval</span></div>
-<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>    <span class="comment">// [-range2/100 , (range2-1)/100]</span></div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>    <span class="keywordtype">int</span> range = 500;          <span class="comment">// sample points full-range</span></div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>    <span class="keywordtype">int</span> range2 = range &gt;&gt; 1;  <span class="comment">// sample points half-range</span></div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>        <span class="keywordtype">double</span> x0 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>        <span class="keywordtype">double</span> x1 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>        X[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a>({x0, x1});</div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>        Y[i] = (x0 + 3. * x1) &gt; -1 ? 1 : -1;</div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>    }</div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span> </div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------- Test 2 -------&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model before fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span> </div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>    ada.fit(X, Y);</div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model after fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span> </div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>    <span class="keywordtype">int</span> N_test_cases = 5;</div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N_test_cases; i++) {</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>        <span class="keywordtype">double</span> x0 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>        <span class="keywordtype">double</span> x1 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span> </div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>        <span class="keywordtype">int</span> predict = ada.predict({x0, x1});</div>
-<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span> </div>
-<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Predict for x=(&quot;</span> &lt;&lt; x0 &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; x1 &lt;&lt; <span class="stringliteral">&quot;): &quot;</span> &lt;&lt; predict;</div>
-<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span> </div>
-<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>        <span class="keywordtype">int</span> expected_val = (x0 + 3. * x1) &gt; -1 ? 1 : -1;</div>
-<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>        assert(predict == expected_val);</div>
-<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; ...passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>    }</div>
-<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  262</span>                              {</div>
+<div class="line"><span class="lineno">  263</span>    <a class="code hl_class" href="../../d6/d30/classmachine__learning_1_1adaline.html">adaline</a> ada(2, eta);  <span class="comment">// 2 features</span></div>
+<div class="line"><span class="lineno">  264</span> </div>
+<div class="line"><span class="lineno">  265</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 50;  <span class="comment">// number of sample points</span></div>
+<div class="line"><span class="lineno">  266</span> </div>
+<div class="line"><span class="lineno">  267</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::vector&lt;double&gt;</a>, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>&gt; X;</div>
+<div class="line"><span class="lineno">  268</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, N&gt;</a> Y{};  <span class="comment">// corresponding y-values</span></div>
+<div class="line"><span class="lineno">  269</span> </div>
+<div class="line"><span class="lineno">  270</span>    <span class="comment">// generate sample points in the interval</span></div>
+<div class="line"><span class="lineno">  271</span>    <span class="comment">// [-range2/100 , (range2-1)/100]</span></div>
+<div class="line"><span class="lineno">  272</span>    <span class="keywordtype">int</span> range = 500;          <span class="comment">// sample points full-range</span></div>
+<div class="line"><span class="lineno">  273</span>    <span class="keywordtype">int</span> range2 = range &gt;&gt; 1;  <span class="comment">// sample points half-range</span></div>
+<div class="line"><span class="lineno">  274</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
+<div class="line"><span class="lineno">  275</span>        <span class="keywordtype">double</span> x0 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><span class="lineno">  276</span>        <span class="keywordtype">double</span> x1 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><span class="lineno">  277</span>        X[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a>({x0, x1});</div>
+<div class="line"><span class="lineno">  278</span>        Y[i] = (x0 + 3. * x1) &gt; -1 ? 1 : -1;</div>
+<div class="line"><span class="lineno">  279</span>    }</div>
+<div class="line"><span class="lineno">  280</span> </div>
+<div class="line"><span class="lineno">  281</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------- Test 2 -------&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  282</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model before fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  283</span> </div>
+<div class="line"><span class="lineno">  284</span>    ada.fit(X, Y);</div>
+<div class="line"><span class="lineno">  285</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model after fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  286</span> </div>
+<div class="line"><span class="lineno">  287</span>    <span class="keywordtype">int</span> N_test_cases = 5;</div>
+<div class="line"><span class="lineno">  288</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N_test_cases; i++) {</div>
+<div class="line"><span class="lineno">  289</span>        <span class="keywordtype">double</span> x0 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><span class="lineno">  290</span>        <span class="keywordtype">double</span> x1 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><span class="lineno">  291</span> </div>
+<div class="line"><span class="lineno">  292</span>        <span class="keywordtype">int</span> predict = ada.predict({x0, x1});</div>
+<div class="line"><span class="lineno">  293</span> </div>
+<div class="line"><span class="lineno">  294</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Predict for x=(&quot;</span> &lt;&lt; x0 &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; x1 &lt;&lt; <span class="stringliteral">&quot;): &quot;</span> &lt;&lt; predict;</div>
+<div class="line"><span class="lineno">  295</span> </div>
+<div class="line"><span class="lineno">  296</span>        <span class="keywordtype">int</span> expected_val = (x0 + 3. * x1) &gt; -1 ? 1 : -1;</div>
+<div class="line"><span class="lineno">  297</span>        assert(predict == expected_val);</div>
+<div class="line"><span class="lineno">  298</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; ...passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  299</span>    }</div>
+<div class="line"><span class="lineno">  300</span>}</div>
 <div class="ttc" id="arand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a></div><div class="ttdeci">T rand(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d5/db0/adaline__learning_8cpp_a379f7488a305f2571f2932b319931f82_cgraph.svg" width="100%" height="556"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d5/db0/adaline__learning_8cpp_a379f7488a305f2571f2932b319931f82_cgraph.svg" width="100%" height="594"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
 </div>
 </div>
 
@@ -375,52 +375,52 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span>                              {</div>
-<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span>    <a class="code hl_class" href="../../d6/d30/classmachine__learning_1_1adaline.html">adaline</a> ada(6, eta);  <span class="comment">// 2 features</span></div>
-<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span> </div>
-<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 100;  <span class="comment">// number of sample points</span></div>
-<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span> </div>
-<div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::vector&lt;double&gt;</a>, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>&gt; X;</div>
-<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, N&gt;</a> Y{};  <span class="comment">// corresponding y-values</span></div>
-<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span> </div>
-<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>    <span class="comment">// generate sample points in the interval</span></div>
-<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>    <span class="comment">// [-range2/100 , (range2-1)/100]</span></div>
-<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>    <span class="keywordtype">int</span> range = 200;          <span class="comment">// sample points full-range</span></div>
-<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>    <span class="keywordtype">int</span> range2 = range &gt;&gt; 1;  <span class="comment">// sample points half-range</span></div>
-<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
-<div class="line"><a id="l00326" name="l00326"></a><span class="lineno">  326</span>        <span class="keywordtype">double</span> x0 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a id="l00327" name="l00327"></a><span class="lineno">  327</span>        <span class="keywordtype">double</span> x1 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a id="l00328" name="l00328"></a><span class="lineno">  328</span>        <span class="keywordtype">double</span> x2 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a id="l00329" name="l00329"></a><span class="lineno">  329</span>        X[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a>({x0, x1, x2, x0 * x0, x1 * x1, x2 * x2});</div>
-<div class="line"><a id="l00330" name="l00330"></a><span class="lineno">  330</span>        Y[i] = ((x0 * x0) + (x1 * x1) + (x2 * x2)) &lt;= 1.f ? 1 : -1;</div>
-<div class="line"><a id="l00331" name="l00331"></a><span class="lineno">  331</span>    }</div>
-<div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span> </div>
-<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------- Test 3 -------&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model before fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span> </div>
-<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span>    ada.fit(X, Y);</div>
-<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model after fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span> </div>
-<div class="line"><a id="l00339" name="l00339"></a><span class="lineno">  339</span>    <span class="keywordtype">int</span> N_test_cases = 5;</div>
-<div class="line"><a id="l00340" name="l00340"></a><span class="lineno">  340</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N_test_cases; i++) {</div>
-<div class="line"><a id="l00341" name="l00341"></a><span class="lineno">  341</span>        <span class="keywordtype">double</span> x0 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a id="l00342" name="l00342"></a><span class="lineno">  342</span>        <span class="keywordtype">double</span> x1 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a id="l00343" name="l00343"></a><span class="lineno">  343</span>        <span class="keywordtype">double</span> x2 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
-<div class="line"><a id="l00344" name="l00344"></a><span class="lineno">  344</span> </div>
-<div class="line"><a id="l00345" name="l00345"></a><span class="lineno">  345</span>        <span class="keywordtype">int</span> predict = ada.predict({x0, x1, x2, x0 * x0, x1 * x1, x2 * x2});</div>
-<div class="line"><a id="l00346" name="l00346"></a><span class="lineno">  346</span> </div>
-<div class="line"><a id="l00347" name="l00347"></a><span class="lineno">  347</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Predict for x=(&quot;</span> &lt;&lt; x0 &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; x1 &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; x2</div>
-<div class="line"><a id="l00348" name="l00348"></a><span class="lineno">  348</span>                  &lt;&lt; <span class="stringliteral">&quot;): &quot;</span> &lt;&lt; predict;</div>
-<div class="line"><a id="l00349" name="l00349"></a><span class="lineno">  349</span> </div>
-<div class="line"><a id="l00350" name="l00350"></a><span class="lineno">  350</span>        <span class="keywordtype">int</span> expected_val = ((x0 * x0) + (x1 * x1) + (x2 * x2)) &lt;= 1.f ? 1 : -1;</div>
-<div class="line"><a id="l00351" name="l00351"></a><span class="lineno">  351</span>        assert(predict == expected_val);</div>
-<div class="line"><a id="l00352" name="l00352"></a><span class="lineno">  352</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; ...passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span>    }</div>
-<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  313</span>                              {</div>
+<div class="line"><span class="lineno">  314</span>    <a class="code hl_class" href="../../d6/d30/classmachine__learning_1_1adaline.html">adaline</a> ada(6, eta);  <span class="comment">// 2 features</span></div>
+<div class="line"><span class="lineno">  315</span> </div>
+<div class="line"><span class="lineno">  316</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 100;  <span class="comment">// number of sample points</span></div>
+<div class="line"><span class="lineno">  317</span> </div>
+<div class="line"><span class="lineno">  318</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::vector&lt;double&gt;</a>, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>&gt; X;</div>
+<div class="line"><span class="lineno">  319</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, N&gt;</a> Y{};  <span class="comment">// corresponding y-values</span></div>
+<div class="line"><span class="lineno">  320</span> </div>
+<div class="line"><span class="lineno">  321</span>    <span class="comment">// generate sample points in the interval</span></div>
+<div class="line"><span class="lineno">  322</span>    <span class="comment">// [-range2/100 , (range2-1)/100]</span></div>
+<div class="line"><span class="lineno">  323</span>    <span class="keywordtype">int</span> range = 200;          <span class="comment">// sample points full-range</span></div>
+<div class="line"><span class="lineno">  324</span>    <span class="keywordtype">int</span> range2 = range &gt;&gt; 1;  <span class="comment">// sample points half-range</span></div>
+<div class="line"><span class="lineno">  325</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
+<div class="line"><span class="lineno">  326</span>        <span class="keywordtype">double</span> x0 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><span class="lineno">  327</span>        <span class="keywordtype">double</span> x1 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><span class="lineno">  328</span>        <span class="keywordtype">double</span> x2 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><span class="lineno">  329</span>        X[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a>({x0, x1, x2, x0 * x0, x1 * x1, x2 * x2});</div>
+<div class="line"><span class="lineno">  330</span>        Y[i] = ((x0 * x0) + (x1 * x1) + (x2 * x2)) &lt;= 1.f ? 1 : -1;</div>
+<div class="line"><span class="lineno">  331</span>    }</div>
+<div class="line"><span class="lineno">  332</span> </div>
+<div class="line"><span class="lineno">  333</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------- Test 3 -------&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  334</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model before fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  335</span> </div>
+<div class="line"><span class="lineno">  336</span>    ada.fit(X, Y);</div>
+<div class="line"><span class="lineno">  337</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model after fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  338</span> </div>
+<div class="line"><span class="lineno">  339</span>    <span class="keywordtype">int</span> N_test_cases = 5;</div>
+<div class="line"><span class="lineno">  340</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N_test_cases; i++) {</div>
+<div class="line"><span class="lineno">  341</span>        <span class="keywordtype">double</span> x0 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><span class="lineno">  342</span>        <span class="keywordtype">double</span> x1 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><span class="lineno">  343</span>        <span class="keywordtype">double</span> x2 = (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><span class="lineno">  344</span> </div>
+<div class="line"><span class="lineno">  345</span>        <span class="keywordtype">int</span> predict = ada.predict({x0, x1, x2, x0 * x0, x1 * x1, x2 * x2});</div>
+<div class="line"><span class="lineno">  346</span> </div>
+<div class="line"><span class="lineno">  347</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Predict for x=(&quot;</span> &lt;&lt; x0 &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; x1 &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; x2</div>
+<div class="line"><span class="lineno">  348</span>                  &lt;&lt; <span class="stringliteral">&quot;): &quot;</span> &lt;&lt; predict;</div>
+<div class="line"><span class="lineno">  349</span> </div>
+<div class="line"><span class="lineno">  350</span>        <span class="keywordtype">int</span> expected_val = ((x0 * x0) + (x1 * x1) + (x2 * x2)) &lt;= 1.f ? 1 : -1;</div>
+<div class="line"><span class="lineno">  351</span>        assert(predict == expected_val);</div>
+<div class="line"><span class="lineno">  352</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; ...passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  353</span>    }</div>
+<div class="line"><span class="lineno">  354</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
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@@ -432,7 +432,7 @@ Here is the call graph for this function:</div>
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+<p>Implementation to [From the right, set the Kth bit in the binary representation of N] (<a href="https://practice.geeksforgeeks.org/problems/set-kth-bit3724/1/">https://practice.geeksforgeeks.org/problems/set-kth-bit3724/1/</a>) in an integer.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for set_kth_bit.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/d43/set__kth__bit_8cpp__incl.svg" width="174" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="namespaces" name="namespaces"></a>
+Namespaces</h2></td></tr>
+<tr class="memitem:d7/d81/namespacebit__manipulation"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d81/namespacebit__manipulation.html">bit_manipulation</a></td></tr>
+<tr class="memdesc:d7/d81/namespacebit__manipulation"><td class="mdescLeft">&#160;</td><td class="mdescRight">for IO operations <br /></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:d8/d88/namespaceset_kth_bit"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d88/namespaceset_kth_bit.html">setKthBit</a></td></tr>
+<tr class="memdesc:d8/d88/namespaceset_kth_bit"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for the [From the right, set the Kth bit in the binary representation of N] (<a href="https://practice.geeksforgeeks.org/problems/set-kth-bit3724/1/">https://practice.geeksforgeeks.org/problems/set-kth-bit3724/1/</a>) implementation. <br /></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:ad4d0ffd9331242c42a28834ee19f5fd9"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint64_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/db5/set__kth__bit_8cpp.html#ad4d0ffd9331242c42a28834ee19f5fd9">bit_manipulation::set_kth_bit::setKthBit</a> (std ::int64_t N, std ::int64_t k)</td></tr>
+<tr class="memdesc:ad4d0ffd9331242c42a28834ee19f5fd9"><td class="mdescLeft">&#160;</td><td class="mdescRight">The main function implements set kth bit.  <a href="../../d5/db5/set__kth__bit_8cpp.html#ad4d0ffd9331242c42a28834ee19f5fd9">More...</a><br /></td></tr>
+<tr class="separator:ad4d0ffd9331242c42a28834ee19f5fd9"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/db5/set__kth__bit_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
+<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations.  <a href="../../d5/db5/set__kth__bit_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
+<tr class="separator:aa8dca7b867074164d5f45b0f3851269d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/db5/set__kth__bit_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function.  <a href="../../d5/db5/set__kth__bit_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p >Implementation to [From the right, set the Kth bit in the binary representation of N] (<a href="https://practice.geeksforgeeks.org/problems/set-kth-bit3724/1/">https://practice.geeksforgeeks.org/problems/set-kth-bit3724/1/</a>) in an integer. </p>
+<p >Given a number N and a value K. From the right, set the Kth bit in the binary representation of N. The position of Least Significant Bit(or last bit) is 0, the second last bit is 1 and so on. in it.</p>
+<p >A binary number consists of two digits. They are 0 &amp; 1. Digit 1 is known as set bit in computer terms. Worst Case Time Complexity: O(1) Space complexity: O(1)</p>
+<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/aman2000raj" target="_blank">Aman Raj</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramtype">void&#160;</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Main function. </p>
+<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
+<div class="fragment"><div class="line"><span class="lineno">   76</span>           {</div>
+<div class="line"><span class="lineno">   77</span>    <a class="code hl_function" href="../../d5/db5/set__kth__bit_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
+<div class="line"><span class="lineno">   78</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">   79</span>}</div>
+<div class="ttc" id="aset__kth__bit_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d5/db5/set__kth__bit_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition:</b> set_kth_bit.cpp:60</div></div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
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+</div>
+</div>
+
+</div>
+</div>
+<a id="ad4d0ffd9331242c42a28834ee19f5fd9" name="ad4d0ffd9331242c42a28834ee19f5fd9"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ad4d0ffd9331242c42a28834ee19f5fd9">&#9670;&nbsp;</a></span>setKthBit()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint64_t</a> bit_manipulation::set_kth_bit::setKthBit </td>
+          <td>(</td>
+          <td class="paramtype">std ::int64_t&#160;</td>
+          <td class="paramname"><em>N</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">std ::int64_t&#160;</td>
+          <td class="paramname"><em>k</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>The main function implements set kth bit. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">N</td><td>is the number whose kth bit will be set </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>returns an integer after setting the K'th bit in N </dd></dl>
+<div class="fragment"><div class="line"><span class="lineno">   43</span>                                       {  <span class="comment">// int64_t is preferred over int so</span></div>
+<div class="line"><span class="lineno">   44</span>                                            <span class="comment">// that no Overflow can be there.</span></div>
+<div class="line"><span class="lineno">   45</span> </div>
+<div class="line"><span class="lineno">   46</span>    <span class="keywordtype">int</span> pos =</div>
+<div class="line"><span class="lineno">   47</span>        1 &lt;&lt; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>;  <span class="comment">// &quot;pos&quot; variable is used to store 1 at kth postion and</span></div>
+<div class="line"><span class="lineno">   48</span>                 <span class="comment">// rest bits are 0. in binary representation of number &#39;n&#39;</span></div>
+<div class="line"><span class="lineno">   49</span> </div>
+<div class="line"><span class="lineno">   50</span>    <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> | pos;  <span class="comment">// by taking or with the pos and the N we set the bit of N</span></div>
+<div class="line"><span class="lineno">   51</span>                     <span class="comment">// at kth position.</span></div>
+<div class="line"><span class="lineno">   52</span>}</div>
+<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
+<div class="ttc" id="adata__structures_2sparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:47</div></div>
+</div><!-- fragment -->
+</div>
+</div>
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+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
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+      </table>
+  </td>
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+<p>Self-test implementations. </p>
+<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
+<div class="fragment"><div class="line"><span class="lineno">   60</span>                   {</div>
+<div class="line"><span class="lineno">   61</span>    <span class="comment">// n = 10,2 return 14</span></div>
+<div class="line"><span class="lineno">   62</span>    assert(bit_manipulation::set_kth_bit::setKthBit(10, 2) == 14);</div>
+<div class="line"><span class="lineno">   63</span>    <span class="comment">// n = 25,1 return 27</span></div>
+<div class="line"><span class="lineno">   64</span>    assert(bit_manipulation::set_kth_bit::setKthBit(25, 1) == 27);</div>
+<div class="line"><span class="lineno">   65</span>    <span class="comment">// n = 400001,5 return 400033</span></div>
+<div class="line"><span class="lineno">   66</span>    assert(bit_manipulation::set_kth_bit::setKthBit(400001, 5) == 400033);</div>
+<div class="line"><span class="lineno">   67</span>    <span class="comment">// n = 123 return 123</span></div>
+<div class="line"><span class="lineno">   68</span>    assert(bit_manipulation::set_kth_bit::setKthBit(123, 3) == 123);</div>
+<div class="line"><span class="lineno">   69</span> </div>
+<div class="line"><span class="lineno">   70</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All test cases successfully passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="fragment"><div class="line"><span class="lineno">   56</span>            {</div>
+<div class="line"><span class="lineno">   57</span>    <span class="comment">// are_amicable(220, 284) returns true.</span></div>
+<div class="line"><span class="lineno">   58</span>    assert(<a class="code hl_function" href="../../d5/df6/check__amicable__pair_8cpp.html#afeb67e204ec7de02ad152c11df4d1e01">are_amicable</a>(220, 284) == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">   59</span>    <span class="comment">// are_amicable(6232, 6368) returns true.</span></div>
+<div class="line"><span class="lineno">   60</span>    assert(<a class="code hl_function" href="../../d5/df6/check__amicable__pair_8cpp.html#afeb67e204ec7de02ad152c11df4d1e01">are_amicable</a>(6368, 6232) == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">   61</span>    <span class="comment">// are_amicable(458, 232) returns false.</span></div>
+<div class="line"><span class="lineno">   62</span>    assert(<a class="code hl_function" href="../../d5/df6/check__amicable__pair_8cpp.html#afeb67e204ec7de02ad152c11df4d1e01">are_amicable</a>(458, 232) == <span class="keyword">false</span>);</div>
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 <p>Delete element from back of the queue. </p>
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-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   75</span>                         {</div>
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+<div class="line"><span class="lineno">   78</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nstack is empty &quot;</span>;</div>
+<div class="line"><span class="lineno">   79</span>        <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">   80</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d6/d04/classdata__structures_1_1queue__using__array_1_1_queue___array.html#a2f676f2f249eb36dfd49711a03e9e67e">front</a> == <a class="code hl_variable" href="../../d6/d04/classdata__structures_1_1queue__using__array_1_1_queue___array.html#a9883dfcceede9a42227d2d313ae86f85">rear</a>) {</div>
+<div class="line"><span class="lineno">   81</span>        d = <a class="code hl_variable" href="../../d6/d04/classdata__structures_1_1queue__using__array_1_1_queue___array.html#ae69a0bf6c9921b37c516c8a4d2fb904d">arr</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/at.html">at</a>(<a class="code hl_variable" href="../../d6/d04/classdata__structures_1_1queue__using__array_1_1_queue___array.html#a2f676f2f249eb36dfd49711a03e9e67e">front</a>);</div>
+<div class="line"><span class="lineno">   82</span>        <a class="code hl_variable" href="../../d6/d04/classdata__structures_1_1queue__using__array_1_1_queue___array.html#a2f676f2f249eb36dfd49711a03e9e67e">front</a> = <a class="code hl_variable" href="../../d6/d04/classdata__structures_1_1queue__using__array_1_1_queue___array.html#a9883dfcceede9a42227d2d313ae86f85">rear</a> = -1;</div>
+<div class="line"><span class="lineno">   83</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   84</span>        d = <a class="code hl_variable" href="../../d6/d04/classdata__structures_1_1queue__using__array_1_1_queue___array.html#ae69a0bf6c9921b37c516c8a4d2fb904d">arr</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/at.html">at</a>(<a class="code hl_variable" href="../../d6/d04/classdata__structures_1_1queue__using__array_1_1_queue___array.html#a2f676f2f249eb36dfd49711a03e9e67e">front</a>++);</div>
+<div class="line"><span class="lineno">   85</span>    }</div>
+<div class="line"><span class="lineno">   86</span> </div>
+<div class="line"><span class="lineno">   87</span>    <span class="keywordflow">return</span> d;</div>
+<div class="line"><span class="lineno">   88</span>}</div>
+<div class="ttc" id="aat_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array/at.html">std::array::at</a></div><div class="ttdeci">T at(T... args)</div></div>
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@@ -163,10 +163,10 @@ Algorithm</h3>
 
 <p>Main function. </p>
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@@ -202,29 +202,29 @@ Here is the call graph for this function:</div>
 
 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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+<div class="line"><span class="lineno">  175</span>    <span class="comment">// 1st test</span></div>
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+<div class="line"><span class="lineno">   56</span>            q = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(q, price[j - 1] + profit[i - j]);</div>
+<div class="line"><span class="lineno">   57</span>        }</div>
+<div class="line"><span class="lineno">   58</span>        profit[i] = q;</div>
+<div class="line"><span class="lineno">   59</span>    }</div>
+<div class="line"><span class="lineno">   60</span>    <span class="keyword">const</span> int16_t <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = profit[n];</div>
+<div class="line"><span class="lineno">   61</span>    <span class="keyword">delete</span>[] profit;</div>
+<div class="line"><span class="lineno">   62</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;  <span class="comment">// returning maximum profit</span></div>
+<div class="line"><span class="lineno">   63</span>}</div>
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 <div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
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@@ -280,40 +280,40 @@ Here is the call graph for this function:</div>
 
 <p>Function to test above algorithm. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>                   {</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    <span class="comment">// Test 1</span></div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <span class="keyword">const</span> int16_t n1 = 8;                                        <span class="comment">// size of rod</span></div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int32_t, n1&gt;</a> price1 = {1,2,4,6,8,45,21,9};  <span class="comment">// price array</span></div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    <span class="keyword">const</span> int64_t max_profit1 =</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        <a class="code hl_function" href="../../d6/d10/cut__rod_8cpp.html#a1cc523a30c18c63eac58220c3c494cfa">dynamic_programming::cut_rod::maxProfitByCuttingRod</a>(price1, n1);</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <span class="keyword">const</span> int64_t expected_max_profit1 = 47;</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    assert(max_profit1 == expected_max_profit1);</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Maximum profit with &quot;</span> &lt;&lt; n1 &lt;&lt; <span class="stringliteral">&quot; inch road is &quot;</span> &lt;&lt; max_profit1</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span> </div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <span class="comment">// Test 2</span></div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    <span class="keyword">const</span> int16_t n2 = 30;  <span class="comment">// size of rod</span></div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int32_t, n2&gt;</a> price2 = {</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>        1,  5,  8,  9,  10, 17, 17, 20, 24, 30,  <span class="comment">// price array</span></div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>        31, 32, 33, 34, 35, 36, 37, 38, 39, 40,</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>        41, 42, 43, 44, 45, 46, 47, 48, 49, 50};</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span> </div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    <span class="keyword">const</span> int64_t max_profit2=</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>        <a class="code hl_function" href="../../d6/d10/cut__rod_8cpp.html#a1cc523a30c18c63eac58220c3c494cfa">dynamic_programming::cut_rod::maxProfitByCuttingRod</a>(price2, n2);</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    <span class="keyword">const</span> int32_t expected_max_profit2 = 90;</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    assert(max_profit2 == expected_max_profit2);</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Maximum profit with &quot;</span> &lt;&lt; n2 &lt;&lt; <span class="stringliteral">&quot; inch road is &quot;</span> &lt;&lt; max_profit2</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>     <span class="comment">// Test 3</span></div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    <span class="keyword">const</span> int16_t n3 = 5;                                        <span class="comment">// size of rod</span></div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int32_t, n3&gt;</a> price3 = {2,9,17,23,45};  <span class="comment">// price array</span></div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    <span class="keyword">const</span> int64_t max_profit3 =</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>        <a class="code hl_function" href="../../d6/d10/cut__rod_8cpp.html#a1cc523a30c18c63eac58220c3c494cfa">dynamic_programming::cut_rod::maxProfitByCuttingRod</a>(price3, n3);</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    <span class="keyword">const</span> int64_t expected_max_profit3 = 45;</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    assert(max_profit3 == expected_max_profit3);</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Maximum profit with &quot;</span> &lt;&lt; n3 &lt;&lt; <span class="stringliteral">&quot; inch road is &quot;</span> &lt;&lt; max_profit3</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   71</span>                   {</div>
+<div class="line"><span class="lineno">   72</span>    <span class="comment">// Test 1</span></div>
+<div class="line"><span class="lineno">   73</span>    <span class="keyword">const</span> int16_t n1 = 8;                                        <span class="comment">// size of rod</span></div>
+<div class="line"><span class="lineno">   74</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int32_t, n1&gt;</a> price1 = {1,2,4,6,8,45,21,9};  <span class="comment">// price array</span></div>
+<div class="line"><span class="lineno">   75</span>    <span class="keyword">const</span> int64_t max_profit1 =</div>
+<div class="line"><span class="lineno">   76</span>        <a class="code hl_function" href="../../d6/d10/cut__rod_8cpp.html#a1cc523a30c18c63eac58220c3c494cfa">dynamic_programming::cut_rod::maxProfitByCuttingRod</a>(price1, n1);</div>
+<div class="line"><span class="lineno">   77</span>    <span class="keyword">const</span> int64_t expected_max_profit1 = 47;</div>
+<div class="line"><span class="lineno">   78</span>    assert(max_profit1 == expected_max_profit1);</div>
+<div class="line"><span class="lineno">   79</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Maximum profit with &quot;</span> &lt;&lt; n1 &lt;&lt; <span class="stringliteral">&quot; inch road is &quot;</span> &lt;&lt; max_profit1</div>
+<div class="line"><span class="lineno">   80</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   81</span> </div>
+<div class="line"><span class="lineno">   82</span>    <span class="comment">// Test 2</span></div>
+<div class="line"><span class="lineno">   83</span>    <span class="keyword">const</span> int16_t n2 = 30;  <span class="comment">// size of rod</span></div>
+<div class="line"><span class="lineno">   84</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int32_t, n2&gt;</a> price2 = {</div>
+<div class="line"><span class="lineno">   85</span>        1,  5,  8,  9,  10, 17, 17, 20, 24, 30,  <span class="comment">// price array</span></div>
+<div class="line"><span class="lineno">   86</span>        31, 32, 33, 34, 35, 36, 37, 38, 39, 40,</div>
+<div class="line"><span class="lineno">   87</span>        41, 42, 43, 44, 45, 46, 47, 48, 49, 50};</div>
+<div class="line"><span class="lineno">   88</span> </div>
+<div class="line"><span class="lineno">   89</span>    <span class="keyword">const</span> int64_t max_profit2=</div>
+<div class="line"><span class="lineno">   90</span>        <a class="code hl_function" href="../../d6/d10/cut__rod_8cpp.html#a1cc523a30c18c63eac58220c3c494cfa">dynamic_programming::cut_rod::maxProfitByCuttingRod</a>(price2, n2);</div>
+<div class="line"><span class="lineno">   91</span>    <span class="keyword">const</span> int32_t expected_max_profit2 = 90;</div>
+<div class="line"><span class="lineno">   92</span>    assert(max_profit2 == expected_max_profit2);</div>
+<div class="line"><span class="lineno">   93</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Maximum profit with &quot;</span> &lt;&lt; n2 &lt;&lt; <span class="stringliteral">&quot; inch road is &quot;</span> &lt;&lt; max_profit2</div>
+<div class="line"><span class="lineno">   94</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   95</span>     <span class="comment">// Test 3</span></div>
+<div class="line"><span class="lineno">   96</span>    <span class="keyword">const</span> int16_t n3 = 5;                                        <span class="comment">// size of rod</span></div>
+<div class="line"><span class="lineno">   97</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int32_t, n3&gt;</a> price3 = {2,9,17,23,45};  <span class="comment">// price array</span></div>
+<div class="line"><span class="lineno">   98</span>    <span class="keyword">const</span> int64_t max_profit3 =</div>
+<div class="line"><span class="lineno">   99</span>        <a class="code hl_function" href="../../d6/d10/cut__rod_8cpp.html#a1cc523a30c18c63eac58220c3c494cfa">dynamic_programming::cut_rod::maxProfitByCuttingRod</a>(price3, n3);</div>
+<div class="line"><span class="lineno">  100</span>    <span class="keyword">const</span> int64_t expected_max_profit3 = 45;</div>
+<div class="line"><span class="lineno">  101</span>    assert(max_profit3 == expected_max_profit3);</div>
+<div class="line"><span class="lineno">  102</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Maximum profit with &quot;</span> &lt;&lt; n3 &lt;&lt; <span class="stringliteral">&quot; inch road is &quot;</span> &lt;&lt; max_profit3</div>
+<div class="line"><span class="lineno">  103</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   73</span>                   {</div>
+<div class="line"><span class="lineno">   74</span>    <span class="comment">// 1st test</span></div>
+<div class="line"><span class="lineno">   75</span>    <span class="comment">// [1, 0, 2, 1] return [0, 1, 1, 2]</span></div>
+<div class="line"><span class="lineno">   76</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> array1 = {0, 1, 1, 2};</div>
+<div class="line"><span class="lineno">   77</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1... &quot;</span>;</div>
+<div class="line"><span class="lineno">   78</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> arr1 = <a class="code hl_function" href="../../d6/d1a/dnf__sort_8cpp.html#a621767fe711db64fe57a2ac4987b11f0">sorting::dnf_sort::dnfSort</a>(array1);</div>
+<div class="line"><span class="lineno">   79</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr1), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr1)));</div>
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+<div class="line"><span class="lineno">   81</span>    <span class="comment">// 2nd test</span></div>
+<div class="line"><span class="lineno">   82</span>    <span class="comment">// [1, 0, 0, 1, 1, 0, 2, 1] return [0, 0, 0, 1, 1, 1, 1, 2]</span></div>
+<div class="line"><span class="lineno">   83</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> array2 = {1, 0, 0, 1, 1, 0, 2, 1};</div>
+<div class="line"><span class="lineno">   84</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2... &quot;</span>;</div>
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+<div class="line"><span class="lineno">   86</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr2), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr2)));</div>
+<div class="line"><span class="lineno">   87</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   88</span>    <span class="comment">// 3rd test</span></div>
+<div class="line"><span class="lineno">   89</span>    <span class="comment">// [1, 1, 0, 0, 1, 2, 2, 0, 2, 1] return [0, 0, 0, 1, 1, 1, 1, 2, 2, 2]</span></div>
+<div class="line"><span class="lineno">   90</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> array3 = {1, 1, 0, 0, 1, 2, 2, 0, 2, 1};</div>
+<div class="line"><span class="lineno">   91</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3... &quot;</span>;</div>
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+<div class="line"><span class="lineno">   93</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr3), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr3)));</div>
+<div class="line"><span class="lineno">   94</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   95</span>    <span class="comment">// 4th test</span></div>
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+<div class="line"><span class="lineno">  101</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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-<div class="line"><a id="l00460" name="l00460"></a><span class="lineno">  460</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  458</span>                                                                          {</div>
+<div class="line"><span class="lineno">  459</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#ad667fa0860977f6d6d443fa1dbcd80aa">codec</a>(text, decrypt_key);</div>
+<div class="line"><span class="lineno">  460</span>    }</div>
 <div class="ttc" id="aclassciphers_1_1_hill_cipher_html_ad667fa0860977f6d6d443fa1dbcd80aa"><div class="ttname"><a href="../../d6/d26/classciphers_1_1_hill_cipher.html#ad667fa0860977f6d6d443fa1dbcd80aa">ciphers::HillCipher::codec</a></div><div class="ttdeci">static const std::string codec(const std::string &amp;text, const matrix&lt; int &gt; &amp;key)</div><div class="ttdoc">Convenience function to perform block cipher operations. The operations are identical for both encryp...</div><div class="ttdef"><b>Definition:</b> hill_cipher.cpp:210</div></div>
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@@ -343,9 +343,9 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>encrypted text </dd></dl>
-<div class="fragment"><div class="line"><a id="l00446" name="l00446"></a><span class="lineno">  446</span>                                                                          {</div>
-<div class="line"><a id="l00447" name="l00447"></a><span class="lineno">  447</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#ad667fa0860977f6d6d443fa1dbcd80aa">codec</a>(text, encrypt_key);</div>
-<div class="line"><a id="l00448" name="l00448"></a><span class="lineno">  448</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  446</span>                                                                          {</div>
+<div class="line"><span class="lineno">  447</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#ad667fa0860977f6d6d443fa1dbcd80aa">codec</a>(text, encrypt_key);</div>
+<div class="line"><span class="lineno">  448</span>    }</div>
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@@ -400,18 +400,18 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>GCD of \(a\) and \(b\) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>                                 {</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        <span class="keywordflow">if</span> (b &gt; a)  <span class="comment">// ensure always a &lt; b</span></div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(a, b);</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span> </div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>        <span class="keywordflow">while</span> (b != 0) {</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>            T tmp = b;</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>            b = a % b;</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>            a = tmp;</div>
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-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>        <span class="keywordflow">return</span> a;</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  138</span>                                 {</div>
+<div class="line"><span class="lineno">  139</span>        <span class="keywordflow">if</span> (b &gt; a)  <span class="comment">// ensure always a &lt; b</span></div>
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+<div class="line"><span class="lineno">  141</span> </div>
+<div class="line"><span class="lineno">  142</span>        <span class="keywordflow">while</span> (b != 0) {</div>
+<div class="line"><span class="lineno">  143</span>            T tmp = b;</div>
+<div class="line"><span class="lineno">  144</span>            b = a % b;</div>
+<div class="line"><span class="lineno">  145</span>            a = tmp;</div>
+<div class="line"><span class="lineno">  146</span>        }</div>
+<div class="line"><span class="lineno">  147</span> </div>
+<div class="line"><span class="lineno">  148</span>        <span class="keywordflow">return</span> a;</div>
+<div class="line"><span class="lineno">  149</span>    }</div>
 <div class="ttc" id="aswap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a></div><div class="ttdeci">T swap(T... args)</div></div>
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@@ -454,47 +454,47 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>Decryption martix </dd></dl>
-<div class="fragment"><div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span>                                                                               {</div>
-<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span>        <span class="keywordtype">size_t</span> size = encrypt_key.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
-<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>        <span class="keywordtype">int</span> L = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/strlen.html">std::strlen</a>(<a class="code hl_variable" href="../../d6/d4e/namespaceciphers.html#ab9aec0ccf4b6809f652bb540be87c216">STRKEY</a>);</div>
-<div class="line"><a id="l00374" name="l00374"></a><span class="lineno">  374</span> </div>
-<div class="line"><a id="l00375" name="l00375"></a><span class="lineno">  375</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> decrypt_key(size, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;int&gt;</a>(size));</div>
-<div class="line"><a id="l00376" name="l00376"></a><span class="lineno">  376</span>        <span class="keywordtype">int</span> det_encrypt = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(<a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(encrypt_key));</div>
-<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span> </div>
-<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span>        <span class="keywordtype">int</span> mat_determinant = det_encrypt &lt; 0 ? det_encrypt % L : det_encrypt;</div>
-<div class="line"><a id="l00379" name="l00379"></a><span class="lineno">  379</span> </div>
-<div class="line"><a id="l00380" name="l00380"></a><span class="lineno">  380</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> tmp_inverse = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#a2eb58750b978a93ac5e6eb29e3e570b7">get_inverse</a>(encrypt_key);</div>
-<div class="line"><a id="l00381" name="l00381"></a><span class="lineno">  381</span>        <span class="keywordtype">double</span> d2 = <a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(decrypt_key);</div>
-<div class="line"><a id="l00382" name="l00382"></a><span class="lineno">  382</span> </div>
-<div class="line"><a id="l00383" name="l00383"></a><span class="lineno">  383</span>        <span class="comment">// find co-prime factor for inversion</span></div>
-<div class="line"><a id="l00384" name="l00384"></a><span class="lineno">  384</span>        <span class="keywordtype">int</span> det_inv = -1;</div>
-<div class="line"><a id="l00385" name="l00385"></a><span class="lineno">  385</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; L; i++) {</div>
-<div class="line"><a id="l00386" name="l00386"></a><span class="lineno">  386</span>            <span class="keywordflow">if</span> (modulo(mat_determinant * i, L) == 1) {</div>
-<div class="line"><a id="l00387" name="l00387"></a><span class="lineno">  387</span>                det_inv = i;</div>
-<div class="line"><a id="l00388" name="l00388"></a><span class="lineno">  388</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00389" name="l00389"></a><span class="lineno">  389</span>            }</div>
-<div class="line"><a id="l00390" name="l00390"></a><span class="lineno">  390</span>        }</div>
-<div class="line"><a id="l00391" name="l00391"></a><span class="lineno">  391</span> </div>
-<div class="line"><a id="l00392" name="l00392"></a><span class="lineno">  392</span>        <span class="keywordflow">if</span> (det_inv == -1) {</div>
-<div class="line"><a id="l00393" name="l00393"></a><span class="lineno">  393</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Could not find a co-prime for inversion\n&quot;</span>;</div>
-<div class="line"><a id="l00394" name="l00394"></a><span class="lineno">  394</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
-<div class="line"><a id="l00395" name="l00395"></a><span class="lineno">  395</span>        }</div>
-<div class="line"><a id="l00396" name="l00396"></a><span class="lineno">  396</span> </div>
-<div class="line"><a id="l00397" name="l00397"></a><span class="lineno">  397</span>        mat_determinant = det_inv * det_encrypt;</div>
-<div class="line"><a id="l00398" name="l00398"></a><span class="lineno">  398</span> </div>
-<div class="line"><a id="l00399" name="l00399"></a><span class="lineno">  399</span>        <span class="comment">// perform modular inverse of encryption matrix</span></div>
-<div class="line"><a id="l00400" name="l00400"></a><span class="lineno">  400</span>        <span class="keywordtype">int</span> i;</div>
-<div class="line"><a id="l00401" name="l00401"></a><span class="lineno">  401</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00402" name="l00402"></a><span class="lineno">  402</span><span class="preprocessor">#pragma parallel omp for private(i)</span></div>
-<div class="line"><a id="l00403" name="l00403"></a><span class="lineno">  403</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00404" name="l00404"></a><span class="lineno">  404</span>        <span class="keywordflow">for</span> (i = 0; i &lt; size; i++) {</div>
-<div class="line"><a id="l00405" name="l00405"></a><span class="lineno">  405</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; size; j++) {</div>
-<div class="line"><a id="l00406" name="l00406"></a><span class="lineno">  406</span>                <span class="keywordtype">int</span> temp = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(tmp_inverse[i][j] * mat_determinant);</div>
-<div class="line"><a id="l00407" name="l00407"></a><span class="lineno">  407</span>                decrypt_key[i][j] = modulo(temp, L);</div>
-<div class="line"><a id="l00408" name="l00408"></a><span class="lineno">  408</span>            }</div>
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-<div class="line"><a id="l00410" name="l00410"></a><span class="lineno">  410</span>        <span class="keywordflow">return</span> decrypt_key;</div>
-<div class="line"><a id="l00411" name="l00411"></a><span class="lineno">  411</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  371</span>                                                                               {</div>
+<div class="line"><span class="lineno">  372</span>        <span class="keywordtype">size_t</span> size = encrypt_key.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">  373</span>        <span class="keywordtype">int</span> L = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/strlen.html">std::strlen</a>(<a class="code hl_variable" href="../../d6/d4e/namespaceciphers.html#ab9aec0ccf4b6809f652bb540be87c216">STRKEY</a>);</div>
+<div class="line"><span class="lineno">  374</span> </div>
+<div class="line"><span class="lineno">  375</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> decrypt_key(size, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;int&gt;</a>(size));</div>
+<div class="line"><span class="lineno">  376</span>        <span class="keywordtype">int</span> det_encrypt = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(<a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(encrypt_key));</div>
+<div class="line"><span class="lineno">  377</span> </div>
+<div class="line"><span class="lineno">  378</span>        <span class="keywordtype">int</span> mat_determinant = det_encrypt &lt; 0 ? det_encrypt % L : det_encrypt;</div>
+<div class="line"><span class="lineno">  379</span> </div>
+<div class="line"><span class="lineno">  380</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> tmp_inverse = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#a2eb58750b978a93ac5e6eb29e3e570b7">get_inverse</a>(encrypt_key);</div>
+<div class="line"><span class="lineno">  381</span>        <span class="keywordtype">double</span> d2 = <a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(decrypt_key);</div>
+<div class="line"><span class="lineno">  382</span> </div>
+<div class="line"><span class="lineno">  383</span>        <span class="comment">// find co-prime factor for inversion</span></div>
+<div class="line"><span class="lineno">  384</span>        <span class="keywordtype">int</span> det_inv = -1;</div>
+<div class="line"><span class="lineno">  385</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; L; i++) {</div>
+<div class="line"><span class="lineno">  386</span>            <span class="keywordflow">if</span> (modulo(mat_determinant * i, L) == 1) {</div>
+<div class="line"><span class="lineno">  387</span>                det_inv = i;</div>
+<div class="line"><span class="lineno">  388</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  389</span>            }</div>
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+<div class="line"><span class="lineno">  392</span>        <span class="keywordflow">if</span> (det_inv == -1) {</div>
+<div class="line"><span class="lineno">  393</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Could not find a co-prime for inversion\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  394</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><span class="lineno">  395</span>        }</div>
+<div class="line"><span class="lineno">  396</span> </div>
+<div class="line"><span class="lineno">  397</span>        mat_determinant = det_inv * det_encrypt;</div>
+<div class="line"><span class="lineno">  398</span> </div>
+<div class="line"><span class="lineno">  399</span>        <span class="comment">// perform modular inverse of encryption matrix</span></div>
+<div class="line"><span class="lineno">  400</span>        <span class="keywordtype">int</span> i;</div>
+<div class="line"><span class="lineno">  401</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  402</span><span class="preprocessor">#pragma parallel omp for private(i)</span></div>
+<div class="line"><span class="lineno">  403</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  404</span>        <span class="keywordflow">for</span> (i = 0; i &lt; size; i++) {</div>
+<div class="line"><span class="lineno">  405</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; size; j++) {</div>
+<div class="line"><span class="lineno">  406</span>                <span class="keywordtype">int</span> temp = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(tmp_inverse[i][j] * mat_determinant);</div>
+<div class="line"><span class="lineno">  407</span>                decrypt_key[i][j] = modulo(temp, L);</div>
+<div class="line"><span class="lineno">  408</span>            }</div>
+<div class="line"><span class="lineno">  409</span>        }</div>
+<div class="line"><span class="lineno">  410</span>        <span class="keywordflow">return</span> decrypt_key;</div>
+<div class="line"><span class="lineno">  411</span>    }</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div></div>
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 <div class="ttc" id="aexit_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a></div><div class="ttdeci">T exit(T... args)</div></div>
@@ -559,30 +559,30 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>Encryption martix </dd></dl>
-<div class="fragment"><div class="line"><a id="l00340" name="l00340"></a><span class="lineno">  340</span>                                                                {</div>
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-<div class="line"><a id="l00342" name="l00342"></a><span class="lineno">  342</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> min_mat = encrypt_key;</div>
-<div class="line"><a id="l00343" name="l00343"></a><span class="lineno">  343</span>        <span class="keywordtype">int</span> mat_determinant = -1;  <span class="comment">// because matrix has only ints, the</span></div>
-<div class="line"><a id="l00344" name="l00344"></a><span class="lineno">  344</span>                                   <span class="comment">// determinant will also be an int</span></div>
-<div class="line"><a id="l00345" name="l00345"></a><span class="lineno">  345</span>        <span class="keywordtype">int</span> L = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/strlen.html">std::strlen</a>(<a class="code hl_variable" href="../../d6/d4e/namespaceciphers.html#ab9aec0ccf4b6809f652bb540be87c216">STRKEY</a>);</div>
-<div class="line"><a id="l00346" name="l00346"></a><span class="lineno">  346</span> </div>
-<div class="line"><a id="l00347" name="l00347"></a><span class="lineno">  347</span>        <span class="keywordtype">double</span> dd;</div>
-<div class="line"><a id="l00348" name="l00348"></a><span class="lineno">  348</span>        <span class="keywordflow">do</span> {</div>
-<div class="line"><a id="l00349" name="l00349"></a><span class="lineno">  349</span>            <span class="comment">// keeping the random number range smaller generates better</span></div>
-<div class="line"><a id="l00350" name="l00350"></a><span class="lineno">  350</span>            <span class="comment">// defined matrices with more ease of cracking</span></div>
-<div class="line"><a id="l00351" name="l00351"></a><span class="lineno">  351</span>            dd = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#a629be41c1ab78850963e4ce14e1d11d9">rand_range</a>(&amp;encrypt_key, limit1, limit2);</div>
-<div class="line"><a id="l00352" name="l00352"></a><span class="lineno">  352</span>            mat_determinant = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(dd);</div>
-<div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span> </div>
-<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span>            <span class="keywordflow">if</span> (mat_determinant &lt; 0)</div>
-<div class="line"><a id="l00355" name="l00355"></a><span class="lineno">  355</span>                mat_determinant = (mat_determinant % L);</div>
-<div class="line"><a id="l00356" name="l00356"></a><span class="lineno">  356</span>        } <span class="keywordflow">while</span> (std::abs(dd) &gt; 1e3 ||  <span class="comment">// while ill-defined</span></div>
-<div class="line"><a id="l00357" name="l00357"></a><span class="lineno">  357</span>                 dd &lt; 0.1 ||  <span class="comment">// while singular or negative determinant</span></div>
-<div class="line"><a id="l00358" name="l00358"></a><span class="lineno">  358</span>                 !<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/isfinite.html">std::isfinite</a>(dd) ||  <span class="comment">// while determinant is not finite</span></div>
-<div class="line"><a id="l00359" name="l00359"></a><span class="lineno">  359</span>                 <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#a7760f3665651a0a37937c79c62f219c0">gcd</a>(mat_determinant, L) != 1);  <span class="comment">// while no common factors</span></div>
-<div class="line"><a id="l00360" name="l00360"></a><span class="lineno">  360</span>        <span class="comment">// std::cout &lt;&lt;</span></div>
-<div class="line"><a id="l00361" name="l00361"></a><span class="lineno">  361</span> </div>
-<div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span>        <span class="keywordflow">return</span> encrypt_key;</div>
-<div class="line"><a id="l00363" name="l00363"></a><span class="lineno">  363</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  340</span>                                                                {</div>
+<div class="line"><span class="lineno">  341</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> encrypt_key(size, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;int&gt;</a>(size));</div>
+<div class="line"><span class="lineno">  342</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> min_mat = encrypt_key;</div>
+<div class="line"><span class="lineno">  343</span>        <span class="keywordtype">int</span> mat_determinant = -1;  <span class="comment">// because matrix has only ints, the</span></div>
+<div class="line"><span class="lineno">  344</span>                                   <span class="comment">// determinant will also be an int</span></div>
+<div class="line"><span class="lineno">  345</span>        <span class="keywordtype">int</span> L = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/strlen.html">std::strlen</a>(<a class="code hl_variable" href="../../d6/d4e/namespaceciphers.html#ab9aec0ccf4b6809f652bb540be87c216">STRKEY</a>);</div>
+<div class="line"><span class="lineno">  346</span> </div>
+<div class="line"><span class="lineno">  347</span>        <span class="keywordtype">double</span> dd;</div>
+<div class="line"><span class="lineno">  348</span>        <span class="keywordflow">do</span> {</div>
+<div class="line"><span class="lineno">  349</span>            <span class="comment">// keeping the random number range smaller generates better</span></div>
+<div class="line"><span class="lineno">  350</span>            <span class="comment">// defined matrices with more ease of cracking</span></div>
+<div class="line"><span class="lineno">  351</span>            dd = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#a629be41c1ab78850963e4ce14e1d11d9">rand_range</a>(&amp;encrypt_key, limit1, limit2);</div>
+<div class="line"><span class="lineno">  352</span>            mat_determinant = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(dd);</div>
+<div class="line"><span class="lineno">  353</span> </div>
+<div class="line"><span class="lineno">  354</span>            <span class="keywordflow">if</span> (mat_determinant &lt; 0)</div>
+<div class="line"><span class="lineno">  355</span>                mat_determinant = (mat_determinant % L);</div>
+<div class="line"><span class="lineno">  356</span>        } <span class="keywordflow">while</span> (std::abs(dd) &gt; 1e3 ||  <span class="comment">// while ill-defined</span></div>
+<div class="line"><span class="lineno">  357</span>                 dd &lt; 0.1 ||  <span class="comment">// while singular or negative determinant</span></div>
+<div class="line"><span class="lineno">  358</span>                 !<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/isfinite.html">std::isfinite</a>(dd) ||  <span class="comment">// while determinant is not finite</span></div>
+<div class="line"><span class="lineno">  359</span>                 <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#a7760f3665651a0a37937c79c62f219c0">gcd</a>(mat_determinant, L) != 1);  <span class="comment">// while no common factors</span></div>
+<div class="line"><span class="lineno">  360</span>        <span class="comment">// std::cout &lt;&lt;</span></div>
+<div class="line"><span class="lineno">  361</span> </div>
+<div class="line"><span class="lineno">  362</span>        <span class="keywordflow">return</span> encrypt_key;</div>
+<div class="line"><span class="lineno">  363</span>    }</div>
 <div class="ttc" id="aclassciphers_1_1_hill_cipher_html_a629be41c1ab78850963e4ce14e1d11d9"><div class="ttname"><a href="../../d6/d26/classciphers_1_1_hill_cipher.html#a629be41c1ab78850963e4ce14e1d11d9">ciphers::HillCipher::rand_range</a></div><div class="ttdeci">static const T2 rand_range(T1 a, T1 b)</div><div class="ttdoc">Function to generate a random integer in a given interval.</div><div class="ttdef"><b>Definition:</b> hill_cipher.cpp:92</div></div>
 <div class="ttc" id="aclassciphers_1_1_hill_cipher_html_a7760f3665651a0a37937c79c62f219c0"><div class="ttname"><a href="../../d6/d26/classciphers_1_1_hill_cipher.html#a7760f3665651a0a37937c79c62f219c0">ciphers::HillCipher::gcd</a></div><div class="ttdeci">static const T gcd(T a, T b)</div><div class="ttdoc">Compute GCD of two integers using Euler's algorithm.</div><div class="ttdef"><b>Definition:</b> hill_cipher.cpp:138</div></div>
 <div class="ttc" id="aisfinite_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/isfinite.html">std::isfinite</a></div><div class="ttdeci">T isfinite(T... args)</div></div>
@@ -640,17 +640,17 @@ Here is the call graph for this function:</div>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt;matrix&lt;int&gt;, matrix&lt;int&gt;&gt; encryption and decryption keys as a pair</dd></dl>
 <dl class="section see"><dt>See also</dt><dd>::generate_encryption_key </dd></dl>
-<div class="fragment"><div class="line"><a id="l00426" name="l00426"></a><span class="lineno">  426</span>                                                                              {</div>
-<div class="line"><a id="l00427" name="l00427"></a><span class="lineno">  427</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> encrypt_key = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#a642f70fb54cb50b00fb6df7c3f2b120e">generate_encryption_key</a>(size);</div>
-<div class="line"><a id="l00428" name="l00428"></a><span class="lineno">  428</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> decrypt_key = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#ab02c7563889bf1e363deb8e21967b706">generate_decryption_key</a>(encrypt_key);</div>
-<div class="line"><a id="l00429" name="l00429"></a><span class="lineno">  429</span>        <span class="keywordtype">double</span> det2 = <a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(decrypt_key);</div>
-<div class="line"><a id="l00430" name="l00430"></a><span class="lineno">  430</span>        <span class="keywordflow">while</span> (std::abs(det2) &lt; 0.1 || std::abs(det2) &gt; 1e3) {</div>
-<div class="line"><a id="l00431" name="l00431"></a><span class="lineno">  431</span>            encrypt_key = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#a642f70fb54cb50b00fb6df7c3f2b120e">generate_encryption_key</a>(size, limit1, limit2);</div>
-<div class="line"><a id="l00432" name="l00432"></a><span class="lineno">  432</span>            decrypt_key = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#ab02c7563889bf1e363deb8e21967b706">generate_decryption_key</a>(encrypt_key);</div>
-<div class="line"><a id="l00433" name="l00433"></a><span class="lineno">  433</span>            det2 = <a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(decrypt_key);</div>
-<div class="line"><a id="l00434" name="l00434"></a><span class="lineno">  434</span>        }</div>
-<div class="line"><a id="l00435" name="l00435"></a><span class="lineno">  435</span>        <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(encrypt_key, decrypt_key);</div>
-<div class="line"><a id="l00436" name="l00436"></a><span class="lineno">  436</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  426</span>                                                                              {</div>
+<div class="line"><span class="lineno">  427</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> encrypt_key = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#a642f70fb54cb50b00fb6df7c3f2b120e">generate_encryption_key</a>(size);</div>
+<div class="line"><span class="lineno">  428</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> decrypt_key = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#ab02c7563889bf1e363deb8e21967b706">generate_decryption_key</a>(encrypt_key);</div>
+<div class="line"><span class="lineno">  429</span>        <span class="keywordtype">double</span> det2 = <a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(decrypt_key);</div>
+<div class="line"><span class="lineno">  430</span>        <span class="keywordflow">while</span> (std::abs(det2) &lt; 0.1 || std::abs(det2) &gt; 1e3) {</div>
+<div class="line"><span class="lineno">  431</span>            encrypt_key = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#a642f70fb54cb50b00fb6df7c3f2b120e">generate_encryption_key</a>(size, limit1, limit2);</div>
+<div class="line"><span class="lineno">  432</span>            decrypt_key = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#ab02c7563889bf1e363deb8e21967b706">generate_decryption_key</a>(encrypt_key);</div>
+<div class="line"><span class="lineno">  433</span>            det2 = <a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(decrypt_key);</div>
+<div class="line"><span class="lineno">  434</span>        }</div>
+<div class="line"><span class="lineno">  435</span>        <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(encrypt_key, decrypt_key);</div>
+<div class="line"><span class="lineno">  436</span>    }</div>
 <div class="ttc" id="aclassciphers_1_1_hill_cipher_html_a642f70fb54cb50b00fb6df7c3f2b120e"><div class="ttname"><a href="../../d6/d26/classciphers_1_1_hill_cipher.html#a642f70fb54cb50b00fb6df7c3f2b120e">ciphers::HillCipher::generate_encryption_key</a></div><div class="ttdeci">static matrix&lt; int &gt; generate_encryption_key(size_t size, int limit1=0, int limit2=10)</div><div class="ttdoc">Generate encryption matrix of a given size. Larger size matrices are difficult to generate but provid...</div><div class="ttdef"><b>Definition:</b> hill_cipher.cpp:339</div></div>
 <div class="ttc" id="aclassciphers_1_1_hill_cipher_html_ab02c7563889bf1e363deb8e21967b706"><div class="ttname"><a href="../../d6/d26/classciphers_1_1_hill_cipher.html#ab02c7563889bf1e363deb8e21967b706">ciphers::HillCipher::generate_decryption_key</a></div><div class="ttdeci">static matrix&lt; int &gt; generate_decryption_key(matrix&lt; int &gt; const &amp;encrypt_key)</div><div class="ttdoc">Generate decryption matrix from an encryption matrix key.</div><div class="ttdef"><b>Definition:</b> hill_cipher.cpp:371</div></div>
 <div class="ttc" id="amake_pair_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a></div><div class="ttdeci">T make_pair(T... args)</div></div>
@@ -689,17 +689,17 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>index of character </dd></dl>
-<div class="fragment"><div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>                                                      {</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>        <span class="keywordtype">size_t</span> L = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/strlen.html">std::strlen</a>(<a class="code hl_variable" href="../../d6/d4e/namespaceciphers.html#ab9aec0ccf4b6809f652bb540be87c216">STRKEY</a>);</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span> </div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> idx = 0; idx &lt;= L; idx++)</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d6/d4e/namespaceciphers.html#ab9aec0ccf4b6809f652bb540be87c216">STRKEY</a>[idx] == ch)</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>                <span class="keywordflow">return</span> idx;</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span> </div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;:&quot;</span> &lt;&lt; __LINE__ &lt;&lt; <span class="stringliteral">&quot;: (&quot;</span> &lt;&lt; ch</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>                  &lt;&lt; <span class="stringliteral">&quot;) Should not reach here!\n&quot;</span>;</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>        <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  190</span>                                                      {</div>
+<div class="line"><span class="lineno">  191</span>        <span class="keywordtype">size_t</span> L = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/strlen.html">std::strlen</a>(<a class="code hl_variable" href="../../d6/d4e/namespaceciphers.html#ab9aec0ccf4b6809f652bb540be87c216">STRKEY</a>);</div>
+<div class="line"><span class="lineno">  192</span> </div>
+<div class="line"><span class="lineno">  193</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> idx = 0; idx &lt;= L; idx++)</div>
+<div class="line"><span class="lineno">  194</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d6/d4e/namespaceciphers.html#ab9aec0ccf4b6809f652bb540be87c216">STRKEY</a>[idx] == ch)</div>
+<div class="line"><span class="lineno">  195</span>                <span class="keywordflow">return</span> idx;</div>
+<div class="line"><span class="lineno">  196</span> </div>
+<div class="line"><span class="lineno">  197</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;:&quot;</span> &lt;&lt; __LINE__ &lt;&lt; <span class="stringliteral">&quot;: (&quot;</span> &lt;&lt; ch</div>
+<div class="line"><span class="lineno">  198</span>                  &lt;&lt; <span class="stringliteral">&quot;) Should not reach here!\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  199</span>        <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  200</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -741,7 +741,7 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>character at the index </dd></dl>
-<div class="fragment"><div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d6/d4e/namespaceciphers.html#ab9aec0ccf4b6809f652bb540be87c216">STRKEY</a>[idx]; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  182</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d6/d4e/namespaceciphers.html#ab9aec0ccf4b6809f652bb540be87c216">STRKEY</a>[idx]; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -771,69 +771,69 @@ template&lt;typename T &gt; </div>
 </table>
 </div><div class="memdoc">
 <p >Get matrix inverse using Row-transformations. Given matrix must be a square and non-singular. </p><dl class="section return"><dt>Returns</dt><dd>inverse matrix </dd></dl>
-<div class="fragment"><div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>                                                          {</div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>        <span class="comment">// Assuming A is square matrix</span></div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>        <span class="keywordtype">size_t</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span> </div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> inverse(N, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(N));</div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row++) {</div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; col++) {</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>                <span class="comment">// create identity matrix</span></div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>                inverse[row][col] = (row == col) ? 1.f : 0.f;</div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>            }</div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>        }</div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span> </div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>        <span class="keywordflow">if</span> (A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() != A[0].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) {</div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;A must be a square matrix!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>            <span class="keywordflow">return</span> inverse;</div>
-<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>        }</div>
-<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span> </div>
-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>        <span class="comment">// preallocate a temporary matrix identical to A</span></div>
-<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> temp(N, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(N));</div>
-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row++) {</div>
-<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; col++)</div>
-<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>                temp[row][col] = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(A[row][col]);</div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>        }</div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span> </div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>        <span class="comment">// start transformations</span></div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row++) {</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = row; row2 &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> &amp;&amp; temp[row][row] == 0; row2++) {</div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>                <span class="comment">// this to ensure diagonal elements are not 0</span></div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>                temp[row] = temp[row] + temp[row2];</div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>                inverse[row] = inverse[row] + inverse[row2];</div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>            }</div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span> </div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col2 = row; col2 &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> &amp;&amp; temp[row][row] == 0; col2++) {</div>
-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>                <span class="comment">// this to further ensure diagonal elements are not 0</span></div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>                <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = 0; row2 &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row2++) {</div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>                    temp[row2][row] = temp[row2][row] + temp[row2][col2];</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>                    inverse[row2][row] =</div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>                        inverse[row2][row] + inverse[row2][col2];</div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>                }</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>            }</div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span> </div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>            <span class="keywordflow">if</span> (temp[row][row] == 0) {</div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>                <span class="comment">// Probably a low-rank matrix and hence singular</span></div>
-<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Low-rank matrix, no inverse!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>                <span class="keywordflow">return</span> inverse;</div>
-<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span>            }</div>
-<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span> </div>
-<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>            <span class="comment">// set diagonal to 1</span></div>
-<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>            <span class="keywordtype">double</span> divisor = temp[row][row];</div>
-<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>            temp[row] = temp[row] / divisor;</div>
-<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span>            inverse[row] = inverse[row] / divisor;</div>
-<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span>            <span class="comment">// Row transformations</span></div>
-<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = 0; row2 &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row2++) {</div>
-<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span>                <span class="keywordflow">if</span> (row2 == row)</div>
-<div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span>                    <span class="keywordflow">continue</span>;</div>
-<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span>                <span class="keywordtype">double</span> factor = temp[row2][row];</div>
-<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>                temp[row2] = temp[row2] - factor * temp[row];</div>
-<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>                inverse[row2] = inverse[row2] - factor * inverse[row];</div>
-<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>            }</div>
-<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span>        }</div>
-<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span> </div>
-<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>        <span class="keywordflow">return</span> inverse;</div>
-<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  250</span>                                                          {</div>
+<div class="line"><span class="lineno">  251</span>        <span class="comment">// Assuming A is square matrix</span></div>
+<div class="line"><span class="lineno">  252</span>        <span class="keywordtype">size_t</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">  253</span> </div>
+<div class="line"><span class="lineno">  254</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> inverse(N, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(N));</div>
+<div class="line"><span class="lineno">  255</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row++) {</div>
+<div class="line"><span class="lineno">  256</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; col++) {</div>
+<div class="line"><span class="lineno">  257</span>                <span class="comment">// create identity matrix</span></div>
+<div class="line"><span class="lineno">  258</span>                inverse[row][col] = (row == col) ? 1.f : 0.f;</div>
+<div class="line"><span class="lineno">  259</span>            }</div>
+<div class="line"><span class="lineno">  260</span>        }</div>
+<div class="line"><span class="lineno">  261</span> </div>
+<div class="line"><span class="lineno">  262</span>        <span class="keywordflow">if</span> (A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() != A[0].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) {</div>
+<div class="line"><span class="lineno">  263</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;A must be a square matrix!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  264</span>            <span class="keywordflow">return</span> inverse;</div>
+<div class="line"><span class="lineno">  265</span>        }</div>
+<div class="line"><span class="lineno">  266</span> </div>
+<div class="line"><span class="lineno">  267</span>        <span class="comment">// preallocate a temporary matrix identical to A</span></div>
+<div class="line"><span class="lineno">  268</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> temp(N, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(N));</div>
+<div class="line"><span class="lineno">  269</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row++) {</div>
+<div class="line"><span class="lineno">  270</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; col++)</div>
+<div class="line"><span class="lineno">  271</span>                temp[row][col] = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(A[row][col]);</div>
+<div class="line"><span class="lineno">  272</span>        }</div>
+<div class="line"><span class="lineno">  273</span> </div>
+<div class="line"><span class="lineno">  274</span>        <span class="comment">// start transformations</span></div>
+<div class="line"><span class="lineno">  275</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row++) {</div>
+<div class="line"><span class="lineno">  276</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = row; row2 &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> &amp;&amp; temp[row][row] == 0; row2++) {</div>
+<div class="line"><span class="lineno">  277</span>                <span class="comment">// this to ensure diagonal elements are not 0</span></div>
+<div class="line"><span class="lineno">  278</span>                temp[row] = temp[row] + temp[row2];</div>
+<div class="line"><span class="lineno">  279</span>                inverse[row] = inverse[row] + inverse[row2];</div>
+<div class="line"><span class="lineno">  280</span>            }</div>
+<div class="line"><span class="lineno">  281</span> </div>
+<div class="line"><span class="lineno">  282</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col2 = row; col2 &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> &amp;&amp; temp[row][row] == 0; col2++) {</div>
+<div class="line"><span class="lineno">  283</span>                <span class="comment">// this to further ensure diagonal elements are not 0</span></div>
+<div class="line"><span class="lineno">  284</span>                <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = 0; row2 &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row2++) {</div>
+<div class="line"><span class="lineno">  285</span>                    temp[row2][row] = temp[row2][row] + temp[row2][col2];</div>
+<div class="line"><span class="lineno">  286</span>                    inverse[row2][row] =</div>
+<div class="line"><span class="lineno">  287</span>                        inverse[row2][row] + inverse[row2][col2];</div>
+<div class="line"><span class="lineno">  288</span>                }</div>
+<div class="line"><span class="lineno">  289</span>            }</div>
+<div class="line"><span class="lineno">  290</span> </div>
+<div class="line"><span class="lineno">  291</span>            <span class="keywordflow">if</span> (temp[row][row] == 0) {</div>
+<div class="line"><span class="lineno">  292</span>                <span class="comment">// Probably a low-rank matrix and hence singular</span></div>
+<div class="line"><span class="lineno">  293</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Low-rank matrix, no inverse!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  294</span>                <span class="keywordflow">return</span> inverse;</div>
+<div class="line"><span class="lineno">  295</span>            }</div>
+<div class="line"><span class="lineno">  296</span> </div>
+<div class="line"><span class="lineno">  297</span>            <span class="comment">// set diagonal to 1</span></div>
+<div class="line"><span class="lineno">  298</span>            <span class="keywordtype">double</span> divisor = temp[row][row];</div>
+<div class="line"><span class="lineno">  299</span>            temp[row] = temp[row] / divisor;</div>
+<div class="line"><span class="lineno">  300</span>            inverse[row] = inverse[row] / divisor;</div>
+<div class="line"><span class="lineno">  301</span>            <span class="comment">// Row transformations</span></div>
+<div class="line"><span class="lineno">  302</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = 0; row2 &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row2++) {</div>
+<div class="line"><span class="lineno">  303</span>                <span class="keywordflow">if</span> (row2 == row)</div>
+<div class="line"><span class="lineno">  304</span>                    <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno">  305</span>                <span class="keywordtype">double</span> factor = temp[row2][row];</div>
+<div class="line"><span class="lineno">  306</span>                temp[row2] = temp[row2] - factor * temp[row];</div>
+<div class="line"><span class="lineno">  307</span>                inverse[row2] = inverse[row2] - factor * inverse[row];</div>
+<div class="line"><span class="lineno">  308</span>            }</div>
+<div class="line"><span class="lineno">  309</span>        }</div>
+<div class="line"><span class="lineno">  310</span> </div>
+<div class="line"><span class="lineno">  311</span>        <span class="keywordflow">return</span> inverse;</div>
+<div class="line"><span class="lineno">  312</span>    }</div>
 <div class="ttc" id="adata__structures_2sparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:47</div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -888,21 +888,21 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>corresponding encrypted or decrypted text </dd></dl>
-<div class="fragment"><div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>                                                                    {</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;uint8_t&gt;</a> out(vector);  <span class="comment">// make a copy</span></div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span> </div>
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 <dl class="section warning"><dt>Warning</dt><dd>There will need to be a balance between the matrix size and the range of random numbers. If the matrix is large, the range of random numbers must be small to have a well defined keys. Or if the matrix is smaller, the random numbers range can be larger. For an 8x8 matrix, range should be no more than \([0,10]\) </dd></dl>
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 Here is the call graph for this function:</div>
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+<div class="fragment"><div class="line"><span class="lineno">   66</span>                   {</div>
+<div class="line"><span class="lineno">   67</span>    <span class="comment">// Test 1</span></div>
+<div class="line"><span class="lineno">   68</span>    <span class="comment">// [1, 2, 3, 1] return 4</span></div>
+<div class="line"><span class="lineno">   69</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> array1 = {1, 2, 3, 1};</div>
+<div class="line"><span class="lineno">   70</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1... &quot;</span>;</div>
+<div class="line"><span class="lineno">   71</span>    assert(</div>
+<div class="line"><span class="lineno">   72</span>        dynamic_programming::house_robber::houseRobber(array1, array1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) ==</div>
+<div class="line"><span class="lineno">   73</span>        4);  <span class="comment">// here the two non-adjacent houses that are robbed are first and</span></div>
+<div class="line"><span class="lineno">   74</span>             <span class="comment">// third with total sum money as 4</span></div>
+<div class="line"><span class="lineno">   75</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   76</span> </div>
+<div class="line"><span class="lineno">   77</span>    <span class="comment">// Test 2</span></div>
+<div class="line"><span class="lineno">   78</span>    <span class="comment">// [6, 7, 1, 3, 8, 2, 4] return 19</span></div>
+<div class="line"><span class="lineno">   79</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> array2 = {6, 7, 1, 3, 8, 2, 4};</div>
+<div class="line"><span class="lineno">   80</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2... &quot;</span>;</div>
+<div class="line"><span class="lineno">   81</span>    assert(</div>
+<div class="line"><span class="lineno">   82</span>        dynamic_programming::house_robber::houseRobber(array2, array2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) ==</div>
+<div class="line"><span class="lineno">   83</span>        19);  <span class="comment">// here the four non-adjacent houses that are robbed are first,</span></div>
+<div class="line"><span class="lineno">   84</span>              <span class="comment">// third, fifth and seventh with total sum money as 19</span></div>
+<div class="line"><span class="lineno">   85</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   86</span> </div>
+<div class="line"><span class="lineno">   87</span>    <span class="comment">// Test 3</span></div>
+<div class="line"><span class="lineno">   88</span>    <span class="comment">// [] return 0</span></div>
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+<div class="line"><span class="lineno">   90</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3... &quot;</span>;</div>
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+<div class="line"><span class="lineno">   92</span>        dynamic_programming::house_robber::houseRobber(array3, array3.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) ==</div>
+<div class="line"><span class="lineno">   93</span>        0);  <span class="comment">// since there is no house no money can be robbed</span></div>
+<div class="line"><span class="lineno">   94</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   95</span> </div>
+<div class="line"><span class="lineno">   96</span>    <span class="comment">// Test 4</span></div>
+<div class="line"><span class="lineno">   97</span>    <span class="comment">// [2,7,9,3,1] return 12</span></div>
+<div class="line"><span class="lineno">   98</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> array4 = {2, 7, 9, 3, 1};</div>
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-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> text1 = <span class="stringliteral">&quot;ALANTURING&quot;</span>;</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> encrypted1 = <a class="code hl_function" href="../../d6/d2c/caesar__cipher_8cpp.html#ac3381121289548640b1c27a58a8524c3">ciphers::caesar::encrypt</a>(text1, 17);</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> decrypted1 = <a class="code hl_function" href="../../d6/d2c/caesar__cipher_8cpp.html#a355e69511cd2006b5c4c80ae95b71056">ciphers::caesar::decrypt</a>(encrypted1, 17);</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    assert(text1 == decrypted1);</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Original text : &quot;</span> &lt;&lt; text1;</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; , Encrypted text (with shift = 21) : &quot;</span> &lt;&lt; encrypted1;</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; , Decrypted text : &quot;</span>&lt;&lt; decrypted1 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <span class="comment">// Test 2</span></div>
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-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> decrypted2 = <a class="code hl_function" href="../../d6/d2c/caesar__cipher_8cpp.html#a355e69511cd2006b5c4c80ae95b71056">ciphers::caesar::decrypt</a>(encrypted2, 1729);</div>
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-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  100</span>            {</div>
+<div class="line"><span class="lineno">  101</span>    <span class="comment">// Test 1</span></div>
+<div class="line"><span class="lineno">  102</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> text1 = <span class="stringliteral">&quot;ALANTURING&quot;</span>;</div>
+<div class="line"><span class="lineno">  103</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> encrypted1 = <a class="code hl_function" href="../../d6/d2c/caesar__cipher_8cpp.html#ac3381121289548640b1c27a58a8524c3">ciphers::caesar::encrypt</a>(text1, 17);</div>
+<div class="line"><span class="lineno">  104</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> decrypted1 = <a class="code hl_function" href="../../d6/d2c/caesar__cipher_8cpp.html#a355e69511cd2006b5c4c80ae95b71056">ciphers::caesar::decrypt</a>(encrypted1, 17);</div>
+<div class="line"><span class="lineno">  105</span>    assert(text1 == decrypted1);</div>
+<div class="line"><span class="lineno">  106</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Original text : &quot;</span> &lt;&lt; text1;</div>
+<div class="line"><span class="lineno">  107</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; , Encrypted text (with shift = 21) : &quot;</span> &lt;&lt; encrypted1;</div>
+<div class="line"><span class="lineno">  108</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; , Decrypted text : &quot;</span>&lt;&lt; decrypted1 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  109</span>    <span class="comment">// Test 2</span></div>
+<div class="line"><span class="lineno">  110</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> text2 = <span class="stringliteral">&quot;HELLOWORLD&quot;</span>;</div>
+<div class="line"><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> encrypted2 = <a class="code hl_function" href="../../d6/d2c/caesar__cipher_8cpp.html#ac3381121289548640b1c27a58a8524c3">ciphers::caesar::encrypt</a>(text2, 1729);</div>
+<div class="line"><span class="lineno">  112</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> decrypted2 = <a class="code hl_function" href="../../d6/d2c/caesar__cipher_8cpp.html#a355e69511cd2006b5c4c80ae95b71056">ciphers::caesar::decrypt</a>(encrypted2, 1729);</div>
+<div class="line"><span class="lineno">  113</span>    assert(text2 == decrypted2);</div>
+<div class="line"><span class="lineno">  114</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Original text : &quot;</span> &lt;&lt; text2;</div>
+<div class="line"><span class="lineno">  115</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; , Encrypted text (with shift = 1729) : &quot;</span> &lt;&lt; encrypted2;</div>
+<div class="line"><span class="lineno">  116</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; , Decrypted text : &quot;</span>&lt;&lt; decrypted2 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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 <div class="ttc" id="acaesar__cipher_8cpp_html_ac3381121289548640b1c27a58a8524c3"><div class="ttname"><a href="../../d6/d2c/caesar__cipher_8cpp.html#ac3381121289548640b1c27a58a8524c3">ciphers::caesar::encrypt</a></div><div class="ttdeci">std::string encrypt(const std::string &amp;text, const int &amp;shift)</div><div class="ttdef"><b>Definition:</b> caesar_cipher.cpp:65</div></div>
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+<div class="line"><span class="lineno">   73</span> </div>
+<div class="line"><span class="lineno">   74</span>    assert(fenwick_tree.sum_range(0, 0) == 1);</div>
+<div class="line"><span class="lineno">   75</span>    assert(fenwick_tree.sum_range(0, 1) == 3);</div>
+<div class="line"><span class="lineno">   76</span>    assert(fenwick_tree.sum_range(0, 2) == 6);</div>
+<div class="line"><span class="lineno">   77</span>    fenwick_tree.update(0, 6);</div>
+<div class="line"><span class="lineno">   78</span>    assert(fenwick_tree.sum_range(0, 0) == 6);</div>
+<div class="line"><span class="lineno">   79</span>    assert(fenwick_tree.sum_range(0, 1) == 8);</div>
+<div class="line"><span class="lineno">   80</span>    assert(fenwick_tree.sum_range(0, 2) == 11);</div>
+<div class="line"><span class="lineno">   81</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">   82</span>}</div>
 <div class="ttc" id="aclass_fenwick_tree_html"><div class="ttname"><a href="../../dd/d91/class_fenwick_tree.html">FenwickTree</a></div><div class="ttdef"><b>Definition:</b> fenwick_tree.cpp:17</div></div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int &gt;</a></div></div>
 </div><!-- fragment --><div class="dynheader">
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   <ul>
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+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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  <tbody>
- <tr style="height: 56px;">
-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
+  <td id="projectalign">
    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
    </div>
    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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-<!-- Generated by Doxygen 1.9.2 -->
+<!-- Generated by Doxygen 1.9.3 -->
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@@ -99,6 +99,12 @@ $(document).ready(function(){initNavTree('d6/d30/classmachine__learning_1_1adali
   <div class="headertitle"><div class="title">machine_learning::adaline Class Reference</div></div>
 </div><!--header-->
 <div class="contents">
+<div class="dynheader">
+Collaboration diagram for machine_learning::adaline:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../da/dd3/classmachine__learning_1_1adaline__coll__graph.svg" width="183" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+<center><span class="legend">[<a target="top" href="../../graph_legend.html">legend</a>]</span></center></div>
 <table class="memberdecls">
 <tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
 Public Member Functions</h2></td></tr>
@@ -187,28 +193,28 @@ Friends</h2></td></tr>
   </table>
   </dd>
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-<div class="fragment"><div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>        : <a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#a28160d17e492597a2f112e0d38551cda">eta</a>(<a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#a28160d17e492597a2f112e0d38551cda">eta</a>), <a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#aa23d60262f917f35836ef4b1c1d9f7d3">accuracy</a>(<a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#aa23d60262f917f35836ef4b1c1d9f7d3">accuracy</a>) {</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#a28160d17e492597a2f112e0d38551cda">eta</a> &lt;= 0) {</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;learning rate should be positive and nonzero&quot;</span></div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>                      &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        }</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span> </div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        <a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a>(</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>            num_features +</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>            1);  <span class="comment">// additional weight is for the constant bias term</span></div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span> </div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        <span class="comment">// initialize with random weights in the range [-50, 49]</span></div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        <span class="keywordflow">for</span> (<span class="keywordtype">double</span> &amp;weight : <a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>) weight = 1.f;</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        <span class="comment">// weights[i] = (static_cast&lt;double&gt;(std::rand() % 100) - 50);</span></div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   57</span>        : <a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#a28160d17e492597a2f112e0d38551cda">eta</a>(<a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#a28160d17e492597a2f112e0d38551cda">eta</a>), <a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#aa23d60262f917f35836ef4b1c1d9f7d3">accuracy</a>(<a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#aa23d60262f917f35836ef4b1c1d9f7d3">accuracy</a>) {</div>
+<div class="line"><span class="lineno">   58</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#a28160d17e492597a2f112e0d38551cda">eta</a> &lt;= 0) {</div>
+<div class="line"><span class="lineno">   59</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;learning rate should be positive and nonzero&quot;</span></div>
+<div class="line"><span class="lineno">   60</span>                      &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   61</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><span class="lineno">   62</span>        }</div>
+<div class="line"><span class="lineno">   63</span> </div>
+<div class="line"><span class="lineno">   64</span>        <a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a>(</div>
+<div class="line"><span class="lineno">   65</span>            num_features +</div>
+<div class="line"><span class="lineno">   66</span>            1);  <span class="comment">// additional weight is for the constant bias term</span></div>
+<div class="line"><span class="lineno">   67</span> </div>
+<div class="line"><span class="lineno">   68</span>        <span class="comment">// initialize with random weights in the range [-50, 49]</span></div>
+<div class="line"><span class="lineno">   69</span>        <span class="keywordflow">for</span> (<span class="keywordtype">double</span> &amp;weight : <a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>) weight = 1.f;</div>
+<div class="line"><span class="lineno">   70</span>        <span class="comment">// weights[i] = (static_cast&lt;double&gt;(std::rand() % 100) - 50);</span></div>
+<div class="line"><span class="lineno">   71</span>    }</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div></div>
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 <div class="ttc" id="aclassmachine__learning_1_1adaline_html_aa23d60262f917f35836ef4b1c1d9f7d3"><div class="ttname"><a href="../../d6/d30/classmachine__learning_1_1adaline.html#aa23d60262f917f35836ef4b1c1d9f7d3">machine_learning::adaline::accuracy</a></div><div class="ttdeci">const double accuracy</div><div class="ttdoc">model fit convergence accuracy</div><div class="ttdef"><b>Definition:</b> adaline_learning.cpp:208</div></div>
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-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; double &gt;</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -252,7 +258,7 @@ Here is the call graph for this function:</div>
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 </dl>
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-<div class="fragment"><div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>{ <span class="keywordflow">return</span> x &gt; 0 ? 1 : -1; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  186</span>{ <span class="keywordflow">return</span> x &gt; 0 ? 1 : -1; }</div>
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@@ -288,16 +294,16 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> size matches </dd>
 <dd>
 <code>false</code> size does not match </dd></dl>
-<div class="fragment"><div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>                                                      {</div>
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-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;: &quot;</span></div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>                      &lt;&lt; <span class="stringliteral">&quot;Number of features in x does not match the feature &quot;</span></div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>                         <span class="stringliteral">&quot;dimension in model!&quot;</span></div>
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-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  196</span>                                                      {</div>
+<div class="line"><span class="lineno">  197</span>        <span class="keywordflow">if</span> (x.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() != (<a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() - 1)) {</div>
+<div class="line"><span class="lineno">  198</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;: &quot;</span></div>
+<div class="line"><span class="lineno">  199</span>                      &lt;&lt; <span class="stringliteral">&quot;Number of features in x does not match the feature &quot;</span></div>
+<div class="line"><span class="lineno">  200</span>                         <span class="stringliteral">&quot;dimension in model!&quot;</span></div>
+<div class="line"><span class="lineno">  201</span>                      &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  202</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  203</span>        }</div>
+<div class="line"><span class="lineno">  204</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  205</span>    }</div>
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   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>correction factor </dd></dl>
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-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span> </div>
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-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>        <span class="keywordflow">return</span> correction_factor;</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  119</span>                                                         {</div>
+<div class="line"><span class="lineno">  120</span>        <span class="keywordflow">if</span> (!<a class="code hl_function" href="../../d6/d30/classmachine__learning_1_1adaline.html#ac8a9c2aaaa63b0f27ea176857e1e7d56">check_size_match</a>(x)) {</div>
+<div class="line"><span class="lineno">  121</span>            <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  122</span>        }</div>
+<div class="line"><span class="lineno">  123</span> </div>
+<div class="line"><span class="lineno">  124</span>        <span class="comment">/* output of the model with current weights */</span></div>
+<div class="line"><span class="lineno">  125</span>        <span class="keywordtype">int</span> p = <a class="code hl_function" href="../../d6/d30/classmachine__learning_1_1adaline.html#ab11242d9ad5b03a75911e29b04f78fd3">predict</a>(x);</div>
+<div class="line"><span class="lineno">  126</span>        <span class="keywordtype">int</span> prediction_error = y - p;  <span class="comment">// error in estimation</span></div>
+<div class="line"><span class="lineno">  127</span>        <span class="keywordtype">double</span> correction_factor = <a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#a28160d17e492597a2f112e0d38551cda">eta</a> * prediction_error;</div>
+<div class="line"><span class="lineno">  128</span> </div>
+<div class="line"><span class="lineno">  129</span>        <span class="comment">/* update each weight, the last weight is the bias term */</span></div>
+<div class="line"><span class="lineno">  130</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; x.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
+<div class="line"><span class="lineno">  131</span>            <a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>[i] += correction_factor * x[i];</div>
+<div class="line"><span class="lineno">  132</span>        }</div>
+<div class="line"><span class="lineno">  133</span>        <a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>[x.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()] += correction_factor;  <span class="comment">// update bias</span></div>
+<div class="line"><span class="lineno">  134</span> </div>
+<div class="line"><span class="lineno">  135</span>        <span class="keywordflow">return</span> correction_factor;</div>
+<div class="line"><span class="lineno">  136</span>    }</div>
 <div class="ttc" id="aclassmachine__learning_1_1adaline_html_ab11242d9ad5b03a75911e29b04f78fd3"><div class="ttname"><a href="../../d6/d30/classmachine__learning_1_1adaline.html#ab11242d9ad5b03a75911e29b04f78fd3">machine_learning::adaline::predict</a></div><div class="ttdeci">int predict(const std::vector&lt; double &gt; &amp;x, double *out=nullptr)</div><div class="ttdef"><b>Definition:</b> adaline_learning.cpp:95</div></div>
 <div class="ttc" id="aclassmachine__learning_1_1adaline_html_ac8a9c2aaaa63b0f27ea176857e1e7d56"><div class="ttname"><a href="../../d6/d30/classmachine__learning_1_1adaline.html#ac8a9c2aaaa63b0f27ea176857e1e7d56">machine_learning::adaline::check_size_match</a></div><div class="ttdeci">bool check_size_match(const std::vector&lt; double &gt; &amp;x)</div><div class="ttdef"><b>Definition:</b> adaline_learning.cpp:196</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d6/d30/classmachine__learning_1_1adaline_a74e3c6c037b67895014414c5d75465e5_cgraph.svg" width="100%" height="542"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d6/d30/classmachine__learning_1_1adaline_a74e3c6c037b67895014414c5d75465e5_cgraph.svg" width="100%" height="577"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
 </div>
 </div>
 
@@ -420,42 +426,42 @@ template&lt;size_t N&gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>                                        {</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>        <span class="keywordtype">double</span> avg_pred_error = 1.f;</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span> </div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>        <span class="keywordtype">int</span> iter = 0;</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>        <span class="keywordflow">for</span> (iter = 0; (iter &lt; <a class="code hl_variable" href="../../d9/d66/group__machine__learning.html#ga5118e5cbc4f0886e27b3a7a2544dded1">MAX_ITER</a>) &amp;&amp; (avg_pred_error &gt; <a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#aa23d60262f917f35836ef4b1c1d9f7d3">accuracy</a>);</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>             iter++) {</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>            avg_pred_error = 0.f;</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span> </div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>            <span class="comment">// perform fit for each sample</span></div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>                <span class="keywordtype">double</span> err = <a class="code hl_function" href="../../d6/d30/classmachine__learning_1_1adaline.html#a74e3c6c037b67895014414c5d75465e5">fit</a>(X[i], Y[i]);</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>                avg_pred_error += std::abs(err);</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>            }</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>            avg_pred_error /= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>;</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span> </div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>            <span class="comment">// Print updates every 200th iteration</span></div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>            <span class="comment">// if (iter % 100 == 0)</span></div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tIter &quot;</span> &lt;&lt; iter &lt;&lt; <span class="stringliteral">&quot;: Training weights: &quot;</span> &lt;&lt; *<span class="keyword">this</span></div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>                      &lt;&lt; <span class="stringliteral">&quot;\tAvg error: &quot;</span> &lt;&lt; avg_pred_error &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>        }</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span> </div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>        <span class="keywordflow">if</span> (iter &lt; <a class="code hl_variable" href="../../d9/d66/group__machine__learning.html#ga5118e5cbc4f0886e27b3a7a2544dded1">MAX_ITER</a>) {</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Converged after &quot;</span> &lt;&lt; iter &lt;&lt; <span class="stringliteral">&quot; iterations.&quot;</span></div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>                      &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Did not converge after &quot;</span> &lt;&lt; iter &lt;&lt; <span class="stringliteral">&quot; iterations.&quot;</span></div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>                      &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>        }</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  146</span>                                        {</div>
+<div class="line"><span class="lineno">  147</span>        <span class="keywordtype">double</span> avg_pred_error = 1.f;</div>
+<div class="line"><span class="lineno">  148</span> </div>
+<div class="line"><span class="lineno">  149</span>        <span class="keywordtype">int</span> iter = 0;</div>
+<div class="line"><span class="lineno">  150</span>        <span class="keywordflow">for</span> (iter = 0; (iter &lt; <a class="code hl_variable" href="../../d9/d66/group__machine__learning.html#ga5118e5cbc4f0886e27b3a7a2544dded1">MAX_ITER</a>) &amp;&amp; (avg_pred_error &gt; <a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#aa23d60262f917f35836ef4b1c1d9f7d3">accuracy</a>);</div>
+<div class="line"><span class="lineno">  151</span>             iter++) {</div>
+<div class="line"><span class="lineno">  152</span>            avg_pred_error = 0.f;</div>
+<div class="line"><span class="lineno">  153</span> </div>
+<div class="line"><span class="lineno">  154</span>            <span class="comment">// perform fit for each sample</span></div>
+<div class="line"><span class="lineno">  155</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
+<div class="line"><span class="lineno">  156</span>                <span class="keywordtype">double</span> err = <a class="code hl_function" href="../../d6/d30/classmachine__learning_1_1adaline.html#a74e3c6c037b67895014414c5d75465e5">fit</a>(X[i], Y[i]);</div>
+<div class="line"><span class="lineno">  157</span>                avg_pred_error += std::abs(err);</div>
+<div class="line"><span class="lineno">  158</span>            }</div>
+<div class="line"><span class="lineno">  159</span>            avg_pred_error /= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>;</div>
+<div class="line"><span class="lineno">  160</span> </div>
+<div class="line"><span class="lineno">  161</span>            <span class="comment">// Print updates every 200th iteration</span></div>
+<div class="line"><span class="lineno">  162</span>            <span class="comment">// if (iter % 100 == 0)</span></div>
+<div class="line"><span class="lineno">  163</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tIter &quot;</span> &lt;&lt; iter &lt;&lt; <span class="stringliteral">&quot;: Training weights: &quot;</span> &lt;&lt; *<span class="keyword">this</span></div>
+<div class="line"><span class="lineno">  164</span>                      &lt;&lt; <span class="stringliteral">&quot;\tAvg error: &quot;</span> &lt;&lt; avg_pred_error &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  165</span>        }</div>
+<div class="line"><span class="lineno">  166</span> </div>
+<div class="line"><span class="lineno">  167</span>        <span class="keywordflow">if</span> (iter &lt; <a class="code hl_variable" href="../../d9/d66/group__machine__learning.html#ga5118e5cbc4f0886e27b3a7a2544dded1">MAX_ITER</a>) {</div>
+<div class="line"><span class="lineno">  168</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Converged after &quot;</span> &lt;&lt; iter &lt;&lt; <span class="stringliteral">&quot; iterations.&quot;</span></div>
+<div class="line"><span class="lineno">  169</span>                      &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  170</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  171</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Did not converge after &quot;</span> &lt;&lt; iter &lt;&lt; <span class="stringliteral">&quot; iterations.&quot;</span></div>
+<div class="line"><span class="lineno">  172</span>                      &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  173</span>        }</div>
+<div class="line"><span class="lineno">  174</span>    }</div>
 <div class="ttc" id="aclassmachine__learning_1_1adaline_html_a74e3c6c037b67895014414c5d75465e5"><div class="ttname"><a href="../../d6/d30/classmachine__learning_1_1adaline.html#a74e3c6c037b67895014414c5d75465e5">machine_learning::adaline::fit</a></div><div class="ttdeci">double fit(const std::vector&lt; double &gt; &amp;x, const int &amp;y)</div><div class="ttdef"><b>Definition:</b> adaline_learning.cpp:119</div></div>
 <div class="ttc" id="adata__structures_2sparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:47</div></div>
 <div class="ttc" id="agroup__machine__learning_html_ga5118e5cbc4f0886e27b3a7a2544dded1"><div class="ttname"><a href="../../d9/d66/group__machine__learning.html#ga5118e5cbc4f0886e27b3a7a2544dded1">MAX_ITER</a></div><div class="ttdeci">constexpr int MAX_ITER</div><div class="ttdef"><b>Definition:</b> adaline_learning.cpp:40</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d6/d30/classmachine__learning_1_1adaline_a8d61f9ed872eef26bca39388cbda6a91_cgraph.svg" width="100%" height="576"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d6/d30/classmachine__learning_1_1adaline_a8d61f9ed872eef26bca39388cbda6a91_cgraph.svg" width="100%" height="600"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
 </div>
 </div>
 
@@ -502,22 +508,23 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>model prediction output </dd></dl>
-<div class="fragment"><div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>                                                                   {</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>        <span class="keywordflow">if</span> (!<a class="code hl_function" href="../../d6/d30/classmachine__learning_1_1adaline.html#ac8a9c2aaaa63b0f27ea176857e1e7d56">check_size_match</a>(x)) {</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>            <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>        }</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span> </div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>        <span class="keywordtype">double</span> y = <a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>.back();  <span class="comment">// assign bias value</span></div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span> </div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>        <span class="comment">// for (int i = 0; i &lt; x.size(); i++) y += x[i] * weights[i];</span></div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        y = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/inner_product.html">std::inner_product</a>(x.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), x.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>(), <a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>.begin(), y);</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span> </div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>        <span class="keywordflow">if</span> (out != <span class="keyword">nullptr</span>) {  <span class="comment">// if out variable is provided</span></div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>            *out = y;</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>        }</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span> </div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d6/d30/classmachine__learning_1_1adaline.html#a082f758fb55fe19f22b3df66f89b2325">activation</a>(y);  <span class="comment">// quantizer: apply ADALINE threshold function</span></div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   95</span>                                                                   {</div>
+<div class="line"><span class="lineno">   96</span>        <span class="keywordflow">if</span> (!<a class="code hl_function" href="../../d6/d30/classmachine__learning_1_1adaline.html#ac8a9c2aaaa63b0f27ea176857e1e7d56">check_size_match</a>(x)) {</div>
+<div class="line"><span class="lineno">   97</span>            <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">   98</span>        }</div>
+<div class="line"><span class="lineno">   99</span> </div>
+<div class="line"><span class="lineno">  100</span>        <span class="keywordtype">double</span> y = <a class="code hl_variable" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/back.html">back</a>();  <span class="comment">// assign bias value</span></div>
+<div class="line"><span class="lineno">  101</span> </div>
+<div class="line"><span class="lineno">  102</span>        <span class="comment">// for (int i = 0; i &lt; x.size(); i++) y += x[i] * weights[i];</span></div>
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+<div class="line"><span class="lineno">  149</span>    }</div>
+<div class="line"><span class="lineno">  150</span>    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  151</span>}</div>
 <div class="ttc" id="amiller__rabin_8cpp_html_a6f9c31c1047aa3191676d64571d4c506"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a6f9c31c1047aa3191676d64571d4c506">miller_test</a></div><div class="ttdeci">bool miller_test(T d, T num)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:73</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -271,36 +271,36 @@ template&lt;typename T &gt; </div>
 <dl class="section return"><dt>Returns</dt><dd>'false' if n is composite </dd>
 <dd>
 'true' if n is (probably) prime. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>                             {</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    <span class="comment">// random number seed</span></div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/random_device.html">std::random_device</a> rd_seed;</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>    <span class="comment">// random number generator</span></div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/mersenne_twister_engine.html">std::mt19937</a> gen(rd_seed());</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    <span class="comment">// Uniformly distributed range [2, num - 2] for random numbers</span></div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/uniform_int_distribution.html">std::uniform_int_distribution&lt;&gt;</a> distribution(2, num - 2);</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    <span class="comment">// Random number generated in the range [2, num -2].</span></div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    T random = distribution(gen);</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <span class="comment">// vector for reverse binary of the power</span></div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">power</a> = <a class="code hl_function" href="../../d6/d42/miller__rabin_8cpp.html#a091662a787d5ad4866713021f580fddb">reverse_binary</a>(d);</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    <span class="comment">// x = random ^ d % num</span></div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    T x = <a class="code hl_function" href="../../d6/d42/miller__rabin_8cpp.html#ad6c2c67ea416d0e80003a88623f98b29">modular_exponentiation</a>(random, power, num);</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>    <span class="comment">// miller conditions</span></div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    <span class="keywordflow">if</span> (x == 1 || x == num - 1) {</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    }</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span> </div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    <span class="keywordflow">while</span> (d != num - 1) {</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>        x = (x * x) % num;</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>        d *= 2;</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>        <span class="keywordflow">if</span> (x == 1) {</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>        }</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>        <span class="keywordflow">if</span> (x == num - 1) {</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>        }</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    }</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   73</span>                             {</div>
+<div class="line"><span class="lineno">   74</span>    <span class="comment">// random number seed</span></div>
+<div class="line"><span class="lineno">   75</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/random_device.html">std::random_device</a> rd_seed;</div>
+<div class="line"><span class="lineno">   76</span>    <span class="comment">// random number generator</span></div>
+<div class="line"><span class="lineno">   77</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/mersenne_twister_engine.html">std::mt19937</a> gen(rd_seed());</div>
+<div class="line"><span class="lineno">   78</span>    <span class="comment">// Uniformly distributed range [2, num - 2] for random numbers</span></div>
+<div class="line"><span class="lineno">   79</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/uniform_int_distribution.html">std::uniform_int_distribution&lt;&gt;</a> distribution(2, num - 2);</div>
+<div class="line"><span class="lineno">   80</span>    <span class="comment">// Random number generated in the range [2, num -2].</span></div>
+<div class="line"><span class="lineno">   81</span>    T random = distribution(gen);</div>
+<div class="line"><span class="lineno">   82</span>    <span class="comment">// vector for reverse binary of the power</span></div>
+<div class="line"><span class="lineno">   83</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">power</a> = <a class="code hl_function" href="../../d6/d42/miller__rabin_8cpp.html#a091662a787d5ad4866713021f580fddb">reverse_binary</a>(d);</div>
+<div class="line"><span class="lineno">   84</span>    <span class="comment">// x = random ^ d % num</span></div>
+<div class="line"><span class="lineno">   85</span>    T x = <a class="code hl_function" href="../../d6/d42/miller__rabin_8cpp.html#ad6c2c67ea416d0e80003a88623f98b29">modular_exponentiation</a>(random, power, num);</div>
+<div class="line"><span class="lineno">   86</span>    <span class="comment">// miller conditions</span></div>
+<div class="line"><span class="lineno">   87</span>    <span class="keywordflow">if</span> (x == 1 || x == num - 1) {</div>
+<div class="line"><span class="lineno">   88</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   89</span>    }</div>
+<div class="line"><span class="lineno">   90</span> </div>
+<div class="line"><span class="lineno">   91</span>    <span class="keywordflow">while</span> (d != num - 1) {</div>
+<div class="line"><span class="lineno">   92</span>        x = (x * x) % num;</div>
+<div class="line"><span class="lineno">   93</span>        d *= 2;</div>
+<div class="line"><span class="lineno">   94</span>        <span class="keywordflow">if</span> (x == 1) {</div>
+<div class="line"><span class="lineno">   95</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   96</span>        }</div>
+<div class="line"><span class="lineno">   97</span>        <span class="keywordflow">if</span> (x == num - 1) {</div>
+<div class="line"><span class="lineno">   98</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   99</span>        }</div>
+<div class="line"><span class="lineno">  100</span>    }</div>
+<div class="line"><span class="lineno">  101</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  102</span>}</div>
 <div class="ttc" id="afibonacci__sum_8cpp_html_a7cf5feaf168b88e74544da59ed830311"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">math::fibonacci_sum::power</a></div><div class="ttdeci">math::fibonacci_sum::matrix power(math::fibonacci_sum::matrix T, uint64_t ex)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:57</div></div>
 <div class="ttc" id="amersenne_twister_engine_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/mersenne_twister_engine.html">std::mt19937</a></div></div>
 <div class="ttc" id="amiller__rabin_8cpp_html_a091662a787d5ad4866713021f580fddb"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a091662a787d5ad4866713021f580fddb">reverse_binary</a></div><div class="ttdeci">std::vector&lt; T &gt; reverse_binary(T num)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:19</div></div>
@@ -359,25 +359,25 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>r the modular exponentiation of \(a^{n} \equiv r \mod{m}\) where \(n\) is the base 10 representation of rev_binary_exponent and \(m = mod \) parameter. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>                                {</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>    <span class="keywordflow">if</span> (mod == 1)</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>        <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>    T b = 1;</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <span class="keywordflow">if</span> (rev_binary_exponent.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() == 0)</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        <span class="keywordflow">return</span> b;</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    T A = base;</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    <span class="keywordflow">if</span> (rev_binary_exponent[0] == 1)</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>        b = base;</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span> </div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>    <span class="keywordflow">for</span> (<span class="keyword">typename</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;::const_iterator</a> it =</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>             rev_binary_exponent.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">cbegin</a>() + 1;</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>         it != rev_binary_exponent.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">cend</a>(); ++it) {</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>        A = A * A % mod;</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>        <span class="keywordflow">if</span> (*it == 1)</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>            b = A * b % mod;</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    }</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    <span class="keywordflow">return</span> b;</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   44</span>                                {</div>
+<div class="line"><span class="lineno">   45</span>    <span class="keywordflow">if</span> (mod == 1)</div>
+<div class="line"><span class="lineno">   46</span>        <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">   47</span>    T b = 1;</div>
+<div class="line"><span class="lineno">   48</span>    <span class="keywordflow">if</span> (rev_binary_exponent.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() == 0)</div>
+<div class="line"><span class="lineno">   49</span>        <span class="keywordflow">return</span> b;</div>
+<div class="line"><span class="lineno">   50</span>    T A = base;</div>
+<div class="line"><span class="lineno">   51</span>    <span class="keywordflow">if</span> (rev_binary_exponent[0] == 1)</div>
+<div class="line"><span class="lineno">   52</span>        b = base;</div>
+<div class="line"><span class="lineno">   53</span> </div>
+<div class="line"><span class="lineno">   54</span>    <span class="keywordflow">for</span> (<span class="keyword">typename</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;::const_iterator</a> it =</div>
+<div class="line"><span class="lineno">   55</span>             rev_binary_exponent.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">cbegin</a>() + 1;</div>
+<div class="line"><span class="lineno">   56</span>         it != rev_binary_exponent.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">cend</a>(); ++it) {</div>
+<div class="line"><span class="lineno">   57</span>        A = A * A % mod;</div>
+<div class="line"><span class="lineno">   58</span>        <span class="keywordflow">if</span> (*it == 1)</div>
+<div class="line"><span class="lineno">   59</span>            b = A * b % mod;</div>
+<div class="line"><span class="lineno">   60</span>    }</div>
+<div class="line"><span class="lineno">   61</span>    <span class="keywordflow">return</span> b;</div>
+<div class="line"><span class="lineno">   62</span>}</div>
 <div class="ttc" id="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/begin.html">std::vector::cbegin</a></div><div class="ttdeci">T cbegin(T... args)</div></div>
 <div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/end.html">std::vector::cend</a></div><div class="ttdeci">T cend(T... args)</div></div>
 <div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
@@ -414,15 +414,15 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>result vector of the number input in reverse binary </dd></dl>
-<div class="fragment"><div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span>                                   {</div>
-<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>    T temp = num;</div>
-<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>    <span class="keywordflow">while</span> (temp &gt; 0) {</div>
-<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.push_back(temp % 2);</div>
-<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span>        temp = temp / 2;</div>
-<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>    }</div>
-<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   19</span>                                   {</div>
+<div class="line"><span class="lineno">   20</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">   21</span>    T temp = num;</div>
+<div class="line"><span class="lineno">   22</span>    <span class="keywordflow">while</span> (temp &gt; 0) {</div>
+<div class="line"><span class="lineno">   23</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.push_back(temp % 2);</div>
+<div class="line"><span class="lineno">   24</span>        temp = temp / 2;</div>
+<div class="line"><span class="lineno">   25</span>    }</div>
+<div class="line"><span class="lineno">   26</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">   27</span>}</div>
 <div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
 </div><!-- fragment -->
 </div>
@@ -442,28 +442,28 @@ template&lt;typename T &gt; </div>
       </table>
 </div><div class="memdoc">
 <p >Functions for testing the <a class="el" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test()</a> function with some assert statements. </p>
-<div class="fragment"><div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>             {</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    <span class="comment">// First test on 2</span></div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>    assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;2 is prime but function says otherwise.\n&quot;</span>,</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>            <a class="code hl_function" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a>(2, 1) == <span class="keyword">true</span>));</div>
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 <p >Calculates the probability of the events A or B for dependent events note that if value of B_given_A is unknown, use chainrule to find it \parama [in] A probability of event A \parama [in] B probability of event B \parama [in] B_given_A probability of event B condition A </p><dl class="section return"><dt>Returns</dt><dd>probability of A and B </dd></dl>
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 <p >calculates the probability of the independent events A or B for independent events \parama [in] A probability of event A \parama [in] B probability of event B </p><dl class="section return"><dt>Returns</dt><dd>probability of A and B </dd></dl>
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-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>        x += dx;                            <span class="comment">// update step</span></div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    } <span class="keywordflow">while</span> (x &lt;= x_max);  <span class="comment">// till upper limit of independent variable</span></div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    <span class="comment">/* end of integration */</span></div>
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-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span> </div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    <span class="keywordflow">if</span> (fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/close.html">close</a>();</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    }</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span> </div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>    <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(t2 - t1) / CLOCKS_PER_SEC;</div>
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+<div class="fragment"><div class="line"><span class="lineno">  103</span>                                                                        {</div>
+<div class="line"><span class="lineno">  104</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> dy = *y;</div>
+<div class="line"><span class="lineno">  105</span> </div>
+<div class="line"><span class="lineno">  106</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp;</div>
+<div class="line"><span class="lineno">  107</span>    <span class="keywordflow">if</span> (save_to_file) {</div>
+<div class="line"><span class="lineno">  108</span>        fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">open</a>(<span class="stringliteral">&quot;forward_euler.csv&quot;</span>, std::ofstream::out);</div>
+<div class="line"><span class="lineno">  109</span>        <span class="keywordflow">if</span> (!fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
+<div class="line"><span class="lineno">  110</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a>(<span class="stringliteral">&quot;Error! &quot;</span>);</div>
+<div class="line"><span class="lineno">  111</span>        }</div>
+<div class="line"><span class="lineno">  112</span>    }</div>
+<div class="line"><span class="lineno">  113</span> </div>
+<div class="line"><span class="lineno">  114</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> L = y-&gt;size();</div>
+<div class="line"><span class="lineno">  115</span> </div>
+<div class="line"><span class="lineno">  116</span>    <span class="comment">/* start integration */</span></div>
+<div class="line"><span class="lineno">  117</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t1 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  118</span>    <span class="keywordtype">double</span> x = x0;</div>
+<div class="line"><span class="lineno">  119</span> </div>
+<div class="line"><span class="lineno">  120</span>    <span class="keywordflow">do</span> {  <span class="comment">// iterate for each step of independent variable</span></div>
+<div class="line"><span class="lineno">  121</span>        <span class="keywordflow">if</span> (save_to_file &amp;&amp; fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
+<div class="line"><span class="lineno">  122</span>            <span class="comment">// write to file</span></div>
+<div class="line"><span class="lineno">  123</span>            fp &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><span class="lineno">  124</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; L - 1; i++) {</div>
+<div class="line"><span class="lineno">  125</span>                fp &lt;&lt; y[0][i] &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;  <span class="comment">// NOLINT</span></div>
+<div class="line"><span class="lineno">  126</span>            }</div>
+<div class="line"><span class="lineno">  127</span>            fp &lt;&lt; y[0][L - 1] &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;  <span class="comment">// NOLINT</span></div>
+<div class="line"><span class="lineno">  128</span>        }</div>
+<div class="line"><span class="lineno">  129</span> </div>
+<div class="line"><span class="lineno">  130</span>        <a class="code hl_function" href="../../d6/d60/group__ode.html#ga195d23bbdfcb80e83c9cda45c9ad5723">forward_euler_step</a>(dx, x, y, &amp;dy);  <span class="comment">// perform integration</span></div>
+<div class="line"><span class="lineno">  131</span>        x += dx;                            <span class="comment">// update step</span></div>
+<div class="line"><span class="lineno">  132</span>    } <span class="keywordflow">while</span> (x &lt;= x_max);  <span class="comment">// till upper limit of independent variable</span></div>
+<div class="line"><span class="lineno">  133</span>    <span class="comment">/* end of integration */</span></div>
+<div class="line"><span class="lineno">  134</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t2 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  135</span> </div>
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+<div class="line"><span class="lineno">  139</span> </div>
+<div class="line"><span class="lineno">  140</span>    <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(t2 - t1) / CLOCKS_PER_SEC;</div>
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-<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a></div></div>
+<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt; double &gt;</a></div></div>
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@@ -285,10 +285,10 @@ Here is the call graph for this function:</div>
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-<div class="fragment"><div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>                                                                         {</div>
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-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   87</span>                                                                         {</div>
+<div class="line"><span class="lineno">   88</span>    <a class="code hl_function" href="../../db/dd3/ode__forward__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a>(x, y, dy);</div>
+<div class="line"><span class="lineno">   89</span>    *y += *dy * dx;</div>
+<div class="line"><span class="lineno">   90</span>}</div>
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@@ -355,43 +355,43 @@ Here is the call graph for this function:</div>
   </dd>
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 <dl class="section return"><dt>Returns</dt><dd>time taken for computation in seconds </dd></dl>
-<div class="fragment"><div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>                                                                         {</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> dy = y[0];</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span> </div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp;</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    <span class="keywordflow">if</span> (save_to_file) {</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">open</a>(<span class="stringliteral">&quot;midpoint_euler.csv&quot;</span>, std::ofstream::out);</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>        <span class="keywordflow">if</span> (!fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a>(<span class="stringliteral">&quot;Error! &quot;</span>);</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>        }</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    }</div>
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-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    <span class="comment">/* start integration */</span></div>
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-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <span class="keywordtype">double</span> x = x0;</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    <span class="keywordflow">do</span> {  <span class="comment">// iterate for each step of independent variable</span></div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>        <span class="keywordflow">if</span> (save_to_file &amp;&amp; fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>            <span class="comment">// write to file</span></div>
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-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; L - 1; i++) {</div>
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-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    } <span class="keywordflow">while</span> (x &lt;= x_max);  <span class="comment">// till upper limit of independent variable</span></div>
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-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>    <span class="keywordflow">if</span> (fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>())</div>
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+<div class="line"><span class="lineno">  114</span>        <span class="keywordflow">if</span> (!fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
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+<div class="line"><span class="lineno">  121</span>    <span class="comment">/* start integration */</span></div>
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+<div class="line"><span class="lineno">  124</span>    <span class="keywordflow">do</span> {  <span class="comment">// iterate for each step of independent variable</span></div>
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+<div class="line"><span class="lineno">  126</span>            <span class="comment">// write to file</span></div>
+<div class="line"><span class="lineno">  127</span>            fp &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><span class="lineno">  128</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; L - 1; i++) {</div>
+<div class="line"><span class="lineno">  129</span>                fp &lt;&lt; y[0][i] &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><span class="lineno">  130</span>            }</div>
+<div class="line"><span class="lineno">  131</span>            fp &lt;&lt; y[0][L - 1] &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  132</span>        }</div>
+<div class="line"><span class="lineno">  133</span> </div>
+<div class="line"><span class="lineno">  134</span>        <a class="code hl_function" href="../../d6/d60/group__ode.html#ga8c319db420c3d97a83e9dcca803b6812">midpoint_euler_step</a>(dx, x, y, &amp;dy);  <span class="comment">// perform integration</span></div>
+<div class="line"><span class="lineno">  135</span>        x += dx;                             <span class="comment">// update step</span></div>
+<div class="line"><span class="lineno">  136</span>    } <span class="keywordflow">while</span> (x &lt;= x_max);  <span class="comment">// till upper limit of independent variable</span></div>
+<div class="line"><span class="lineno">  137</span>    <span class="comment">/* end of integration */</span></div>
+<div class="line"><span class="lineno">  138</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t2 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  139</span> </div>
+<div class="line"><span class="lineno">  140</span>    <span class="keywordflow">if</span> (fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>())</div>
+<div class="line"><span class="lineno">  141</span>        fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/close.html">close</a>();</div>
+<div class="line"><span class="lineno">  142</span> </div>
+<div class="line"><span class="lineno">  143</span>    <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(t2 - t1) / CLOCKS_PER_SEC;</div>
+<div class="line"><span class="lineno">  144</span>}</div>
 <div class="ttc" id="agroup__ode_html_ga8c319db420c3d97a83e9dcca803b6812"><div class="ttname"><a href="../../d6/d60/group__ode.html#ga8c319db420c3d97a83e9dcca803b6812">midpoint_euler_step</a></div><div class="ttdeci">void midpoint_euler_step(const double dx, const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Compute next step approximation using the midpoint-Euler method.</div><div class="ttdef"><b>Definition:</b> ode_midpoint_euler.cpp:85</div></div>
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   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>                                                                          {</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    <a class="code hl_function" href="../../d6/dd3/ode__midpoint__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a>(x, y, dy);</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    <span class="keywordtype">double</span> tmp_x = x + 0.5 * dx;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span> </div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> tmp_y = y[0] + dy[0] * (0.5 * dx);</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span> </div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    <a class="code hl_function" href="../../d6/dd3/ode__midpoint__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a>(tmp_x, &amp;tmp_y, dy);</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span> </div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>    y[0] += dy[0] * dx;</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   86</span>                                                                          {</div>
+<div class="line"><span class="lineno">   87</span>    <a class="code hl_function" href="../../d6/dd3/ode__midpoint__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a>(x, y, dy);</div>
+<div class="line"><span class="lineno">   88</span>    <span class="keywordtype">double</span> tmp_x = x + 0.5 * dx;</div>
+<div class="line"><span class="lineno">   89</span> </div>
+<div class="line"><span class="lineno">   90</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> tmp_y = y[0] + dy[0] * (0.5 * dx);</div>
+<div class="line"><span class="lineno">   91</span> </div>
+<div class="line"><span class="lineno">   92</span>    <a class="code hl_function" href="../../d6/dd3/ode__midpoint__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a>(tmp_x, &amp;tmp_y, dy);</div>
+<div class="line"><span class="lineno">   93</span> </div>
+<div class="line"><span class="lineno">   94</span>    y[0] += dy[0] * dx;</div>
+<div class="line"><span class="lineno">   95</span>}</div>
 <div class="ttc" id="aode__midpoint__euler_8cpp_html_abaeae8f62a018d197f0187a1c80a90fe"><div class="ttname"><a href="../../d6/dd3/ode__midpoint__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a></div><div class="ttdeci">void problem(const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Problem statement for a system with first-order differential equations. Updates the system differenti...</div><div class="ttdef"><b>Definition:</b> ode_midpoint_euler.cpp:53</div></div>
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   </dd>
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 <dl class="section return"><dt>Returns</dt><dd>time taken for computation in seconds </dd></dl>
-<div class="fragment"><div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>                                                      {</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> dy = y[0];</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span> </div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp;</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <span class="keywordflow">if</span> (save_to_file) {</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">open</a>(<span class="stringliteral">&quot;semi_implicit_euler.csv&quot;</span>, std::ofstream::out);</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>        <span class="keywordflow">if</span> (!fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a>(<span class="stringliteral">&quot;Error! &quot;</span>);</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        }</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    }</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span> </div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> L = y-&gt;size();</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span> </div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    <span class="comment">/* start integration */</span></div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t1 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <span class="keywordtype">double</span> x = x0;</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    <span class="keywordflow">do</span> {  <span class="comment">// iterate for each step of independent variable</span></div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>        <span class="keywordflow">if</span> (save_to_file &amp;&amp; fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>            <span class="comment">// write to file</span></div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>            fp &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; L - 1; i++) {</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>                fp &lt;&lt; y[0][i] &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>            }</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>            fp &lt;&lt; y[0][L - 1] &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>        }</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span> </div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>        <a class="code hl_function" href="../../d6/d60/group__ode.html#ga827bf009831ddc477c5fa8891d5cb35f">semi_implicit_euler_step</a>(dx, x, y, &amp;dy);  <span class="comment">// perform integration</span></div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>        x += dx;                                  <span class="comment">// update step</span></div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    } <span class="keywordflow">while</span> (x &lt;= x_max);  <span class="comment">// till upper limit of independent variable</span></div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    <span class="comment">/* end of integration */</span></div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t2 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span> </div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    <span class="keywordflow">if</span> (fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>())</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>        fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/close.html">close</a>();</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span> </div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>    <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(t2 - t1) / CLOCKS_PER_SEC;</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  105</span>                                                      {</div>
+<div class="line"><span class="lineno">  106</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> dy = y[0];</div>
+<div class="line"><span class="lineno">  107</span> </div>
+<div class="line"><span class="lineno">  108</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp;</div>
+<div class="line"><span class="lineno">  109</span>    <span class="keywordflow">if</span> (save_to_file) {</div>
+<div class="line"><span class="lineno">  110</span>        fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">open</a>(<span class="stringliteral">&quot;semi_implicit_euler.csv&quot;</span>, std::ofstream::out);</div>
+<div class="line"><span class="lineno">  111</span>        <span class="keywordflow">if</span> (!fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
+<div class="line"><span class="lineno">  112</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a>(<span class="stringliteral">&quot;Error! &quot;</span>);</div>
+<div class="line"><span class="lineno">  113</span>        }</div>
+<div class="line"><span class="lineno">  114</span>    }</div>
+<div class="line"><span class="lineno">  115</span> </div>
+<div class="line"><span class="lineno">  116</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> L = y-&gt;size();</div>
+<div class="line"><span class="lineno">  117</span> </div>
+<div class="line"><span class="lineno">  118</span>    <span class="comment">/* start integration */</span></div>
+<div class="line"><span class="lineno">  119</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t1 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  120</span>    <span class="keywordtype">double</span> x = x0;</div>
+<div class="line"><span class="lineno">  121</span>    <span class="keywordflow">do</span> {  <span class="comment">// iterate for each step of independent variable</span></div>
+<div class="line"><span class="lineno">  122</span>        <span class="keywordflow">if</span> (save_to_file &amp;&amp; fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
+<div class="line"><span class="lineno">  123</span>            <span class="comment">// write to file</span></div>
+<div class="line"><span class="lineno">  124</span>            fp &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><span class="lineno">  125</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; L - 1; i++) {</div>
+<div class="line"><span class="lineno">  126</span>                fp &lt;&lt; y[0][i] &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><span class="lineno">  127</span>            }</div>
+<div class="line"><span class="lineno">  128</span>            fp &lt;&lt; y[0][L - 1] &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  129</span>        }</div>
+<div class="line"><span class="lineno">  130</span> </div>
+<div class="line"><span class="lineno">  131</span>        <a class="code hl_function" href="../../d6/d60/group__ode.html#ga827bf009831ddc477c5fa8891d5cb35f">semi_implicit_euler_step</a>(dx, x, y, &amp;dy);  <span class="comment">// perform integration</span></div>
+<div class="line"><span class="lineno">  132</span>        x += dx;                                  <span class="comment">// update step</span></div>
+<div class="line"><span class="lineno">  133</span>    } <span class="keywordflow">while</span> (x &lt;= x_max);  <span class="comment">// till upper limit of independent variable</span></div>
+<div class="line"><span class="lineno">  134</span>    <span class="comment">/* end of integration */</span></div>
+<div class="line"><span class="lineno">  135</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t2 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  136</span> </div>
+<div class="line"><span class="lineno">  137</span>    <span class="keywordflow">if</span> (fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>())</div>
+<div class="line"><span class="lineno">  138</span>        fp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/close.html">close</a>();</div>
+<div class="line"><span class="lineno">  139</span> </div>
+<div class="line"><span class="lineno">  140</span>    <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(t2 - t1) / CLOCKS_PER_SEC;</div>
+<div class="line"><span class="lineno">  141</span>}</div>
 <div class="ttc" id="agroup__ode_html_ga827bf009831ddc477c5fa8891d5cb35f"><div class="ttname"><a href="../../d6/d60/group__ode.html#ga827bf009831ddc477c5fa8891d5cb35f">semi_implicit_euler_step</a></div><div class="ttdeci">void semi_implicit_euler_step(const double dx, const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Compute next step approximation using the semi-implicit-Euler method.</div><div class="ttdef"><b>Definition:</b> ode_semi_implicit_euler.cpp:82</div></div>
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   </table>
   </dd>
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-<div class="fragment"><div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>                                                       {</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    <a class="code hl_function" href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a>(x, y, dy);         <span class="comment">// update dy once</span></div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>    y[0][0] += dx * dy[0][0];  <span class="comment">// update y0</span></div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    <a class="code hl_function" href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a>(x, y, dy);         <span class="comment">// update dy once more</span></div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span> </div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    dy[0][0] = 0.f;      <span class="comment">// ignore y0</span></div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    y[0] += dy[0] * dx;  <span class="comment">// update remaining using new dy</span></div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   84</span>                                                       {</div>
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 <p >Main function </p>
-<div class="fragment"><div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>           {</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>.precision(9);</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span> </div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Computations performed with machine epsilon: &quot;</span> &lt;&lt; <a class="code hl_define" href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>              &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span> </div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>();</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span> </div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  139</span>           {</div>
+<div class="line"><span class="lineno">  140</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>.precision(9);</div>
+<div class="line"><span class="lineno">  141</span> </div>
+<div class="line"><span class="lineno">  142</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Computations performed with machine epsilon: &quot;</span> &lt;&lt; <a class="code hl_define" href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div>
+<div class="line"><span class="lineno">  143</span>              &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  144</span> </div>
+<div class="line"><span class="lineno">  145</span>    <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
+<div class="line"><span class="lineno">  146</span>    <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
+<div class="line"><span class="lineno">  147</span>    <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>();</div>
+<div class="line"><span class="lineno">  148</span> </div>
+<div class="line"><span class="lineno">  149</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  150</span>}</div>
 <div class="ttc" id="agolden__search__extrema_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../d6/d7a/golden__search__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdoc">Test function to find maxima for the function  in the interval    Expected result: .</div><div class="ttdef"><b>Definition:</b> golden_search_extrema.cpp:100</div></div>
 <div class="ttc" id="agolden__search__extrema_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="../../d6/d7a/golden__search__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdoc">Test function to find minima for the function  in the interval    Expected result = 2.</div><div class="ttdef"><b>Definition:</b> golden_search_extrema.cpp:78</div></div>
 <div class="ttc" id="agolden__search__extrema_8cpp_html_a6d0455dd5c30adda100e95f0423c786e"><div class="ttname"><a href="../../d6/d7a/golden__search__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a></div><div class="ttdeci">void test3()</div><div class="ttdoc">Test function to find maxima for the function  in the interval    Expected result: .</div><div class="ttdef"><b>Definition:</b> golden_search_extrema.cpp:123</div></div>
@@ -304,21 +304,21 @@ Here is the call graph for this function:</div>
 
 <p>Test function to find minima for the function \(f(x)= (x-2)^2\) in the interval \([1,5]\) <br  />
  Expected result = 2. </p>
-<div class="fragment"><div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>             {</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <span class="comment">// define the function to minimize as a lambda function</span></div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(<span class="keywordtype">double</span>)&gt; f1 = [](<span class="keywordtype">double</span> x) {</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>        <span class="keywordflow">return</span> (x - 2) * (x - 2);</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    };</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span> </div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1.... &quot;</span>;</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span> </div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>    <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(f1, 1, 5);</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span> </div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minima &lt;&lt; <span class="stringliteral">&quot;...&quot;</span>;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span> </div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    assert(std::abs(minima - 2) &lt; <a class="code hl_define" href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   78</span>             {</div>
+<div class="line"><span class="lineno">   79</span>    <span class="comment">// define the function to minimize as a lambda function</span></div>
+<div class="line"><span class="lineno">   80</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(<span class="keywordtype">double</span>)&gt; f1 = [](<span class="keywordtype">double</span> x) {</div>
+<div class="line"><span class="lineno">   81</span>        <span class="keywordflow">return</span> (x - 2) * (x - 2);</div>
+<div class="line"><span class="lineno">   82</span>    };</div>
+<div class="line"><span class="lineno">   83</span> </div>
+<div class="line"><span class="lineno">   84</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1.... &quot;</span>;</div>
+<div class="line"><span class="lineno">   85</span> </div>
+<div class="line"><span class="lineno">   86</span>    <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(f1, 1, 5);</div>
+<div class="line"><span class="lineno">   87</span> </div>
+<div class="line"><span class="lineno">   88</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minima &lt;&lt; <span class="stringliteral">&quot;...&quot;</span>;</div>
+<div class="line"><span class="lineno">   89</span> </div>
+<div class="line"><span class="lineno">   90</span>    assert(std::abs(minima - 2) &lt; <a class="code hl_define" href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
+<div class="line"><span class="lineno">   91</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   92</span>}</div>
 <div class="ttc" id="afunction_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a></div></div>
 <div class="ttc" id="agolden__search__extrema_8cpp_html_a1aa76a6d5fd4d333f9072beff1dc486b"><div class="ttname"><a href="../../d6/d7a/golden__search__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a></div><div class="ttdeci">double get_minima(const std::function&lt; double(double)&gt; &amp;f, double lim_a, double lim_b)</div><div class="ttdoc">Get the minima of a function in the given interval. To get the maxima, simply negate the function....</div><div class="ttdef"><b>Definition:</b> golden_search_extrema.cpp:29</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -347,22 +347,22 @@ Here is the call graph for this function:</div>
 
 <p>Test function to find <em>maxima</em> for the function \(f(x)= x^{\frac{1}{x}}\) in the interval \([-2,10]\) <br  />
  Expected result: \(e\approx 2.71828182845904509\). </p>
-<div class="fragment"><div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>             {</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <span class="comment">// define the function to maximize as a lambda function</span></div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <span class="comment">// since we are maximixing, we negated the function return value</span></div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(<span class="keywordtype">double</span>)&gt; func = [](<span class="keywordtype">double</span> x) {</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>        <span class="keywordflow">return</span> -<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(x, 1.f / x);</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    };</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span> </div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2.... &quot;</span>;</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span> </div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(func, -2, 10);</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span> </div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minima &lt;&lt; <span class="stringliteral">&quot; (&quot;</span> &lt;&lt; M_E &lt;&lt; <span class="stringliteral">&quot;)...&quot;</span>;</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span> </div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    assert(std::abs(minima - M_E) &lt; <a class="code hl_define" href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  100</span>             {</div>
+<div class="line"><span class="lineno">  101</span>    <span class="comment">// define the function to maximize as a lambda function</span></div>
+<div class="line"><span class="lineno">  102</span>    <span class="comment">// since we are maximixing, we negated the function return value</span></div>
+<div class="line"><span class="lineno">  103</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(<span class="keywordtype">double</span>)&gt; func = [](<span class="keywordtype">double</span> x) {</div>
+<div class="line"><span class="lineno">  104</span>        <span class="keywordflow">return</span> -<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(x, 1.f / x);</div>
+<div class="line"><span class="lineno">  105</span>    };</div>
+<div class="line"><span class="lineno">  106</span> </div>
+<div class="line"><span class="lineno">  107</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2.... &quot;</span>;</div>
+<div class="line"><span class="lineno">  108</span> </div>
+<div class="line"><span class="lineno">  109</span>    <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(func, -2, 10);</div>
+<div class="line"><span class="lineno">  110</span> </div>
+<div class="line"><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minima &lt;&lt; <span class="stringliteral">&quot; (&quot;</span> &lt;&lt; M_E &lt;&lt; <span class="stringliteral">&quot;)...&quot;</span>;</div>
+<div class="line"><span class="lineno">  112</span> </div>
+<div class="line"><span class="lineno">  113</span>    assert(std::abs(minima - M_E) &lt; <a class="code hl_define" href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
+<div class="line"><span class="lineno">  114</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  115</span>}</div>
 <div class="ttc" id="apow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a></div><div class="ttdeci">T pow(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -390,20 +390,20 @@ Here is the call graph for this function:</div>
 
 <p>Test function to find <em>maxima</em> for the function \(f(x)= \cos x\) in the interval \([0,12]\) <br  />
  Expected result: \(\pi\approx 3.14159265358979312\). </p>
-<div class="fragment"><div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>             {</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    <span class="comment">// define the function to maximize as a lambda function</span></div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>    <span class="comment">// since we are maximixing, we negated the function return value</span></div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(<span class="keywordtype">double</span>)&gt; func = [](<span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a>(x); };</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span> </div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3.... &quot;</span>;</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span> </div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(func, -4, 12);</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span> </div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minima &lt;&lt; <span class="stringliteral">&quot; (&quot;</span> &lt;&lt; M_PI &lt;&lt; <span class="stringliteral">&quot;)...&quot;</span>;</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span> </div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    assert(std::abs(minima - M_PI) &lt; <a class="code hl_define" href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  123</span>             {</div>
+<div class="line"><span class="lineno">  124</span>    <span class="comment">// define the function to maximize as a lambda function</span></div>
+<div class="line"><span class="lineno">  125</span>    <span class="comment">// since we are maximixing, we negated the function return value</span></div>
+<div class="line"><span class="lineno">  126</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(<span class="keywordtype">double</span>)&gt; func = [](<span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a>(x); };</div>
+<div class="line"><span class="lineno">  127</span> </div>
+<div class="line"><span class="lineno">  128</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3.... &quot;</span>;</div>
+<div class="line"><span class="lineno">  129</span> </div>
+<div class="line"><span class="lineno">  130</span>    <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../d6/d7a/golden__search__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(func, -4, 12);</div>
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+<div class="line"><span class="lineno">  132</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minima &lt;&lt; <span class="stringliteral">&quot; (&quot;</span> &lt;&lt; M_PI &lt;&lt; <span class="stringliteral">&quot;)...&quot;</span>;</div>
+<div class="line"><span class="lineno">  133</span> </div>
+<div class="line"><span class="lineno">  134</span>    assert(std::abs(minima - M_PI) &lt; <a class="code hl_define" href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
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 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
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-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> V = 9;</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;int, V&gt;</a>, V&gt; mat = {</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>{5, 3, 0, 0, 7, 0, 0, 0, 0},</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>{6, 0, 0, 1, 9, 5, 0, 0, 0},</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>{0, 9, 8, 0, 0, 0, 0, 6, 0},</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>{8, 0, 0, 0, 6, 0, 0, 0, 3},</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>{4, 0, 0, 8, 0, 3, 0, 0, 1},</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>{7, 0, 0, 0, 2, 0, 0, 0, 6},</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>{0, 6, 0, 0, 0, 0, 2, 8, 0},</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>{0, 0, 0, 4, 1, 9, 0, 0, 5},</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>{0, 0, 0, 0, 8, 0, 0, 7, 9}};</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span> </div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>    backtracking::sudoku_solver::printMat&lt;V&gt;(mat, mat, 9);</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Solution &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;int, V&gt;</a>, V&gt; starting_mat = mat;</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>    backtracking::sudoku_solver::solveSudoku&lt;V&gt;(mat, starting_mat, 0, 0);</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span> </div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  154</span>           {</div>
+<div class="line"><span class="lineno">  155</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> V = 9;</div>
+<div class="line"><span class="lineno">  156</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;int, V&gt;</a>, V&gt; mat = {</div>
+<div class="line"><span class="lineno">  157</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>{5, 3, 0, 0, 7, 0, 0, 0, 0},</div>
+<div class="line"><span class="lineno">  158</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>{6, 0, 0, 1, 9, 5, 0, 0, 0},</div>
+<div class="line"><span class="lineno">  159</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>{0, 9, 8, 0, 0, 0, 0, 6, 0},</div>
+<div class="line"><span class="lineno">  160</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>{8, 0, 0, 0, 6, 0, 0, 0, 3},</div>
+<div class="line"><span class="lineno">  161</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>{4, 0, 0, 8, 0, 3, 0, 0, 1},</div>
+<div class="line"><span class="lineno">  162</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>{7, 0, 0, 0, 2, 0, 0, 0, 6},</div>
+<div class="line"><span class="lineno">  163</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>{0, 6, 0, 0, 0, 0, 2, 8, 0},</div>
+<div class="line"><span class="lineno">  164</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>{0, 0, 0, 4, 1, 9, 0, 0, 5},</div>
+<div class="line"><span class="lineno">  165</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>{0, 0, 0, 0, 8, 0, 0, 7, 9}};</div>
+<div class="line"><span class="lineno">  166</span> </div>
+<div class="line"><span class="lineno">  167</span>    backtracking::sudoku_solver::printMat&lt;V&gt;(mat, mat, 9);</div>
+<div class="line"><span class="lineno">  168</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Solution &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  169</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;int, V&gt;</a>, V&gt; starting_mat = mat;</div>
+<div class="line"><span class="lineno">  170</span>    backtracking::sudoku_solver::solveSudoku&lt;V&gt;(mat, starting_mat, 0, 0);</div>
+<div class="line"><span class="lineno">  171</span> </div>
+<div class="line"><span class="lineno">  172</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  173</span>}</div>
 <div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
@@ -341,25 +341,25 @@ template&lt;size_t V&gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>                                                                        {</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>            <span class="keywordflow">if</span> (starting_mat[i][j] != mat[i][j]) {</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\033[93m&quot;</span> &lt;&lt; mat[i][j] &lt;&lt; <span class="stringliteral">&quot;\033[0m&quot;</span></div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>                          &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; mat[i][j] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>            }</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>            <span class="keywordflow">if</span> ((j + 1) % 3 == 0) {</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="charliteral">&#39;\t&#39;</span>;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>            }</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>        }</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>        <span class="keywordflow">if</span> ((i + 1) % 3 == 0) {</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>        }</div>
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-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>    }</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   78</span>                                                                        {</div>
+<div class="line"><span class="lineno">   79</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">   80</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
+<div class="line"><span class="lineno">   81</span>            <span class="keywordflow">if</span> (starting_mat[i][j] != mat[i][j]) {</div>
+<div class="line"><span class="lineno">   82</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\033[93m&quot;</span> &lt;&lt; mat[i][j] &lt;&lt; <span class="stringliteral">&quot;\033[0m&quot;</span></div>
+<div class="line"><span class="lineno">   83</span>                          &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">   84</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   85</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; mat[i][j] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">   86</span>            }</div>
+<div class="line"><span class="lineno">   87</span>            <span class="keywordflow">if</span> ((j + 1) % 3 == 0) {</div>
+<div class="line"><span class="lineno">   88</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="charliteral">&#39;\t&#39;</span>;</div>
+<div class="line"><span class="lineno">   89</span>            }</div>
+<div class="line"><span class="lineno">   90</span>        }</div>
+<div class="line"><span class="lineno">   91</span>        <span class="keywordflow">if</span> ((i + 1) % 3 == 0) {</div>
+<div class="line"><span class="lineno">   92</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   93</span>        }</div>
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+<div class="line"><span class="lineno">   95</span>    }</div>
+<div class="line"><span class="lineno">   96</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -436,41 +436,41 @@ template&lt;size_t V&gt; </div>
 <p >Place the 'no' - assuming a solution will exist</p>
 <p >Couldn't find a solution loop will place the next <code>no</code>.</p>
 <p ><a class="el" href="../../dd/d4f/class_solution.html">Solution</a> couldn't be found for any of the numbers provided</p>
-<div class="fragment"><div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>                        {<span class="comment"></span></div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span><span class="comment">    /// Base Case</span></div>
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-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span><span class="comment"></span>        printMat&lt;V&gt;(mat, starting_mat, 9);</div>
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-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span><span class="comment"></span> </div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span><span class="comment">    /// Crossed the last  Cell in the row</span></div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span><span class="comment"></span>    <span class="keywordflow">if</span> (j == 9) {</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>        <span class="keywordflow">return</span> solveSudoku&lt;V&gt;(mat, starting_mat, i + 1, 0);</div>
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-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span><span class="comment"></span> </div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span><span class="comment">    /// Blue Cell - Skip</span></div>
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-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>        <span class="keywordflow">return</span> solveSudoku&lt;V&gt;(mat, starting_mat, i, j + 1);</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    }<span class="comment"></span></div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span><span class="comment">    /// White Cell</span></div>
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-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    }<span class="comment"></span></div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span><span class="comment">    /// Solution couldn&#39;t be found for any of the numbers provided</span></div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span><span class="comment"></span>    mat[i][j] = 0;</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  112</span>                        {<span class="comment"></span></div>
+<div class="line"><span class="lineno">  113</span><span class="comment">    /// Base Case</span></div>
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+<div class="line"><span class="lineno">  115</span><span class="comment">        /// Solved for 9 rows already</span></div>
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+<div class="line"><span class="lineno">  129</span><span class="comment">    /// White Cell</span></div>
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-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>            }</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>            <span class="keywordflow">case</span> 4:</div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter element to generate hash = &quot;</span>;</div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hash of &quot;</span> &lt;&lt; key</div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>                          &lt;&lt; <span class="stringliteral">&quot; is = &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a0d90726ed1de7b3d2ae261baed048003">double_hashing::hashFxn</a>(key);</div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>            <span class="keywordflow">case</span> 5:</div>
-<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>                <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a1e901418c759627557eff359b8db38cd">double_hashing::display</a>();</div>
-<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span>            <span class="keywordflow">default</span>:</div>
-<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>                loop = <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>                <span class="comment">// delete[] table;</span></div>
-<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>        }</div>
-<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span>    }</div>
-<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  250</span>           {</div>
+<div class="line"><span class="lineno">  251</span>    <span class="keywordtype">int</span> cmd = 0, <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hash</a> = 0, key = 0;</div>
+<div class="line"><span class="lineno">  252</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the initial size of Hash Table. = &quot;</span>;</div>
+<div class="line"><span class="lineno">  253</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; totalSize;</div>
+<div class="line"><span class="lineno">  254</span>    table = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Entry&gt;</a>(totalSize);</div>
+<div class="line"><span class="lineno">  255</span>    <span class="keywordtype">bool</span> loop = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  256</span>    <span class="keywordflow">while</span> (loop) {</div>
+<div class="line"><span class="lineno">  257</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  258</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;PLEASE CHOOSE -&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  259</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1. Add key. (Numeric only)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  260</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2. Remove key.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  261</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3. Find key.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  262</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4. Generate Hash. (Numeric only)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  263</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;5. Display Hash table.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  264</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;6. Exit.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  265</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; cmd;</div>
+<div class="line"><span class="lineno">  266</span>        <span class="keywordflow">switch</span> (cmd) {</div>
+<div class="line"><span class="lineno">  267</span>            <span class="keywordflow">case</span> 1:</div>
+<div class="line"><span class="lineno">  268</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to add = &quot;</span>;</div>
+<div class="line"><span class="lineno">  269</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
+<div class="line"><span class="lineno">  270</span>                <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a9c652b2e467e5d250dfe3bed83b12560">double_hashing::addInfo</a>(key);</div>
+<div class="line"><span class="lineno">  271</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  272</span>            <span class="keywordflow">case</span> 2:</div>
+<div class="line"><span class="lineno">  273</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to remove = &quot;</span>;</div>
+<div class="line"><span class="lineno">  274</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
+<div class="line"><span class="lineno">  275</span>                <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a5d06e4598569526294f10104875f6824">double_hashing::removalInfo</a>(key);</div>
+<div class="line"><span class="lineno">  276</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  277</span>            <span class="keywordflow">case</span> 3: {</div>
+<div class="line"><span class="lineno">  278</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to search = &quot;</span>;</div>
+<div class="line"><span class="lineno">  279</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
+<div class="line"><span class="lineno">  280</span>                <a class="code hl_struct" href="../../d9/dde/structdouble__hashing_1_1_entry.html">Entry</a> entry = table[<a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a8f8ff4fb018e1bb32d67d8a1885d3200">double_hashing::doubleHash</a>(key, <span class="keyword">true</span>)];</div>
+<div class="line"><span class="lineno">  281</span>                <span class="keywordflow">if</span> (entry.<a class="code hl_variable" href="../../d9/dde/structdouble__hashing_1_1_entry.html#ae114967c89dbba3b754dc4976bba3248">key</a> == double_hashing::notPresent) {</div>
+<div class="line"><span class="lineno">  282</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Key not present&quot;</span>;</div>
+<div class="line"><span class="lineno">  283</span>                }</div>
+<div class="line"><span class="lineno">  284</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  285</span>            }</div>
+<div class="line"><span class="lineno">  286</span>            <span class="keywordflow">case</span> 4:</div>
+<div class="line"><span class="lineno">  287</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter element to generate hash = &quot;</span>;</div>
+<div class="line"><span class="lineno">  288</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
+<div class="line"><span class="lineno">  289</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hash of &quot;</span> &lt;&lt; key</div>
+<div class="line"><span class="lineno">  290</span>                          &lt;&lt; <span class="stringliteral">&quot; is = &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a0d90726ed1de7b3d2ae261baed048003">double_hashing::hashFxn</a>(key);</div>
+<div class="line"><span class="lineno">  291</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  292</span>            <span class="keywordflow">case</span> 5:</div>
+<div class="line"><span class="lineno">  293</span>                <a class="code hl_function" href="../../d0/d65/namespacedouble__hashing.html#a1e901418c759627557eff359b8db38cd">double_hashing::display</a>();</div>
+<div class="line"><span class="lineno">  294</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  295</span>            <span class="keywordflow">default</span>:</div>
+<div class="line"><span class="lineno">  296</span>                loop = <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  297</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  298</span>                <span class="comment">// delete[] table;</span></div>
+<div class="line"><span class="lineno">  299</span>        }</div>
+<div class="line"><span class="lineno">  300</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  301</span>    }</div>
+<div class="line"><span class="lineno">  302</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  303</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
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 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
@@ -278,7 +278,7 @@ bool&#160;</td><td class="memItemRight" valign="bottom"><b>double_hashing::rehas
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- <tr style="height: 56px;">
-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
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-<!-- Generated by Doxygen 1.9.2 -->
+<!-- Generated by Doxygen 1.9.3 -->
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@@ -94,17 +94,17 @@ $(document).ready(function(){initNavTree('d6/d8d/namespacemorse.html','../../');
 </div><!--header-->
 <div class="contents">
 
-<p>Functions for <a href="https://en.wikipedia.org/wiki/Morse_code" target="_blank">Morse Code</a>.  
+<p>Functions for [Morse Code] (<a href="https://en.wikipedia.org/wiki/Morse_code">https://en.wikipedia.org/wiki/Morse_code</a>).  
 <a href="../../d6/d8d/namespacemorse.html#details">More...</a></p>
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-<div class="textblock"><p >Functions for <a href="https://en.wikipedia.org/wiki/Morse_code" target="_blank">Morse Code</a>. </p>
+<div class="textblock"><p >Functions for [Morse Code] (<a href="https://en.wikipedia.org/wiki/Morse_code">https://en.wikipedia.org/wiki/Morse_code</a>). </p>
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+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
+  <td id="projectalign">
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+<!-- Generated by Doxygen 1.9.3 -->
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@@ -149,36 +149,36 @@ Functions</h2></td></tr>
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-<div class="fragment"><div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>                                 {</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    <span class="keywordtype">int</span> number, i;</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span> </div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    <span class="keywordflow">if</span> (argc == 2) {</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>        number = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">atoi</a>(argv[1]);</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the value of n(n starts from 0 ): &quot;</span>;</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; number;</div>
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-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span> </div>
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-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>              &lt;&lt; <span class="stringliteral">&quot;Number of digits: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.num_digits() &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
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+<div class="line"><span class="lineno">   94</span>    } <span class="keywordflow">else</span> {</div>
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+<div class="line"><span class="lineno">   96</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; number;</div>
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+<div class="line"><span class="lineno">  102</span>    <span class="keywordflow">for</span> (i = 2; i &lt;= number; i++) <span class="comment">/* Multiply every number from 2 thru N */</span></div>
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+<div class="line"><span class="lineno">  106</span>        <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(end_time - start_time) / CLOCKS_PER_SEC;</div>
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+<div class="line"><span class="lineno">  108</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; number &lt;&lt; <span class="stringliteral">&quot;! = &quot;</span> &lt;&lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
+<div class="line"><span class="lineno">  109</span>              &lt;&lt; <span class="stringliteral">&quot;Number of digits: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.num_digits() &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
+<div class="line"><span class="lineno">  110</span>              &lt;&lt; <span class="stringliteral">&quot;Time taken: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/fixed.html">std::scientific</a> &lt;&lt; time_taken &lt;&lt; <span class="stringliteral">&quot; s&quot;</span></div>
+<div class="line"><span class="lineno">  111</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  112</span> </div>
+<div class="line"><span class="lineno">  113</span>    <a class="code hl_function" href="../../d6/d9d/large__factorial_8cpp.html#a3f93b60e229b6683e24c4754a7106ee8">test1</a>();</div>
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+<div class="line"><span class="lineno">  116</span> </div>
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 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
@@ -214,34 +214,34 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Test implementation for 10! Result must be 3628800. </p><dl class="section return"><dt>Returns</dt><dd>True if test pass else False </dd></dl>
-<div class="fragment"><div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span>             {</div>
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-<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>    <span class="keywordflow">for</span> (i = 2; i &lt;= number; i++) <span class="comment">/* Multiply every number from 2 thru N */</span></div>
-<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>        result *= i;</div>
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-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>                  &lt;&lt; <span class="stringliteral">&quot; != &quot;</span> &lt;&lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.num_digits() &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span> </div>
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-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
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-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>                      &lt;&lt; <span class="stringliteral">&quot; != &quot;</span> &lt;&lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.digit_char(i) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><span class="lineno">   21</span>    <span class="keywordflow">for</span> (i = 2; i &lt;= number; i++) <span class="comment">/* Multiply every number from 2 thru N */</span></div>
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 <div class="ttc" id="aclassothers_1_1lru__cache_1_1_l_r_u_cache_html_a1aafd0444b410e0fcb66287e9954c893"><div class="ttname"><a href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a1aafd0444b410e0fcb66287e9954c893">others::lru_cache::LRUCache::pageFrame</a></div><div class="ttdeci">uint64_t pageFrame</div><div class="ttdoc">Page frame, or total size of the cache.</div><div class="ttdef"><b>Definition:</b> lru_cache.cpp:68</div></div>
 </div><!-- fragment -->
 </div>
@@ -204,12 +210,12 @@ uint64_t&#160;</td><td class="memItemRight" valign="bottom"><b>pageFrame</b></td
 
 <p>A function to display the current cache. </p>
 <dl class="section return"><dt>Returns</dt><dd>Void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>                   {</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>        <span class="keywordflow">for</span> (uint64_t &amp;it : <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a3ee3560a6b90e6f50f6e063d690ba8e8">cache</a>) {</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; it &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>        }</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  120</span>                   {</div>
+<div class="line"><span class="lineno">  121</span>        <span class="keywordflow">for</span> (uint64_t &amp;it : <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a3ee3560a6b90e6f50f6e063d690ba8e8">cache</a>) {</div>
+<div class="line"><span class="lineno">  122</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; it &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">  123</span>        }</div>
+<div class="line"><span class="lineno">  124</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  125</span>    }</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aclassothers_1_1lru__cache_1_1_l_r_u_cache_html_a3ee3560a6b90e6f50f6e063d690ba8e8"><div class="ttname"><a href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a3ee3560a6b90e6f50f6e063d690ba8e8">others::lru_cache::LRUCache::cache</a></div><div class="ttdeci">std::list&lt; uint64_t &gt; cache</div><div class="ttdoc">Cache linked list (using the STL)</div><div class="ttdef"><b>Definition:</b> lru_cache.cpp:69</div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
@@ -247,7 +253,7 @@ Here is the call graph for this function:</div>
 
 <p>A function to get page hits. </p>
 <dl class="section return"><dt>Returns</dt><dd>int </dd></dl>
-<div class="fragment"><div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a5f33913e7ddfbb38062362e7bd859154">hits</a>; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  130</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a5f33913e7ddfbb38062362e7bd859154">hits</a>; }</div>
 <div class="ttc" id="aclassothers_1_1lru__cache_1_1_l_r_u_cache_html_a5f33913e7ddfbb38062362e7bd859154"><div class="ttname"><a href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a5f33913e7ddfbb38062362e7bd859154">others::lru_cache::LRUCache::hits</a></div><div class="ttdeci">uint64_t hits</div><div class="ttdoc">was found in cache.</div><div class="ttdef"><b>Definition:</b> lru_cache.cpp:73</div></div>
 </div><!-- fragment -->
 </div>
@@ -277,7 +283,7 @@ Here is the call graph for this function:</div>
 
 <p>A function to get page fault. </p>
 <dl class="section return"><dt>Returns</dt><dd>int </dd></dl>
-<div class="fragment"><div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a09cbe562b0c396329607f5d388d57c9c">pageFault</a>; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  135</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a09cbe562b0c396329607f5d388d57c9c">pageFault</a>; }</div>
 <div class="ttc" id="aclassothers_1_1lru__cache_1_1_l_r_u_cache_html_a09cbe562b0c396329607f5d388d57c9c"><div class="ttname"><a href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a09cbe562b0c396329607f5d388d57c9c">others::lru_cache::LRUCache::pageFault</a></div><div class="ttdeci">uint64_t pageFault</div><div class="ttdef"><b>Definition:</b> lru_cache.cpp:76</div></div>
 </div><!-- fragment -->
 </div>
@@ -315,32 +321,46 @@ Here is the call graph for this function:</div>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
 <p >&lt; Increase the page fault by one.</p>
-<div class="fragment"><div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>                              {</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>        <span class="comment">// If the page requested not in cache.</span></div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#aa4d6db56109af196ffc7e5f72bc9907c">pageMap</a>.find(page) == <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#aa4d6db56109af196ffc7e5f72bc9907c">pageMap</a>.end()) {</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>            <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a09cbe562b0c396329607f5d388d57c9c">pageFault</a>++;  <span class="comment">///&lt; Increase the page fault by one.</span></div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span> </div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>            <span class="comment">// Check if the cache is full</span></div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a3ee3560a6b90e6f50f6e063d690ba8e8">cache</a>.size() == <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a1aafd0444b410e0fcb66287e9954c893">pageFrame</a>) {</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>                <span class="comment">// delete the last page from cache</span></div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>                uint64_t lastPage = <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a3ee3560a6b90e6f50f6e063d690ba8e8">cache</a>.back();</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>                <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a3ee3560a6b90e6f50f6e063d690ba8e8">cache</a>.pop_back();</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>                <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#aa4d6db56109af196ffc7e5f72bc9907c">pageMap</a>.erase(lastPage);</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>            }</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        }</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>        <span class="comment">// The requested page is in the cache</span></div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>        <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>            <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a5f33913e7ddfbb38062362e7bd859154">hits</a>++;</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>            <span class="comment">// present in cache, erase from current position to bring in front</span></div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>            <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a3ee3560a6b90e6f50f6e063d690ba8e8">cache</a>.erase(<a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#aa4d6db56109af196ffc7e5f72bc9907c">pageMap</a>[page]);</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>        }</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        <span class="comment">// Push it in the front of the cache and update the page reference in</span></div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>        <span class="comment">// page map.</span></div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>        <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a3ee3560a6b90e6f50f6e063d690ba8e8">cache</a>.push_front(page);</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#aa4d6db56109af196ffc7e5f72bc9907c">pageMap</a>[page] = <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a3ee3560a6b90e6f50f6e063d690ba8e8">cache</a>.begin();</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   91</span>                              {</div>
+<div class="line"><span class="lineno">   92</span>        <span class="comment">// If the page requested not in cache.</span></div>
+<div class="line"><span class="lineno">   93</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#aa4d6db56109af196ffc7e5f72bc9907c">pageMap</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/find.html">find</a>(page) == <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#aa4d6db56109af196ffc7e5f72bc9907c">pageMap</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/end.html">end</a>()) {</div>
+<div class="line"><span class="lineno">   94</span>            <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a09cbe562b0c396329607f5d388d57c9c">pageFault</a>++;  <span class="comment">///&lt; Increase the page fault by one.</span></div>
+<div class="line"><span class="lineno">   95</span> </div>
+<div class="line"><span class="lineno">   96</span>            <span class="comment">// Check if the cache is full</span></div>
+<div class="line"><span class="lineno">   97</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a3ee3560a6b90e6f50f6e063d690ba8e8">cache</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/size.html">size</a>() == <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a1aafd0444b410e0fcb66287e9954c893">pageFrame</a>) {</div>
+<div class="line"><span class="lineno">   98</span>                <span class="comment">// delete the last page from cache</span></div>
+<div class="line"><span class="lineno">   99</span>                uint64_t lastPage = <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a3ee3560a6b90e6f50f6e063d690ba8e8">cache</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/back.html">back</a>();</div>
+<div class="line"><span class="lineno">  100</span>                <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a3ee3560a6b90e6f50f6e063d690ba8e8">cache</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/pop_back.html">pop_back</a>();</div>
+<div class="line"><span class="lineno">  101</span>                <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#aa4d6db56109af196ffc7e5f72bc9907c">pageMap</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/erase.html">erase</a>(lastPage);</div>
+<div class="line"><span class="lineno">  102</span>            }</div>
+<div class="line"><span class="lineno">  103</span>        }</div>
+<div class="line"><span class="lineno">  104</span>        <span class="comment">// The requested page is in the cache</span></div>
+<div class="line"><span class="lineno">  105</span>        <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  106</span>            <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a5f33913e7ddfbb38062362e7bd859154">hits</a>++;</div>
+<div class="line"><span class="lineno">  107</span>            <span class="comment">// present in cache, erase from current position to bring in front</span></div>
+<div class="line"><span class="lineno">  108</span>            <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a3ee3560a6b90e6f50f6e063d690ba8e8">cache</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/erase.html">erase</a>(<a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#aa4d6db56109af196ffc7e5f72bc9907c">pageMap</a>[page]);</div>
+<div class="line"><span class="lineno">  109</span>        }</div>
+<div class="line"><span class="lineno">  110</span>        <span class="comment">// Push it in the front of the cache and update the page reference in</span></div>
+<div class="line"><span class="lineno">  111</span>        <span class="comment">// page map.</span></div>
+<div class="line"><span class="lineno">  112</span>        <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a3ee3560a6b90e6f50f6e063d690ba8e8">cache</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/push_front.html">push_front</a>(page);</div>
+<div class="line"><span class="lineno">  113</span>        <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#aa4d6db56109af196ffc7e5f72bc9907c">pageMap</a>[page] = <a class="code hl_variable" href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#a3ee3560a6b90e6f50f6e063d690ba8e8">cache</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/begin.html">begin</a>();</div>
+<div class="line"><span class="lineno">  114</span>    }</div>
+<div class="ttc" id="aback_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list/back.html">std::list::back</a></div><div class="ttdeci">T back(T... args)</div></div>
+<div class="ttc" id="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list/begin.html">std::list::begin</a></div><div class="ttdeci">T begin(T... args)</div></div>
 <div class="ttc" id="aclassothers_1_1lru__cache_1_1_l_r_u_cache_html_aa4d6db56109af196ffc7e5f72bc9907c"><div class="ttname"><a href="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html#aa4d6db56109af196ffc7e5f72bc9907c">others::lru_cache::LRUCache::pageMap</a></div><div class="ttdeci">std::unordered_map&lt; uint64_t, std::list&lt; uint64_t &gt;::iterator &gt; pageMap</div><div class="ttdoc">Hash map containing pages and their addresses.</div><div class="ttdef"><b>Definition:</b> lru_cache.cpp:71</div></div>
-</div><!-- fragment -->
+<div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/unordered_map/end.html">std::unordered_map::end</a></div><div class="ttdeci">T end(T... args)</div></div>
+<div class="ttc" id="aerase_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/unordered_map/erase.html">std::unordered_map::erase</a></div><div class="ttdeci">T erase(T... args)</div></div>
+<div class="ttc" id="afind_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/unordered_map/find.html">std::unordered_map::find</a></div><div class="ttdeci">T find(T... args)</div></div>
+<div class="ttc" id="apop_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list/pop_back.html">std::list::pop_back</a></div><div class="ttdeci">T pop_back(T... args)</div></div>
+<div class="ttc" id="apush_front_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list/push_front.html">std::list::push_front</a></div><div class="ttdeci">T push_front(T... args)</div></div>
+<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list/size.html">std::list::size</a></div><div class="ttdeci">T size(T... args)</div></div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache_a7dbf04bf7e1472c48639694f0b110602_cgraph.svg" width="356" height="475"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
 </div>
 </div>
 <h2 class="groupheader">Member Data Documentation</h2>
@@ -403,7 +423,7 @@ Here is the call graph for this function:</div>
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-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        <a class="code hl_namespace" href="../../d4/ded/namespaceprobability.html">probability</a> += <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a78d36635232e54b5d71fcbf1eac9a49a">nCr</a>(n, i) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(p, i) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(1 - p, n - i);</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    }</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    <span class="keywordflow">return</span> <a class="code hl_namespace" href="../../d4/ded/namespaceprobability.html">probability</a>;</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   75</span>                                                    {</div>
+<div class="line"><span class="lineno">   76</span>    <span class="keywordtype">double</span> <a class="code hl_namespace" href="../../d4/ded/namespaceprobability.html">probability</a> = 0;</div>
+<div class="line"><span class="lineno">   77</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = lower_bound; i &lt;= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/upper_bound.html">upper_bound</a>; i++) {</div>
+<div class="line"><span class="lineno">   78</span>        <a class="code hl_namespace" href="../../d4/ded/namespaceprobability.html">probability</a> += <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a78d36635232e54b5d71fcbf1eac9a49a">nCr</a>(n, i) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(p, i) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(1 - p, n - i);</div>
+<div class="line"><span class="lineno">   79</span>    }</div>
+<div class="line"><span class="lineno">   80</span>    <span class="keywordflow">return</span> <a class="code hl_namespace" href="../../d4/ded/namespaceprobability.html">probability</a>;</div>
+<div class="line"><span class="lineno">   81</span>}</div>
 <div class="ttc" id="abinomial__dist_8cpp_html_a78d36635232e54b5d71fcbf1eac9a49a"><div class="ttname"><a href="../../d6/db0/binomial__dist_8cpp.html#a78d36635232e54b5d71fcbf1eac9a49a">nCr</a></div><div class="ttdeci">double nCr(double n, double r)</div><div class="ttdef"><b>Definition:</b> binomial_dist.cpp:47</div></div>
 <div class="ttc" id="anamespaceprobability_html"><div class="ttname"><a href="../../d4/ded/namespaceprobability.html">probability</a></div><div class="ttdoc">Probability algorithms.</div></div>
 <div class="ttc" id="apow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a></div><div class="ttdeci">T pow(T... args)</div></div>
@@ -261,9 +261,9 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>\(\sigma = \sqrt{\sigma^2} = \sqrt{n\cdot p\cdot (1-p)}\) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>                                                       {</div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(<a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a>(n, p));</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   36</span>                                                       {</div>
+<div class="line"><span class="lineno">   37</span>    <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(<a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a>(n, p));</div>
+<div class="line"><span class="lineno">   38</span>}</div>
 <div class="ttc" id="abinomial__dist_8cpp_html_acd4dd4558031e4c5d045c801f73d8861"><div class="ttname"><a href="../../d6/db0/binomial__dist_8cpp.html#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a></div><div class="ttdeci">double binomial_variance(double n, double p)</div><div class="ttdef"><b>Definition:</b> binomial_dist.cpp:29</div></div>
 <div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -308,7 +308,7 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>\(\sigma^2 = n\cdot p\cdot (1-p)\) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>{ <span class="keywordflow">return</span> n * p * (1 - p); }</div>
+<div class="fragment"><div class="line"><span class="lineno">   29</span>{ <span class="keywordflow">return</span> n * p * (1 - p); }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -344,9 +344,9 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >calculates the probability of exactly x successes </p><dl class="section return"><dt>Returns</dt><dd>\(\displaystyle P(n,p,x) = {n\choose x} p^x (1-p)^{n-x}\) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>                                                          {</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a78d36635232e54b5d71fcbf1eac9a49a">nCr</a>(n, x) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(p, x) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(1 - p, n - x);</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   65</span>                                                          {</div>
+<div class="line"><span class="lineno">   66</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a78d36635232e54b5d71fcbf1eac9a49a">nCr</a>(n, x) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(p, x) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(1 - p, n - x);</div>
+<div class="line"><span class="lineno">   67</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -372,23 +372,23 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >main function </p>
-<div class="fragment"><div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>           {</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;expected value : &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a4416a7bc7fa87201883c54cdc4c82813">binomial_expected</a>(100, 0.5)</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span> </div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;variance : &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a>(100, 0.5) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span> </div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;standard deviation : &quot;</span></div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>              &lt;&lt; <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#af09e51f513cee647d41192ab0a872cdc">binomial_standard_deviation</a>(100, 0.5) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span> </div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;exactly 30 successes : &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a19ae0a6a2bd200fd1eb0e31b2bf4cc76">binomial_x_successes</a>(100, 0.5, 30)</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span> </div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;45 or more successes : &quot;</span></div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>              &lt;&lt; <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a76ed6ce71415fb400b65f0656cef3d25">binomial_range_successes</a>(100, 0.5, 45, 100) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span> </div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   84</span>           {</div>
+<div class="line"><span class="lineno">   85</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;expected value : &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a4416a7bc7fa87201883c54cdc4c82813">binomial_expected</a>(100, 0.5)</div>
+<div class="line"><span class="lineno">   86</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   87</span> </div>
+<div class="line"><span class="lineno">   88</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;variance : &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a>(100, 0.5) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   89</span> </div>
+<div class="line"><span class="lineno">   90</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;standard deviation : &quot;</span></div>
+<div class="line"><span class="lineno">   91</span>              &lt;&lt; <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#af09e51f513cee647d41192ab0a872cdc">binomial_standard_deviation</a>(100, 0.5) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   92</span> </div>
+<div class="line"><span class="lineno">   93</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;exactly 30 successes : &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a19ae0a6a2bd200fd1eb0e31b2bf4cc76">binomial_x_successes</a>(100, 0.5, 30)</div>
+<div class="line"><span class="lineno">   94</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   95</span> </div>
+<div class="line"><span class="lineno">   96</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;45 or more successes : &quot;</span></div>
+<div class="line"><span class="lineno">   97</span>              &lt;&lt; <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a76ed6ce71415fb400b65f0656cef3d25">binomial_range_successes</a>(100, 0.5, 45, 100) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   98</span> </div>
+<div class="line"><span class="lineno">   99</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  100</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="abinomial__dist_8cpp_html_a19ae0a6a2bd200fd1eb0e31b2bf4cc76"><div class="ttname"><a href="../../d6/db0/binomial__dist_8cpp.html#a19ae0a6a2bd200fd1eb0e31b2bf4cc76">binomial_x_successes</a></div><div class="ttdeci">double binomial_x_successes(double n, double p, double x)</div><div class="ttdef"><b>Definition:</b> binomial_dist.cpp:65</div></div>
 <div class="ttc" id="abinomial__dist_8cpp_html_a4416a7bc7fa87201883c54cdc4c82813"><div class="ttname"><a href="../../d6/db0/binomial__dist_8cpp.html#a4416a7bc7fa87201883c54cdc4c82813">binomial_expected</a></div><div class="ttdeci">double binomial_expected(double n, double p)</div><div class="ttdef"><b>Definition:</b> binomial_dist.cpp:22</div></div>
@@ -437,20 +437,20 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>\(\displaystyle {n\choose r} = \frac{n!}{r!(n-r)!} = \frac{n\times(n-1)\times(n-2)\times\cdots(n-r)}{r!} \) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>                               {</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <span class="keywordtype">double</span> numerator = n;</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    <span class="keywordtype">double</span> denominator = r;</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span> </div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = n - 1; i &gt;= ((n - r) + 1); i--) {</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>        numerator *= i;</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    }</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span> </div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt; r; i++) {</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>        denominator *= i;</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    }</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span> </div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <span class="keywordflow">return</span> numerator / denominator;</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   47</span>                               {</div>
+<div class="line"><span class="lineno">   48</span>    <span class="keywordtype">double</span> numerator = n;</div>
+<div class="line"><span class="lineno">   49</span>    <span class="keywordtype">double</span> denominator = r;</div>
+<div class="line"><span class="lineno">   50</span> </div>
+<div class="line"><span class="lineno">   51</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = n - 1; i &gt;= ((n - r) + 1); i--) {</div>
+<div class="line"><span class="lineno">   52</span>        numerator *= i;</div>
+<div class="line"><span class="lineno">   53</span>    }</div>
+<div class="line"><span class="lineno">   54</span> </div>
+<div class="line"><span class="lineno">   55</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt; r; i++) {</div>
+<div class="line"><span class="lineno">   56</span>        denominator *= i;</div>
+<div class="line"><span class="lineno">   57</span>    }</div>
+<div class="line"><span class="lineno">   58</span> </div>
+<div class="line"><span class="lineno">   59</span>    <span class="keywordflow">return</span> numerator / denominator;</div>
+<div class="line"><span class="lineno">   60</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -460,7 +460,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_82e494173a87936756866de2fa774307.html">probability</a></li><li class="navelem"><a class="el" href="../../d6/db0/binomial__dist_8cpp.html">binomial_dist.cpp</a></li>
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+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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diff --git a/d6/db0/binomial__dist_8cpp_a19ae0a6a2bd200fd1eb0e31b2bf4cc76_cgraph.map b/d6/db0/binomial__dist_8cpp_a19ae0a6a2bd200fd1eb0e31b2bf4cc76_cgraph.map
index ce41bdc85..85d4afbfc 100644
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-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   28</span>                           {</div>
+<div class="line"><span class="lineno">   29</span>    <span class="keyword">using</span> Tint = <span class="keyword">typename</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/conditional.html">std::conditional</a>&lt;<span class="keyword">sizeof</span>(T) == 8, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int64_t</a>,</div>
+<div class="line"><span class="lineno">   30</span>                                           <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int32_t</a>&gt;::type;</div>
+<div class="line"><span class="lineno">   31</span>    T y = x;</div>
+<div class="line"><span class="lineno">   32</span>    T x2 = y * 0.5;</div>
+<div class="line"><span class="lineno">   33</span> </div>
+<div class="line"><span class="lineno">   34</span>    Tint i =</div>
+<div class="line"><span class="lineno">   35</span>        *<span class="keyword">reinterpret_cast&lt;</span>Tint *<span class="keyword">&gt;</span>(&amp;y);  <span class="comment">// Store floating-point bits in integer</span></div>
+<div class="line"><span class="lineno">   36</span> </div>
+<div class="line"><span class="lineno">   37</span>    i = (<span class="keyword">sizeof</span>(T) == 8 ? 0x5fe6eb50c7b537a9 : 0x5f3759df) -</div>
+<div class="line"><span class="lineno">   38</span>        (i &gt;&gt; 1);  <span class="comment">// Initial guess for Newton&#39;s method</span></div>
+<div class="line"><span class="lineno">   39</span> </div>
+<div class="line"><span class="lineno">   40</span>    y = *<span class="keyword">reinterpret_cast&lt;</span>T *<span class="keyword">&gt;</span>(&amp;i);  <span class="comment">// Convert new bits into float</span></div>
+<div class="line"><span class="lineno">   41</span> </div>
+<div class="line"><span class="lineno">   42</span>    y = y * (1.5 - (x2 * y * y));  <span class="comment">// 1st iteration Newton&#39;s method</span></div>
+<div class="line"><span class="lineno">   43</span>    <span class="keywordflow">if</span> (iterations == 2) {</div>
+<div class="line"><span class="lineno">   44</span>        y = y * (1.5 - (x2 * y * y));  <span class="comment">// 2nd iteration, the more exact result</span></div>
+<div class="line"><span class="lineno">   45</span>    }</div>
+<div class="line"><span class="lineno">   46</span>    <span class="keywordflow">return</span> y;</div>
+<div class="line"><span class="lineno">   47</span>}</div>
 <div class="ttc" id="aconditional_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/conditional.html">std::conditional</a></div></div>
 <div class="ttc" id="ainteger_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/integer.html">std::int64_t</a></div></div>
 </div><!-- fragment -->
@@ -215,23 +215,23 @@ template&lt;typename T  = double, char iterations = 2&gt; </div>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>           {</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    <a class="code hl_function" href="../../d6/db8/inv__sqrt_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The Fast inverse square root of 36 is: &quot;</span></div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>              &lt;&lt; Fast_InvSqrt&lt;float, 1&gt;(36.0f) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The Fast inverse square root of 36 is: &quot;</span></div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>              &lt;&lt; Fast_InvSqrt&lt;double, 2&gt;(36.0f) &lt;&lt; <span class="stringliteral">&quot; (2 iterations)&quot;</span></div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The Fast inverse square root of 100 is: &quot;</span></div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>              &lt;&lt; <a class="code hl_function" href="../../d6/db8/inv__sqrt_8cpp.html#ad219034bf5fba657f5035ec5a1d50f52">Fast_InvSqrt</a>(100.0f)</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>              &lt;&lt; <span class="stringliteral">&quot; (With default template type and iterations: double, 2)&quot;</span></div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The Standard inverse square root of 36 is: &quot;</span></div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>              &lt;&lt; Standard_InvSqrt&lt;float&gt;(36.0f) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The Standard inverse square root of 100 is: &quot;</span></div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>              &lt;&lt; <a class="code hl_function" href="../../d6/db8/inv__sqrt_8cpp.html#aa2703e5cf3fecde8becd9066b9666b97">Standard_InvSqrt</a>(100.0f)</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>              &lt;&lt; <span class="stringliteral">&quot; (With default template type: double)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   87</span>           {</div>
+<div class="line"><span class="lineno">   88</span>    <a class="code hl_function" href="../../d6/db8/inv__sqrt_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
+<div class="line"><span class="lineno">   89</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The Fast inverse square root of 36 is: &quot;</span></div>
+<div class="line"><span class="lineno">   90</span>              &lt;&lt; Fast_InvSqrt&lt;float, 1&gt;(36.0f) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   91</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The Fast inverse square root of 36 is: &quot;</span></div>
+<div class="line"><span class="lineno">   92</span>              &lt;&lt; Fast_InvSqrt&lt;double, 2&gt;(36.0f) &lt;&lt; <span class="stringliteral">&quot; (2 iterations)&quot;</span></div>
+<div class="line"><span class="lineno">   93</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   94</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The Fast inverse square root of 100 is: &quot;</span></div>
+<div class="line"><span class="lineno">   95</span>              &lt;&lt; <a class="code hl_function" href="../../d6/db8/inv__sqrt_8cpp.html#ad219034bf5fba657f5035ec5a1d50f52">Fast_InvSqrt</a>(100.0f)</div>
+<div class="line"><span class="lineno">   96</span>              &lt;&lt; <span class="stringliteral">&quot; (With default template type and iterations: double, 2)&quot;</span></div>
+<div class="line"><span class="lineno">   97</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   98</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The Standard inverse square root of 36 is: &quot;</span></div>
+<div class="line"><span class="lineno">   99</span>              &lt;&lt; Standard_InvSqrt&lt;float&gt;(36.0f) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  100</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The Standard inverse square root of 100 is: &quot;</span></div>
+<div class="line"><span class="lineno">  101</span>              &lt;&lt; <a class="code hl_function" href="../../d6/db8/inv__sqrt_8cpp.html#aa2703e5cf3fecde8becd9066b9666b97">Standard_InvSqrt</a>(100.0f)</div>
+<div class="line"><span class="lineno">  102</span>              &lt;&lt; <span class="stringliteral">&quot; (With default template type: double)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  103</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
 <div class="ttc" id="ainv__sqrt_8cpp_html_aa2703e5cf3fecde8becd9066b9666b97"><div class="ttname"><a href="../../d6/db8/inv__sqrt_8cpp.html#aa2703e5cf3fecde8becd9066b9666b97">Standard_InvSqrt</a></div><div class="ttdeci">T Standard_InvSqrt(T number)</div><div class="ttdoc">This is the function that calculates the fast inverse square root. The following code is the fast inv...</div><div class="ttdef"><b>Definition:</b> inv_sqrt.cpp:59</div></div>
@@ -278,10 +278,10 @@ template&lt;typename T  = double&gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>the inverse square root </dd></dl>
-<div class="fragment"><div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>                             {</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    T squareRoot = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">sqrt</a>(number);</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    <span class="keywordflow">return</span> 1.0f / squareRoot;</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   59</span>                             {</div>
+<div class="line"><span class="lineno">   60</span>    T squareRoot = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">sqrt</a>(number);</div>
+<div class="line"><span class="lineno">   61</span>    <span class="keywordflow">return</span> 1.0f / squareRoot;</div>
+<div class="line"><span class="lineno">   62</span>}</div>
 <div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
 </div><!-- fragment -->
 </div>
@@ -311,20 +311,20 @@ template&lt;typename T  = double&gt; </div>
 
 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>                   {</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    <span class="keyword">const</span> <span class="keywordtype">float</span> epsilon = 1e-3f;</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span> </div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    <span class="comment">/* Tests with multiple values */</span></div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(Standard_InvSqrt&lt;float&gt;(100.0f) - 0.0998449f) &lt; epsilon);</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(Standard_InvSqrt&lt;double&gt;(36.0f) - 0.166667f) &lt; epsilon);</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(<a class="code hl_function" href="../../d6/db8/inv__sqrt_8cpp.html#aa2703e5cf3fecde8becd9066b9666b97">Standard_InvSqrt</a>(12.0f) - 0.288423f) &lt; epsilon);</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(Standard_InvSqrt&lt;double&gt;(5.0f) - 0.447141f) &lt; epsilon);</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span> </div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(Fast_InvSqrt&lt;float, 1&gt;(100.0f) - 0.0998449f) &lt; epsilon);</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(Fast_InvSqrt&lt;double, 1&gt;(36.0f) - 0.166667f) &lt; epsilon);</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(<a class="code hl_function" href="../../d6/db8/inv__sqrt_8cpp.html#ad219034bf5fba657f5035ec5a1d50f52">Fast_InvSqrt</a>(12.0f) - 0.288423) &lt; epsilon);</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(Fast_InvSqrt&lt;double&gt;(5.0f) - 0.447141) &lt; epsilon);</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   68</span>                   {</div>
+<div class="line"><span class="lineno">   69</span>    <span class="keyword">const</span> <span class="keywordtype">float</span> epsilon = 1e-3f;</div>
+<div class="line"><span class="lineno">   70</span> </div>
+<div class="line"><span class="lineno">   71</span>    <span class="comment">/* Tests with multiple values */</span></div>
+<div class="line"><span class="lineno">   72</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(Standard_InvSqrt&lt;float&gt;(100.0f) - 0.0998449f) &lt; epsilon);</div>
+<div class="line"><span class="lineno">   73</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(Standard_InvSqrt&lt;double&gt;(36.0f) - 0.166667f) &lt; epsilon);</div>
+<div class="line"><span class="lineno">   74</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(<a class="code hl_function" href="../../d6/db8/inv__sqrt_8cpp.html#aa2703e5cf3fecde8becd9066b9666b97">Standard_InvSqrt</a>(12.0f) - 0.288423f) &lt; epsilon);</div>
+<div class="line"><span class="lineno">   75</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(Standard_InvSqrt&lt;double&gt;(5.0f) - 0.447141f) &lt; epsilon);</div>
+<div class="line"><span class="lineno">   76</span> </div>
+<div class="line"><span class="lineno">   77</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(Fast_InvSqrt&lt;float, 1&gt;(100.0f) - 0.0998449f) &lt; epsilon);</div>
+<div class="line"><span class="lineno">   78</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(Fast_InvSqrt&lt;double, 1&gt;(36.0f) - 0.166667f) &lt; epsilon);</div>
+<div class="line"><span class="lineno">   79</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(<a class="code hl_function" href="../../d6/db8/inv__sqrt_8cpp.html#ad219034bf5fba657f5035ec5a1d50f52">Fast_InvSqrt</a>(12.0f) - 0.288423) &lt; epsilon);</div>
+<div class="line"><span class="lineno">   80</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(Fast_InvSqrt&lt;double&gt;(5.0f) - 0.447141) &lt; epsilon);</div>
+<div class="line"><span class="lineno">   81</span>}</div>
 <div class="ttc" id="afabs_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a></div><div class="ttdeci">T fabs(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -341,7 +341,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d6/db8/inv__sqrt_8cpp.html">inv_sqrt.cpp</a></li>
-    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.2 </li>
+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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diff --git a/d6/db8/inv__sqrt_8cpp_aa8dca7b867074164d5f45b0f3851269d_cgraph.map b/d6/db8/inv__sqrt_8cpp_aa8dca7b867074164d5f45b0f3851269d_cgraph.map
index 6cce02b43..01c109ff8 100644
--- a/d6/db8/inv__sqrt_8cpp_aa8dca7b867074164d5f45b0f3851269d_cgraph.map
+++ b/d6/db8/inv__sqrt_8cpp_aa8dca7b867074164d5f45b0f3851269d_cgraph.map
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  <a href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#details">More...</a></p>
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 <table class="memberdecls">
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 <p>the p from (nCr % p) </p>
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 <p >Finds the value of x, y such that a*x + b*y = gcd(a,b)</p>
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 <p >Find modular inverse of a with m i.e. a number x such that (a*x)m = 1</p>
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+<div class="fragment"><div class="line"><span class="lineno">   76</span>                                                             {</div>
+<div class="line"><span class="lineno">   77</span>        int64_t x = 0, y = 0;</div>
+<div class="line"><span class="lineno">   78</span>        uint64_t <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = <a class="code hl_function" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#afde201f4687740454302c444f507a926">gcdExtended</a>(a, m, &amp;x, &amp;y);</div>
+<div class="line"><span class="lineno">   79</span>        <span class="keywordflow">if</span> (g != 1) {  <span class="comment">// modular inverse doesn&#39;t exist</span></div>
+<div class="line"><span class="lineno">   80</span>            <span class="keywordflow">return</span> -1;</div>
+<div class="line"><span class="lineno">   81</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   82</span>            int64_t res = ((x + m) % m);</div>
+<div class="line"><span class="lineno">   83</span>            <span class="keywordflow">return</span> res;</div>
+<div class="line"><span class="lineno">   84</span>        }</div>
+<div class="line"><span class="lineno">   85</span>    }</div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a2f67508d5f392b0321772169342c98ad"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">numerical_methods::simpson_method::g</a></div><div class="ttdeci">double g(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:115</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -343,28 +349,28 @@ Here is the call graph for this function:</div>
 </div><div class="memdoc">
 <p >Find nCr % p</p>
 <p >@params[in] the numbers 'n', 'r' and 'p' </p><dl class="section return"><dt>Returns</dt><dd>the value nCr % p </dd></dl>
-<div class="fragment"><div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>                                                                         {</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>        <span class="comment">// Base cases</span></div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>        <span class="keywordflow">if</span> (r &gt; n) {</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>            <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>        }</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>        <span class="keywordflow">if</span> (r == 1) {</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>            <span class="keywordflow">return</span> n % <a class="code hl_variable" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a57c168cd6eb85718eab97da658a698ad">p</a>;</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>        }</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>        <span class="keywordflow">if</span> (r == 0 || r == n) {</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>            <span class="keywordflow">return</span> 1;</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>        }</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        <span class="comment">// fac is a global array with fac[r] = (r! % p)</span></div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>        int64_t denominator = <a class="code hl_function" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a0431ec5c876e1154d8e1e5f89e1ab34a">modInverse</a>(fac[r], <a class="code hl_variable" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a57c168cd6eb85718eab97da658a698ad">p</a>);</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>        <span class="keywordflow">if</span> (denominator &lt; 0) {  <span class="comment">// modular inverse doesn&#39;t exist</span></div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>            <span class="keywordflow">return</span> -1;</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>        }</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>        denominator = (denominator * <a class="code hl_function" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a0431ec5c876e1154d8e1e5f89e1ab34a">modInverse</a>(fac[n - r], <a class="code hl_variable" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a57c168cd6eb85718eab97da658a698ad">p</a>)) % <a class="code hl_variable" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a57c168cd6eb85718eab97da658a698ad">p</a>;</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>        <span class="keywordflow">if</span> (denominator &lt; 0) {  <span class="comment">// modular inverse doesn&#39;t exist</span></div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>            <span class="keywordflow">return</span> -1;</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>        }</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>        <span class="keywordflow">return</span> (fac[n] * denominator) % <a class="code hl_variable" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a57c168cd6eb85718eab97da658a698ad">p</a>;</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   92</span>                                                                         {</div>
+<div class="line"><span class="lineno">   93</span>        <span class="comment">// Base cases</span></div>
+<div class="line"><span class="lineno">   94</span>        <span class="keywordflow">if</span> (r &gt; n) {</div>
+<div class="line"><span class="lineno">   95</span>            <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">   96</span>        }</div>
+<div class="line"><span class="lineno">   97</span>        <span class="keywordflow">if</span> (r == 1) {</div>
+<div class="line"><span class="lineno">   98</span>            <span class="keywordflow">return</span> n % <a class="code hl_variable" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a57c168cd6eb85718eab97da658a698ad">p</a>;</div>
+<div class="line"><span class="lineno">   99</span>        }</div>
+<div class="line"><span class="lineno">  100</span>        <span class="keywordflow">if</span> (r == 0 || r == n) {</div>
+<div class="line"><span class="lineno">  101</span>            <span class="keywordflow">return</span> 1;</div>
+<div class="line"><span class="lineno">  102</span>        }</div>
+<div class="line"><span class="lineno">  103</span>        <span class="comment">// fac is a global array with fac[r] = (r! % p)</span></div>
+<div class="line"><span class="lineno">  104</span>        int64_t denominator = <a class="code hl_function" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a0431ec5c876e1154d8e1e5f89e1ab34a">modInverse</a>(fac[r], <a class="code hl_variable" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a57c168cd6eb85718eab97da658a698ad">p</a>);</div>
+<div class="line"><span class="lineno">  105</span>        <span class="keywordflow">if</span> (denominator &lt; 0) {  <span class="comment">// modular inverse doesn&#39;t exist</span></div>
+<div class="line"><span class="lineno">  106</span>            <span class="keywordflow">return</span> -1;</div>
+<div class="line"><span class="lineno">  107</span>        }</div>
+<div class="line"><span class="lineno">  108</span>        denominator = (denominator * <a class="code hl_function" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a0431ec5c876e1154d8e1e5f89e1ab34a">modInverse</a>(fac[n - r], <a class="code hl_variable" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a57c168cd6eb85718eab97da658a698ad">p</a>)) % <a class="code hl_variable" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a57c168cd6eb85718eab97da658a698ad">p</a>;</div>
+<div class="line"><span class="lineno">  109</span>        <span class="keywordflow">if</span> (denominator &lt; 0) {  <span class="comment">// modular inverse doesn&#39;t exist</span></div>
+<div class="line"><span class="lineno">  110</span>            <span class="keywordflow">return</span> -1;</div>
+<div class="line"><span class="lineno">  111</span>        }</div>
+<div class="line"><span class="lineno">  112</span>        <span class="keywordflow">return</span> (fac[n] * denominator) % <a class="code hl_variable" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a57c168cd6eb85718eab97da658a698ad">p</a>;</div>
+<div class="line"><span class="lineno">  113</span>    }</div>
 <div class="ttc" id="aclassmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p_html_a0431ec5c876e1154d8e1e5f89e1ab34a"><div class="ttname"><a href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a0431ec5c876e1154d8e1e5f89e1ab34a">math::ncr_modulo_p::NCRModuloP::modInverse</a></div><div class="ttdeci">int64_t modInverse(const uint64_t &amp;a, const uint64_t &amp;m)</div><div class="ttdef"><b>Definition:</b> ncr_modulo_p.cpp:76</div></div>
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 Here is the call graph for this function:</div>
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@@ -30,8 +30,8 @@ MathJax.Hub.Config({
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- <tr style="height: 56px;">
-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
+  <td id="projectalign">
    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
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    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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-<!-- Generated by Doxygen 1.9.2 -->
+<!-- Generated by Doxygen 1.9.3 -->
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@@ -124,7 +124,7 @@ Contributor</h2>
 - Make sure the file extensions should be &lt;tt&gt;*.hpp&lt;/tt&gt;, &lt;tt&gt;*.h&lt;/tt&gt; or &lt;tt&gt;*.cpp&lt;/tt&gt;.
 - Don't use **&lt;tt&gt;bits/stdc++.h&lt;/tt&gt;** because this is quite Linux-specific and slows down the compilation process.
 - Organize your code using **&lt;tt&gt;struct&lt;/tt&gt;**, **&lt;tt&gt;class&lt;/tt&gt;**, and/or **&lt;tt&gt;namespace&lt;/tt&gt;** keywords.
-- If an implementation of the algorithm already exists, please refer to the &lt;a href="#new-file-name-guidelines" target="_blank" &gt;file-name section below&lt;/a&gt;.
+- If an implementation of the algorithm already exists, please refer to the @ref new-file-name-guidelines "file-name section below".
 - You can suggest reasonable changes to existing algorithms.
 - Strictly use snake_case (underscore_separated) in filenames.
 - If you have added or modified code, please make sure the code compiles before submitting.
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+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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diff --git a/d6/dce/rabin__karp_8cpp.html b/d6/dce/rabin__karp_8cpp.html
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@@ -30,8 +30,8 @@ MathJax.Hub.Config({
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 <table cellspacing="0" cellpadding="0">
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- <tr style="height: 56px;">
-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
+  <td id="projectalign">
    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
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    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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@@ -156,13 +156,13 @@ Functions</h2></td></tr>
       </table>
 </div><div class="memdoc">
 <p >Main function </p>
-<div class="fragment"><div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>               {</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    assert(<a class="code hl_function" href="../../d9/d03/namespacestring__search.html#a21c673d56cbf67b1d2ee4d869185b7d9">rabin_karp</a>(<span class="stringliteral">&quot;helloWorld&quot;</span>, <span class="stringliteral">&quot;world&quot;</span>) == -1);</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    assert(<a class="code hl_function" href="../../d9/d03/namespacestring__search.html#a21c673d56cbf67b1d2ee4d869185b7d9">rabin_karp</a>(<span class="stringliteral">&quot;helloWorld&quot;</span>, <span class="stringliteral">&quot;World&quot;</span>) == 5);</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    assert(<a class="code hl_function" href="../../d9/d03/namespacestring__search.html#a21c673d56cbf67b1d2ee4d869185b7d9">rabin_karp</a>(<span class="stringliteral">&quot;this_is_c++&quot;</span>, <span class="stringliteral">&quot;c++&quot;</span>) == 8);</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    assert(<a class="code hl_function" href="../../d9/d03/namespacestring__search.html#a21c673d56cbf67b1d2ee4d869185b7d9">rabin_karp</a>(<span class="stringliteral">&quot;happy_coding&quot;</span>, <span class="stringliteral">&quot;happy&quot;</span>) == 0);</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  105</span>               {</div>
+<div class="line"><span class="lineno">  106</span>    assert(<a class="code hl_function" href="../../d9/d03/namespacestring__search.html#a21c673d56cbf67b1d2ee4d869185b7d9">rabin_karp</a>(<span class="stringliteral">&quot;helloWorld&quot;</span>, <span class="stringliteral">&quot;world&quot;</span>) == -1);</div>
+<div class="line"><span class="lineno">  107</span>    assert(<a class="code hl_function" href="../../d9/d03/namespacestring__search.html#a21c673d56cbf67b1d2ee4d869185b7d9">rabin_karp</a>(<span class="stringliteral">&quot;helloWorld&quot;</span>, <span class="stringliteral">&quot;World&quot;</span>) == 5);</div>
+<div class="line"><span class="lineno">  108</span>    assert(<a class="code hl_function" href="../../d9/d03/namespacestring__search.html#a21c673d56cbf67b1d2ee4d869185b7d9">rabin_karp</a>(<span class="stringliteral">&quot;this_is_c++&quot;</span>, <span class="stringliteral">&quot;c++&quot;</span>) == 8);</div>
+<div class="line"><span class="lineno">  109</span>    assert(<a class="code hl_function" href="../../d9/d03/namespacestring__search.html#a21c673d56cbf67b1d2ee4d869185b7d9">rabin_karp</a>(<span class="stringliteral">&quot;happy_coding&quot;</span>, <span class="stringliteral">&quot;happy&quot;</span>) == 0);</div>
+<div class="line"><span class="lineno">  110</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  111</span>}</div>
 <div class="ttc" id="anamespacestring__search_html_a21c673d56cbf67b1d2ee4d869185b7d9"><div class="ttname"><a href="../../d9/d03/namespacestring__search.html#a21c673d56cbf67b1d2ee4d869185b7d9">string_search::rabin_karp</a></div><div class="ttdeci">int rabin_karp(const std::string &amp;str, const std::string &amp;pat)</div><div class="ttdef"><b>Definition:</b> rabin_karp.cpp:83</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -179,7 +179,7 @@ Here is the call graph for this function:</div>
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 <p >Main function </p>
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 <p >creating graph G2 with 3 vertices</p>
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@@ -159,10 +159,10 @@ Algorithm</h3>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>           {</div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>    <a class="code hl_function" href="../../d7/d00/list__array_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// Execute the tests</span></div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  247</span>           {</div>
+<div class="line"><span class="lineno">  248</span>    <a class="code hl_function" href="../../d7/d00/list__array_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// Execute the tests</span></div>
+<div class="line"><span class="lineno">  249</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  250</span>}</div>
 <div class="ttc" id="alist__array_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d7/d00/list__array_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Test implementations.</div><div class="ttdef"><b>Definition:</b> list_array.cpp:205</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -198,43 +198,43 @@ Here is the call graph for this function:</div>
 
 <p>Test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>                   {</div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    <a class="code hl_struct" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html">data_structures::list_array::list</a> L;</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span> </div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    <span class="comment">// Insert testing</span></div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0f44d5e3a52d35f8ff23ace9569c6305">insert</a>(11);</div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0f44d5e3a52d35f8ff23ace9569c6305">insert</a>(12);</div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>    assert(L.top == 2);</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0f44d5e3a52d35f8ff23ace9569c6305">insert</a>(15);</div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0f44d5e3a52d35f8ff23ace9569c6305">insert</a>(10);</div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0f44d5e3a52d35f8ff23ace9569c6305">insert</a>(12);</div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0f44d5e3a52d35f8ff23ace9569c6305">insert</a>(20);</div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0f44d5e3a52d35f8ff23ace9569c6305">insert</a>(18);</div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>    assert(L.top == 7);</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#ae5c15d93819c4e437ebb7a1b41f2d594">show</a>(); <span class="comment">// To print the array</span></div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span> </div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>    <span class="comment">// Remove testing</span></div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0499455a80156134cc79c98eabb376d9">remove</a>(12); <span class="comment">// Remove Duplicate value in the list</span></div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0499455a80156134cc79c98eabb376d9">remove</a>(15); <span class="comment">// Remove the existing value in the list</span></div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>    assert(L.top == 5);</div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0499455a80156134cc79c98eabb376d9">remove</a>(50); <span class="comment">// Try to remove the non-existing value in the list</span></div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>    assert(L.top == 5);</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span> </div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>    <span class="comment">// LinearSearch testing</span></div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    assert(L.search(11) == 0); <span class="comment">// search for the existing element</span></div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>    assert(L.search(12) == 2);</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>    assert(L.search(50) == -1); <span class="comment">// search for the non-existing element</span></div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span> </div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>    <span class="comment">// Sort testing</span></div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a39a712c8413b0d7861695ec019474469">sort</a>();</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>    assert(L.isSorted == <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#ae5c15d93819c4e437ebb7a1b41f2d594">show</a>();</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span> </div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>    <span class="comment">// BinarySearch testing</span></div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>    assert(L.search(11) == 1); <span class="comment">// search for the existing element</span></div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>    assert(L.search(12) == 2);</div>
-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>    assert(L.search(50) == -1); <span class="comment">// search for the non-existing element</span></div>
-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  205</span>                   {</div>
+<div class="line"><span class="lineno">  206</span>    <a class="code hl_struct" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html">data_structures::list_array::list</a> L;</div>
+<div class="line"><span class="lineno">  207</span> </div>
+<div class="line"><span class="lineno">  208</span>    <span class="comment">// Insert testing</span></div>
+<div class="line"><span class="lineno">  209</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0f44d5e3a52d35f8ff23ace9569c6305">insert</a>(11);</div>
+<div class="line"><span class="lineno">  210</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0f44d5e3a52d35f8ff23ace9569c6305">insert</a>(12);</div>
+<div class="line"><span class="lineno">  211</span>    assert(L.top == 2);</div>
+<div class="line"><span class="lineno">  212</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0f44d5e3a52d35f8ff23ace9569c6305">insert</a>(15);</div>
+<div class="line"><span class="lineno">  213</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0f44d5e3a52d35f8ff23ace9569c6305">insert</a>(10);</div>
+<div class="line"><span class="lineno">  214</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0f44d5e3a52d35f8ff23ace9569c6305">insert</a>(12);</div>
+<div class="line"><span class="lineno">  215</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0f44d5e3a52d35f8ff23ace9569c6305">insert</a>(20);</div>
+<div class="line"><span class="lineno">  216</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0f44d5e3a52d35f8ff23ace9569c6305">insert</a>(18);</div>
+<div class="line"><span class="lineno">  217</span>    assert(L.top == 7);</div>
+<div class="line"><span class="lineno">  218</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#ae5c15d93819c4e437ebb7a1b41f2d594">show</a>(); <span class="comment">// To print the array</span></div>
+<div class="line"><span class="lineno">  219</span> </div>
+<div class="line"><span class="lineno">  220</span>    <span class="comment">// Remove testing</span></div>
+<div class="line"><span class="lineno">  221</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0499455a80156134cc79c98eabb376d9">remove</a>(12); <span class="comment">// Remove Duplicate value in the list</span></div>
+<div class="line"><span class="lineno">  222</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0499455a80156134cc79c98eabb376d9">remove</a>(15); <span class="comment">// Remove the existing value in the list</span></div>
+<div class="line"><span class="lineno">  223</span>    assert(L.top == 5);</div>
+<div class="line"><span class="lineno">  224</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0499455a80156134cc79c98eabb376d9">remove</a>(50); <span class="comment">// Try to remove the non-existing value in the list</span></div>
+<div class="line"><span class="lineno">  225</span>    assert(L.top == 5);</div>
+<div class="line"><span class="lineno">  226</span> </div>
+<div class="line"><span class="lineno">  227</span>    <span class="comment">// LinearSearch testing</span></div>
+<div class="line"><span class="lineno">  228</span>    assert(L.search(11) == 0); <span class="comment">// search for the existing element</span></div>
+<div class="line"><span class="lineno">  229</span>    assert(L.search(12) == 2);</div>
+<div class="line"><span class="lineno">  230</span>    assert(L.search(50) == -1); <span class="comment">// search for the non-existing element</span></div>
+<div class="line"><span class="lineno">  231</span> </div>
+<div class="line"><span class="lineno">  232</span>    <span class="comment">// Sort testing</span></div>
+<div class="line"><span class="lineno">  233</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a39a712c8413b0d7861695ec019474469">sort</a>();</div>
+<div class="line"><span class="lineno">  234</span>    assert(L.isSorted == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  235</span>    L.<a class="code hl_function" href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#ae5c15d93819c4e437ebb7a1b41f2d594">show</a>();</div>
+<div class="line"><span class="lineno">  236</span> </div>
+<div class="line"><span class="lineno">  237</span>    <span class="comment">// BinarySearch testing</span></div>
+<div class="line"><span class="lineno">  238</span>    assert(L.search(11) == 1); <span class="comment">// search for the existing element</span></div>
+<div class="line"><span class="lineno">  239</span>    assert(L.search(12) == 2);</div>
+<div class="line"><span class="lineno">  240</span>    assert(L.search(50) == -1); <span class="comment">// search for the non-existing element</span></div>
+<div class="line"><span class="lineno">  241</span>}</div>
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 <div class="ttc" id="astructdata__structures_1_1list__array_1_1list_html_a0499455a80156134cc79c98eabb376d9"><div class="ttname"><a href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0499455a80156134cc79c98eabb376d9">data_structures::list_array::list::remove</a></div><div class="ttdeci">void remove(const uint64_t &amp;val)</div><div class="ttdoc">To remove the element from the list.</div><div class="ttdef"><b>Definition:</b> list_array.cpp:171</div></div>
 <div class="ttc" id="astructdata__structures_1_1list__array_1_1list_html_a0f44d5e3a52d35f8ff23ace9569c6305"><div class="ttname"><a href="../../d5/dab/structdata__structures_1_1list__array_1_1list.html#a0f44d5e3a52d35f8ff23ace9569c6305">data_structures::list_array::list::insert</a></div><div class="ttdeci">void insert(const uint64_t &amp;val)</div><div class="ttdoc">Insert the new element in the list.</div><div class="ttdef"><b>Definition:</b> list_array.cpp:132</div></div>
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-<p><a href="https://www.coursera.org/learn/algorithms-on-graphs/lecture/7ml18/bidirectional-dijkstra" target="_blank">Bidirectional Dijkstra Shortest Path Algorithm</a>  
+<p>[Bidirectional Dijkstra Shortest Path Algorithm] (<a href="https://www.coursera.org/learn/algorithms-on-graphs/lecture/7ml18/bidirectional-dijkstra">https://www.coursera.org/learn/algorithms-on-graphs/lecture/7ml18/bidirectional-dijkstra</a>)  
 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;cassert&gt;</code><br />
 <code>#include &lt;iostream&gt;</code><br />
@@ -119,7 +119,7 @@ Namespaces</h2></td></tr>
 <tr class="memdesc:df/dce/namespacegraph"><td class="mdescLeft">&#160;</td><td class="mdescRight"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> Algorithms. <br /></td></tr>
 <tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
 <tr class="memitem:d4/d13/namespacebidirectional__dijkstra"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d13/namespacebidirectional__dijkstra.html">bidirectional_dijkstra</a></td></tr>
-<tr class="memdesc:d4/d13/namespacebidirectional__dijkstra"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for <a href="https://www.coursera.org/learn/algorithms-on-graphs/lecture/7ml18/bidirectional-dijkstra" target="_blank">Bidirectional Dijkstra Shortest Path</a> algorithm. <br /></td></tr>
+<tr class="memdesc:d4/d13/namespacebidirectional__dijkstra"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for [Bidirectional Dijkstra Shortest Path] (<a href="https://www.coursera.org/learn/algorithms-on-graphs/lecture/7ml18/bidirectional-dijkstra">https://www.coursera.org/learn/algorithms-on-graphs/lecture/7ml18/bidirectional-dijkstra</a>) algorithm. <br /></td></tr>
 <tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
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 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
-<div class="textblock"><p ><a href="https://www.coursera.org/learn/algorithms-on-graphs/lecture/7ml18/bidirectional-dijkstra" target="_blank">Bidirectional Dijkstra Shortest Path Algorithm</a> </p>
+<div class="textblock"><p >[Bidirectional Dijkstra Shortest Path Algorithm] (<a href="https://www.coursera.org/learn/algorithms-on-graphs/lecture/7ml18/bidirectional-dijkstra">https://www.coursera.org/learn/algorithms-on-graphs/lecture/7ml18/bidirectional-dijkstra</a>) </p>
 <dl class="section author"><dt>Author</dt><dd><a href="http://github.com/Marinovsky" target="_blank">Marinovksy</a></dd></dl>
 <p>This is basically the same Dijkstra Algorithm but faster because it goes from the source to the target and from target to the source and stops when finding a vertex visited already by the direct search or the reverse one. Here some simulations of it: <a href="https://www.youtube.com/watch?v=DINCL5cd_w0&t=24s">https://www.youtube.com/watch?v=DINCL5cd_w0&amp;t=24s</a> </p>
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-<div class="fragment"><div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>                                                 {</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    (*adj1)[u - 1].push_back(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(v - 1, w));</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    (*adj2)[v - 1].push_back(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(u - 1, w));</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    <span class="comment">// (*adj)[v - 1].push_back(std::make_pair(u - 1, w));</span></div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>}</div>
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+<div class="line"><span class="lineno">   48</span>    (*adj1)[u - 1].push_back(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(v - 1, w));</div>
+<div class="line"><span class="lineno">   49</span>    (*adj2)[v - 1].push_back(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(u - 1, w));</div>
+<div class="line"><span class="lineno">   50</span>    <span class="comment">// (*adj)[v - 1].push_back(std::make_pair(u - 1, w));</span></div>
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 <p >for all the reachable vertex from the currently exploring vertex we will try to minimize the distance</p>
 <p >minimizing distances</p>
 <p >check if currentNode has already been visited</p>
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-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span><span class="comment">    /// n denotes the number of vertices in graph</span></div>
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-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span><span class="comment">    /// pq[0] contains the min heap for the direct search</span></div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span><span class="comment">    /// pq[1] contains the min heap for the reverse search</span></div>
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-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue.html">std::priority_queue&lt;std::pair&lt;uint64_t, uint64_t&gt;</a>,</div>
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-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span><span class="comment"></span> </div>
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-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span><span class="comment"></span>    pq[0].push(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(0, s));</div>
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-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span><span class="comment"></span> </div>
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-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>        visited[currentNode] = <span class="keyword">true</span>;<span class="comment"></span></div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span><span class="comment">        /// reversed search</span></div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span><span class="comment"></span> </div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>        <span class="comment">// If pq[1].size() is equal to zero then the node/ vertex is not</span></div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>        <span class="comment">// reachable from t</span></div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>        <span class="keywordflow">if</span> (pq[1].size() == 0) {</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>            <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>        }<span class="comment"></span></div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span><span class="comment">        /// second element of pair denotes the node / vertex</span></div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span><span class="comment"></span>        currentNode = pq[1].top().second;</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span><span class="comment"></span> </div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span><span class="comment">        /// first element of pair denotes the distance</span></div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span><span class="comment"></span>        currentDist = pq[1].top().first;</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span> </div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>        pq[1].pop();</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span><span class="comment"></span> </div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span><span class="comment">        /// for all the reachable vertex from the currently exploring vertex</span></div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span><span class="comment">        /// we will try to minimize the distance</span></div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span><span class="comment"></span>        <span class="keywordflow">for</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;int, int&gt;</a> edge : (*adj2)[currentNode]) {<span class="comment"></span></div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span><span class="comment">            /// minimizing distances</span></div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span><span class="comment"></span>            <span class="keywordflow">if</span> (currentDist + edge.second &lt; dist[1][edge.first]) {</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>                dist[1][edge.first] = currentDist + edge.second;</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>                pq[1].push(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(dist[1][edge.first], edge.first));</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>            }</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>        }</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>        <span class="comment">// store the processed node/ vertex</span></div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>        workset.push_back(currentNode);</div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span><span class="comment"></span> </div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span><span class="comment">        /// check if currentNode has already been visited</span></div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span><span class="comment"></span>        <span class="keywordflow">if</span> (visited[currentNode] == 1) {</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a22f1b7277e1dd4190f25014b48487ce6">Shortest_Path_Distance</a>(workset, dist);</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>        }</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>        visited[currentNode] = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>    }</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>    <span class="keywordflow">return</span> -1;</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   88</span>                                       {<span class="comment"></span></div>
+<div class="line"><span class="lineno">   89</span><span class="comment">    /// n denotes the number of vertices in graph</span></div>
+<div class="line"><span class="lineno">   90</span><span class="comment"></span>    uint64_t n = adj1-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   91</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   92</span><span class="comment">    /// setting all the distances initially to INF</span></div>
+<div class="line"><span class="lineno">   93</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint64_t&gt;</a>&gt; dist(2, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(n, <a class="code hl_variable" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a330a2b0a904f01802ada1f8f3b28e76c">INF</a>));</div>
+<div class="line"><span class="lineno">   94</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   95</span><span class="comment">    /// creating a a vector of min heap using priority queue</span></div>
+<div class="line"><span class="lineno">   96</span><span class="comment">    /// pq[0] contains the min heap for the direct search</span></div>
+<div class="line"><span class="lineno">   97</span><span class="comment">    /// pq[1] contains the min heap for the reverse search</span></div>
+<div class="line"><span class="lineno">   98</span><span class="comment"></span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   99</span><span class="comment">    /// first element of pair contains the distance</span></div>
+<div class="line"><span class="lineno">  100</span><span class="comment">    /// second element of pair contains the vertex</span></div>
+<div class="line"><span class="lineno">  101</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;</div>
+<div class="line"><span class="lineno">  102</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue.html">std::priority_queue&lt;std::pair&lt;uint64_t, uint64_t&gt;</a>,</div>
+<div class="line"><span class="lineno">  103</span>                            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;,</div>
+<div class="line"><span class="lineno">  104</span>                            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/greater.html">std::greater&lt;std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;&gt;&gt;</div>
+<div class="line"><span class="lineno">  105</span>        pq(2);<span class="comment"></span></div>
+<div class="line"><span class="lineno">  106</span><span class="comment">    /// vector for store the nodes or vertices in the shortest path</span></div>
+<div class="line"><span class="lineno">  107</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> workset(n);<span class="comment"></span></div>
+<div class="line"><span class="lineno">  108</span><span class="comment">    /// vector for store the nodes or vertices visited</span></div>
+<div class="line"><span class="lineno">  109</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> visited(n);</div>
+<div class="line"><span class="lineno">  110</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  111</span><span class="comment">    /// pushing the source vertex &#39;s&#39; with 0 distance in pq[0] min heap</span></div>
+<div class="line"><span class="lineno">  112</span><span class="comment"></span>    pq[0].push(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(0, s));</div>
+<div class="line"><span class="lineno">  113</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  114</span><span class="comment">    /// marking the distance of source as 0</span></div>
+<div class="line"><span class="lineno">  115</span><span class="comment"></span>    dist[0][s] = 0;</div>
+<div class="line"><span class="lineno">  116</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  117</span><span class="comment">    /// pushing the target vertex &#39;t&#39; with 0 distance in pq[1] min heap</span></div>
+<div class="line"><span class="lineno">  118</span><span class="comment"></span>    pq[1].push(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(0, t));</div>
+<div class="line"><span class="lineno">  119</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  120</span><span class="comment">    /// marking the distance of target as 0</span></div>
+<div class="line"><span class="lineno">  121</span><span class="comment"></span>    dist[1][t] = 0;</div>
+<div class="line"><span class="lineno">  122</span> </div>
+<div class="line"><span class="lineno">  123</span>    <span class="keywordflow">while</span> (<span class="keyword">true</span>) {<span class="comment"></span></div>
+<div class="line"><span class="lineno">  124</span><span class="comment">        /// direct search</span></div>
+<div class="line"><span class="lineno">  125</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  126</span>        <span class="comment">// If pq[0].size() is equal to zero then the node/ vertex is not</span></div>
+<div class="line"><span class="lineno">  127</span>        <span class="comment">// reachable from s</span></div>
+<div class="line"><span class="lineno">  128</span>        <span class="keywordflow">if</span> (pq[0].size() == 0) {</div>
+<div class="line"><span class="lineno">  129</span>            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  130</span>        }<span class="comment"></span></div>
+<div class="line"><span class="lineno">  131</span><span class="comment">        /// second element of pair denotes the node / vertex</span></div>
+<div class="line"><span class="lineno">  132</span><span class="comment"></span>        uint64_t currentNode = pq[0].top().second;</div>
+<div class="line"><span class="lineno">  133</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  134</span><span class="comment">        /// first element of pair denotes the distance</span></div>
+<div class="line"><span class="lineno">  135</span><span class="comment"></span>        uint64_t currentDist = pq[0].top().first;</div>
+<div class="line"><span class="lineno">  136</span> </div>
+<div class="line"><span class="lineno">  137</span>        pq[0].pop();</div>
+<div class="line"><span class="lineno">  138</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  139</span><span class="comment">        /// for all the reachable vertex from the currently exploring vertex</span></div>
+<div class="line"><span class="lineno">  140</span><span class="comment">        /// we will try to minimize the distance</span></div>
+<div class="line"><span class="lineno">  141</span><span class="comment"></span>        <span class="keywordflow">for</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;int, int&gt;</a> edge : (*adj1)[currentNode]) {<span class="comment"></span></div>
+<div class="line"><span class="lineno">  142</span><span class="comment">            /// minimizing distances</span></div>
+<div class="line"><span class="lineno">  143</span><span class="comment"></span>            <span class="keywordflow">if</span> (currentDist + edge.second &lt; dist[0][edge.first]) {</div>
+<div class="line"><span class="lineno">  144</span>                dist[0][edge.first] = currentDist + edge.second;</div>
+<div class="line"><span class="lineno">  145</span>                pq[0].push(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(dist[0][edge.first], edge.first));</div>
+<div class="line"><span class="lineno">  146</span>            }</div>
+<div class="line"><span class="lineno">  147</span>        }</div>
+<div class="line"><span class="lineno">  148</span>        <span class="comment">// store the processed node/ vertex</span></div>
+<div class="line"><span class="lineno">  149</span>        workset.push_back(currentNode);</div>
+<div class="line"><span class="lineno">  150</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  151</span><span class="comment">        /// check if currentNode has already been visited</span></div>
+<div class="line"><span class="lineno">  152</span><span class="comment"></span>        <span class="keywordflow">if</span> (visited[currentNode] == 1) {</div>
+<div class="line"><span class="lineno">  153</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a22f1b7277e1dd4190f25014b48487ce6">Shortest_Path_Distance</a>(workset, dist);</div>
+<div class="line"><span class="lineno">  154</span>        }</div>
+<div class="line"><span class="lineno">  155</span>        visited[currentNode] = <span class="keyword">true</span>;<span class="comment"></span></div>
+<div class="line"><span class="lineno">  156</span><span class="comment">        /// reversed search</span></div>
+<div class="line"><span class="lineno">  157</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  158</span>        <span class="comment">// If pq[1].size() is equal to zero then the node/ vertex is not</span></div>
+<div class="line"><span class="lineno">  159</span>        <span class="comment">// reachable from t</span></div>
+<div class="line"><span class="lineno">  160</span>        <span class="keywordflow">if</span> (pq[1].size() == 0) {</div>
+<div class="line"><span class="lineno">  161</span>            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  162</span>        }<span class="comment"></span></div>
+<div class="line"><span class="lineno">  163</span><span class="comment">        /// second element of pair denotes the node / vertex</span></div>
+<div class="line"><span class="lineno">  164</span><span class="comment"></span>        currentNode = pq[1].top().second;</div>
+<div class="line"><span class="lineno">  165</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  166</span><span class="comment">        /// first element of pair denotes the distance</span></div>
+<div class="line"><span class="lineno">  167</span><span class="comment"></span>        currentDist = pq[1].top().first;</div>
+<div class="line"><span class="lineno">  168</span> </div>
+<div class="line"><span class="lineno">  169</span>        pq[1].pop();</div>
+<div class="line"><span class="lineno">  170</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  171</span><span class="comment">        /// for all the reachable vertex from the currently exploring vertex</span></div>
+<div class="line"><span class="lineno">  172</span><span class="comment">        /// we will try to minimize the distance</span></div>
+<div class="line"><span class="lineno">  173</span><span class="comment"></span>        <span class="keywordflow">for</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;int, int&gt;</a> edge : (*adj2)[currentNode]) {<span class="comment"></span></div>
+<div class="line"><span class="lineno">  174</span><span class="comment">            /// minimizing distances</span></div>
+<div class="line"><span class="lineno">  175</span><span class="comment"></span>            <span class="keywordflow">if</span> (currentDist + edge.second &lt; dist[1][edge.first]) {</div>
+<div class="line"><span class="lineno">  176</span>                dist[1][edge.first] = currentDist + edge.second;</div>
+<div class="line"><span class="lineno">  177</span>                pq[1].push(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(dist[1][edge.first], edge.first));</div>
+<div class="line"><span class="lineno">  178</span>            }</div>
+<div class="line"><span class="lineno">  179</span>        }</div>
+<div class="line"><span class="lineno">  180</span>        <span class="comment">// store the processed node/ vertex</span></div>
+<div class="line"><span class="lineno">  181</span>        workset.push_back(currentNode);</div>
+<div class="line"><span class="lineno">  182</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  183</span><span class="comment">        /// check if currentNode has already been visited</span></div>
+<div class="line"><span class="lineno">  184</span><span class="comment"></span>        <span class="keywordflow">if</span> (visited[currentNode] == 1) {</div>
+<div class="line"><span class="lineno">  185</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a22f1b7277e1dd4190f25014b48487ce6">Shortest_Path_Distance</a>(workset, dist);</div>
+<div class="line"><span class="lineno">  186</span>        }</div>
+<div class="line"><span class="lineno">  187</span>        visited[currentNode] = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  188</span>    }</div>
+<div class="line"><span class="lineno">  189</span>    <span class="keywordflow">return</span> -1;</div>
+<div class="line"><span class="lineno">  190</span>}</div>
 <div class="ttc" id="abidirectional__dijkstra_8cpp_html_a22f1b7277e1dd4190f25014b48487ce6"><div class="ttname"><a href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a22f1b7277e1dd4190f25014b48487ce6">graph::bidirectional_dijkstra::Shortest_Path_Distance</a></div><div class="ttdeci">uint64_t Shortest_Path_Distance(const std::vector&lt; uint64_t &gt; &amp;workset_, const std::vector&lt; std::vector&lt; uint64_t &gt; &gt; &amp;distance_)</div><div class="ttdoc">This function returns the shortest distance from the source to the target if there is path between ve...</div><div class="ttdef"><b>Definition:</b> bidirectional_dijkstra.cpp:61</div></div>
 <div class="ttc" id="abidirectional__dijkstra_8cpp_html_a330a2b0a904f01802ada1f8f3b28e76c"><div class="ttname"><a href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a330a2b0a904f01802ada1f8f3b28e76c">INF</a></div><div class="ttdeci">constexpr int64_t INF</div><div class="ttdoc">for store the graph, the distances, and the path</div><div class="ttdef"><b>Definition:</b> bidirectional_dijkstra.cpp:23</div></div>
 <div class="ttc" id="agreater_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/functional/greater.html">std::greater</a></div></div>
@@ -428,52 +428,52 @@ Here is the call graph for this function:</div>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>           {</div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>();  <span class="comment">// running predefined tests</span></div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>    uint64_t vertices = uint64_t();</div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>    uint64_t edges = uint64_t();</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number of vertices : &quot;</span>;</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; vertices;</div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number of edges : &quot;</span>;</div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; edges;</div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span> </div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;&gt; adj1(</div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>        vertices, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;());</div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;&gt; adj2(</div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>        vertices, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;());</div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span> </div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>    uint64_t u = uint64_t(), v = uint64_t(), w = uint64_t();</div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the edges by three integers in this form: u v w &quot;</span></div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Example: if there is and edge between node 1 and node 4 with &quot;</span></div>
-<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>                 <span class="stringliteral">&quot;weight 7 enter: 1 4 7, and then press enter&quot;</span></div>
-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>    <span class="keywordflow">while</span> (edges--) {</div>
-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; u &gt;&gt; v &gt;&gt; w;</div>
-<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>        <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj1, &amp;adj2, u, v, w);</div>
-<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>        <span class="keywordflow">if</span> (edges != 0) {</div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the next edge&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>        }</div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>    }</div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span> </div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>    uint64_t s = uint64_t(), t = uint64_t();</div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>        &lt;&lt; <span class="stringliteral">&quot;Enter the source node and the target node separated by a space&quot;</span></div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>        &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Example: If the source node is 5 and the target node is 6 &quot;</span></div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>                 <span class="stringliteral">&quot;enter: 5 6 and press enter&quot;</span></div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; s &gt;&gt; t;</div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>    <span class="keywordtype">int</span> dist =</div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>        <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a1b2df3d52a403ad46523ab90d3a723c1">graph::bidirectional_dijkstra::Bidijkstra</a>(&amp;adj1, &amp;adj2, s - 1, t - 1);</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>    <span class="keywordflow">if</span> (dist == -1) {</div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Target not reachable from source&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Shortest Path Distance : &quot;</span> &lt;&lt; dist &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>    }</div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span> </div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  248</span>           {</div>
+<div class="line"><span class="lineno">  249</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>();  <span class="comment">// running predefined tests</span></div>
+<div class="line"><span class="lineno">  250</span>    uint64_t vertices = uint64_t();</div>
+<div class="line"><span class="lineno">  251</span>    uint64_t edges = uint64_t();</div>
+<div class="line"><span class="lineno">  252</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number of vertices : &quot;</span>;</div>
+<div class="line"><span class="lineno">  253</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; vertices;</div>
+<div class="line"><span class="lineno">  254</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number of edges : &quot;</span>;</div>
+<div class="line"><span class="lineno">  255</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; edges;</div>
+<div class="line"><span class="lineno">  256</span> </div>
+<div class="line"><span class="lineno">  257</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;&gt; adj1(</div>
+<div class="line"><span class="lineno">  258</span>        vertices, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;());</div>
+<div class="line"><span class="lineno">  259</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;&gt; adj2(</div>
+<div class="line"><span class="lineno">  260</span>        vertices, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;());</div>
+<div class="line"><span class="lineno">  261</span> </div>
+<div class="line"><span class="lineno">  262</span>    uint64_t u = uint64_t(), v = uint64_t(), w = uint64_t();</div>
+<div class="line"><span class="lineno">  263</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the edges by three integers in this form: u v w &quot;</span></div>
+<div class="line"><span class="lineno">  264</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  265</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Example: if there is and edge between node 1 and node 4 with &quot;</span></div>
+<div class="line"><span class="lineno">  266</span>                 <span class="stringliteral">&quot;weight 7 enter: 1 4 7, and then press enter&quot;</span></div>
+<div class="line"><span class="lineno">  267</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  268</span>    <span class="keywordflow">while</span> (edges--) {</div>
+<div class="line"><span class="lineno">  269</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; u &gt;&gt; v &gt;&gt; w;</div>
+<div class="line"><span class="lineno">  270</span>        <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj1, &amp;adj2, u, v, w);</div>
+<div class="line"><span class="lineno">  271</span>        <span class="keywordflow">if</span> (edges != 0) {</div>
+<div class="line"><span class="lineno">  272</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the next edge&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  273</span>        }</div>
+<div class="line"><span class="lineno">  274</span>    }</div>
+<div class="line"><span class="lineno">  275</span> </div>
+<div class="line"><span class="lineno">  276</span>    uint64_t s = uint64_t(), t = uint64_t();</div>
+<div class="line"><span class="lineno">  277</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
+<div class="line"><span class="lineno">  278</span>        &lt;&lt; <span class="stringliteral">&quot;Enter the source node and the target node separated by a space&quot;</span></div>
+<div class="line"><span class="lineno">  279</span>        &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  280</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Example: If the source node is 5 and the target node is 6 &quot;</span></div>
+<div class="line"><span class="lineno">  281</span>                 <span class="stringliteral">&quot;enter: 5 6 and press enter&quot;</span></div>
+<div class="line"><span class="lineno">  282</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  283</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; s &gt;&gt; t;</div>
+<div class="line"><span class="lineno">  284</span>    <span class="keywordtype">int</span> dist =</div>
+<div class="line"><span class="lineno">  285</span>        <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a1b2df3d52a403ad46523ab90d3a723c1">graph::bidirectional_dijkstra::Bidijkstra</a>(&amp;adj1, &amp;adj2, s - 1, t - 1);</div>
+<div class="line"><span class="lineno">  286</span>    <span class="keywordflow">if</span> (dist == -1) {</div>
+<div class="line"><span class="lineno">  287</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Target not reachable from source&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  288</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  289</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Shortest Path Distance : &quot;</span> &lt;&lt; dist &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  290</span>    }</div>
+<div class="line"><span class="lineno">  291</span> </div>
+<div class="line"><span class="lineno">  292</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  293</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="abidirectional__dijkstra_8cpp_html_a1b2df3d52a403ad46523ab90d3a723c1"><div class="ttname"><a href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a1b2df3d52a403ad46523ab90d3a723c1">graph::bidirectional_dijkstra::Bidijkstra</a></div><div class="ttdeci">int Bidijkstra(std::vector&lt; std::vector&lt; std::pair&lt; uint64_t, uint64_t &gt; &gt; &gt; *adj1, std::vector&lt; std::vector&lt; std::pair&lt; uint64_t, uint64_t &gt; &gt; &gt; *adj2, uint64_t s, uint64_t t)</div><div class="ttdoc">Function runs the dijkstra algorithm for some source vertex and target vertex in the graph and return...</div><div class="ttdef"><b>Definition:</b> bidirectional_dijkstra.cpp:86</div></div>
@@ -523,15 +523,15 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>                                                     {</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    int64_t <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a> = <a class="code hl_variable" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a330a2b0a904f01802ada1f8f3b28e76c">INF</a>;</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <span class="keywordflow">for</span> (uint64_t i : workset_) {</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="keywordflow">if</span> (distance_[0][i] + distance_[1][i] &lt; distance) {</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a> = distance_[0][i] + distance_[1][i];</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        }</div>
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-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>    <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a>;</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   63</span>                                                     {</div>
+<div class="line"><span class="lineno">   64</span>    int64_t <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a> = <a class="code hl_variable" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a330a2b0a904f01802ada1f8f3b28e76c">INF</a>;</div>
+<div class="line"><span class="lineno">   65</span>    <span class="keywordflow">for</span> (uint64_t i : workset_) {</div>
+<div class="line"><span class="lineno">   66</span>        <span class="keywordflow">if</span> (distance_[0][i] + distance_[1][i] &lt; distance) {</div>
+<div class="line"><span class="lineno">   67</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a> = distance_[0][i] + distance_[1][i];</div>
+<div class="line"><span class="lineno">   68</span>        }</div>
+<div class="line"><span class="lineno">   69</span>    }</div>
+<div class="line"><span class="lineno">   70</span>    <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a>;</div>
+<div class="line"><span class="lineno">   71</span>}</div>
 <div class="ttc" id="adistance_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/distance.html">std::distance</a></div><div class="ttdeci">T distance(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -567,50 +567,50 @@ Here is the call graph for this function:</div>
 
 <p>Function to test the provided algorithm above. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>                    {</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiatinig Predefined Tests...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiating Test 1...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;&gt; adj1_1(</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>        4, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;());</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;&gt; adj1_2(</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>        4, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;());</div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj1_1, &amp;adj1_2, 1, 2, 1);</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj1_1, &amp;adj1_2, 4, 1, 2);</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj1_1, &amp;adj1_2, 2, 3, 2);</div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj1_1, &amp;adj1_2, 1, 3, 5);</div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span> </div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>    uint64_t s = 1, t = 3;</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>    assert(graph::bidirectional_dijkstra::Bidijkstra(&amp;adj1_1, &amp;adj1_2, s - 1,</div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>                                                     t - 1) == 3);</div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span> </div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>    s = 4, t = 3;</div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiating Test 2...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>    assert(graph::bidirectional_dijkstra::Bidijkstra(&amp;adj1_1, &amp;adj1_2, s - 1,</div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>                                                     t - 1) == 5);</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span> </div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;&gt; adj2_1(</div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>        5, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;());</div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;&gt; adj2_2(</div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>        5, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;());</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj2_1, &amp;adj2_2, 1, 2, 4);</div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj2_1, &amp;adj2_2, 1, 3, 2);</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj2_1, &amp;adj2_2, 2, 3, 2);</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj2_1, &amp;adj2_2, 3, 2, 1);</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj2_1, &amp;adj2_2, 2, 4, 2);</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj2_1, &amp;adj2_2, 3, 5, 4);</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj2_1, &amp;adj2_2, 5, 4, 1);</div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj2_1, &amp;adj2_2, 2, 5, 3);</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj2_1, &amp;adj2_2, 3, 4, 4);</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span> </div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>    s = 1, t = 5;</div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiating Test 3...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>    assert(graph::bidirectional_dijkstra::Bidijkstra(&amp;adj2_1, &amp;adj2_2, s - 1,</div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>                                                     t - 1) == 6);</div>
-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All Test Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  199</span>                    {</div>
+<div class="line"><span class="lineno">  200</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiatinig Predefined Tests...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  201</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiating Test 1...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  202</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;&gt; adj1_1(</div>
+<div class="line"><span class="lineno">  203</span>        4, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;());</div>
+<div class="line"><span class="lineno">  204</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;&gt; adj1_2(</div>
+<div class="line"><span class="lineno">  205</span>        4, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;());</div>
+<div class="line"><span class="lineno">  206</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj1_1, &amp;adj1_2, 1, 2, 1);</div>
+<div class="line"><span class="lineno">  207</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj1_1, &amp;adj1_2, 4, 1, 2);</div>
+<div class="line"><span class="lineno">  208</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj1_1, &amp;adj1_2, 2, 3, 2);</div>
+<div class="line"><span class="lineno">  209</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj1_1, &amp;adj1_2, 1, 3, 5);</div>
+<div class="line"><span class="lineno">  210</span> </div>
+<div class="line"><span class="lineno">  211</span>    uint64_t s = 1, t = 3;</div>
+<div class="line"><span class="lineno">  212</span>    assert(graph::bidirectional_dijkstra::Bidijkstra(&amp;adj1_1, &amp;adj1_2, s - 1,</div>
+<div class="line"><span class="lineno">  213</span>                                                     t - 1) == 3);</div>
+<div class="line"><span class="lineno">  214</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  215</span> </div>
+<div class="line"><span class="lineno">  216</span>    s = 4, t = 3;</div>
+<div class="line"><span class="lineno">  217</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiating Test 2...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  218</span>    assert(graph::bidirectional_dijkstra::Bidijkstra(&amp;adj1_1, &amp;adj1_2, s - 1,</div>
+<div class="line"><span class="lineno">  219</span>                                                     t - 1) == 5);</div>
+<div class="line"><span class="lineno">  220</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  221</span> </div>
+<div class="line"><span class="lineno">  222</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;&gt; adj2_1(</div>
+<div class="line"><span class="lineno">  223</span>        5, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;());</div>
+<div class="line"><span class="lineno">  224</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;&gt; adj2_2(</div>
+<div class="line"><span class="lineno">  225</span>        5, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint64_t, uint64_t&gt;</a>&gt;());</div>
+<div class="line"><span class="lineno">  226</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj2_1, &amp;adj2_2, 1, 2, 4);</div>
+<div class="line"><span class="lineno">  227</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj2_1, &amp;adj2_2, 1, 3, 2);</div>
+<div class="line"><span class="lineno">  228</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj2_1, &amp;adj2_2, 2, 3, 2);</div>
+<div class="line"><span class="lineno">  229</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj2_1, &amp;adj2_2, 3, 2, 1);</div>
+<div class="line"><span class="lineno">  230</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj2_1, &amp;adj2_2, 2, 4, 2);</div>
+<div class="line"><span class="lineno">  231</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj2_1, &amp;adj2_2, 3, 5, 4);</div>
+<div class="line"><span class="lineno">  232</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj2_1, &amp;adj2_2, 5, 4, 1);</div>
+<div class="line"><span class="lineno">  233</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj2_1, &amp;adj2_2, 2, 5, 3);</div>
+<div class="line"><span class="lineno">  234</span>    <a class="code hl_function" href="../../d7/d07/bidirectional__dijkstra_8cpp.html#a69172365aebde9be1997157f6f80e0cf">graph::bidirectional_dijkstra::addEdge</a>(&amp;adj2_1, &amp;adj2_2, 3, 4, 4);</div>
+<div class="line"><span class="lineno">  235</span> </div>
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-<p>&lt;a href="https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm"  
+<p>[<a class="el" href="../../da/d9a/class_graph.html">Graph</a> Dijkstras Shortest Path Algorithm (Dijkstra's Shortest Path)] (<a href="https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm">https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm</a>)  
 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;cassert&gt;</code><br />
 <code>#include &lt;iostream&gt;</code><br />
@@ -140,8 +140,7 @@ constexpr int64_t&#160;</td><td class="memItemRight" valign="bottom"><b>INF</b>
 <tr class="separator:a330a2b0a904f01802ada1f8f3b28e76c"><td class="memSeparator" colspan="2">&#160;</td></tr>
 </table>
 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
-<div class="textblock"><p >&lt;a href="https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm" </p>
-<p >target="_blank" &gt;<a class="el" href="../../da/d9a/class_graph.html">Graph</a> Dijkstras Shortest Path Algorithm (Dijkstra's Shortest Path)</p>
+<div class="textblock"><p >[<a class="el" href="../../da/d9a/class_graph.html">Graph</a> Dijkstras Shortest Path Algorithm (Dijkstra's Shortest Path)] (<a href="https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm">https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm</a>) </p>
 <dl class="section author"><dt>Author</dt><dd><a href="http://github.com/ayaankhan98" target="_blank">Ayaan Khan</a></dd></dl>
 <p>Dijkstra's Algorithm is used to find the shortest path from a source vertex to all other reachable vertex in the graph. The algorithm initially assumes all the nodes are unreachable from the given source vertex so we mark the distances of all vertices as INF (infinity) from source vertex (INF / infinity denotes unable to reach).</p>
 <p >in similar fashion with BFS we assume the distance of source vertex as 0 and pushes the vertex in a priority queue with it's distance. we maintain the priority queue as a min heap so that we can get the minimum element at the top of heap</p>
@@ -163,35 +162,35 @@ constexpr int64_t&#160;</td><td class="memItemRight" valign="bottom"><b>INF</b>
       </table>
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 <p >Main function </p>
-<div class="fragment"><div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>           {</div>
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-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span> </div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>    <span class="keywordtype">int</span> vertices = int(), edges = int();</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number of vertices : &quot;</span>;</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; vertices;</div>
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-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; edges;</div>
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-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>        vertices, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;int, int&gt;</a>&gt;());</div>
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-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  152</span>           {</div>
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@@ -203,7 +202,7 @@ constexpr int64_t&#160;</td><td class="memItemRight" valign="bottom"><b>INF</b>
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 Here is the call graph for this function:</div>
 <div class="dyncontent">
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 <p >Function to test the Algorithm </p>
-<div class="fragment"><div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>             {</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiatinig Predefined Tests...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiating Test 1...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;int, int&gt;</a>&gt;&gt; adj1(</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>        4, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;int, int&gt;</a>&gt;());</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 1, 2, 1);</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 4, 1, 2);</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 2, 3, 2);</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 1, 3, 5);</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span> </div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <span class="keywordtype">int</span> s = 1, t = 3;</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#adc68cbc8ba09eb1142265935c0d45b84">graph::dijkstra</a>(&amp;adj1, s - 1, t - 1) == 3);</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span> </div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    s = 4, t = 3;</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiating Test 2...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#adc68cbc8ba09eb1142265935c0d45b84">graph::dijkstra</a>(&amp;adj1, s - 1, t - 1) == 5);</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span> </div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;int, int&gt;</a>&gt;&gt; adj2(</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>        5, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;int, int&gt;</a>&gt;());</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 1, 2, 4);</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 1, 3, 2);</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 2, 3, 2);</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 3, 2, 1);</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 2, 4, 2);</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 3, 5, 4);</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 5, 4, 1);</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 2, 5, 3);</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 3, 4, 4);</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span> </div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    s = 1, t = 5;</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiating Test 3...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#adc68cbc8ba09eb1142265935c0d45b84">graph::dijkstra</a>(&amp;adj2, s - 1, t - 1) == 6);</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All Test Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  113</span>             {</div>
+<div class="line"><span class="lineno">  114</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiatinig Predefined Tests...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  115</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiating Test 1...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  116</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;int, int&gt;</a>&gt;&gt; adj1(</div>
+<div class="line"><span class="lineno">  117</span>        4, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;int, int&gt;</a>&gt;());</div>
+<div class="line"><span class="lineno">  118</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 1, 2, 1);</div>
+<div class="line"><span class="lineno">  119</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 4, 1, 2);</div>
+<div class="line"><span class="lineno">  120</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 2, 3, 2);</div>
+<div class="line"><span class="lineno">  121</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 1, 3, 5);</div>
+<div class="line"><span class="lineno">  122</span> </div>
+<div class="line"><span class="lineno">  123</span>    <span class="keywordtype">int</span> s = 1, t = 3;</div>
+<div class="line"><span class="lineno">  124</span>    assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#adc68cbc8ba09eb1142265935c0d45b84">graph::dijkstra</a>(&amp;adj1, s - 1, t - 1) == 3);</div>
+<div class="line"><span class="lineno">  125</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  126</span> </div>
+<div class="line"><span class="lineno">  127</span>    s = 4, t = 3;</div>
+<div class="line"><span class="lineno">  128</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiating Test 2...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  129</span>    assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#adc68cbc8ba09eb1142265935c0d45b84">graph::dijkstra</a>(&amp;adj1, s - 1, t - 1) == 5);</div>
+<div class="line"><span class="lineno">  130</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  131</span> </div>
+<div class="line"><span class="lineno">  132</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;int, int&gt;</a>&gt;&gt; adj2(</div>
+<div class="line"><span class="lineno">  133</span>        5, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;int, int&gt;</a>&gt;());</div>
+<div class="line"><span class="lineno">  134</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 1, 2, 4);</div>
+<div class="line"><span class="lineno">  135</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 1, 3, 2);</div>
+<div class="line"><span class="lineno">  136</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 2, 3, 2);</div>
+<div class="line"><span class="lineno">  137</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 3, 2, 1);</div>
+<div class="line"><span class="lineno">  138</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 2, 4, 2);</div>
+<div class="line"><span class="lineno">  139</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 3, 5, 4);</div>
+<div class="line"><span class="lineno">  140</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 5, 4, 1);</div>
+<div class="line"><span class="lineno">  141</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 2, 5, 3);</div>
+<div class="line"><span class="lineno">  142</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 3, 4, 4);</div>
+<div class="line"><span class="lineno">  143</span> </div>
+<div class="line"><span class="lineno">  144</span>    s = 1, t = 5;</div>
+<div class="line"><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiating Test 3...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  146</span>    assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#adc68cbc8ba09eb1142265935c0d45b84">graph::dijkstra</a>(&amp;adj2, s - 1, t - 1) == 6);</div>
+<div class="line"><span class="lineno">  147</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  148</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All Test Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  149</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../d7/d1e/graph_2dijkstra_8cpp_a88ec9ad42717780d6caaff9d3d6977f9_cgraph.svg" width="223" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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@@ -276,7 +275,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_12552d7fa429bf94a2e32e5cf39f7e69.html">graph</a></li><li class="navelem"><a class="el" href="../../d7/d1e/graph_2dijkstra_8cpp.html">dijkstra.cpp</a></li>
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+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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diff --git a/d7/d1e/graph_2dijkstra_8cpp_a88ec9ad42717780d6caaff9d3d6977f9_cgraph.map b/d7/d1e/graph_2dijkstra_8cpp_a88ec9ad42717780d6caaff9d3d6977f9_cgraph.map
index a9762f88b..e210bef32 100644
--- a/d7/d1e/graph_2dijkstra_8cpp_a88ec9ad42717780d6caaff9d3d6977f9_cgraph.map
+++ b/d7/d1e/graph_2dijkstra_8cpp_a88ec9ad42717780d6caaff9d3d6977f9_cgraph.map
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-<div class="fragment"><div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>             {</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    <span class="keywordflow">if</span> (n == 0)</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>        <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>    <span class="keywordflow">if</span> (n &lt;= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>)</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a>[n - 1];</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    <span class="comment">// F1</span></div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;ll&gt;</a> F1(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1);</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    <span class="keywordflow">for</span> (ll i = 1; i &lt;= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) F1[i] = <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a>[i - 1];</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span> </div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    <span class="comment">// Transpose matrix</span></div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;vector&lt;ll&gt;</a>&gt; T(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;ll&gt;</a>(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1));</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <span class="keywordflow">for</span> (ll i = 1; i &lt;= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        <span class="keywordflow">for</span> (ll j = 1; j &lt;= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; j++) {</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>            <span class="keywordflow">if</span> (i &lt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>) {</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>                <span class="keywordflow">if</span> (j == i + 1)</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>                    T[i][j] = 1;</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>                <span class="keywordflow">else</span></div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>                    T[i][j] = 0;</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>                <span class="keywordflow">continue</span>;</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>            }</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>            T[i][j] = fib_c[<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> - j];</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>        }</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    }</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    <span class="comment">// T^n-1</span></div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    T = <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#a702a9fc90e79b05b863cc4efa26ae2ec">power</a>(T, n - 1);</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span> </div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    <span class="comment">// T*F1</span></div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    ll res = 0;</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    <span class="keywordflow">for</span> (ll i = 1; i &lt;= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        res = (res + (T[1][i] * F1[i]) % MOD) % MOD;</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    }</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    <span class="keywordflow">return</span> res;</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   91</span>             {</div>
+<div class="line"><span class="lineno">   92</span>    <span class="keywordflow">if</span> (n == 0)</div>
+<div class="line"><span class="lineno">   93</span>        <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">   94</span>    <span class="keywordflow">if</span> (n &lt;= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>)</div>
+<div class="line"><span class="lineno">   95</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a>[n - 1];</div>
+<div class="line"><span class="lineno">   96</span>    <span class="comment">// F1</span></div>
+<div class="line"><span class="lineno">   97</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;ll&gt;</a> F1(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1);</div>
+<div class="line"><span class="lineno">   98</span>    <span class="keywordflow">for</span> (ll i = 1; i &lt;= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) F1[i] = <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a>[i - 1];</div>
+<div class="line"><span class="lineno">   99</span> </div>
+<div class="line"><span class="lineno">  100</span>    <span class="comment">// Transpose matrix</span></div>
+<div class="line"><span class="lineno">  101</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;vector&lt;ll&gt;</a>&gt; T(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;ll&gt;</a>(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1));</div>
+<div class="line"><span class="lineno">  102</span>    <span class="keywordflow">for</span> (ll i = 1; i &lt;= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
+<div class="line"><span class="lineno">  103</span>        <span class="keywordflow">for</span> (ll j = 1; j &lt;= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; j++) {</div>
+<div class="line"><span class="lineno">  104</span>            <span class="keywordflow">if</span> (i &lt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>) {</div>
+<div class="line"><span class="lineno">  105</span>                <span class="keywordflow">if</span> (j == i + 1)</div>
+<div class="line"><span class="lineno">  106</span>                    T[i][j] = 1;</div>
+<div class="line"><span class="lineno">  107</span>                <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  108</span>                    T[i][j] = 0;</div>
+<div class="line"><span class="lineno">  109</span>                <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno">  110</span>            }</div>
+<div class="line"><span class="lineno">  111</span>            T[i][j] = fib_c[<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> - j];</div>
+<div class="line"><span class="lineno">  112</span>        }</div>
+<div class="line"><span class="lineno">  113</span>    }</div>
+<div class="line"><span class="lineno">  114</span>    <span class="comment">// T^n-1</span></div>
+<div class="line"><span class="lineno">  115</span>    T = <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#a702a9fc90e79b05b863cc4efa26ae2ec">power</a>(T, n - 1);</div>
+<div class="line"><span class="lineno">  116</span> </div>
+<div class="line"><span class="lineno">  117</span>    <span class="comment">// T*F1</span></div>
+<div class="line"><span class="lineno">  118</span>    ll res = 0;</div>
+<div class="line"><span class="lineno">  119</span>    <span class="keywordflow">for</span> (ll i = 1; i &lt;= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
+<div class="line"><span class="lineno">  120</span>        res = (res + (T[1][i] * F1[i]) % MOD) % MOD;</div>
+<div class="line"><span class="lineno">  121</span>    }</div>
+<div class="line"><span class="lineno">  122</span>    <span class="keywordflow">return</span> res;</div>
+<div class="line"><span class="lineno">  123</span>}</div>
 <div class="ttc" id="amatrix__exponentiation_8cpp_html_a35b7c98af53ad2ec18658679ad7d43de"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a></div><div class="ttdeci">vector&lt; ll &gt; fib_b</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:50</div></div>
 <div class="ttc" id="amatrix__exponentiation_8cpp_html_a702a9fc90e79b05b863cc4efa26ae2ec"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a702a9fc90e79b05b863cc4efa26ae2ec">power</a></div><div class="ttdeci">vector&lt; vector&lt; ll &gt; &gt; power(const vector&lt; vector&lt; ll &gt; &gt; &amp;A, ll p)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:76</div></div>
 <div class="ttc" id="amatrix__exponentiation_8cpp_html_a9977ad12548c4a49dee9dc3f0685aa54"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a></div><div class="ttdeci">ll mat_size</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:45</div></div>
@@ -284,29 +284,29 @@ This way you can find the \(10^{18}\) fibonacci numberMOD. I have given a genera
       </table>
 </div><div class="memdoc">
 <p >Main function </p>
-<div class="fragment"><div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>           {</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a>.tie(0);</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a>.tie(0);</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    ll t;</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> &gt;&gt; t;</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    ll i, j, x;</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    <span class="keywordflow">while</span> (t--) {</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> &gt;&gt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>;</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>        <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> &gt;&gt; x;</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>            <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a>.pb(x);</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        }</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>        <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> &gt;&gt; x;</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>            fib_c.pb(x);</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>        }</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> &gt;&gt; x;</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>(x) &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>        <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a>.clear();</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>        fib_c.clear();</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    }</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  126</span>           {</div>
+<div class="line"><span class="lineno">  127</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a>.tie(0);</div>
+<div class="line"><span class="lineno">  128</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a>.tie(0);</div>
+<div class="line"><span class="lineno">  129</span>    ll t;</div>
+<div class="line"><span class="lineno">  130</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> &gt;&gt; t;</div>
+<div class="line"><span class="lineno">  131</span>    ll i, j, x;</div>
+<div class="line"><span class="lineno">  132</span>    <span class="keywordflow">while</span> (t--) {</div>
+<div class="line"><span class="lineno">  133</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> &gt;&gt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>;</div>
+<div class="line"><span class="lineno">  134</span>        <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
+<div class="line"><span class="lineno">  135</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> &gt;&gt; x;</div>
+<div class="line"><span class="lineno">  136</span>            <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a>.pb(x);</div>
+<div class="line"><span class="lineno">  137</span>        }</div>
+<div class="line"><span class="lineno">  138</span>        <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
+<div class="line"><span class="lineno">  139</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> &gt;&gt; x;</div>
+<div class="line"><span class="lineno">  140</span>            fib_c.pb(x);</div>
+<div class="line"><span class="lineno">  141</span>        }</div>
+<div class="line"><span class="lineno">  142</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> &gt;&gt; x;</div>
+<div class="line"><span class="lineno">  143</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>(x) &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
+<div class="line"><span class="lineno">  144</span>        <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a>.clear();</div>
+<div class="line"><span class="lineno">  145</span>        fib_c.clear();</div>
+<div class="line"><span class="lineno">  146</span>    }</div>
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-<p>Implementation to <a href="https://www.geeksforgeeks.org/count-number-of-bits-to-be-flipped-to-convert-a-to-b/" target="_blank">Count number of bits to be flipped to convert A to B</a> in an integer.  
+<p>Implementation to [Count number of bits to be flipped to convert A to B] (<a href="https://www.geeksforgeeks.org/count-number-of-bits-to-be-flipped-to-convert-a-to-b/">https://www.geeksforgeeks.org/count-number-of-bits-to-be-flipped-to-convert-a-to-b/</a>) in an integer.  
 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;cassert&gt;</code><br />
 <code>#include &lt;iostream&gt;</code><br />
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 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
-<div class="textblock"><p >Implementation to <a href="https://www.geeksforgeeks.org/count-number-of-bits-to-be-flipped-to-convert-a-to-b/" target="_blank">Count number of bits to be flipped to convert A to B</a> in an integer. </p>
+<div class="textblock"><p >Implementation to [Count number of bits to be flipped to convert A to B] (<a href="https://www.geeksforgeeks.org/count-number-of-bits-to-be-flipped-to-convert-a-to-b/">https://www.geeksforgeeks.org/count-number-of-bits-to-be-flipped-to-convert-a-to-b/</a>) in an integer. </p>
 <p >We are given two numbers A and B. Our task is to count the number of bits needed to be flipped to convert A to B.</p>
 <p >Explanation:</p>
 <p >A = 01010 B = 10100 As we can see, the bits of A that need to be flipped are 01010. If we flipthese bits, we get 10100, which is B.</p>
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   </dd>
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-<div class="fragment"><div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>                  {  <span class="comment">// int64_t is preferred over int so that</span></div>
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-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   44</span>                  {  <span class="comment">// int64_t is preferred over int so that</span></div>
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+<div class="line"><span class="lineno">   46</span> </div>
+<div class="line"><span class="lineno">   47</span>    <span class="keywordtype">int</span> count =</div>
+<div class="line"><span class="lineno">   48</span>        0;  <span class="comment">// &quot;count&quot; variable is used to count number of bits flip of the</span></div>
+<div class="line"><span class="lineno">   49</span>            <span class="comment">// number A to form B in binary representation of number &#39;n&#39;</span></div>
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-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   64</span>                   {</div>
+<div class="line"><span class="lineno">   65</span>    <span class="comment">// A = 10, B = 20 return 4</span></div>
+<div class="line"><span class="lineno">   66</span>    assert(bit_manipulation::count_bits_flip::countBitsFlip(10, 20) == 4);</div>
+<div class="line"><span class="lineno">   67</span>    <span class="comment">// A = 20, B = 25 return 3</span></div>
+<div class="line"><span class="lineno">   68</span>    assert(bit_manipulation::count_bits_flip::countBitsFlip(20, 25) == 3);</div>
+<div class="line"><span class="lineno">   69</span>    <span class="comment">// A = 7, B = 10 return 3</span></div>
+<div class="line"><span class="lineno">   70</span>    assert(bit_manipulation::count_bits_flip::countBitsFlip(7, 10) == 3);</div>
+<div class="line"><span class="lineno">   71</span>    <span class="comment">// A = 17, B = 25 return 1</span></div>
+<div class="line"><span class="lineno">   72</span>    assert(bit_manipulation::count_bits_flip::countBitsFlip(17, 25) == 1);</div>
+<div class="line"><span class="lineno">   73</span>    <span class="comment">// A = 11, B = 8 return 2</span></div>
+<div class="line"><span class="lineno">   74</span>    assert(bit_manipulation::count_bits_flip::countBitsFlip(11, 8) == 2);</div>
+<div class="line"><span class="lineno">   75</span>    <span class="comment">// A = 21, B = 22 return 2</span></div>
+<div class="line"><span class="lineno">   76</span>    assert(bit_manipulation::count_bits_flip::countBitsFlip(21, 22) == 2);</div>
+<div class="line"><span class="lineno">   77</span>    <span class="comment">// A = 7, B = 786 return 5</span></div>
+<div class="line"><span class="lineno">   78</span>    assert(bit_manipulation::count_bits_flip::countBitsFlip(7, 786) == 5);</div>
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+ <tr id="projectrow">
+  <td id="projectalign">
    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
    </div>
    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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+<!-- Generated by Doxygen 1.9.3 -->
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@@ -153,22 +153,22 @@ related <a class="el" href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#ab
       </table>
 </div><div class="memdoc">
 <p >Main function (driver code) </p>
-<div class="fragment"><div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>           {</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>    <span class="comment">// test for implementation</span></div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    <a class="code hl_function" href="../../d7/d65/shortest__common__supersequence_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span> </div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    <span class="comment">// user input</span></div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s1, s2;</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; s1;</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; s2;</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span> </div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span> </div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>    <span class="comment">// user output</span></div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>    <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = <a class="code hl_function" href="../../d7/d65/shortest__common__supersequence_8cpp.html#ad2ee8d7e67da9f6eb85146b08dad95e6">dynamic_programming::shortest_common_supersequence::scs</a>(s1, s2);</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  164</span>           {</div>
+<div class="line"><span class="lineno">  165</span>    <span class="comment">// test for implementation</span></div>
+<div class="line"><span class="lineno">  166</span>    <a class="code hl_function" href="../../d7/d65/shortest__common__supersequence_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
+<div class="line"><span class="lineno">  167</span> </div>
+<div class="line"><span class="lineno">  168</span>    <span class="comment">// user input</span></div>
+<div class="line"><span class="lineno">  169</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s1, s2;</div>
+<div class="line"><span class="lineno">  170</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; s1;</div>
+<div class="line"><span class="lineno">  171</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; s2;</div>
+<div class="line"><span class="lineno">  172</span> </div>
+<div class="line"><span class="lineno">  173</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
+<div class="line"><span class="lineno">  174</span> </div>
+<div class="line"><span class="lineno">  175</span>    <span class="comment">// user output</span></div>
+<div class="line"><span class="lineno">  176</span>    <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = <a class="code hl_function" href="../../d7/d65/shortest__common__supersequence_8cpp.html#ad2ee8d7e67da9f6eb85146b08dad95e6">dynamic_programming::shortest_common_supersequence::scs</a>(s1, s2);</div>
+<div class="line"><span class="lineno">  177</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
+<div class="line"><span class="lineno">  178</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  179</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
@@ -217,81 +217,81 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>string 'Z', superSequence of X and Y </dd></dl>
-<div class="fragment"><div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>                                                                    {</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span> </div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>            <span class="comment">// Edge cases</span></div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>            <span class="comment">// If either str1 or str2 or both are empty</span></div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>            <span class="keywordflow">if</span>(str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/empty.html">empty</a>() &amp;&amp; str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/empty.html">empty</a>()) {</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>                <span class="keywordflow">return</span> <span class="stringliteral">&quot;&quot;</span>;</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>            }</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span>(str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/empty.html">empty</a>()) {</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>                <span class="keywordflow">return</span> str2;</div>
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-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span>(str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/empty.html">empty</a>()) {</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>                <span class="keywordflow">return</span> str1;</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>            }</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span> </div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>            <span class="comment">// creating lookup table</span></div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector &lt;std::vector &lt;int&gt;</a>&gt; lookup(str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>() + 1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector &lt;int&gt;</a> (str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>() + 1, 0));</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>      </div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>            <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=1; i &lt;= str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>(); i++) {</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>                <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=1; j &lt;= str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>(); j++) {</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>                    <span class="keywordflow">if</span>(str1[i-1] == str2[j-1]) {</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>                        lookup[i][j] = lookup[i-1][j-1] + 1;</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>                    }</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>                    <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>                        lookup[i][j] = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(lookup[i-1][j], lookup[i][j-1]);</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>                    }</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>                }</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>            }</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span> </div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>            <span class="comment">// making supersequence</span></div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>            <span class="comment">// i and j are initially pointed towards end of strings</span></div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>            <span class="comment">// Super-sequence will be constructed backwards</span></div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>            <span class="keywordtype">int</span> i=str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>();</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>            <span class="keywordtype">int</span> j=str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>();</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s;</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>      </div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>            <span class="keywordflow">while</span>(i&gt;0 &amp;&amp; j&gt;0) {</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span> </div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>                <span class="comment">// If the characters at i and j of both strings are same</span></div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>                <span class="comment">// We only need to add them once in s</span></div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>                <span class="keywordflow">if</span>(str1[i-1] == str2[j-1]) {</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>                    s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/push_back.html">push_back</a>(str1[i-1]);</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>                    i--;</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>                    j--;</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>                }</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>                <span class="comment">// otherwise we check lookup table for recurrences of characters</span></div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>                <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>                    <span class="keywordflow">if</span>(lookup[i-1][j] &gt; lookup[i][j-1]) {</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>                        s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/push_back.html">push_back</a>(str1[i-1]);</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>                        i--;</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>                    }</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>                    <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>                        s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/push_back.html">push_back</a>(str2[j-1]);</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>                        j--;</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>                    }</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>                }</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>            }</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span> </div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>            <span class="comment">// copying remaining elements</span></div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>            <span class="comment">// if j becomes 0 before i</span></div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>            <span class="keywordflow">while</span>(i &gt; 0) {</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>                s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/push_back.html">push_back</a>(str1[i-1]);</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>                i--;</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>            }</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span> </div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>            <span class="comment">// if i becomes 0 before j</span></div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>            <span class="keywordflow">while</span>(j &gt; 0) {</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>                s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/push_back.html">push_back</a>(str2[j-1]);</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>                j--;</div>
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-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span> </div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>            <span class="comment">// As the super sequence is constructd backwards</span></div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>            <span class="comment">// reversing the string before returning gives us the correct output  </span></div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/reverse.html">reverse</a>(s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/begin.html">begin</a>(), s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/end.html">end</a>());</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>            <span class="keywordflow">return</span> s;</div>
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+<div class="line"><span class="lineno">   43</span> </div>
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+<div class="line"><span class="lineno">   45</span>            <span class="comment">// If either str1 or str2 or both are empty</span></div>
+<div class="line"><span class="lineno">   46</span>            <span class="keywordflow">if</span>(str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/empty.html">empty</a>() &amp;&amp; str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/empty.html">empty</a>()) {</div>
+<div class="line"><span class="lineno">   47</span>                <span class="keywordflow">return</span> <span class="stringliteral">&quot;&quot;</span>;</div>
+<div class="line"><span class="lineno">   48</span>            }</div>
+<div class="line"><span class="lineno">   49</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span>(str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/empty.html">empty</a>()) {</div>
+<div class="line"><span class="lineno">   50</span>                <span class="keywordflow">return</span> str2;</div>
+<div class="line"><span class="lineno">   51</span>            }</div>
+<div class="line"><span class="lineno">   52</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span>(str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/empty.html">empty</a>()) {</div>
+<div class="line"><span class="lineno">   53</span>                <span class="keywordflow">return</span> str1;</div>
+<div class="line"><span class="lineno">   54</span>            }</div>
+<div class="line"><span class="lineno">   55</span> </div>
+<div class="line"><span class="lineno">   56</span>            <span class="comment">// creating lookup table</span></div>
+<div class="line"><span class="lineno">   57</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector &lt;std::vector &lt;int&gt;</a>&gt; lookup(str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>() + 1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector &lt;int&gt;</a> (str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>() + 1, 0));</div>
+<div class="line"><span class="lineno">   58</span>      </div>
+<div class="line"><span class="lineno">   59</span>            <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=1; i &lt;= str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>(); i++) {</div>
+<div class="line"><span class="lineno">   60</span>                <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=1; j &lt;= str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>(); j++) {</div>
+<div class="line"><span class="lineno">   61</span>                    <span class="keywordflow">if</span>(str1[i-1] == str2[j-1]) {</div>
+<div class="line"><span class="lineno">   62</span>                        lookup[i][j] = lookup[i-1][j-1] + 1;</div>
+<div class="line"><span class="lineno">   63</span>                    }</div>
+<div class="line"><span class="lineno">   64</span>                    <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   65</span>                        lookup[i][j] = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(lookup[i-1][j], lookup[i][j-1]);</div>
+<div class="line"><span class="lineno">   66</span>                    }</div>
+<div class="line"><span class="lineno">   67</span>                }</div>
+<div class="line"><span class="lineno">   68</span>            }</div>
+<div class="line"><span class="lineno">   69</span> </div>
+<div class="line"><span class="lineno">   70</span>            <span class="comment">// making supersequence</span></div>
+<div class="line"><span class="lineno">   71</span>            <span class="comment">// i and j are initially pointed towards end of strings</span></div>
+<div class="line"><span class="lineno">   72</span>            <span class="comment">// Super-sequence will be constructed backwards</span></div>
+<div class="line"><span class="lineno">   73</span>            <span class="keywordtype">int</span> i=str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>();</div>
+<div class="line"><span class="lineno">   74</span>            <span class="keywordtype">int</span> j=str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>();</div>
+<div class="line"><span class="lineno">   75</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s;</div>
+<div class="line"><span class="lineno">   76</span>      </div>
+<div class="line"><span class="lineno">   77</span>            <span class="keywordflow">while</span>(i&gt;0 &amp;&amp; j&gt;0) {</div>
+<div class="line"><span class="lineno">   78</span> </div>
+<div class="line"><span class="lineno">   79</span>                <span class="comment">// If the characters at i and j of both strings are same</span></div>
+<div class="line"><span class="lineno">   80</span>                <span class="comment">// We only need to add them once in s</span></div>
+<div class="line"><span class="lineno">   81</span>                <span class="keywordflow">if</span>(str1[i-1] == str2[j-1]) {</div>
+<div class="line"><span class="lineno">   82</span>                    s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/push_back.html">push_back</a>(str1[i-1]);</div>
+<div class="line"><span class="lineno">   83</span>                    i--;</div>
+<div class="line"><span class="lineno">   84</span>                    j--;</div>
+<div class="line"><span class="lineno">   85</span>                }</div>
+<div class="line"><span class="lineno">   86</span>                <span class="comment">// otherwise we check lookup table for recurrences of characters</span></div>
+<div class="line"><span class="lineno">   87</span>                <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   88</span>                    <span class="keywordflow">if</span>(lookup[i-1][j] &gt; lookup[i][j-1]) {</div>
+<div class="line"><span class="lineno">   89</span>                        s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/push_back.html">push_back</a>(str1[i-1]);</div>
+<div class="line"><span class="lineno">   90</span>                        i--;</div>
+<div class="line"><span class="lineno">   91</span>                    }</div>
+<div class="line"><span class="lineno">   92</span>                    <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   93</span>                        s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/push_back.html">push_back</a>(str2[j-1]);</div>
+<div class="line"><span class="lineno">   94</span>                        j--;</div>
+<div class="line"><span class="lineno">   95</span>                    }</div>
+<div class="line"><span class="lineno">   96</span>                }</div>
+<div class="line"><span class="lineno">   97</span>            }</div>
+<div class="line"><span class="lineno">   98</span> </div>
+<div class="line"><span class="lineno">   99</span>            <span class="comment">// copying remaining elements</span></div>
+<div class="line"><span class="lineno">  100</span>            <span class="comment">// if j becomes 0 before i</span></div>
+<div class="line"><span class="lineno">  101</span>            <span class="keywordflow">while</span>(i &gt; 0) {</div>
+<div class="line"><span class="lineno">  102</span>                s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/push_back.html">push_back</a>(str1[i-1]);</div>
+<div class="line"><span class="lineno">  103</span>                i--;</div>
+<div class="line"><span class="lineno">  104</span>            }</div>
+<div class="line"><span class="lineno">  105</span> </div>
+<div class="line"><span class="lineno">  106</span>            <span class="comment">// if i becomes 0 before j</span></div>
+<div class="line"><span class="lineno">  107</span>            <span class="keywordflow">while</span>(j &gt; 0) {</div>
+<div class="line"><span class="lineno">  108</span>                s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/push_back.html">push_back</a>(str2[j-1]);</div>
+<div class="line"><span class="lineno">  109</span>                j--;</div>
+<div class="line"><span class="lineno">  110</span>            }</div>
+<div class="line"><span class="lineno">  111</span> </div>
+<div class="line"><span class="lineno">  112</span>            <span class="comment">// As the super sequence is constructd backwards</span></div>
+<div class="line"><span class="lineno">  113</span>            <span class="comment">// reversing the string before returning gives us the correct output  </span></div>
+<div class="line"><span class="lineno">  114</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/reverse.html">reverse</a>(s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/begin.html">begin</a>(), s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/end.html">end</a>());</div>
+<div class="line"><span class="lineno">  115</span>            <span class="keywordflow">return</span> s;</div>
+<div class="line"><span class="lineno">  116</span>        }</div>
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@@ -332,44 +332,44 @@ Here is the call graph for this function:</div>
 </table>
 </div><div class="memdoc">
 <p >Test Function </p><dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>                   {</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>    <span class="comment">// custom input vector</span></div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector &lt;std::vector &lt;std::string&gt;</a>&gt; scsStrings {</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>        {<span class="stringliteral">&quot;ABCXYZ&quot;</span>, <span class="stringliteral">&quot;ABZ&quot;</span>},</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>        {<span class="stringliteral">&quot;ABZ&quot;</span>, <span class="stringliteral">&quot;ABCXYZ&quot;</span>},</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>        {<span class="stringliteral">&quot;AGGTAB&quot;</span>, <span class="stringliteral">&quot;GXTXAYB&quot;</span>},</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>        {<span class="stringliteral">&quot;X&quot;</span>, <span class="stringliteral">&quot;Y&quot;</span>},</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    };</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span> </div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    <span class="comment">// calculated output vector by scs function</span></div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector &lt;std::string&gt;</a> calculatedOutput(4, <span class="stringliteral">&quot;&quot;</span>);</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    <span class="keywordtype">int</span> i=0;</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    <span class="keywordflow">for</span>(<span class="keyword">auto</span> &amp; scsString : scsStrings) {</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        </div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>        calculatedOutput[i] = <a class="code hl_function" href="../../d7/d65/shortest__common__supersequence_8cpp.html#ad2ee8d7e67da9f6eb85146b08dad95e6">dynamic_programming::shortest_common_supersequence::scs</a>(</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>            scsString[0], scsString[1]</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>        );</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>        i++;</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    }</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span> </div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    <span class="comment">// expected output vector acc to problem statement</span></div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector &lt;std::string&gt;</a> expectedOutput {</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>        <span class="stringliteral">&quot;ABCXYZ&quot;</span>,</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>        <span class="stringliteral">&quot;ABCXYZ&quot;</span>,</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>        <span class="stringliteral">&quot;AGGXTXAYB&quot;</span>,</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>        <span class="stringliteral">&quot;XY&quot;</span></div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    };</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span> </div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>    <span class="comment">// Testing implementation via assert function</span></div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>    <span class="comment">// It will throw error if any of the expected test fails</span></div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>    <span class="comment">// Else it will give nothing</span></div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0; i &lt; scsStrings.size(); i++) {</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>        assert(expectedOutput[i] == calculatedOutput[i]);</div>
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-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span> </div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All tests passed successfully!\n&quot;</span>;</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>    <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  124</span>                   {</div>
+<div class="line"><span class="lineno">  125</span>    <span class="comment">// custom input vector</span></div>
+<div class="line"><span class="lineno">  126</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector &lt;std::vector &lt;std::string&gt;</a>&gt; scsStrings {</div>
+<div class="line"><span class="lineno">  127</span>        {<span class="stringliteral">&quot;ABCXYZ&quot;</span>, <span class="stringliteral">&quot;ABZ&quot;</span>},</div>
+<div class="line"><span class="lineno">  128</span>        {<span class="stringliteral">&quot;ABZ&quot;</span>, <span class="stringliteral">&quot;ABCXYZ&quot;</span>},</div>
+<div class="line"><span class="lineno">  129</span>        {<span class="stringliteral">&quot;AGGTAB&quot;</span>, <span class="stringliteral">&quot;GXTXAYB&quot;</span>},</div>
+<div class="line"><span class="lineno">  130</span>        {<span class="stringliteral">&quot;X&quot;</span>, <span class="stringliteral">&quot;Y&quot;</span>},</div>
+<div class="line"><span class="lineno">  131</span>    };</div>
+<div class="line"><span class="lineno">  132</span> </div>
+<div class="line"><span class="lineno">  133</span>    <span class="comment">// calculated output vector by scs function</span></div>
+<div class="line"><span class="lineno">  134</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector &lt;std::string&gt;</a> calculatedOutput(4, <span class="stringliteral">&quot;&quot;</span>);</div>
+<div class="line"><span class="lineno">  135</span>    <span class="keywordtype">int</span> i=0;</div>
+<div class="line"><span class="lineno">  136</span>    <span class="keywordflow">for</span>(<span class="keyword">auto</span> &amp; scsString : scsStrings) {</div>
+<div class="line"><span class="lineno">  137</span>        </div>
+<div class="line"><span class="lineno">  138</span>        calculatedOutput[i] = <a class="code hl_function" href="../../d7/d65/shortest__common__supersequence_8cpp.html#ad2ee8d7e67da9f6eb85146b08dad95e6">dynamic_programming::shortest_common_supersequence::scs</a>(</div>
+<div class="line"><span class="lineno">  139</span>            scsString[0], scsString[1]</div>
+<div class="line"><span class="lineno">  140</span>        );</div>
+<div class="line"><span class="lineno">  141</span>        i++;</div>
+<div class="line"><span class="lineno">  142</span>    }</div>
+<div class="line"><span class="lineno">  143</span> </div>
+<div class="line"><span class="lineno">  144</span>    <span class="comment">// expected output vector acc to problem statement</span></div>
+<div class="line"><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector &lt;std::string&gt;</a> expectedOutput {</div>
+<div class="line"><span class="lineno">  146</span>        <span class="stringliteral">&quot;ABCXYZ&quot;</span>,</div>
+<div class="line"><span class="lineno">  147</span>        <span class="stringliteral">&quot;ABCXYZ&quot;</span>,</div>
+<div class="line"><span class="lineno">  148</span>        <span class="stringliteral">&quot;AGGXTXAYB&quot;</span>,</div>
+<div class="line"><span class="lineno">  149</span>        <span class="stringliteral">&quot;XY&quot;</span></div>
+<div class="line"><span class="lineno">  150</span>    };</div>
+<div class="line"><span class="lineno">  151</span> </div>
+<div class="line"><span class="lineno">  152</span>    <span class="comment">// Testing implementation via assert function</span></div>
+<div class="line"><span class="lineno">  153</span>    <span class="comment">// It will throw error if any of the expected test fails</span></div>
+<div class="line"><span class="lineno">  154</span>    <span class="comment">// Else it will give nothing</span></div>
+<div class="line"><span class="lineno">  155</span>    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0; i &lt; scsStrings.size(); i++) {</div>
+<div class="line"><span class="lineno">  156</span>        assert(expectedOutput[i] == calculatedOutput[i]);</div>
+<div class="line"><span class="lineno">  157</span>    }</div>
+<div class="line"><span class="lineno">  158</span> </div>
+<div class="line"><span class="lineno">  159</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All tests passed successfully!\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  160</span>    <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  161</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
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+<div class="line"><span class="lineno">  136</span>                    memo[i][j] = <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  137</span>                } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  138</span>                    memo[i][j] = memo[i - 1][j];</div>
+<div class="line"><span class="lineno">  139</span>                }</div>
+<div class="line"><span class="lineno">  140</span>            }</div>
+<div class="line"><span class="lineno">  141</span>        }</div>
+<div class="line"><span class="lineno">  142</span>    }</div>
+<div class="line"><span class="lineno">  143</span>    <span class="keywordflow">return</span> memo.back().back();</div>
+<div class="line"><span class="lineno">  144</span>}</div>
 <div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
 <div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">std::string::size</a></div><div class="ttdeci">T size(T... args)</div></div>
 <div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
@@ -294,57 +294,57 @@ Here is the call graph for this function:</div>
 <li>convert it to capitalized letter and move both to next pointer <code>(i + 1, j + 1)</code></li>
 <li>Discard the character <code>(str[i])</code> and move to next char <code>(i + 1, j)</code></li>
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-<div class="fragment"><div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>                                                                           {</div>
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-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    <span class="keywordflow">if</span> (str_idx == str.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() &amp;&amp; result_idx == <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.size()) {</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (str_idx == str.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() &amp;&amp; result_idx != <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.size()) {</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="comment">// result `t` is not converted, return false</span></div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (!visited-&gt;at(str_idx).at(result_idx)) {<span class="comment"></span></div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span><span class="comment">        /**</span></div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span><span class="comment">         * `(str[i] == result[j])`: if str char at position i is equal to</span></div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span><span class="comment">         * `result` char at position j, then s character is a capitalized one,</span></div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span><span class="comment">         * move on to next character `str[i] - 32 == result[j]`:</span></div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span><span class="comment">         * if `str[i]` character is lowercase of `result[j]` then explore two</span></div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span><span class="comment">         * possibilites:</span></div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span><span class="comment">         * 1. convert it to capitalized letter and move both to next pointer</span></div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span><span class="comment">         * `(i + 1, j + 1)`</span></div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span><span class="comment">         * 2. Discard the character `(str[i])` and move to next char `(i + 1,</span></div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span><span class="comment">         * j)`</span></div>
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-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>        <span class="keywordflow">if</span> (str[str_idx] == result[result_idx]) {</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>            <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = <a class="code hl_function" href="../../d7/d73/abbreviation_8cpp.html#add60b8858720bf217df22d992d0fefaa">abbreviation_recursion</a>(memo, visited, str, result,</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>                                         str_idx + 1, result_idx + 1);</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (str[str_idx] - 32 == result[result_idx]) {</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>            <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = <a class="code hl_function" href="../../d7/d73/abbreviation_8cpp.html#add60b8858720bf217df22d992d0fefaa">abbreviation_recursion</a>(memo, visited, str, result,</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>                                         str_idx + 1, result_idx + 1) ||</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>                  <a class="code hl_function" href="../../d7/d73/abbreviation_8cpp.html#add60b8858720bf217df22d992d0fefaa">abbreviation_recursion</a>(memo, visited, str, result,</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>                                         str_idx + 1, result_idx);</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        } <span class="keywordflow">else</span> {</div>
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-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>                                             str_idx + 1, result_idx);</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>            }</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>        }</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    }</div>
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-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    (*visited)[str_idx][result_idx] = <span class="keyword">true</span>;</div>
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-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   61</span>                                                                           {</div>
+<div class="line"><span class="lineno">   62</span>    <span class="keywordtype">bool</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = memo-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/at.html">at</a>(str_idx).at(result_idx);</div>
+<div class="line"><span class="lineno">   63</span>    <span class="keywordflow">if</span> (str_idx == str.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() &amp;&amp; result_idx == <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.size()) {</div>
+<div class="line"><span class="lineno">   64</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   65</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (str_idx == str.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() &amp;&amp; result_idx != <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.size()) {</div>
+<div class="line"><span class="lineno">   66</span>        <span class="comment">// result `t` is not converted, return false</span></div>
+<div class="line"><span class="lineno">   67</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   68</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (!visited-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/at.html">at</a>(str_idx).at(result_idx)) {<span class="comment"></span></div>
+<div class="line"><span class="lineno">   69</span><span class="comment">        /**</span></div>
+<div class="line"><span class="lineno">   70</span><span class="comment">         * `(str[i] == result[j])`: if str char at position i is equal to</span></div>
+<div class="line"><span class="lineno">   71</span><span class="comment">         * `result` char at position j, then s character is a capitalized one,</span></div>
+<div class="line"><span class="lineno">   72</span><span class="comment">         * move on to next character `str[i] - 32 == result[j]`:</span></div>
+<div class="line"><span class="lineno">   73</span><span class="comment">         * if `str[i]` character is lowercase of `result[j]` then explore two</span></div>
+<div class="line"><span class="lineno">   74</span><span class="comment">         * possibilites:</span></div>
+<div class="line"><span class="lineno">   75</span><span class="comment">         * 1. convert it to capitalized letter and move both to next pointer</span></div>
+<div class="line"><span class="lineno">   76</span><span class="comment">         * `(i + 1, j + 1)`</span></div>
+<div class="line"><span class="lineno">   77</span><span class="comment">         * 2. Discard the character `(str[i])` and move to next char `(i + 1,</span></div>
+<div class="line"><span class="lineno">   78</span><span class="comment">         * j)`</span></div>
+<div class="line"><span class="lineno">   79</span><span class="comment">         */</span></div>
+<div class="line"><span class="lineno">   80</span>        <span class="keywordflow">if</span> (str[str_idx] == result[result_idx]) {</div>
+<div class="line"><span class="lineno">   81</span>            <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = <a class="code hl_function" href="../../d7/d73/abbreviation_8cpp.html#add60b8858720bf217df22d992d0fefaa">abbreviation_recursion</a>(memo, visited, str, result,</div>
+<div class="line"><span class="lineno">   82</span>                                         str_idx + 1, result_idx + 1);</div>
+<div class="line"><span class="lineno">   83</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (str[str_idx] - 32 == result[result_idx]) {</div>
+<div class="line"><span class="lineno">   84</span>            <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = <a class="code hl_function" href="../../d7/d73/abbreviation_8cpp.html#add60b8858720bf217df22d992d0fefaa">abbreviation_recursion</a>(memo, visited, str, result,</div>
+<div class="line"><span class="lineno">   85</span>                                         str_idx + 1, result_idx + 1) ||</div>
+<div class="line"><span class="lineno">   86</span>                  <a class="code hl_function" href="../../d7/d73/abbreviation_8cpp.html#add60b8858720bf217df22d992d0fefaa">abbreviation_recursion</a>(memo, visited, str, result,</div>
+<div class="line"><span class="lineno">   87</span>                                         str_idx + 1, result_idx);</div>
+<div class="line"><span class="lineno">   88</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   89</span>            <span class="comment">// if `str[i]` is uppercase, then cannot be converted, return</span></div>
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+<div class="line"><span class="lineno">   91</span>            <span class="comment">// else `str[i]` is lowercase, only option is to discard this</span></div>
+<div class="line"><span class="lineno">   92</span>            <span class="comment">// character</span></div>
+<div class="line"><span class="lineno">   93</span>            <span class="keywordflow">if</span> (str[str_idx] &gt;= <span class="charliteral">&#39;A&#39;</span> &amp;&amp; str[str_idx] &lt;= <span class="charliteral">&#39;Z&#39;</span>) {</div>
+<div class="line"><span class="lineno">   94</span>                <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   95</span>            } <span class="keywordflow">else</span> {</div>
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+<div class="line"><span class="lineno">   97</span>                                             str_idx + 1, result_idx);</div>
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 <div class="ttc" id="aat_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/at.html">std::vector::at</a></div><div class="ttdeci">T at(T... args)</div></div>
 <div class="ttc" id="amatrix__exponentiation_8cpp_html_ad8389ed58fd0ec66df248014775ad1fa"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a></div><div class="ttdeci">ll ans(ll n)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:91</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
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+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d7/d73/abbreviation_8cpp_add60b8858720bf217df22d992d0fefaa_cgraph.svg" width="350" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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@@ -368,10 +368,10 @@ Here is the call graph for this function:</div>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>           {</div>
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+<div class="fragment"><div class="line"><span class="lineno">  191</span>           {</div>
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+<div class="line"><span class="lineno">  193</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  194</span>}</div>
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 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -407,40 +407,40 @@ Here is the call graph for this function:</div>
 
 <p>Self test-implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>                   {</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s = <span class="stringliteral">&quot;daBcd&quot;</span>, t = <span class="stringliteral">&quot;ABC&quot;</span>;</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;bool&gt;</a>&gt; memo(s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() + 1,</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>                                        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>(t.size() + 1, <span class="keyword">false</span>)),</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>        visited(s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() + 1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>(t.size() + 1, <span class="keyword">false</span>));</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span> </div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    assert(dynamic_programming::abbreviation::abbreviation_recursion(</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>               &amp;memo, &amp;visited, s, t) == <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>    assert(dynamic_programming::abbreviation::abbreviation(s, t) == <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>    s = <span class="stringliteral">&quot;XXVVnDEFYgYeMXzWINQYHAQKKOZEYgSRCzLZAmUYGUGILjMDET&quot;</span>;</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>    t = <span class="stringliteral">&quot;XXVVDEFYYMXWINQYHAQKKOZEYSRCLZAUYGUGILMDETQVWU&quot;</span>;</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>    memo = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;bool&gt;</a>&gt;(</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>        s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() + 1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>(t.size() + 1, <span class="keyword">false</span>));</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span> </div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    visited = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;bool&gt;</a>&gt;(</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>        s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() + 1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>(t.size() + 1, <span class="keyword">false</span>));</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span> </div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>    assert(dynamic_programming::abbreviation::abbreviation_recursion(</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>               &amp;memo, &amp;visited, s, t) == <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>    assert(dynamic_programming::abbreviation::abbreviation(s, t) == <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span> </div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>    s = <span class="stringliteral">&quot;DRFNLZZVHLPZWIupjwdmqafmgkg&quot;</span>;</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>    t = <span class="stringliteral">&quot;DRFNLZZVHLPZWI&quot;</span>;</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span> </div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>    memo = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;bool&gt;</a>&gt;(</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>        s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() + 1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>(t.size() + 1, <span class="keyword">false</span>));</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span> </div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>    visited = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;bool&gt;</a>&gt;(</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>        s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() + 1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>(t.size() + 1, <span class="keyword">false</span>));</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span> </div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>    assert(dynamic_programming::abbreviation::abbreviation_recursion(</div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>               &amp;memo, &amp;visited, s, t) == <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>    assert(dynamic_programming::abbreviation::abbreviation(s, t) == <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  152</span>                   {</div>
+<div class="line"><span class="lineno">  153</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s = <span class="stringliteral">&quot;daBcd&quot;</span>, t = <span class="stringliteral">&quot;ABC&quot;</span>;</div>
+<div class="line"><span class="lineno">  154</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;bool&gt;</a>&gt; memo(s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() + 1,</div>
+<div class="line"><span class="lineno">  155</span>                                        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>(t.size() + 1, <span class="keyword">false</span>)),</div>
+<div class="line"><span class="lineno">  156</span>        visited(s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() + 1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>(t.size() + 1, <span class="keyword">false</span>));</div>
+<div class="line"><span class="lineno">  157</span> </div>
+<div class="line"><span class="lineno">  158</span>    assert(dynamic_programming::abbreviation::abbreviation_recursion(</div>
+<div class="line"><span class="lineno">  159</span>               &amp;memo, &amp;visited, s, t) == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  160</span>    assert(dynamic_programming::abbreviation::abbreviation(s, t) == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  161</span>    s = <span class="stringliteral">&quot;XXVVnDEFYgYeMXzWINQYHAQKKOZEYgSRCzLZAmUYGUGILjMDET&quot;</span>;</div>
+<div class="line"><span class="lineno">  162</span>    t = <span class="stringliteral">&quot;XXVVDEFYYMXWINQYHAQKKOZEYSRCLZAUYGUGILMDETQVWU&quot;</span>;</div>
+<div class="line"><span class="lineno">  163</span>    memo = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;bool&gt;</a>&gt;(</div>
+<div class="line"><span class="lineno">  164</span>        s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() + 1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>(t.size() + 1, <span class="keyword">false</span>));</div>
+<div class="line"><span class="lineno">  165</span> </div>
+<div class="line"><span class="lineno">  166</span>    visited = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;bool&gt;</a>&gt;(</div>
+<div class="line"><span class="lineno">  167</span>        s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() + 1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>(t.size() + 1, <span class="keyword">false</span>));</div>
+<div class="line"><span class="lineno">  168</span> </div>
+<div class="line"><span class="lineno">  169</span>    assert(dynamic_programming::abbreviation::abbreviation_recursion(</div>
+<div class="line"><span class="lineno">  170</span>               &amp;memo, &amp;visited, s, t) == <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  171</span>    assert(dynamic_programming::abbreviation::abbreviation(s, t) == <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  172</span> </div>
+<div class="line"><span class="lineno">  173</span>    s = <span class="stringliteral">&quot;DRFNLZZVHLPZWIupjwdmqafmgkg&quot;</span>;</div>
+<div class="line"><span class="lineno">  174</span>    t = <span class="stringliteral">&quot;DRFNLZZVHLPZWI&quot;</span>;</div>
+<div class="line"><span class="lineno">  175</span> </div>
+<div class="line"><span class="lineno">  176</span>    memo = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;bool&gt;</a>&gt;(</div>
+<div class="line"><span class="lineno">  177</span>        s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() + 1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>(t.size() + 1, <span class="keyword">false</span>));</div>
+<div class="line"><span class="lineno">  178</span> </div>
+<div class="line"><span class="lineno">  179</span>    visited = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;bool&gt;</a>&gt;(</div>
+<div class="line"><span class="lineno">  180</span>        s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() + 1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>(t.size() + 1, <span class="keyword">false</span>));</div>
+<div class="line"><span class="lineno">  181</span> </div>
+<div class="line"><span class="lineno">  182</span>    assert(dynamic_programming::abbreviation::abbreviation_recursion(</div>
+<div class="line"><span class="lineno">  183</span>               &amp;memo, &amp;visited, s, t) == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  184</span>    assert(dynamic_programming::abbreviation::abbreviation(s, t) == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  185</span>}</div>
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+<div class="line"><span class="lineno">   92</span>            c = a * b; <span class="comment">// Multiplication of numbers</span></div>
+<div class="line"><span class="lineno">   93</span>            <a class="code hl_function" href="../../dc/dc5/paranthesis__matching_8cpp.html#aae41c72130114bf31204cde6873b6095">others::postfix_expression::push</a>(c, <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>);</div>
+<div class="line"><span class="lineno">   94</span>            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">   95</span> </div>
+<div class="line"><span class="lineno">   96</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;/&#39;</span>:</div>
+<div class="line"><span class="lineno">   97</span>            c = a / b; <span class="comment">// Division of numbers</span></div>
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+<div class="line"><span class="lineno">   99</span>            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  100</span> </div>
+<div class="line"><span class="lineno">  101</span>        <span class="keywordflow">default</span>:</div>
+<div class="line"><span class="lineno">  102</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Operator not defined\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  103</span>            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  104</span>    }</div>
+<div class="line"><span class="lineno">  105</span>}</div>
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+<div class="fragment"><div class="line"><span class="lineno">   65</span>                                   {</div>
+<div class="line"><span class="lineno">   66</span>    <span class="keywordflow">return</span> !s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/empty.html">empty</a>() &amp;&amp; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/all_any_none_of.html">std::all_of</a>(s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/begin.html">begin</a>(), s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/end.html">end</a>(), ::isdigit);</div>
+<div class="line"><span class="lineno">   67</span>}</div>
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@@ -309,14 +309,14 @@ Here is the call graph for this function:</div>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>           {</div>
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-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span> </div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nTest implementations passed!\n&quot;</span>;</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span> </div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  171</span>           {</div>
+<div class="line"><span class="lineno">  172</span>    <a class="code hl_function" href="../../d7/d75/postfix__evaluation_8cpp.html#a6a8eeb7d346d5cd6335d9780fb7c0f15">test_function_1</a>();</div>
+<div class="line"><span class="lineno">  173</span>    <a class="code hl_function" href="../../d7/d75/postfix__evaluation_8cpp.html#a5b97d12e8b61484f756a8721992bfae1">test_function_2</a>();</div>
+<div class="line"><span class="lineno">  174</span> </div>
+<div class="line"><span class="lineno">  175</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nTest implementations passed!\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  176</span> </div>
+<div class="line"><span class="lineno">  177</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  178</span>}</div>
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 <div class="ttc" id="apostfix__evaluation_8cpp_html_a6a8eeb7d346d5cd6335d9780fb7c0f15"><div class="ttname"><a href="../../d7/d75/postfix__evaluation_8cpp.html#a6a8eeb7d346d5cd6335d9780fb7c0f15">test_function_1</a></div><div class="ttdeci">static void test_function_1()</div><div class="ttdoc">Test function 1 with input array {'2', '3', '1', '*', '+', '9', '-'}.</div><div class="ttdef"><b>Definition:</b> postfix_evaluation.cpp:146</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -352,11 +352,11 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>operand float on top of stack </dd></dl>
-<div class="fragment"><div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>                        {</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <span class="keywordtype">float</span> operand = <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>-&gt;<a class="code hl_function" href="../../d1/dc2/classstack.html#a5b64337ec34b12e98458bb9b9d5f8f83">stack</a>[<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>-&gt;<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>];</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>-&gt;<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>--;</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    <span class="keywordflow">return</span> operand;</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   54</span>                        {</div>
+<div class="line"><span class="lineno">   55</span>    <span class="keywordtype">float</span> operand = <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>-&gt;<a class="code hl_function" href="../../d1/dc2/classstack.html#a5b64337ec34b12e98458bb9b9d5f8f83">stack</a>[<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>-&gt;<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>];</div>
+<div class="line"><span class="lineno">   56</span>    <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>-&gt;<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>--;</div>
+<div class="line"><span class="lineno">   57</span>    <span class="keywordflow">return</span> operand;</div>
+<div class="line"><span class="lineno">   58</span>}</div>
 <div class="ttc" id="aclassstack_html_a5b64337ec34b12e98458bb9b9d5f8f83"><div class="ttname"><a href="../../d1/dc2/classstack.html#a5b64337ec34b12e98458bb9b9d5f8f83">stack::stack</a></div><div class="ttdeci">stack()</div><div class="ttdef"><b>Definition:</b> stack.h:41</div></div>
 <div class="ttc" id="aclassstack_html_a7289037c059aaad492b4d68e6bd54453"><div class="ttname"><a href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stack::stackTop</a></div><div class="ttdeci">node&lt; Type &gt; * stackTop</div><div class="ttdef"><b>Definition:</b> stack.h:146</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -400,28 +400,28 @@ template&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>stack[stackTop] returns the top value from the stack </dd></dl>
-<div class="fragment"><div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>                                                       {</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    Stack <a class="code hl_variable" href="../../dc/dc5/paranthesis__matching_8cpp.html#aa37d24a036d239b3b528f13b9de880c7">stack</a>;</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    <span class="keywordtype">int</span> j = 0;</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span> </div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    <span class="keywordflow">while</span> (j &lt; N) {</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> scan = input[j];</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d7/d75/postfix__evaluation_8cpp.html#a4c27f949c9d6659be9f5bd2ccbe1360a">is_number</a>(scan)) {</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>            <a class="code hl_function" href="../../dc/dc5/paranthesis__matching_8cpp.html#aae41c72130114bf31204cde6873b6095">push</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/stof.html">std::stof</a>(scan), &amp;<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>);</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span> </div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>            <span class="keywordtype">float</span> op2 = <a class="code hl_function" href="../../dc/dc5/paranthesis__matching_8cpp.html#a6d25c7dfbfeb52c3cb9d1b56ab49b664">pop</a>(&amp;<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>);</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>            <span class="keywordtype">float</span> op1 = <a class="code hl_function" href="../../dc/dc5/paranthesis__matching_8cpp.html#a6d25c7dfbfeb52c3cb9d1b56ab49b664">pop</a>(&amp;<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>);</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span> </div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>            <a class="code hl_function" href="../../d7/d75/postfix__evaluation_8cpp.html#a59fd597e0ea394abe027ced4d2ea3338">evaluate</a>(op1, op2, scan, &amp;<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>);</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>        }</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>        j++;</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    }</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span> </div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a5b64337ec34b12e98458bb9b9d5f8f83">stack</a>[<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>] &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span> </div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    <span class="keywordflow">return</span> <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a5b64337ec34b12e98458bb9b9d5f8f83">stack</a>[<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>];</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  115</span>                                                       {</div>
+<div class="line"><span class="lineno">  116</span>    Stack <a class="code hl_variable" href="../../dc/dc5/paranthesis__matching_8cpp.html#aa37d24a036d239b3b528f13b9de880c7">stack</a>;</div>
+<div class="line"><span class="lineno">  117</span>    <span class="keywordtype">int</span> j = 0;</div>
+<div class="line"><span class="lineno">  118</span> </div>
+<div class="line"><span class="lineno">  119</span>    <span class="keywordflow">while</span> (j &lt; N) {</div>
+<div class="line"><span class="lineno">  120</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> scan = input[j];</div>
+<div class="line"><span class="lineno">  121</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d7/d75/postfix__evaluation_8cpp.html#a4c27f949c9d6659be9f5bd2ccbe1360a">is_number</a>(scan)) {</div>
+<div class="line"><span class="lineno">  122</span>            <a class="code hl_function" href="../../dc/dc5/paranthesis__matching_8cpp.html#aae41c72130114bf31204cde6873b6095">push</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/stof.html">std::stof</a>(scan), &amp;<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>);</div>
+<div class="line"><span class="lineno">  123</span> </div>
+<div class="line"><span class="lineno">  124</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  125</span>            <span class="keywordtype">float</span> op2 = <a class="code hl_function" href="../../dc/dc5/paranthesis__matching_8cpp.html#a6d25c7dfbfeb52c3cb9d1b56ab49b664">pop</a>(&amp;<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>);</div>
+<div class="line"><span class="lineno">  126</span>            <span class="keywordtype">float</span> op1 = <a class="code hl_function" href="../../dc/dc5/paranthesis__matching_8cpp.html#a6d25c7dfbfeb52c3cb9d1b56ab49b664">pop</a>(&amp;<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>);</div>
+<div class="line"><span class="lineno">  127</span> </div>
+<div class="line"><span class="lineno">  128</span>            <a class="code hl_function" href="../../d7/d75/postfix__evaluation_8cpp.html#a59fd597e0ea394abe027ced4d2ea3338">evaluate</a>(op1, op2, scan, &amp;<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>);</div>
+<div class="line"><span class="lineno">  129</span>        }</div>
+<div class="line"><span class="lineno">  130</span>        j++;</div>
+<div class="line"><span class="lineno">  131</span>    }</div>
+<div class="line"><span class="lineno">  132</span> </div>
+<div class="line"><span class="lineno">  133</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a5b64337ec34b12e98458bb9b9d5f8f83">stack</a>[<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>] &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  134</span> </div>
+<div class="line"><span class="lineno">  135</span>    <span class="keywordflow">return</span> <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a5b64337ec34b12e98458bb9b9d5f8f83">stack</a>[<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>];</div>
+<div class="line"><span class="lineno">  136</span>}</div>
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   </dd>
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 <dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
-<div class="fragment"><div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>                                       {</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>    <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>-&gt;<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>++;</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>    <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>-&gt;<a class="code hl_function" href="../../d1/dc2/classstack.html#a5b64337ec34b12e98458bb9b9d5f8f83">stack</a>[<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>-&gt;<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>] = operand;</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   44</span>                                       {</div>
+<div class="line"><span class="lineno">   45</span>    <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>-&gt;<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>++;</div>
+<div class="line"><span class="lineno">   46</span>    <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>-&gt;<a class="code hl_function" href="../../d1/dc2/classstack.html#a5b64337ec34b12e98458bb9b9d5f8f83">stack</a>[<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>-&gt;<a class="code hl_variable" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>] = operand;</div>
+<div class="line"><span class="lineno">   47</span>}</div>
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@@ -510,13 +510,13 @@ Here is the call graph for this function:</div>
 
 <p>Test function 1 with input array {'2', '3', '1', '*', '+', '9', '-'}. </p>
 <dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
-<div class="fragment"><div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>                              {</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::string, 7&gt;</a> input = {<span class="stringliteral">&quot;2&quot;</span>, <span class="stringliteral">&quot;3&quot;</span>, <span class="stringliteral">&quot;1&quot;</span>, <span class="stringliteral">&quot;*&quot;</span>, <span class="stringliteral">&quot;+&quot;</span>, <span class="stringliteral">&quot;9&quot;</span>, <span class="stringliteral">&quot;-&quot;</span>};</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span> </div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>    <span class="keywordtype">float</span> answer = <a class="code hl_function" href="../../d7/d75/postfix__evaluation_8cpp.html#ae38bd3a177a6d61da3859a281233bbe1">others::postfix_expression::postfix_evaluation</a>(input);</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span> </div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    assert(answer == -4);</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  146</span>                              {</div>
+<div class="line"><span class="lineno">  147</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::string, 7&gt;</a> input = {<span class="stringliteral">&quot;2&quot;</span>, <span class="stringliteral">&quot;3&quot;</span>, <span class="stringliteral">&quot;1&quot;</span>, <span class="stringliteral">&quot;*&quot;</span>, <span class="stringliteral">&quot;+&quot;</span>, <span class="stringliteral">&quot;9&quot;</span>, <span class="stringliteral">&quot;-&quot;</span>};</div>
+<div class="line"><span class="lineno">  148</span> </div>
+<div class="line"><span class="lineno">  149</span>    <span class="keywordtype">float</span> answer = <a class="code hl_function" href="../../d7/d75/postfix__evaluation_8cpp.html#ae38bd3a177a6d61da3859a281233bbe1">others::postfix_expression::postfix_evaluation</a>(input);</div>
+<div class="line"><span class="lineno">  150</span> </div>
+<div class="line"><span class="lineno">  151</span>    assert(answer == -4);</div>
+<div class="line"><span class="lineno">  152</span>}</div>
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@@ -547,13 +547,13 @@ Here is the call graph for this function:</div>
 
 <p>Test function 2 with input array {'1', '2', '+', '2', '/', '5', '*', '7', '+'}. </p>
 <dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
-<div class="fragment"><div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>                              {</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::string, 9&gt;</a> input = {<span class="stringliteral">&quot;100&quot;</span>, <span class="stringliteral">&quot;200&quot;</span>, <span class="stringliteral">&quot;+&quot;</span>, <span class="stringliteral">&quot;2&quot;</span>, <span class="stringliteral">&quot;/&quot;</span>,</div>
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-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>    <span class="keywordtype">float</span> answer = <a class="code hl_function" href="../../d7/d75/postfix__evaluation_8cpp.html#ae38bd3a177a6d61da3859a281233bbe1">others::postfix_expression::postfix_evaluation</a>(input);</div>
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-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>    assert(answer == 757);</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  159</span>                              {</div>
+<div class="line"><span class="lineno">  160</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::string, 9&gt;</a> input = {<span class="stringliteral">&quot;100&quot;</span>, <span class="stringliteral">&quot;200&quot;</span>, <span class="stringliteral">&quot;+&quot;</span>, <span class="stringliteral">&quot;2&quot;</span>, <span class="stringliteral">&quot;/&quot;</span>,</div>
+<div class="line"><span class="lineno">  161</span>                                        <span class="stringliteral">&quot;5&quot;</span>,   <span class="stringliteral">&quot;*&quot;</span>,   <span class="stringliteral">&quot;7&quot;</span>, <span class="stringliteral">&quot;+&quot;</span>};</div>
+<div class="line"><span class="lineno">  162</span>    <span class="keywordtype">float</span> answer = <a class="code hl_function" href="../../d7/d75/postfix__evaluation_8cpp.html#ae38bd3a177a6d61da3859a281233bbe1">others::postfix_expression::postfix_evaluation</a>(input);</div>
+<div class="line"><span class="lineno">  163</span> </div>
+<div class="line"><span class="lineno">  164</span>    assert(answer == 757);</div>
+<div class="line"><span class="lineno">  165</span>}</div>
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+<div class="line"><span class="lineno">  195</span>    <span class="comment">// Following lines of code give erroneous output</span></div>
+<div class="line"><span class="lineno">  196</span>    <span class="comment">// root.deleteString(&quot;hello&quot;, 0);</span></div>
+<div class="line"><span class="lineno">  197</span>    <span class="comment">// assert(!root.search(&quot;hello&quot;, 0));</span></div>
+<div class="line"><span class="lineno">  198</span>    <span class="comment">// std::cout &lt;&lt; &quot;hello - &quot; &lt;&lt; root.search(&quot;world&quot;, 0) &lt;&lt; &quot;\n&quot;;</span></div>
+<div class="line"><span class="lineno">  199</span>}</div>
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+<div class="ttc" id="ainsert_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/insert.html">std::vector::insert</a></div><div class="ttdeci">T insert(T... args)</div></div>
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@@ -141,15 +141,15 @@ It is also called as semifactorial of a number and is denoted by \(n!!\) </p>
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+<div class="line"><span class="lineno">   18</span>    uint64_t res = 1;</div>
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+<div class="line"><span class="lineno">   24</span>    <span class="keywordflow">return</span> res;</div>
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 <p >Compute double factorial using resursive method. <br  />
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+<div class="line"><span class="lineno">   33</span>    <span class="keywordflow">return</span> n * <a class="code hl_function" href="../../d7/d89/double__factorial_8cpp.html#a68ba20fed2ce427f6469c7689437829d">double_factorial_recursive</a>(n - 2);</div>
+<div class="line"><span class="lineno">   34</span>}</div>
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+<div class="line"><span class="lineno">   69</span>    <span class="keywordflow">return</span> 0;</div>
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 Here is the call graph for this function:</div>
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+<div class="line"><span class="lineno">   43</span>    assert(<a class="code hl_function" href="../../d7/d89/double__factorial_8cpp.html#a0a3c417360400093891a9ccddaa4be26">double_factorial_iterative</a>(n) == expected);</div>
+<div class="line"><span class="lineno">   44</span>    assert(<a class="code hl_function" href="../../d7/d89/double__factorial_8cpp.html#a68ba20fed2ce427f6469c7689437829d">double_factorial_recursive</a>(n) == expected);</div>
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-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2:\t n=15\t...&quot;</span>;</div>
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-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3:\t n=0\t...&quot;</span>;</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <a class="code hl_function" href="../../d7/d89/double__factorial_8cpp.html#abbbcebf3a2d0c67f4c3cfb5511a97981">test</a>(0, 1);</div>
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+<div class="line"><span class="lineno">   56</span>    <a class="code hl_function" href="../../d7/d89/double__factorial_8cpp.html#abbbcebf3a2d0c67f4c3cfb5511a97981">test</a>(15, 2027025);</div>
+<div class="line"><span class="lineno">   57</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
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 <p >Main function </p>
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-<div class="line"><a id="l00533" name="l00533"></a><span class="lineno">  533</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
-<div class="line"><a id="l00534" name="l00534"></a><span class="lineno">  534</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Key dictionary: (&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/strlen.html">std::strlen</a>(<a class="code hl_variable" href="../../d6/d4e/namespaceciphers.html#ab9aec0ccf4b6809f652bb540be87c216">ciphers::STRKEY</a>) &lt;&lt; <span class="stringliteral">&quot;)\n\t&quot;</span></div>
-<div class="line"><a id="l00535" name="l00535"></a><span class="lineno">  535</span>              &lt;&lt; <a class="code hl_variable" href="../../d6/d4e/namespaceciphers.html#ab9aec0ccf4b6809f652bb540be87c216">ciphers::STRKEY</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00536" name="l00536"></a><span class="lineno">  536</span> </div>
-<div class="line"><a id="l00537" name="l00537"></a><span class="lineno">  537</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> text = <span class="stringliteral">&quot;This is a simple text with numb3r5 and exclamat!0n.&quot;</span>;</div>
-<div class="line"><a id="l00538" name="l00538"></a><span class="lineno">  538</span> </div>
-<div class="line"><a id="l00539" name="l00539"></a><span class="lineno">  539</span>    <a class="code hl_function" href="../../d7/db9/hill__cipher_8cpp.html#a3147ad576f8a94a2a6b66948672b452b">test1</a>(text);</div>
-<div class="line"><a id="l00540" name="l00540"></a><span class="lineno">  540</span>    <a class="code hl_function" href="../../d7/db9/hill__cipher_8cpp.html#a04391124480d2a49f2dec900237b0712">test2</a>(text);</div>
-<div class="line"><a id="l00541" name="l00541"></a><span class="lineno">  541</span> </div>
-<div class="line"><a id="l00542" name="l00542"></a><span class="lineno">  542</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00543" name="l00543"></a><span class="lineno">  543</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  532</span>           {</div>
+<div class="line"><span class="lineno">  533</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
+<div class="line"><span class="lineno">  534</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Key dictionary: (&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/strlen.html">std::strlen</a>(<a class="code hl_variable" href="../../d6/d4e/namespaceciphers.html#ab9aec0ccf4b6809f652bb540be87c216">ciphers::STRKEY</a>) &lt;&lt; <span class="stringliteral">&quot;)\n\t&quot;</span></div>
+<div class="line"><span class="lineno">  535</span>              &lt;&lt; <a class="code hl_variable" href="../../d6/d4e/namespaceciphers.html#ab9aec0ccf4b6809f652bb540be87c216">ciphers::STRKEY</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  536</span> </div>
+<div class="line"><span class="lineno">  537</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> text = <span class="stringliteral">&quot;This is a simple text with numb3r5 and exclamat!0n.&quot;</span>;</div>
+<div class="line"><span class="lineno">  538</span> </div>
+<div class="line"><span class="lineno">  539</span>    <a class="code hl_function" href="../../d7/db9/hill__cipher_8cpp.html#a3147ad576f8a94a2a6b66948672b452b">test1</a>(text);</div>
+<div class="line"><span class="lineno">  540</span>    <a class="code hl_function" href="../../d7/db9/hill__cipher_8cpp.html#a04391124480d2a49f2dec900237b0712">test2</a>(text);</div>
+<div class="line"><span class="lineno">  541</span> </div>
+<div class="line"><span class="lineno">  542</span>    <span class="keywordflow">return</span> 0;</div>
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 <div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
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@@ -242,19 +242,19 @@ template&lt;typename T &gt; </div>
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 <p >operator to print a matrix </p>
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-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> width = 15;</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">&#39; &#39;</span>;</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span> </div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; v.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); row++) {</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; v[row].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); col++)</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>            out &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::left</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(width) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a>(separator)</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>                &lt;&lt; v[row][col];</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        out &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="fragment"><div class="line"><span class="lineno">   54</span>                                                                   {</div>
+<div class="line"><span class="lineno">   55</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> width = 15;</div>
+<div class="line"><span class="lineno">   56</span>    <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">&#39; &#39;</span>;</div>
+<div class="line"><span class="lineno">   57</span> </div>
+<div class="line"><span class="lineno">   58</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; v.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); row++) {</div>
+<div class="line"><span class="lineno">   59</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; v[row].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); col++)</div>
+<div class="line"><span class="lineno">   60</span>            out &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::left</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(width) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a>(separator)</div>
+<div class="line"><span class="lineno">   61</span>                &lt;&lt; v[row][col];</div>
+<div class="line"><span class="lineno">   62</span>        out &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   63</span>    }</div>
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@@ -292,35 +292,35 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
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-<div class="fragment"><div class="line"><a id="l00470" name="l00470"></a><span class="lineno">  470</span>                                  {</div>
-<div class="line"><a id="l00471" name="l00471"></a><span class="lineno">  471</span>    <span class="comment">// std::string text = &quot;Hello world!&quot;;</span></div>
-<div class="line"><a id="l00472" name="l00472"></a><span class="lineno">  472</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;======Test 1 (3x3 key) ======\nOriginal text:\n\t&quot;</span> &lt;&lt; text</div>
-<div class="line"><a id="l00473" name="l00473"></a><span class="lineno">  473</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00474" name="l00474"></a><span class="lineno">  474</span> </div>
-<div class="line"><a id="l00475" name="l00475"></a><span class="lineno">  475</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;matrix&lt;int&gt;</a>, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a>&gt; p =</div>
-<div class="line"><a id="l00476" name="l00476"></a><span class="lineno">  476</span>        <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#a405b0a28d66a61239d3565d5256f9cb5">ciphers::HillCipher::generate_keys</a>(3, 0, 100);</div>
-<div class="line"><a id="l00477" name="l00477"></a><span class="lineno">  477</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> ekey = p.first;</div>
-<div class="line"><a id="l00478" name="l00478"></a><span class="lineno">  478</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> dkey = p.second;</div>
-<div class="line"><a id="l00479" name="l00479"></a><span class="lineno">  479</span> </div>
-<div class="line"><a id="l00480" name="l00480"></a><span class="lineno">  480</span>    <span class="comment">// matrix&lt;int&gt; ekey = {{22, 28, 25}, {5, 26, 15}, {14, 18, 9}};</span></div>
-<div class="line"><a id="l00481" name="l00481"></a><span class="lineno">  481</span>    <span class="comment">// std::cout &lt;&lt; &quot;Encryption key: \n&quot; &lt;&lt; ekey;</span></div>
-<div class="line"><a id="l00482" name="l00482"></a><span class="lineno">  482</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> gibberish = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#aa8bbb6e4a5749f6008b06602d5103917">ciphers::HillCipher::encrypt_text</a>(text, ekey);</div>
-<div class="line"><a id="l00483" name="l00483"></a><span class="lineno">  483</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Encrypted text:\n\t&quot;</span> &lt;&lt; gibberish &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00484" name="l00484"></a><span class="lineno">  484</span> </div>
-<div class="line"><a id="l00485" name="l00485"></a><span class="lineno">  485</span>    <span class="comment">// matrix&lt;int&gt; dkey = ciphers::HillCipher::generate_decryption_key(ekey);</span></div>
-<div class="line"><a id="l00486" name="l00486"></a><span class="lineno">  486</span>    <span class="comment">// std::cout &lt;&lt; &quot;Decryption key: \n&quot; &lt;&lt; dkey;</span></div>
-<div class="line"><a id="l00487" name="l00487"></a><span class="lineno">  487</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> txt_back = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#a427acfac1dbff3f48a2b071d449d965b">ciphers::HillCipher::decrypt_text</a>(gibberish, dkey);</div>
-<div class="line"><a id="l00488" name="l00488"></a><span class="lineno">  488</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Reconstruct text:\n\t&quot;</span> &lt;&lt; txt_back &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00489" name="l00489"></a><span class="lineno">  489</span> </div>
-<div class="line"><a id="l00490" name="l00490"></a><span class="lineno">  490</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> out_file(<span class="stringliteral">&quot;hill_cipher_test1.txt&quot;</span>);</div>
-<div class="line"><a id="l00491" name="l00491"></a><span class="lineno">  491</span>    out_file &lt;&lt; <span class="stringliteral">&quot;Block size: &quot;</span> &lt;&lt; ekey.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00492" name="l00492"></a><span class="lineno">  492</span>    out_file &lt;&lt; <span class="stringliteral">&quot;Encryption Key:\n&quot;</span> &lt;&lt; ekey;</div>
-<div class="line"><a id="l00493" name="l00493"></a><span class="lineno">  493</span>    out_file &lt;&lt; <span class="stringliteral">&quot;\nDecryption Key:\n&quot;</span> &lt;&lt; dkey;</div>
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-<div class="line"><a id="l00495" name="l00495"></a><span class="lineno">  495</span> </div>
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+<div class="line"><span class="lineno">  471</span>    <span class="comment">// std::string text = &quot;Hello world!&quot;;</span></div>
+<div class="line"><span class="lineno">  472</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;======Test 1 (3x3 key) ======\nOriginal text:\n\t&quot;</span> &lt;&lt; text</div>
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+<div class="line"><span class="lineno">  474</span> </div>
+<div class="line"><span class="lineno">  475</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;matrix&lt;int&gt;</a>, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a>&gt; p =</div>
+<div class="line"><span class="lineno">  476</span>        <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#a405b0a28d66a61239d3565d5256f9cb5">ciphers::HillCipher::generate_keys</a>(3, 0, 100);</div>
+<div class="line"><span class="lineno">  477</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> ekey = p.first;</div>
+<div class="line"><span class="lineno">  478</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> dkey = p.second;</div>
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+<div class="line"><span class="lineno">  480</span>    <span class="comment">// matrix&lt;int&gt; ekey = {{22, 28, 25}, {5, 26, 15}, {14, 18, 9}};</span></div>
+<div class="line"><span class="lineno">  481</span>    <span class="comment">// std::cout &lt;&lt; &quot;Encryption key: \n&quot; &lt;&lt; ekey;</span></div>
+<div class="line"><span class="lineno">  482</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> gibberish = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#aa8bbb6e4a5749f6008b06602d5103917">ciphers::HillCipher::encrypt_text</a>(text, ekey);</div>
+<div class="line"><span class="lineno">  483</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Encrypted text:\n\t&quot;</span> &lt;&lt; gibberish &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><span class="lineno">  485</span>    <span class="comment">// matrix&lt;int&gt; dkey = ciphers::HillCipher::generate_decryption_key(ekey);</span></div>
+<div class="line"><span class="lineno">  486</span>    <span class="comment">// std::cout &lt;&lt; &quot;Decryption key: \n&quot; &lt;&lt; dkey;</span></div>
+<div class="line"><span class="lineno">  487</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> txt_back = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#a427acfac1dbff3f48a2b071d449d965b">ciphers::HillCipher::decrypt_text</a>(gibberish, dkey);</div>
+<div class="line"><span class="lineno">  488</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Reconstruct text:\n\t&quot;</span> &lt;&lt; txt_back &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  489</span> </div>
+<div class="line"><span class="lineno">  490</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> out_file(<span class="stringliteral">&quot;hill_cipher_test1.txt&quot;</span>);</div>
+<div class="line"><span class="lineno">  491</span>    out_file &lt;&lt; <span class="stringliteral">&quot;Block size: &quot;</span> &lt;&lt; ekey.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  492</span>    out_file &lt;&lt; <span class="stringliteral">&quot;Encryption Key:\n&quot;</span> &lt;&lt; ekey;</div>
+<div class="line"><span class="lineno">  493</span>    out_file &lt;&lt; <span class="stringliteral">&quot;\nDecryption Key:\n&quot;</span> &lt;&lt; dkey;</div>
+<div class="line"><span class="lineno">  494</span>    out_file.close();</div>
+<div class="line"><span class="lineno">  495</span> </div>
+<div class="line"><span class="lineno">  496</span>    assert(txt_back == text);</div>
+<div class="line"><span class="lineno">  497</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed :)\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  498</span>}</div>
 <div class="ttc" id="abasic_ofstream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a></div></div>
 <div class="ttc" id="aclassciphers_1_1_hill_cipher_html_a405b0a28d66a61239d3565d5256f9cb5"><div class="ttname"><a href="../../d6/d26/classciphers_1_1_hill_cipher.html#a405b0a28d66a61239d3565d5256f9cb5">ciphers::HillCipher::generate_keys</a></div><div class="ttdeci">static std::pair&lt; matrix&lt; int &gt;, matrix&lt; int &gt; &gt; generate_keys(size_t size, int limit1=0, int limit2=10)</div><div class="ttdoc">Generate encryption and decryption key pair.</div><div class="ttdef"><b>Definition:</b> hill_cipher.cpp:424</div></div>
 <div class="ttc" id="aclassciphers_1_1_hill_cipher_html_a427acfac1dbff3f48a2b071d449d965b"><div class="ttname"><a href="../../d6/d26/classciphers_1_1_hill_cipher.html#a427acfac1dbff3f48a2b071d449d965b">ciphers::HillCipher::decrypt_text</a></div><div class="ttdeci">static const std::string decrypt_text(const std::string &amp;text, const matrix&lt; int &gt; &amp;decrypt_key)</div><div class="ttdoc">Decrypt a given text using a given key.</div><div class="ttdef"><b>Definition:</b> hill_cipher.cpp:457</div></div>
@@ -359,31 +359,31 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00505" name="l00505"></a><span class="lineno">  505</span>                                  {</div>
-<div class="line"><a id="l00506" name="l00506"></a><span class="lineno">  506</span>    <span class="comment">// std::string text = &quot;Hello world!&quot;;</span></div>
-<div class="line"><a id="l00507" name="l00507"></a><span class="lineno">  507</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;======Test 2 (8x8 key) ======\nOriginal text:\n\t&quot;</span> &lt;&lt; text</div>
-<div class="line"><a id="l00508" name="l00508"></a><span class="lineno">  508</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00509" name="l00509"></a><span class="lineno">  509</span> </div>
-<div class="line"><a id="l00510" name="l00510"></a><span class="lineno">  510</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;matrix&lt;int&gt;</a>, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a>&gt; p =</div>
-<div class="line"><a id="l00511" name="l00511"></a><span class="lineno">  511</span>        <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#a405b0a28d66a61239d3565d5256f9cb5">ciphers::HillCipher::generate_keys</a>(8, 0, 3);</div>
-<div class="line"><a id="l00512" name="l00512"></a><span class="lineno">  512</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> ekey = p.first;</div>
-<div class="line"><a id="l00513" name="l00513"></a><span class="lineno">  513</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> dkey = p.second;</div>
-<div class="line"><a id="l00514" name="l00514"></a><span class="lineno">  514</span> </div>
-<div class="line"><a id="l00515" name="l00515"></a><span class="lineno">  515</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> gibberish = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#aa8bbb6e4a5749f6008b06602d5103917">ciphers::HillCipher::encrypt_text</a>(text, ekey);</div>
-<div class="line"><a id="l00516" name="l00516"></a><span class="lineno">  516</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Encrypted text:\n\t&quot;</span> &lt;&lt; gibberish &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00517" name="l00517"></a><span class="lineno">  517</span> </div>
-<div class="line"><a id="l00518" name="l00518"></a><span class="lineno">  518</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> txt_back = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#a427acfac1dbff3f48a2b071d449d965b">ciphers::HillCipher::decrypt_text</a>(gibberish, dkey);</div>
-<div class="line"><a id="l00519" name="l00519"></a><span class="lineno">  519</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Reconstruct text:\n\t&quot;</span> &lt;&lt; txt_back &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00520" name="l00520"></a><span class="lineno">  520</span> </div>
-<div class="line"><a id="l00521" name="l00521"></a><span class="lineno">  521</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> out_file(<span class="stringliteral">&quot;hill_cipher_test2.txt&quot;</span>);</div>
-<div class="line"><a id="l00522" name="l00522"></a><span class="lineno">  522</span>    out_file &lt;&lt; <span class="stringliteral">&quot;Block size: &quot;</span> &lt;&lt; ekey.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00523" name="l00523"></a><span class="lineno">  523</span>    out_file &lt;&lt; <span class="stringliteral">&quot;Encryption Key:\n&quot;</span> &lt;&lt; ekey;</div>
-<div class="line"><a id="l00524" name="l00524"></a><span class="lineno">  524</span>    out_file &lt;&lt; <span class="stringliteral">&quot;\nDecryption Key:\n&quot;</span> &lt;&lt; dkey;</div>
-<div class="line"><a id="l00525" name="l00525"></a><span class="lineno">  525</span>    out_file.close();</div>
-<div class="line"><a id="l00526" name="l00526"></a><span class="lineno">  526</span> </div>
-<div class="line"><a id="l00527" name="l00527"></a><span class="lineno">  527</span>    assert(txt_back.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/compare.html">compare</a>(0, text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>(), text) == 0);</div>
-<div class="line"><a id="l00528" name="l00528"></a><span class="lineno">  528</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed :)\n&quot;</span>;</div>
-<div class="line"><a id="l00529" name="l00529"></a><span class="lineno">  529</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  505</span>                                  {</div>
+<div class="line"><span class="lineno">  506</span>    <span class="comment">// std::string text = &quot;Hello world!&quot;;</span></div>
+<div class="line"><span class="lineno">  507</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;======Test 2 (8x8 key) ======\nOriginal text:\n\t&quot;</span> &lt;&lt; text</div>
+<div class="line"><span class="lineno">  508</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  509</span> </div>
+<div class="line"><span class="lineno">  510</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;matrix&lt;int&gt;</a>, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a>&gt; p =</div>
+<div class="line"><span class="lineno">  511</span>        <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#a405b0a28d66a61239d3565d5256f9cb5">ciphers::HillCipher::generate_keys</a>(8, 0, 3);</div>
+<div class="line"><span class="lineno">  512</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> ekey = p.first;</div>
+<div class="line"><span class="lineno">  513</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> dkey = p.second;</div>
+<div class="line"><span class="lineno">  514</span> </div>
+<div class="line"><span class="lineno">  515</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> gibberish = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#aa8bbb6e4a5749f6008b06602d5103917">ciphers::HillCipher::encrypt_text</a>(text, ekey);</div>
+<div class="line"><span class="lineno">  516</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Encrypted text:\n\t&quot;</span> &lt;&lt; gibberish &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  517</span> </div>
+<div class="line"><span class="lineno">  518</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> txt_back = <a class="code hl_function" href="../../d6/d26/classciphers_1_1_hill_cipher.html#a427acfac1dbff3f48a2b071d449d965b">ciphers::HillCipher::decrypt_text</a>(gibberish, dkey);</div>
+<div class="line"><span class="lineno">  519</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Reconstruct text:\n\t&quot;</span> &lt;&lt; txt_back &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  520</span> </div>
+<div class="line"><span class="lineno">  521</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> out_file(<span class="stringliteral">&quot;hill_cipher_test2.txt&quot;</span>);</div>
+<div class="line"><span class="lineno">  522</span>    out_file &lt;&lt; <span class="stringliteral">&quot;Block size: &quot;</span> &lt;&lt; ekey.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  523</span>    out_file &lt;&lt; <span class="stringliteral">&quot;Encryption Key:\n&quot;</span> &lt;&lt; ekey;</div>
+<div class="line"><span class="lineno">  524</span>    out_file &lt;&lt; <span class="stringliteral">&quot;\nDecryption Key:\n&quot;</span> &lt;&lt; dkey;</div>
+<div class="line"><span class="lineno">  525</span>    out_file.close();</div>
+<div class="line"><span class="lineno">  526</span> </div>
+<div class="line"><span class="lineno">  527</span>    assert(txt_back.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/compare.html">compare</a>(0, text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>(), text) == 0);</div>
+<div class="line"><span class="lineno">  528</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed :)\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  529</span>}</div>
 <div class="ttc" id="acompare_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/compare.html">std::string::compare</a></div><div class="ttdeci">T compare(T... args)</div></div>
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 Here is the call graph for this function:</div>
@@ -400,7 +400,7 @@ Here is the call graph for this function:</div>
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-<div class="line"><a id="l00446" name="l00446"></a><span class="lineno">  446</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; root-&gt;SearchPresence(<span class="stringliteral">&quot;tutuv&quot;</span>) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00447" name="l00447"></a><span class="lineno">  447</span> </div>
-<div class="line"><a id="l00448" name="l00448"></a><span class="lineno">  448</span>    root-&gt;SearchSuggestions(<span class="stringliteral">&quot;tutuvs&quot;</span>);</div>
-<div class="line"><a id="l00449" name="l00449"></a><span class="lineno">  449</span> </div>
-<div class="line"><a id="l00450" name="l00450"></a><span class="lineno">  450</span>    root-&gt;SearchFreqSuggestions(</div>
-<div class="line"><a id="l00451" name="l00451"></a><span class="lineno">  451</span>        <span class="stringliteral">&quot;tu&quot;</span>);  <span class="comment">// The top 3 frequent entries with prefix tu are tutu, tutuv &amp;</span></div>
-<div class="line"><a id="l00452" name="l00452"></a><span class="lineno">  452</span>                <span class="comment">// tutuvs respectively</span></div>
-<div class="line"><a id="l00453" name="l00453"></a><span class="lineno">  453</span>    root-&gt;SearchSuggestions(</div>
-<div class="line"><a id="l00454" name="l00454"></a><span class="lineno">  454</span>        <span class="stringliteral">&quot;&quot;</span>);  <span class="comment">// Empty search to list all the entries in the trie</span></div>
-<div class="line"><a id="l00455" name="l00455"></a><span class="lineno">  455</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  422</span>                   {</div>
+<div class="line"><span class="lineno">  423</span>    <span class="keyword">auto</span> root = <span class="keyword">new</span> <a class="code hl_class" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html">operations_on_datastructures::trie_operations::Tnode</a>();</div>
+<div class="line"><span class="lineno">  424</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::string&gt;</a> inputs = {</div>
+<div class="line"><span class="lineno">  425</span>        <span class="stringliteral">&quot;abcde&quot;</span>, <span class="stringliteral">&quot;sss&quot;</span>,    <span class="stringliteral">&quot;ssss&quot;</span>,  <span class="stringliteral">&quot;ssst&quot;</span>, <span class="stringliteral">&quot;sssu&quot;</span>, <span class="stringliteral">&quot;sssv&quot;</span>,</div>
+<div class="line"><span class="lineno">  426</span>        <span class="stringliteral">&quot;sst&quot;</span>,   <span class="stringliteral">&quot;ssts&quot;</span>,   <span class="stringliteral">&quot;sstt&quot;</span>,  <span class="stringliteral">&quot;sstu&quot;</span>, <span class="stringliteral">&quot;tutu&quot;</span>, <span class="stringliteral">&quot;tutuv&quot;</span>,</div>
+<div class="line"><span class="lineno">  427</span>        <span class="stringliteral">&quot;tutuu&quot;</span>, <span class="stringliteral">&quot;tutuvs&quot;</span>, <span class="stringliteral">&quot;tutus&quot;</span>, <span class="stringliteral">&quot;tvst&quot;</span>, <span class="stringliteral">&quot;tvsu&quot;</span>, <span class="stringliteral">&quot;vvvv&quot;</span>};</div>
+<div class="line"><span class="lineno">  428</span> </div>
+<div class="line"><span class="lineno">  429</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;i : inputs) {</div>
+<div class="line"><span class="lineno">  430</span>        root-&gt;Insert(i);</div>
+<div class="line"><span class="lineno">  431</span>    }</div>
+<div class="line"><span class="lineno">  432</span>    <span class="comment">// Search an existing entry</span></div>
+<div class="line"><span class="lineno">  433</span>    assert(root-&gt;SearchPresence(<span class="stringliteral">&quot;vvvv&quot;</span>));</div>
+<div class="line"><span class="lineno">  434</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; root-&gt;SearchPresence(<span class="stringliteral">&quot;vvvv&quot;</span>) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  435</span>    <span class="comment">// Delete it</span></div>
+<div class="line"><span class="lineno">  436</span>    root-&gt;Delete(<span class="stringliteral">&quot;vvvv&quot;</span>);</div>
+<div class="line"><span class="lineno">  437</span>    <span class="comment">// Search for the entry again</span></div>
+<div class="line"><span class="lineno">  438</span>    assert(!root-&gt;SearchPresence(<span class="stringliteral">&quot;vvvv&quot;</span>));</div>
+<div class="line"><span class="lineno">  439</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; root-&gt;SearchPresence(<span class="stringliteral">&quot;vvvv&quot;</span>) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  440</span> </div>
+<div class="line"><span class="lineno">  441</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; root-&gt;SearchPresence(<span class="stringliteral">&quot;tutu&quot;</span>) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  442</span>    root-&gt;SearchSuggestions(<span class="stringliteral">&quot;tutu&quot;</span>);</div>
+<div class="line"><span class="lineno">  443</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; root-&gt;SearchPresence(<span class="stringliteral">&quot;tutu&quot;</span>) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  444</span> </div>
+<div class="line"><span class="lineno">  445</span>    root-&gt;SearchSuggestions(<span class="stringliteral">&quot;tutuv&quot;</span>);</div>
+<div class="line"><span class="lineno">  446</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; root-&gt;SearchPresence(<span class="stringliteral">&quot;tutuv&quot;</span>) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  447</span> </div>
+<div class="line"><span class="lineno">  448</span>    root-&gt;SearchSuggestions(<span class="stringliteral">&quot;tutuvs&quot;</span>);</div>
+<div class="line"><span class="lineno">  449</span> </div>
+<div class="line"><span class="lineno">  450</span>    root-&gt;SearchFreqSuggestions(</div>
+<div class="line"><span class="lineno">  451</span>        <span class="stringliteral">&quot;tu&quot;</span>);  <span class="comment">// The top 3 frequent entries with prefix tu are tutu, tutuv &amp;</span></div>
+<div class="line"><span class="lineno">  452</span>                <span class="comment">// tutuvs respectively</span></div>
+<div class="line"><span class="lineno">  453</span>    root-&gt;SearchSuggestions(</div>
+<div class="line"><span class="lineno">  454</span>        <span class="stringliteral">&quot;&quot;</span>);  <span class="comment">// Empty search to list all the entries in the trie</span></div>
+<div class="line"><span class="lineno">  455</span>}</div>
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-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>                          numbers[j + 1]);  <span class="comment">// by changing swap location.</span></div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>                                            <span class="comment">// I mean, j. If the number is</span></div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>                                            <span class="comment">// greater than j + 1, then it</span></div>
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+<div class="line"><span class="lineno">   57</span> </div>
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+<div class="line"><span class="lineno">   68</span>                                            <span class="comment">// means the location.</span></div>
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@@ -102,6 +102,12 @@ $(document).ready(function(){initNavTree('d8/d28/classrange__queries_1_1per_seg_
 
 <p>Range query here is range sum, but the code can be modified to make different queries like range max or min.  
  <a href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#details">More...</a></p>
+<div class="dynheader">
+Collaboration diagram for range_queries::perSegTree:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d6/d47/classrange__queries_1_1per_seg_tree__coll__graph.svg" width="100%" height="450"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+<center><span class="legend">[<a target="top" href="../../graph_legend.html">legend</a>]</span></center></div>
 <table class="memberdecls">
 <tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="nested-classes" name="nested-classes"></a>
 Classes</h2></td></tr>
@@ -188,19 +194,28 @@ uint32_t&#160;</td><td class="memItemRight" valign="bottom"><b>n</b> = 0</td></t
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    {</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a8ff495d2f389b4aaa54449c26c6078f3">vec</a>.empty()) {</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>            <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>        }</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>        n = <a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a8ff495d2f389b4aaa54449c26c6078f3">vec</a>.size();</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>        this-&gt;vec = <a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a8ff495d2f389b4aaa54449c26c6078f3">vec</a>;</div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>        <span class="keyword">auto</span> root = <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a6d3f2465a7c5803a1ff16c5378bcc5e4">construct</a>(0, n - 1);</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>        <a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a1eac9cf0613dfc8e2b0195009dd5c9d5">ptrs</a>.push_back(root);</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  200</span>    {</div>
+<div class="line"><span class="lineno">  201</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a8ff495d2f389b4aaa54449c26c6078f3">vec</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/empty.html">empty</a>()) {</div>
+<div class="line"><span class="lineno">  202</span>            <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  203</span>        }</div>
+<div class="line"><span class="lineno">  204</span>        n = <a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a8ff495d2f389b4aaa54449c26c6078f3">vec</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">  205</span>        this-&gt;vec = <a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a8ff495d2f389b4aaa54449c26c6078f3">vec</a>;</div>
+<div class="line"><span class="lineno">  206</span>        <span class="keyword">auto</span> root = <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a6d3f2465a7c5803a1ff16c5378bcc5e4">construct</a>(0, n - 1);</div>
+<div class="line"><span class="lineno">  207</span>        <a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a1eac9cf0613dfc8e2b0195009dd5c9d5">ptrs</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(root);</div>
+<div class="line"><span class="lineno">  208</span>    }</div>
 <div class="ttc" id="aclassrange__queries_1_1per_seg_tree_html_a1eac9cf0613dfc8e2b0195009dd5c9d5"><div class="ttname"><a href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a1eac9cf0613dfc8e2b0195009dd5c9d5">range_queries::perSegTree::ptrs</a></div><div class="ttdeci">std::vector&lt; std::shared_ptr&lt; Node &gt; &gt; ptrs</div><div class="ttdoc">number of elements/leaf nodes in the segment tree</div><div class="ttdef"><b>Definition:</b> persistent_seg_tree_lazy_prop.cpp:54</div></div>
 <div class="ttc" id="aclassrange__queries_1_1per_seg_tree_html_a6d3f2465a7c5803a1ff16c5378bcc5e4"><div class="ttname"><a href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a6d3f2465a7c5803a1ff16c5378bcc5e4">range_queries::perSegTree::construct</a></div><div class="ttdeci">std::shared_ptr&lt; Node &gt; construct(const uint32_t &amp;i, const uint32_t &amp;j)</div><div class="ttdoc">Constructing the segment tree with the early passed vector. Every call creates a node to hold the sum...</div><div class="ttdef"><b>Definition:</b> persistent_seg_tree_lazy_prop.cpp:106</div></div>
 <div class="ttc" id="aclassrange__queries_1_1per_seg_tree_html_a8ff495d2f389b4aaa54449c26c6078f3"><div class="ttname"><a href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a8ff495d2f389b4aaa54449c26c6078f3">range_queries::perSegTree::vec</a></div><div class="ttdeci">std::vector&lt; int64_t &gt; vec</div><div class="ttdef"><b>Definition:</b> persistent_seg_tree_lazy_prop.cpp:57</div></div>
-</div><!-- fragment -->
+<div class="ttc" id="aempty_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/empty.html">std::vector::empty</a></div><div class="ttdeci">T empty(T... args)</div></div>
+<div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
+<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/d28/classrange__queries_1_1per_seg_tree_ac83bcabf5a8db8b0d8d156a4c1bcd4c3_cgraph.svg" width="366" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
 </div>
 </div>
 <a id="a6d3f2465a7c5803a1ff16c5378bcc5e4" name="a6d3f2465a7c5803a1ff16c5378bcc5e4"></a>
@@ -246,20 +261,20 @@ uint32_t&#160;</td><td class="memItemRight" valign="bottom"><b>n</b> = 0</td></t
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>pointer to the newly created node </dd></dl>
-<div class="fragment"><div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>                                                                        {</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>        <span class="keyword">auto</span> newNode = std::make_shared&lt;Node&gt;(<a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>());</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>        <span class="keywordflow">if</span> (i == j) {</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>            newNode-&gt;val = <a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a8ff495d2f389b4aaa54449c26c6078f3">vec</a>[i];</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>            uint32_t mid = i + (j - i) / 2;</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>            <span class="keyword">auto</span> leftt = <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a6d3f2465a7c5803a1ff16c5378bcc5e4">construct</a>(i, mid);</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>            <span class="keyword">auto</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> = <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a6d3f2465a7c5803a1ff16c5378bcc5e4">construct</a>(mid + 1, j);</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>            newNode-&gt;val = leftt-&gt;val + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>-&gt;val;</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>            newNode-&gt;left = leftt;</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>            newNode-&gt;right = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>;</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>        }</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>        <span class="keywordflow">return</span> newNode;</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  106</span>                                                                        {</div>
+<div class="line"><span class="lineno">  107</span>        <span class="keyword">auto</span> newNode = std::make_shared&lt;Node&gt;(<a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>());</div>
+<div class="line"><span class="lineno">  108</span>        <span class="keywordflow">if</span> (i == j) {</div>
+<div class="line"><span class="lineno">  109</span>            newNode-&gt;val = <a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a8ff495d2f389b4aaa54449c26c6078f3">vec</a>[i];</div>
+<div class="line"><span class="lineno">  110</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  111</span>            uint32_t mid = i + (j - i) / 2;</div>
+<div class="line"><span class="lineno">  112</span>            <span class="keyword">auto</span> leftt = <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a6d3f2465a7c5803a1ff16c5378bcc5e4">construct</a>(i, mid);</div>
+<div class="line"><span class="lineno">  113</span>            <span class="keyword">auto</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> = <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a6d3f2465a7c5803a1ff16c5378bcc5e4">construct</a>(mid + 1, j);</div>
+<div class="line"><span class="lineno">  114</span>            newNode-&gt;val = leftt-&gt;val + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>-&gt;val;</div>
+<div class="line"><span class="lineno">  115</span>            newNode-&gt;left = leftt;</div>
+<div class="line"><span class="lineno">  116</span>            newNode-&gt;right = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>;</div>
+<div class="line"><span class="lineno">  117</span>        }</div>
+<div class="line"><span class="lineno">  118</span>        <span class="keywordflow">return</span> newNode;</div>
+<div class="line"><span class="lineno">  119</span>    }</div>
 <div class="ttc" id="aleft_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::right</a></div><div class="ttdeci">T right(T... args)</div></div>
 <div class="ttc" id="astruct_node_html"><div class="ttname"><a href="../../db/d8b/struct_node.html">Node</a></div><div class="ttdef"><b>Definition:</b> linkedlist_implentation_usingarray.cpp:14</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -321,19 +336,19 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>                                               {</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>        <span class="keywordflow">if</span> (!curr-&gt;prop) {</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>            <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>        }</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        curr-&gt;val += (j - i + 1) * curr-&gt;prop;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        if (i != j) {</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>            curr-&gt;left = <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a0cec4b77d264521717cf9b0482c45817">newKid</a>(curr-&gt;left);</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>            curr-&gt;right = <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a0cec4b77d264521717cf9b0482c45817">newKid</a>(curr-&gt;right);</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>            curr-&gt;left-&gt;prop += curr-&gt;prop;</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>            curr-&gt;right-&gt;prop += curr-&gt;prop;</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>        }</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>        curr-&gt;prop = 0;</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   84</span>                                               {</div>
+<div class="line"><span class="lineno">   85</span>        <span class="keywordflow">if</span> (!curr-&gt;prop) {</div>
+<div class="line"><span class="lineno">   86</span>            <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">   87</span>        }</div>
+<div class="line"><span class="lineno">   88</span>        curr-&gt;val += (j - i + 1) * curr-&gt;prop;</div>
+<div class="line"><span class="lineno">   89</span>        if (i != j) {</div>
+<div class="line"><span class="lineno">   90</span>            curr-&gt;left = <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a0cec4b77d264521717cf9b0482c45817">newKid</a>(curr-&gt;left);</div>
+<div class="line"><span class="lineno">   91</span>            curr-&gt;right = <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a0cec4b77d264521717cf9b0482c45817">newKid</a>(curr-&gt;right);</div>
+<div class="line"><span class="lineno">   92</span>            curr-&gt;left-&gt;prop += curr-&gt;prop;</div>
+<div class="line"><span class="lineno">   93</span>            curr-&gt;right-&gt;prop += curr-&gt;prop;</div>
+<div class="line"><span class="lineno">   94</span>        }</div>
+<div class="line"><span class="lineno">   95</span>        curr-&gt;prop = 0;</div>
+<div class="line"><span class="lineno">   96</span>    }</div>
 <div class="ttc" id="aclassrange__queries_1_1per_seg_tree_html_a0cec4b77d264521717cf9b0482c45817"><div class="ttname"><a href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a0cec4b77d264521717cf9b0482c45817">range_queries::perSegTree::newKid</a></div><div class="ttdeci">std::shared_ptr&lt; Node &gt; newKid(std::shared_ptr&lt; Node &gt; const &amp;curr)</div><div class="ttdoc">Creating a new node with the same values of curr node.</div><div class="ttdef"><b>Definition:</b> persistent_seg_tree_lazy_prop.cpp:65</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -376,14 +391,14 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>the new node </dd></dl>
-<div class="fragment"><div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>                                                                {</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="keyword">auto</span> newNode = std::make_shared&lt;Node&gt;(<a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>());</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        newNode-&gt;left = curr-&gt;left;</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        newNode-&gt;right = curr-&gt;right;</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        newNode-&gt;prop = curr-&gt;prop;</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        newNode-&gt;val = curr-&gt;val;</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        <span class="keywordflow">return</span> newNode;</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   65</span>                                                                {</div>
+<div class="line"><span class="lineno">   66</span>        <span class="keyword">auto</span> newNode = std::make_shared&lt;Node&gt;(<a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>());</div>
+<div class="line"><span class="lineno">   67</span>        newNode-&gt;left = curr-&gt;left;</div>
+<div class="line"><span class="lineno">   68</span>        newNode-&gt;right = curr-&gt;right;</div>
+<div class="line"><span class="lineno">   69</span>        newNode-&gt;prop = curr-&gt;prop;</div>
+<div class="line"><span class="lineno">   70</span>        newNode-&gt;val = curr-&gt;val;</div>
+<div class="line"><span class="lineno">   71</span>        <span class="keywordflow">return</span> newNode;</div>
+<div class="line"><span class="lineno">   72</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -451,18 +466,18 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>sum of elements whose index x satisfies l&lt;=x&lt;=r </dd></dl>
-<div class="fragment"><div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>                                                                      {</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>        <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ace7f57935b3bb9446f11c239fd89ae79">lazy</a>(i, j, curr);</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>        <span class="keywordflow">if</span> (j &lt; l || r &lt; i) {</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>            <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>        }</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>        <span class="keywordflow">if</span> (i &gt;= l &amp;&amp; j &lt;= r) {</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>            <span class="keywordflow">return</span> curr-&gt;val;</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>        }</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>        uint32_t mid = i + (j - i) / 2;</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ae8ae4b1835e5e8aec32f68c5059ed4d4">query</a>(i, mid, l, r, curr-&gt;left) +</div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>               <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ae8ae4b1835e5e8aec32f68c5059ed4d4">query</a>(mid + 1, j, l, r, curr-&gt;right);</div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  172</span>                                                                      {</div>
+<div class="line"><span class="lineno">  173</span>        <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ace7f57935b3bb9446f11c239fd89ae79">lazy</a>(i, j, curr);</div>
+<div class="line"><span class="lineno">  174</span>        <span class="keywordflow">if</span> (j &lt; l || r &lt; i) {</div>
+<div class="line"><span class="lineno">  175</span>            <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  176</span>        }</div>
+<div class="line"><span class="lineno">  177</span>        <span class="keywordflow">if</span> (i &gt;= l &amp;&amp; j &lt;= r) {</div>
+<div class="line"><span class="lineno">  178</span>            <span class="keywordflow">return</span> curr-&gt;val;</div>
+<div class="line"><span class="lineno">  179</span>        }</div>
+<div class="line"><span class="lineno">  180</span>        uint32_t mid = i + (j - i) / 2;</div>
+<div class="line"><span class="lineno">  181</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ae8ae4b1835e5e8aec32f68c5059ed4d4">query</a>(i, mid, l, r, curr-&gt;left) +</div>
+<div class="line"><span class="lineno">  182</span>               <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ae8ae4b1835e5e8aec32f68c5059ed4d4">query</a>(mid + 1, j, l, r, curr-&gt;right);</div>
+<div class="line"><span class="lineno">  183</span>    }</div>
 <div class="ttc" id="aclassrange__queries_1_1per_seg_tree_html_ace7f57935b3bb9446f11c239fd89ae79"><div class="ttname"><a href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ace7f57935b3bb9446f11c239fd89ae79">range_queries::perSegTree::lazy</a></div><div class="ttdeci">void lazy(const uint32_t &amp;i, const uint32_t &amp;j, std::shared_ptr&lt; Node &gt; const &amp;curr)</div><div class="ttdoc">If there is some value to be propagated to the passed node, value is added to the node and the childr...</div><div class="ttdef"><b>Definition:</b> persistent_seg_tree_lazy_prop.cpp:83</div></div>
 <div class="ttc" id="aclassrange__queries_1_1per_seg_tree_html_ae8ae4b1835e5e8aec32f68c5059ed4d4"><div class="ttname"><a href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ae8ae4b1835e5e8aec32f68c5059ed4d4">range_queries::perSegTree::query</a></div><div class="ttdeci">int64_t query(const uint32_t &amp;i, const uint32_t &amp;j, const uint32_t &amp;l, const uint32_t &amp;r, std::shared_ptr&lt; Node &gt; const &amp;curr)</div><div class="ttdoc">Querying the range from index l to index r, checking at every node if it has some value to be propaga...</div><div class="ttdef"><b>Definition:</b> persistent_seg_tree_lazy_prop.cpp:171</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -524,9 +539,9 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>sum of elements whose index x satisfies l&lt;=x&lt;=r </dd></dl>
-<div class="fragment"><div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>    {</div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ae8ae4b1835e5e8aec32f68c5059ed4d4">query</a>(0, n - 1, l, r, <a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a1eac9cf0613dfc8e2b0195009dd5c9d5">ptrs</a>[version]);</div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  246</span>    {</div>
+<div class="line"><span class="lineno">  247</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ae8ae4b1835e5e8aec32f68c5059ed4d4">query</a>(0, n - 1, l, r, <a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a1eac9cf0613dfc8e2b0195009dd5c9d5">ptrs</a>[version]);</div>
+<div class="line"><span class="lineno">  248</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -561,10 +576,16 @@ Here is the call graph for this function:</div>
 
 <p>Getting the number of versions after updates so far which is equal to the size of the pointers vector. </p>
 <dl class="section return"><dt>Returns</dt><dd>the number of versions </dd></dl>
-<div class="fragment"><div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>    {</div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a1eac9cf0613dfc8e2b0195009dd5c9d5">ptrs</a>.size();</div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>    }</div>
-</div><!-- fragment -->
+<div class="fragment"><div class="line"><span class="lineno">  258</span>    {</div>
+<div class="line"><span class="lineno">  259</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a1eac9cf0613dfc8e2b0195009dd5c9d5">ptrs</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">  260</span>    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/d28/classrange__queries_1_1per_seg_tree_a0fe4e431f3e09c274ecd7d2d58dcb865_cgraph.svg" width="354" height="52"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
 </div>
 </div>
 <a id="a24487eda25123bc4d112e8430821a6c6" name="a24487eda25123bc4d112e8430821a6c6"></a>
@@ -638,26 +659,26 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>pointer to the current newly created node </dd></dl>
-<div class="fragment"><div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>                                                                  {</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ace7f57935b3bb9446f11c239fd89ae79">lazy</a>(i, j, curr);</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>        <span class="keywordflow">if</span> (i &gt;= l &amp;&amp; j &lt;= r) {</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Node&gt;</a> newNode = <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a0cec4b77d264521717cf9b0482c45817">newKid</a>(curr);</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>            newNode-&gt;prop += value;</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>            <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ace7f57935b3bb9446f11c239fd89ae79">lazy</a>(i, j, newNode);</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>            <span class="keywordflow">return</span> newNode;</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>        }</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>        <span class="keywordflow">if</span> (i &gt; r || j &lt; l) {</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>            <span class="keywordflow">return</span> curr;</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>        }</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>        <span class="keyword">auto</span> newNode = std::make_shared&lt;Node&gt;(<a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>());</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>        uint32_t mid = i + (j - i) / 2;</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>        newNode-&gt;left = <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a24487eda25123bc4d112e8430821a6c6">update</a>(i, mid, l, r, value, curr-&gt;left);</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>        newNode-&gt;right = <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a24487eda25123bc4d112e8430821a6c6">update</a>(mid + 1, j, l, r, value, curr-&gt;right);</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>        newNode-&gt;val = newNode-&gt;left-&gt;val + newNode-&gt;right-&gt;val;</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>        <span class="keywordflow">return</span> newNode;</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  138</span>                                                                  {</div>
+<div class="line"><span class="lineno">  139</span>        <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ace7f57935b3bb9446f11c239fd89ae79">lazy</a>(i, j, curr);</div>
+<div class="line"><span class="lineno">  140</span>        <span class="keywordflow">if</span> (i &gt;= l &amp;&amp; j &lt;= r) {</div>
+<div class="line"><span class="lineno">  141</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Node&gt;</a> newNode = <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a0cec4b77d264521717cf9b0482c45817">newKid</a>(curr);</div>
+<div class="line"><span class="lineno">  142</span>            newNode-&gt;prop += value;</div>
+<div class="line"><span class="lineno">  143</span>            <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ace7f57935b3bb9446f11c239fd89ae79">lazy</a>(i, j, newNode);</div>
+<div class="line"><span class="lineno">  144</span>            <span class="keywordflow">return</span> newNode;</div>
+<div class="line"><span class="lineno">  145</span>        }</div>
+<div class="line"><span class="lineno">  146</span>        <span class="keywordflow">if</span> (i &gt; r || j &lt; l) {</div>
+<div class="line"><span class="lineno">  147</span>            <span class="keywordflow">return</span> curr;</div>
+<div class="line"><span class="lineno">  148</span>        }</div>
+<div class="line"><span class="lineno">  149</span>        <span class="keyword">auto</span> newNode = std::make_shared&lt;Node&gt;(<a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>());</div>
+<div class="line"><span class="lineno">  150</span>        uint32_t mid = i + (j - i) / 2;</div>
+<div class="line"><span class="lineno">  151</span>        newNode-&gt;left = <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a24487eda25123bc4d112e8430821a6c6">update</a>(i, mid, l, r, value, curr-&gt;left);</div>
+<div class="line"><span class="lineno">  152</span>        newNode-&gt;right = <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a24487eda25123bc4d112e8430821a6c6">update</a>(mid + 1, j, l, r, value, curr-&gt;right);</div>
+<div class="line"><span class="lineno">  153</span>        newNode-&gt;val = newNode-&gt;left-&gt;val + newNode-&gt;right-&gt;val;</div>
+<div class="line"><span class="lineno">  154</span>        <span class="keywordflow">return</span> newNode;</div>
+<div class="line"><span class="lineno">  155</span>    }</div>
 <div class="ttc" id="aclassrange__queries_1_1per_seg_tree_html_a24487eda25123bc4d112e8430821a6c6"><div class="ttname"><a href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a24487eda25123bc4d112e8430821a6c6">range_queries::perSegTree::update</a></div><div class="ttdeci">std::shared_ptr&lt; Node &gt; update(const uint32_t &amp;i, const uint32_t &amp;j, const uint32_t &amp;l, const uint32_t &amp;r, const int64_t &amp;value, std::shared_ptr&lt; Node &gt; const &amp;curr)</div><div class="ttdoc">Doing range update, checking at every node if it has some value to be propagated. All nodes affected ...</div><div class="ttdef"><b>Definition:</b> persistent_seg_tree_lazy_prop.cpp:135</div></div>
-<div class="ttc" id="ashared_ptr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr</a></div></div>
+<div class="ttc" id="ashared_ptr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt; Node &gt;</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -717,16 +738,16 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>    {</div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>        <a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a1eac9cf0613dfc8e2b0195009dd5c9d5">ptrs</a>.push_back(<a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a24487eda25123bc4d112e8430821a6c6">update</a>(</div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>            0, n - 1, l, r, value,</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>            <a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a1eac9cf0613dfc8e2b0195009dd5c9d5">ptrs</a>[<a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a1eac9cf0613dfc8e2b0195009dd5c9d5">ptrs</a>.size() -</div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>                 1]));  <span class="comment">// saving the root pointer to the new segment tree</span></div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  223</span>    {</div>
+<div class="line"><span class="lineno">  224</span>        <a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a1eac9cf0613dfc8e2b0195009dd5c9d5">ptrs</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(<a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a24487eda25123bc4d112e8430821a6c6">update</a>(</div>
+<div class="line"><span class="lineno">  225</span>            0, n - 1, l, r, value,</div>
+<div class="line"><span class="lineno">  226</span>            <a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a1eac9cf0613dfc8e2b0195009dd5c9d5">ptrs</a>[<a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a1eac9cf0613dfc8e2b0195009dd5c9d5">ptrs</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() -</div>
+<div class="line"><span class="lineno">  227</span>                 1]));  <span class="comment">// saving the root pointer to the new segment tree</span></div>
+<div class="line"><span class="lineno">  228</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d8/d28/classrange__queries_1_1per_seg_tree_af87494e6cf012d28c4f5b9d1c15f9c5d_cgraph.svg" width="100%" height="361"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d8/d28/classrange__queries_1_1per_seg_tree_af87494e6cf012d28c4f5b9d1c15f9c5d_cgraph.svg" width="100%" height="434"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
 </div>
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@@ -765,7 +786,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dd/d69/namespacerange__queries.html">range_queries</a></li><li class="navelem"><a class="el" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html">perSegTree</a></li>
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diff --git a/d8/d28/classrange__queries_1_1per_seg_tree_a0fe4e431f3e09c274ecd7d2d58dcb865_cgraph.map b/d8/d28/classrange__queries_1_1per_seg_tree_a0fe4e431f3e09c274ecd7d2d58dcb865_cgraph.map
new file mode 100644
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@@ -0,0 +1,4 @@
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+<area shape="rect" id="node1" title="Getting the number of versions after updates so far which is equal to the size of the pointers vector..." alt="" coords="5,5,184,47"/>
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new file mode 100644
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 <p >Recursive function to calculate exponent in \(O(\log n)\) using binary exponent. </p>
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+<div class="fragment"><div class="line"><span class="lineno">   51</span>                                   {  <span class="comment">// sorting according to current digit.</span></div>
+<div class="line"><span class="lineno">   52</span>    <span class="keywordtype">int</span> n = ar.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   53</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> position(10, 0);</div>
+<div class="line"><span class="lineno">   54</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
+<div class="line"><span class="lineno">   55</span>        position[(ar[i] / cur_digit) %</div>
+<div class="line"><span class="lineno">   56</span>                 10]++;  <span class="comment">// counting frequency of 0-9 at cur_digit.</span></div>
+<div class="line"><span class="lineno">   57</span>    }</div>
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 <dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
 <p >Test 1</p>
 <p >Test 2</p>
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+<div class="line"><span class="lineno">  103</span><span class="comment">    /// Test 1</span></div>
+<div class="line"><span class="lineno">  104</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> ar1 = {432, 234, 143, 332, 123};</div>
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+<div class="line"><span class="lineno">  106</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(ar1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), ar1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>()));<span class="comment"></span></div>
+<div class="line"><span class="lineno">  107</span><span class="comment">    /// Test 2</span></div>
+<div class="line"><span class="lineno">  108</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> ar2 = {213, 3214, 123, 111, 112, 142,</div>
+<div class="line"><span class="lineno">  109</span>                                 133, 132,  32,  12,  113};</div>
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+<div class="line"><span class="lineno">  111</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(ar2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), ar2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>()));</div>
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 <div class="ttc" id="ais_sorted_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a></div><div class="ttdeci">T is_sorted(T... args)</div></div>
 <div class="ttc" id="aradix__sort2_8cpp_html_ae0cfd94fa3765b53d4ec7893ffaee5f8"><div class="ttname"><a href="../../d8/d61/radix__sort2_8cpp.html#ae0cfd94fa3765b53d4ec7893ffaee5f8">sorting::radix_sort::radix</a></div><div class="ttdeci">std::vector&lt; uint64_t &gt; radix(const std::vector&lt; uint64_t &gt; &amp;ar)</div><div class="ttdoc">Function to sort vector digit by digit.</div><div class="ttdef"><b>Definition:</b> radix_sort2.cpp:80</div></div>
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-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>            <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] = INF; <span class="comment">// set distance as infinite so that this vertex is considered next time for availibility</span></div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>    }</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    }</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span> </div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>    </div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>    <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[NIL] = INF; <span class="comment">// Initialize distance to NIL as infinite</span></div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span> </div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>    <span class="comment">// q is going to contain vertices of left side only.</span></div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>    <span class="keywordflow">while</span> (!q.empty())</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>    {</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>        <span class="keywordtype">int</span> u = q.front();  <span class="comment">// dequeue a vertex</span></div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>        q.pop();</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span> </div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>        <span class="comment">// If this node is not NIL and can provide a shorter path to NIL then</span></div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] &lt; <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[NIL])</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>        {</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>            <span class="comment">// Get all the adjacent vertices of the dequeued vertex u</span></div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">std::list&lt;int&gt;::iterator</a> it;</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>            <span class="keywordflow">for</span> (it = <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a35893def7a1c5cd60907b4893117796f">adj</a>[u].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">begin</a>(); it != <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a35893def7a1c5cd60907b4893117796f">adj</a>[u].end(); ++it)</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>            {</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>                <span class="keywordtype">int</span> v = *it;</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span> </div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>                <span class="comment">// If pair of v is not considered so far i.e. (v, pair_v[v]) is not yet explored edge.</span></div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>                <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]] == INF)</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>                {</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>                    <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]] = <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] + 1; </div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>                    q.push(<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]);    <span class="comment">// Consider the pair and push it to queue</span></div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>                }</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>            }</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>        }</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>    }</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span> </div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>   </div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>   </div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>    <span class="keywordflow">return</span> (<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[NIL] != INF);   <span class="comment">// If we could come back to NIL using alternating path of distinct vertices then there is an augmenting path available</span></div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  134</span>{</div>
+<div class="line"><span class="lineno">  135</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue&lt;int&gt;</a> q; <span class="comment">// an integer queue for bfs</span></div>
+<div class="line"><span class="lineno">  136</span> </div>
+<div class="line"><span class="lineno">  137</span>    <span class="comment">// First layer of vertices (set distance as 0)</span></div>
+<div class="line"><span class="lineno">  138</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> u = 1; u &lt;= <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a3d9101e3b4598159005fd028b9b0ff74">m</a>; u++)</div>
+<div class="line"><span class="lineno">  139</span>    {</div>
+<div class="line"><span class="lineno">  140</span>        <span class="comment">// If this is a free vertex, add it to queue</span></div>
+<div class="line"><span class="lineno">  141</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a86ebff8a70cbfedd05281993d5d1987b">pair_u</a>[u] == NIL){</div>
+<div class="line"><span class="lineno">  142</span>            </div>
+<div class="line"><span class="lineno">  143</span>            <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] = 0; <span class="comment">// u is not matched so distance is 0</span></div>
+<div class="line"><span class="lineno">  144</span>            q.push(u);</div>
+<div class="line"><span class="lineno">  145</span>        }</div>
+<div class="line"><span class="lineno">  146</span> </div>
+<div class="line"><span class="lineno">  147</span>        <span class="keywordflow">else</span>{</div>
+<div class="line"><span class="lineno">  148</span>            <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] = INF; <span class="comment">// set distance as infinite so that this vertex is considered next time for availibility</span></div>
+<div class="line"><span class="lineno">  149</span>    }</div>
+<div class="line"><span class="lineno">  150</span>    }</div>
+<div class="line"><span class="lineno">  151</span> </div>
+<div class="line"><span class="lineno">  152</span>    </div>
+<div class="line"><span class="lineno">  153</span>    <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[NIL] = INF; <span class="comment">// Initialize distance to NIL as infinite</span></div>
+<div class="line"><span class="lineno">  154</span> </div>
+<div class="line"><span class="lineno">  155</span>    <span class="comment">// q is going to contain vertices of left side only.</span></div>
+<div class="line"><span class="lineno">  156</span>    <span class="keywordflow">while</span> (!q.empty())</div>
+<div class="line"><span class="lineno">  157</span>    {</div>
+<div class="line"><span class="lineno">  158</span>        <span class="keywordtype">int</span> u = q.front();  <span class="comment">// dequeue a vertex</span></div>
+<div class="line"><span class="lineno">  159</span>        q.pop();</div>
+<div class="line"><span class="lineno">  160</span> </div>
+<div class="line"><span class="lineno">  161</span>        <span class="comment">// If this node is not NIL and can provide a shorter path to NIL then</span></div>
+<div class="line"><span class="lineno">  162</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] &lt; <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[NIL])</div>
+<div class="line"><span class="lineno">  163</span>        {</div>
+<div class="line"><span class="lineno">  164</span>            <span class="comment">// Get all the adjacent vertices of the dequeued vertex u</span></div>
+<div class="line"><span class="lineno">  165</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">std::list&lt;int&gt;::iterator</a> it;</div>
+<div class="line"><span class="lineno">  166</span>            <span class="keywordflow">for</span> (it = <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a35893def7a1c5cd60907b4893117796f">adj</a>[u].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">begin</a>(); it != <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a35893def7a1c5cd60907b4893117796f">adj</a>[u].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>(); ++it)</div>
+<div class="line"><span class="lineno">  167</span>            {</div>
+<div class="line"><span class="lineno">  168</span>                <span class="keywordtype">int</span> v = *it;</div>
+<div class="line"><span class="lineno">  169</span> </div>
+<div class="line"><span class="lineno">  170</span>                <span class="comment">// If pair of v is not considered so far i.e. (v, pair_v[v]) is not yet explored edge.</span></div>
+<div class="line"><span class="lineno">  171</span>                <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]] == INF)</div>
+<div class="line"><span class="lineno">  172</span>                {</div>
+<div class="line"><span class="lineno">  173</span>                    <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]] = <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] + 1; </div>
+<div class="line"><span class="lineno">  174</span>                    q.push(<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]);    <span class="comment">// Consider the pair and push it to queue</span></div>
+<div class="line"><span class="lineno">  175</span>                }</div>
+<div class="line"><span class="lineno">  176</span>            }</div>
+<div class="line"><span class="lineno">  177</span>        }</div>
+<div class="line"><span class="lineno">  178</span>    }</div>
+<div class="line"><span class="lineno">  179</span> </div>
+<div class="line"><span class="lineno">  180</span>   </div>
+<div class="line"><span class="lineno">  181</span>   </div>
+<div class="line"><span class="lineno">  182</span>    <span class="keywordflow">return</span> (<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[NIL] != INF);   <span class="comment">// If we could come back to NIL using alternating path of distinct vertices then there is an augmenting path available</span></div>
+<div class="line"><span class="lineno">  183</span>}</div>
 <div class="ttc" id="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a></div><div class="ttdeci">T begin(T... args)</div></div>
 <div class="ttc" id="aclassgraph_1_1_h_k_graph_html_a6a0228bbba3818447fcf6b56128b552a"><div class="ttname"><a href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">graph::HKGraph::dist</a></div><div class="ttdeci">std::vector&lt; int &gt; dist</div><div class="ttdoc">dist represents the distance between vertex 'u' and vertex 'v'</div><div class="ttdef"><b>Definition:</b> hopcroft_karp.cpp:77</div></div>
 <div class="ttc" id="aclassgraph_1_1_h_k_graph_html_a86ebff8a70cbfedd05281993d5d1987b"><div class="ttname"><a href="../../d8/d69/classgraph_1_1_h_k_graph.html#a86ebff8a70cbfedd05281993d5d1987b">graph::HKGraph::pair_u</a></div><div class="ttdeci">std::vector&lt; int &gt; pair_u</div><div class="ttdoc">value of vertex 'u' ranges from 1 to m</div><div class="ttdef"><b>Definition:</b> hopcroft_karp.cpp:75</div></div>
 <div class="ttc" id="aclassgraph_1_1_h_k_graph_html_a976ee239402cc2726a280e781c706d77"><div class="ttname"><a href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">graph::HKGraph::pair_v</a></div><div class="ttdeci">std::vector&lt; int &gt; pair_v</div><div class="ttdoc">value of vertex 'v' ranges from 1 to n</div><div class="ttdef"><b>Definition:</b> hopcroft_karp.cpp:76</div></div>
+<div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/end.html">std::vector::end</a></div><div class="ttdeci">T end(T... args)</div></div>
 <div class="ttc" id="alist_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list.html">std::list</a></div></div>
 <div class="ttc" id="aqueue_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue</a></div></div>
-</div><!-- fragment -->
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/d69/classgraph_1_1_h_k_graph_a7491add14d9fc04f679114ca6d6f0f93_cgraph.svg" width="315" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
 </div>
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 <a id="ae794950cb3407b6b47d3dc986cf714c0" name="ae794950cb3407b6b47d3dc986cf714c0"></a>
@@ -350,39 +370,39 @@ const int&#160;</td><td class="memItemRight" valign="bottom"><b>INF</b> {INT_MAX
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if there is an augmenting path beginning with free vertex u </dd>
 <dd>
 <code>false</code> if there is no augmenting path beginning with free vertex u </dd></dl>
-<div class="fragment"><div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>{</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>    <span class="keywordflow">if</span> (u != NIL)</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>    {</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">std::list&lt;int&gt;::iterator</a> it;</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>        <span class="keywordflow">for</span> (it = <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a35893def7a1c5cd60907b4893117796f">adj</a>[u].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">begin</a>(); it != <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a35893def7a1c5cd60907b4893117796f">adj</a>[u].end(); ++it)</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>        {</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>            </div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>            <span class="keywordtype">int</span> v = *it; <span class="comment">// Adjacent vertex of u</span></div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span> </div>
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-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>            {</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>                <span class="comment">// If dfs for pair of v also return true then new matching possible, store the matching</span></div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>                <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d8/d69/classgraph_1_1_h_k_graph.html#ae794950cb3407b6b47d3dc986cf714c0">dfs</a>(<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]) == <span class="keyword">true</span>)</div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>                {   </div>
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-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>                    <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a86ebff8a70cbfedd05281993d5d1987b">pair_u</a>[u] = v;</div>
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-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>                }</div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>            }</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>        }</div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span> </div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>        </div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>        <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] = INF; <span class="comment">// If there is no augmenting path beginning with u then set distance to infinite.</span></div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>    }</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  192</span>{</div>
+<div class="line"><span class="lineno">  193</span>    <span class="keywordflow">if</span> (u != NIL)</div>
+<div class="line"><span class="lineno">  194</span>    {</div>
+<div class="line"><span class="lineno">  195</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">std::list&lt;int&gt;::iterator</a> it;</div>
+<div class="line"><span class="lineno">  196</span>        <span class="keywordflow">for</span> (it = <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a35893def7a1c5cd60907b4893117796f">adj</a>[u].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">begin</a>(); it != <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a35893def7a1c5cd60907b4893117796f">adj</a>[u].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>(); ++it)</div>
+<div class="line"><span class="lineno">  197</span>        {</div>
+<div class="line"><span class="lineno">  198</span>            </div>
+<div class="line"><span class="lineno">  199</span>            <span class="keywordtype">int</span> v = *it; <span class="comment">// Adjacent vertex of u</span></div>
+<div class="line"><span class="lineno">  200</span> </div>
+<div class="line"><span class="lineno">  201</span>            <span class="comment">// Follow the distances set by BFS search</span></div>
+<div class="line"><span class="lineno">  202</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]] == <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] + 1)</div>
+<div class="line"><span class="lineno">  203</span>            {</div>
+<div class="line"><span class="lineno">  204</span>                <span class="comment">// If dfs for pair of v also return true then new matching possible, store the matching</span></div>
+<div class="line"><span class="lineno">  205</span>                <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d8/d69/classgraph_1_1_h_k_graph.html#ae794950cb3407b6b47d3dc986cf714c0">dfs</a>(<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]) == <span class="keyword">true</span>)</div>
+<div class="line"><span class="lineno">  206</span>                {   </div>
+<div class="line"><span class="lineno">  207</span>                    <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a>[v] = u;</div>
+<div class="line"><span class="lineno">  208</span>                    <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a86ebff8a70cbfedd05281993d5d1987b">pair_u</a>[u] = v;</div>
+<div class="line"><span class="lineno">  209</span>                    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  210</span>                }</div>
+<div class="line"><span class="lineno">  211</span>            }</div>
+<div class="line"><span class="lineno">  212</span>        }</div>
+<div class="line"><span class="lineno">  213</span> </div>
+<div class="line"><span class="lineno">  214</span>        </div>
+<div class="line"><span class="lineno">  215</span>        <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] = INF; <span class="comment">// If there is no augmenting path beginning with u then set distance to infinite.</span></div>
+<div class="line"><span class="lineno">  216</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  217</span>    }</div>
+<div class="line"><span class="lineno">  218</span>    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  219</span>}</div>
 <div class="ttc" id="aclassgraph_1_1_h_k_graph_html_ae794950cb3407b6b47d3dc986cf714c0"><div class="ttname"><a href="../../d8/d69/classgraph_1_1_h_k_graph.html#ae794950cb3407b6b47d3dc986cf714c0">graph::HKGraph::dfs</a></div><div class="ttdeci">bool dfs(int u)</div><div class="ttdoc">This functions checks whether an augmenting path is available exists beginning with free vertex u.</div><div class="ttdef"><b>Definition:</b> hopcroft_karp.cpp:191</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/d69/classgraph_1_1_h_k_graph_ae794950cb3407b6b47d3dc986cf714c0_cgraph.svg" width="154" height="62"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/d69/classgraph_1_1_h_k_graph_ae794950cb3407b6b47d3dc986cf714c0_cgraph.svg" width="315" height="62"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
 </div>
 </div>
 
@@ -405,42 +425,42 @@ Here is the call graph for this function:</div>
 
 <p>This function counts the number of augmenting paths between left and right sides of the Bipartite graph. </p>
 <dl class="section return"><dt>Returns</dt><dd>size of maximum matching </dd></dl>
-<div class="fragment"><div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>{</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span> </div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    <span class="comment">// pair_u[u] stores pair of u in matching on left side of Bipartite Graph.</span></div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>    <span class="comment">// If u doesn&#39;t have any pair, then pair_u[u] is NIL</span></div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a86ebff8a70cbfedd05281993d5d1987b">pair_u</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>(<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a3d9101e3b4598159005fd028b9b0ff74">m</a> + 1,NIL); </div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span> </div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <span class="comment">// pair_v[v] stores pair of v in matching on right side of Biparite Graph.</span></div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <span class="comment">// If v doesn&#39;t have any pair, then pair_u[v] is NIL</span></div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>(<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6f5a9fdbb83ef731d739ba6707e21c3c">n</a> + 1,NIL); </div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span> </div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>(<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a3d9101e3b4598159005fd028b9b0ff74">m</a> + 1);  <span class="comment">// dist[u] stores distance of left side vertices</span></div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span> </div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    <span class="keywordtype">int</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = 0;  <span class="comment">// Initialize result</span></div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span> </div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    <span class="comment">// Keep updating the result while there is an augmenting path possible.</span></div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <span class="keywordflow">while</span> (<a class="code hl_function" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a7491add14d9fc04f679114ca6d6f0f93">bfs</a>())</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    {</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        <span class="comment">// Find a free vertex to check for a matching</span></div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> u = 1; u &lt;= <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a3d9101e3b4598159005fd028b9b0ff74">m</a>; u++){</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span> </div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>            <span class="comment">// If current vertex is free and there is</span></div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>            <span class="comment">// an augmenting path from current vertex</span></div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>            <span class="comment">// then increment the result</span></div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a86ebff8a70cbfedd05281993d5d1987b">pair_u</a>[u] == NIL &amp;&amp; <a class="code hl_function" href="../../d8/d69/classgraph_1_1_h_k_graph.html#ae794950cb3407b6b47d3dc986cf714c0">dfs</a>(u)){</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>                <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>++;</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>        }</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    }</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    }</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   96</span>{</div>
+<div class="line"><span class="lineno">   97</span> </div>
+<div class="line"><span class="lineno">   98</span>    <span class="comment">// pair_u[u] stores pair of u in matching on left side of Bipartite Graph.</span></div>
+<div class="line"><span class="lineno">   99</span>    <span class="comment">// If u doesn&#39;t have any pair, then pair_u[u] is NIL</span></div>
+<div class="line"><span class="lineno">  100</span>    <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a86ebff8a70cbfedd05281993d5d1987b">pair_u</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>(<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a3d9101e3b4598159005fd028b9b0ff74">m</a> + 1,NIL); </div>
+<div class="line"><span class="lineno">  101</span> </div>
+<div class="line"><span class="lineno">  102</span>    <span class="comment">// pair_v[v] stores pair of v in matching on right side of Biparite Graph.</span></div>
+<div class="line"><span class="lineno">  103</span>    <span class="comment">// If v doesn&#39;t have any pair, then pair_u[v] is NIL</span></div>
+<div class="line"><span class="lineno">  104</span>    <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>(<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6f5a9fdbb83ef731d739ba6707e21c3c">n</a> + 1,NIL); </div>
+<div class="line"><span class="lineno">  105</span> </div>
+<div class="line"><span class="lineno">  106</span>    <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>(<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a3d9101e3b4598159005fd028b9b0ff74">m</a> + 1);  <span class="comment">// dist[u] stores distance of left side vertices</span></div>
+<div class="line"><span class="lineno">  107</span> </div>
+<div class="line"><span class="lineno">  108</span>    <span class="keywordtype">int</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = 0;  <span class="comment">// Initialize result</span></div>
+<div class="line"><span class="lineno">  109</span> </div>
+<div class="line"><span class="lineno">  110</span>    <span class="comment">// Keep updating the result while there is an augmenting path possible.</span></div>
+<div class="line"><span class="lineno">  111</span>    <span class="keywordflow">while</span> (<a class="code hl_function" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a7491add14d9fc04f679114ca6d6f0f93">bfs</a>())</div>
+<div class="line"><span class="lineno">  112</span>    {</div>
+<div class="line"><span class="lineno">  113</span>        <span class="comment">// Find a free vertex to check for a matching</span></div>
+<div class="line"><span class="lineno">  114</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> u = 1; u &lt;= <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a3d9101e3b4598159005fd028b9b0ff74">m</a>; u++){</div>
+<div class="line"><span class="lineno">  115</span> </div>
+<div class="line"><span class="lineno">  116</span>            <span class="comment">// If current vertex is free and there is</span></div>
+<div class="line"><span class="lineno">  117</span>            <span class="comment">// an augmenting path from current vertex</span></div>
+<div class="line"><span class="lineno">  118</span>            <span class="comment">// then increment the result</span></div>
+<div class="line"><span class="lineno">  119</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a86ebff8a70cbfedd05281993d5d1987b">pair_u</a>[u] == NIL &amp;&amp; <a class="code hl_function" href="../../d8/d69/classgraph_1_1_h_k_graph.html#ae794950cb3407b6b47d3dc986cf714c0">dfs</a>(u)){</div>
+<div class="line"><span class="lineno">  120</span>                <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>++;</div>
+<div class="line"><span class="lineno">  121</span>        }</div>
+<div class="line"><span class="lineno">  122</span>    }</div>
+<div class="line"><span class="lineno">  123</span>    }</div>
+<div class="line"><span class="lineno">  124</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  125</span>}</div>
 <div class="ttc" id="aclassgraph_1_1_h_k_graph_html_a7491add14d9fc04f679114ca6d6f0f93"><div class="ttname"><a href="../../d8/d69/classgraph_1_1_h_k_graph.html#a7491add14d9fc04f679114ca6d6f0f93">graph::HKGraph::bfs</a></div><div class="ttdeci">bool bfs()</div><div class="ttdoc">This function checks for the possibility of augmented path availability.</div><div class="ttdef"><b>Definition:</b> hopcroft_karp.cpp:133</div></div>
 <div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/d69/classgraph_1_1_h_k_graph_a9dbda80d02bdc26c3e8ff7330c9be75d_cgraph.svg" width="372" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/d69/classgraph_1_1_h_k_graph_a9dbda80d02bdc26c3e8ff7330c9be75d_cgraph.svg" width="534" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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@@ -455,7 +475,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../df/dce/namespacegraph.html">graph</a></li><li class="navelem"><a class="el" href="../../d8/d69/classgraph_1_1_h_k_graph.html">HKGraph</a></li>
-    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.2 </li>
+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
   </ul>
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diff --git a/d8/d69/classgraph_1_1_h_k_graph_a3b49011c09cf90a116ab53bef61cd95a_cgraph.map b/d8/d69/classgraph_1_1_h_k_graph_a3b49011c09cf90a116ab53bef61cd95a_cgraph.map
new file mode 100644
index 000000000..80e741455
--- /dev/null
+++ b/d8/d69/classgraph_1_1_h_k_graph_a3b49011c09cf90a116ab53bef61cd95a_cgraph.map
@@ -0,0 +1,4 @@
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-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>        <span class="keywordflow">else</span></div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;\nThere is no left child of the node.  &quot;</span>;</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;\nNode Deleted.&quot;</span>;</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>        <span class="keywordflow">if</span> (p-&gt;left == NULL || p-&gt;right == NULL)</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>            y = p;</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>        <span class="keywordflow">else</span></div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>            y = successor(p);</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>        <span class="keywordflow">if</span> (y-&gt;left != NULL)</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>            q = y-&gt;left;</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>        <span class="keywordflow">else</span></div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>        {</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>            <span class="keywordflow">if</span> (y-&gt;right != NULL)</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>                q = y-&gt;right;</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>            <span class="keywordflow">else</span></div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>                q = NULL;</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>        }</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>        <span class="keywordflow">if</span> (q != NULL)</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>            q-&gt;parent = y-&gt;parent;</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>        <span class="keywordflow">if</span> (y-&gt;parent == NULL)</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>            root = q;</div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>        <span class="keywordflow">else</span></div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>        {</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>            <span class="keywordflow">if</span> (y == y-&gt;parent-&gt;left)</div>
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-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>            <span class="keywordflow">else</span></div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>                y-&gt;parent-&gt;right = q;</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>        }</div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>        <span class="keywordflow">if</span> (y != p)</div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>        {</div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>            p-&gt;color = y-&gt;color;</div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>            p-&gt;key = y-&gt;key;</div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>        }</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>        <span class="keywordflow">if</span> (y-&gt;color == <span class="charliteral">&#39;b&#39;</span>)</div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>            delfix(q);</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>    }</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  136</span>{</div>
+<div class="line"><span class="lineno">  137</span>    <span class="keywordflow">if</span> (root == NULL)</div>
+<div class="line"><span class="lineno">  138</span>    {</div>
+<div class="line"><span class="lineno">  139</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEmpty Tree.&quot;</span>;</div>
+<div class="line"><span class="lineno">  140</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  141</span>    }</div>
+<div class="line"><span class="lineno">  142</span>    <span class="keywordtype">int</span> x;</div>
+<div class="line"><span class="lineno">  143</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEnter the key of the node to be deleted: &quot;</span>;</div>
+<div class="line"><span class="lineno">  144</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> &gt;&gt; x;</div>
+<div class="line"><span class="lineno">  145</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *p;</div>
+<div class="line"><span class="lineno">  146</span>    p = root;</div>
+<div class="line"><span class="lineno">  147</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *y = NULL;</div>
+<div class="line"><span class="lineno">  148</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *q = NULL;</div>
+<div class="line"><span class="lineno">  149</span>    <span class="keywordtype">int</span> found = 0;</div>
+<div class="line"><span class="lineno">  150</span>    <span class="keywordflow">while</span> (p != NULL &amp;&amp; found == 0)</div>
+<div class="line"><span class="lineno">  151</span>    {</div>
+<div class="line"><span class="lineno">  152</span>        <span class="keywordflow">if</span> (p-&gt;key == x)</div>
+<div class="line"><span class="lineno">  153</span>            found = 1;</div>
+<div class="line"><span class="lineno">  154</span>        <span class="keywordflow">if</span> (found == 0)</div>
+<div class="line"><span class="lineno">  155</span>        {</div>
+<div class="line"><span class="lineno">  156</span>            <span class="keywordflow">if</span> (p-&gt;key &lt; x)</div>
+<div class="line"><span class="lineno">  157</span>                p = p-&gt;right;</div>
+<div class="line"><span class="lineno">  158</span>            <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  159</span>                p = p-&gt;left;</div>
+<div class="line"><span class="lineno">  160</span>        }</div>
+<div class="line"><span class="lineno">  161</span>    }</div>
+<div class="line"><span class="lineno">  162</span>    <span class="keywordflow">if</span> (found == 0)</div>
+<div class="line"><span class="lineno">  163</span>    {</div>
+<div class="line"><span class="lineno">  164</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;\nElement Not Found.&quot;</span>;</div>
+<div class="line"><span class="lineno">  165</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  166</span>    }</div>
+<div class="line"><span class="lineno">  167</span>    <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  168</span>    {</div>
+<div class="line"><span class="lineno">  169</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;\nDeleted Element: &quot;</span> &lt;&lt; p-&gt;key;</div>
+<div class="line"><span class="lineno">  170</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;\nColour: &quot;</span>;</div>
+<div class="line"><span class="lineno">  171</span>        <span class="keywordflow">if</span> (p-&gt;color == <span class="charliteral">&#39;b&#39;</span>)</div>
+<div class="line"><span class="lineno">  172</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;Black\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  173</span>        <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  174</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;Red\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  175</span> </div>
+<div class="line"><span class="lineno">  176</span>        <span class="keywordflow">if</span> (p-&gt;parent != NULL)</div>
+<div class="line"><span class="lineno">  177</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;\nParent: &quot;</span> &lt;&lt; p-&gt;parent-&gt;key;</div>
+<div class="line"><span class="lineno">  178</span>        <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  179</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;\nThere is no parent of the node.  &quot;</span>;</div>
+<div class="line"><span class="lineno">  180</span>        <span class="keywordflow">if</span> (p-&gt;right != NULL)</div>
+<div class="line"><span class="lineno">  181</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;\nRight Child: &quot;</span> &lt;&lt; p-&gt;right-&gt;key;</div>
+<div class="line"><span class="lineno">  182</span>        <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  183</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;\nThere is no right child of the node.  &quot;</span>;</div>
+<div class="line"><span class="lineno">  184</span>        <span class="keywordflow">if</span> (p-&gt;left != NULL)</div>
+<div class="line"><span class="lineno">  185</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;\nLeft Child: &quot;</span> &lt;&lt; p-&gt;left-&gt;key;</div>
+<div class="line"><span class="lineno">  186</span>        <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  187</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;\nThere is no left child of the node.  &quot;</span>;</div>
+<div class="line"><span class="lineno">  188</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;\nNode Deleted.&quot;</span>;</div>
+<div class="line"><span class="lineno">  189</span>        <span class="keywordflow">if</span> (p-&gt;left == NULL || p-&gt;right == NULL)</div>
+<div class="line"><span class="lineno">  190</span>            y = p;</div>
+<div class="line"><span class="lineno">  191</span>        <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  192</span>            y = successor(p);</div>
+<div class="line"><span class="lineno">  193</span>        <span class="keywordflow">if</span> (y-&gt;left != NULL)</div>
+<div class="line"><span class="lineno">  194</span>            q = y-&gt;left;</div>
+<div class="line"><span class="lineno">  195</span>        <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  196</span>        {</div>
+<div class="line"><span class="lineno">  197</span>            <span class="keywordflow">if</span> (y-&gt;right != NULL)</div>
+<div class="line"><span class="lineno">  198</span>                q = y-&gt;right;</div>
+<div class="line"><span class="lineno">  199</span>            <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  200</span>                q = NULL;</div>
+<div class="line"><span class="lineno">  201</span>        }</div>
+<div class="line"><span class="lineno">  202</span>        <span class="keywordflow">if</span> (q != NULL)</div>
+<div class="line"><span class="lineno">  203</span>            q-&gt;parent = y-&gt;parent;</div>
+<div class="line"><span class="lineno">  204</span>        <span class="keywordflow">if</span> (y-&gt;parent == NULL)</div>
+<div class="line"><span class="lineno">  205</span>            root = q;</div>
+<div class="line"><span class="lineno">  206</span>        <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  207</span>        {</div>
+<div class="line"><span class="lineno">  208</span>            <span class="keywordflow">if</span> (y == y-&gt;parent-&gt;left)</div>
+<div class="line"><span class="lineno">  209</span>                y-&gt;parent-&gt;left = q;</div>
+<div class="line"><span class="lineno">  210</span>            <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  211</span>                y-&gt;parent-&gt;right = q;</div>
+<div class="line"><span class="lineno">  212</span>        }</div>
+<div class="line"><span class="lineno">  213</span>        <span class="keywordflow">if</span> (y != p)</div>
+<div class="line"><span class="lineno">  214</span>        {</div>
+<div class="line"><span class="lineno">  215</span>            p-&gt;color = y-&gt;color;</div>
+<div class="line"><span class="lineno">  216</span>            p-&gt;key = y-&gt;key;</div>
+<div class="line"><span class="lineno">  217</span>        }</div>
+<div class="line"><span class="lineno">  218</span>        <span class="keywordflow">if</span> (y-&gt;color == <span class="charliteral">&#39;b&#39;</span>)</div>
+<div class="line"><span class="lineno">  219</span>            delfix(q);</div>
+<div class="line"><span class="lineno">  220</span>    }</div>
+<div class="line"><span class="lineno">  221</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="astructnode_html"><div class="ttname"><a href="../../d5/da1/structnode.html">node</a></div><div class="ttdef"><b>Definition:</b> avltree.cpp:13</div></div>
@@ -288,76 +288,76 @@ Private Attributes</h2></td></tr>
         </tr>
       </table>
 </div><div class="memdoc">
-<div class="fragment"><div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>{</div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *s;</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>    <span class="keywordflow">while</span> (p != root &amp;&amp; p-&gt;color == <span class="charliteral">&#39;b&#39;</span>)</div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>    {</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>        <span class="keywordflow">if</span> (p-&gt;parent-&gt;left == p)</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>        {</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>            s = p-&gt;parent-&gt;right;</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>            <span class="keywordflow">if</span> (s-&gt;color == <span class="charliteral">&#39;r&#39;</span>)</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>            {</div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>                s-&gt;color = <span class="charliteral">&#39;b&#39;</span>;</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>                p-&gt;parent-&gt;color = <span class="charliteral">&#39;r&#39;</span>;</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>                leftrotate(p-&gt;parent);</div>
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-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>            }</div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>            <span class="keywordflow">if</span> (s-&gt;right-&gt;color == <span class="charliteral">&#39;b&#39;</span>&amp;&amp;s-&gt;left-&gt;color == <span class="charliteral">&#39;b&#39;</span>)</div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>            {</div>
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-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>                p = p-&gt;parent;</div>
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-<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>            {</div>
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-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>                {</div>
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-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>                    s-&gt;color = <span class="charliteral">&#39;r&#39;</span>;</div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>                    rightrotate(s);</div>
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-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>                p-&gt;parent-&gt;color = <span class="charliteral">&#39;b&#39;</span>;</div>
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@@ -396,50 +396,50 @@ Private Attributes</h2></td></tr>
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-<div class="line"><a id="l00420" name="l00420"></a><span class="lineno">  420</span>}</div>
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-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   71</span>{</div>
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+<div class="line"><span class="lineno">   73</span>    <span class="keywordflow">if</span> (root == t)</div>
+<div class="line"><span class="lineno">   74</span>    {</div>
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+<div class="line"><span class="lineno">   76</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">   77</span>    }</div>
+<div class="line"><span class="lineno">   78</span>    <span class="keywordflow">while</span> (t-&gt;parent != NULL &amp;&amp; t-&gt;parent-&gt;color == <span class="charliteral">&#39;r&#39;</span>)</div>
+<div class="line"><span class="lineno">   79</span>    {</div>
+<div class="line"><span class="lineno">   80</span>        <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = t-&gt;parent-&gt;parent;</div>
+<div class="line"><span class="lineno">   81</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>-&gt;left == t-&gt;parent)</div>
+<div class="line"><span class="lineno">   82</span>        {</div>
+<div class="line"><span class="lineno">   83</span>            <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>-&gt;right != NULL)</div>
+<div class="line"><span class="lineno">   84</span>            {</div>
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+<div class="line"><span class="lineno">   86</span>                <span class="keywordflow">if</span> (u-&gt;color == <span class="charliteral">&#39;r&#39;</span>)</div>
+<div class="line"><span class="lineno">   87</span>                {</div>
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+<div class="line"><span class="lineno">   90</span>                    <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>-&gt;color = <span class="charliteral">&#39;r&#39;</span>;</div>
+<div class="line"><span class="lineno">   91</span>                    t = <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>;</div>
+<div class="line"><span class="lineno">   92</span>                }</div>
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+<div class="line"><span class="lineno">   95</span>            {</div>
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+<div class="line"><span class="lineno">  103</span>                rightrotate(g);</div>
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+<div class="line"><span class="lineno">  107</span>        {</div>
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+<div class="line"><span class="lineno">  111</span>                <span class="keywordflow">if</span> (u-&gt;color == <span class="charliteral">&#39;r&#39;</span>)</div>
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+<div class="line"><span class="lineno">  116</span>                    t = <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>;</div>
+<div class="line"><span class="lineno">  117</span>                }</div>
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+<div class="line"><span class="lineno">  119</span>            <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  120</span>            {</div>
+<div class="line"><span class="lineno">  121</span>                <span class="keywordflow">if</span> (t-&gt;parent-&gt;left == t)</div>
+<div class="line"><span class="lineno">  122</span>                {</div>
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+<div class="line"><span class="lineno">  127</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>-&gt;color = <span class="charliteral">&#39;r&#39;</span>;</div>
+<div class="line"><span class="lineno">  128</span>                leftrotate(g);</div>
+<div class="line"><span class="lineno">  129</span>            }</div>
+<div class="line"><span class="lineno">  130</span>        }</div>
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+<div class="line"><span class="lineno">  132</span>    }</div>
+<div class="line"><span class="lineno">  133</span>}</div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a2f67508d5f392b0321772169342c98ad"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">numerical_methods::simpson_method::g</a></div><div class="ttdeci">double g(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:115</div></div>
 </div><!-- fragment -->
 </div>
@@ -594,34 +594,34 @@ Private Attributes</h2></td></tr>
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-<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>}</div>
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+<div class="line"><span class="lineno">  299</span>    <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  300</span>    {</div>
+<div class="line"><span class="lineno">  301</span>        <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *y = p-&gt;right;</div>
+<div class="line"><span class="lineno">  302</span>        <span class="keywordflow">if</span> (y-&gt;left != NULL)</div>
+<div class="line"><span class="lineno">  303</span>        {</div>
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+<div class="line"><span class="lineno">  307</span>        <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  308</span>            p-&gt;right = NULL;</div>
+<div class="line"><span class="lineno">  309</span>        <span class="keywordflow">if</span> (p-&gt;parent != NULL)</div>
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+<div class="line"><span class="lineno">  313</span>        <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  314</span>        {</div>
+<div class="line"><span class="lineno">  315</span>            <span class="keywordflow">if</span> (p == p-&gt;parent-&gt;left)</div>
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+<div class="line"><span class="lineno">  318</span>                p-&gt;parent-&gt;right = y;</div>
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+<div class="line"><span class="lineno">  322</span>    }</div>
+<div class="line"><span class="lineno">  323</span>}</div>
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@@ -640,34 +640,34 @@ Private Attributes</h2></td></tr>
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 </div><div class="memdoc">
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-<p>Implementation of <a href="https://en.wikipedia.org/wiki/Morse_code" target="_blank">Morse Code</a>.  
+<p>Implementation of [Morse Code] (<a href="https://en.wikipedia.org/wiki/Morse_code">https://en.wikipedia.org/wiki/Morse_code</a>).  
 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;cassert&gt;</code><br />
 <code>#include &lt;iostream&gt;</code><br />
@@ -116,7 +116,7 @@ Namespaces</h2></td></tr>
 <tr class="memdesc:d6/d4e/namespaceciphers"><td class="mdescLeft">&#160;</td><td class="mdescRight">Algorithms for encryption and decryption. <br /></td></tr>
 <tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
 <tr class="memitem:d6/d8d/namespacemorse"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d8d/namespacemorse.html">morse</a></td></tr>
-<tr class="memdesc:d6/d8d/namespacemorse"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for <a href="https://en.wikipedia.org/wiki/Morse_code" target="_blank">Morse Code</a>. <br /></td></tr>
+<tr class="memdesc:d6/d8d/namespacemorse"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for [Morse Code] (<a href="https://en.wikipedia.org/wiki/Morse_code">https://en.wikipedia.org/wiki/Morse_code</a>). <br /></td></tr>
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 </table>
 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
-<div class="textblock"><p >Implementation of <a href="https://en.wikipedia.org/wiki/Morse_code" target="_blank">Morse Code</a>. </p>
+<div class="textblock"><p >Implementation of [Morse Code] (<a href="https://en.wikipedia.org/wiki/Morse_code">https://en.wikipedia.org/wiki/Morse_code</a>). </p>
 <dl class="section author"><dt>Author</dt><dd><a href="https://github.com/imdeep2905" target="_blank">Deep Raval</a></dd></dl>
 <p>Morse code is a method used in telecommunication to encode text characters as standardized sequences of two different signal durations, called dots and dashes or dits and dahs. Morse code is named after Samuel Morse, an inventor of the telegraph. </p>
 </div><h2 class="groupheader">Function Documentation</h2>
@@ -163,86 +163,86 @@ Functions</h2></td></tr>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>morse representation string of character </dd></dl>
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-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>    <span class="comment">// return corresponding morse code</span></div>
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-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;.-&quot;</span>;</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;b&#39;</span>:</div>
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-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   33</span>                                       {</div>
+<div class="line"><span class="lineno">   34</span>    <span class="comment">// return corresponding morse code</span></div>
+<div class="line"><span class="lineno">   35</span>    <span class="keywordflow">switch</span> (c) {</div>
+<div class="line"><span class="lineno">   36</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;a&#39;</span>:</div>
+<div class="line"><span class="lineno">   37</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;.-&quot;</span>;</div>
+<div class="line"><span class="lineno">   38</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;b&#39;</span>:</div>
+<div class="line"><span class="lineno">   39</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;-...&quot;</span>;</div>
+<div class="line"><span class="lineno">   40</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;c&#39;</span>:</div>
+<div class="line"><span class="lineno">   41</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;-.-.&quot;</span>;</div>
+<div class="line"><span class="lineno">   42</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;d&#39;</span>:</div>
+<div class="line"><span class="lineno">   43</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;-..&quot;</span>;</div>
+<div class="line"><span class="lineno">   44</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;e&#39;</span>:</div>
+<div class="line"><span class="lineno">   45</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;.&quot;</span>;</div>
+<div class="line"><span class="lineno">   46</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;f&#39;</span>:</div>
+<div class="line"><span class="lineno">   47</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;..-.&quot;</span>;</div>
+<div class="line"><span class="lineno">   48</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;g&#39;</span>:</div>
+<div class="line"><span class="lineno">   49</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;--.&quot;</span>;</div>
+<div class="line"><span class="lineno">   50</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;h&#39;</span>:</div>
+<div class="line"><span class="lineno">   51</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;....&quot;</span>;</div>
+<div class="line"><span class="lineno">   52</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;i&#39;</span>:</div>
+<div class="line"><span class="lineno">   53</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;..&quot;</span>;</div>
+<div class="line"><span class="lineno">   54</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;j&#39;</span>:</div>
+<div class="line"><span class="lineno">   55</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;.---&quot;</span>;</div>
+<div class="line"><span class="lineno">   56</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;k&#39;</span>:</div>
+<div class="line"><span class="lineno">   57</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;-.-&quot;</span>;</div>
+<div class="line"><span class="lineno">   58</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;l&#39;</span>:</div>
+<div class="line"><span class="lineno">   59</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;.-..&quot;</span>;</div>
+<div class="line"><span class="lineno">   60</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;m&#39;</span>:</div>
+<div class="line"><span class="lineno">   61</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;--&quot;</span>;</div>
+<div class="line"><span class="lineno">   62</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;n&#39;</span>:</div>
+<div class="line"><span class="lineno">   63</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;-.&quot;</span>;</div>
+<div class="line"><span class="lineno">   64</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;o&#39;</span>:</div>
+<div class="line"><span class="lineno">   65</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;---&quot;</span>;</div>
+<div class="line"><span class="lineno">   66</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;p&#39;</span>:</div>
+<div class="line"><span class="lineno">   67</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;.--.&quot;</span>;</div>
+<div class="line"><span class="lineno">   68</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;q&#39;</span>:</div>
+<div class="line"><span class="lineno">   69</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;--.-&quot;</span>;</div>
+<div class="line"><span class="lineno">   70</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;r&#39;</span>:</div>
+<div class="line"><span class="lineno">   71</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;.-.&quot;</span>;</div>
+<div class="line"><span class="lineno">   72</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;s&#39;</span>:</div>
+<div class="line"><span class="lineno">   73</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;...&quot;</span>;</div>
+<div class="line"><span class="lineno">   74</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;t&#39;</span>:</div>
+<div class="line"><span class="lineno">   75</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;-&quot;</span>;</div>
+<div class="line"><span class="lineno">   76</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;u&#39;</span>:</div>
+<div class="line"><span class="lineno">   77</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;..-&quot;</span>;</div>
+<div class="line"><span class="lineno">   78</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;v&#39;</span>:</div>
+<div class="line"><span class="lineno">   79</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;...-&quot;</span>;</div>
+<div class="line"><span class="lineno">   80</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;w&#39;</span>:</div>
+<div class="line"><span class="lineno">   81</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;.--&quot;</span>;</div>
+<div class="line"><span class="lineno">   82</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;x&#39;</span>:</div>
+<div class="line"><span class="lineno">   83</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;-..-&quot;</span>;</div>
+<div class="line"><span class="lineno">   84</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;y&#39;</span>:</div>
+<div class="line"><span class="lineno">   85</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;-.--&quot;</span>;</div>
+<div class="line"><span class="lineno">   86</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;z&#39;</span>:</div>
+<div class="line"><span class="lineno">   87</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;--..&quot;</span>;</div>
+<div class="line"><span class="lineno">   88</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;1&#39;</span>:</div>
+<div class="line"><span class="lineno">   89</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;.----&quot;</span>;</div>
+<div class="line"><span class="lineno">   90</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;2&#39;</span>:</div>
+<div class="line"><span class="lineno">   91</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;..---&quot;</span>;</div>
+<div class="line"><span class="lineno">   92</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;3&#39;</span>:</div>
+<div class="line"><span class="lineno">   93</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;...--&quot;</span>;</div>
+<div class="line"><span class="lineno">   94</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;4&#39;</span>:</div>
+<div class="line"><span class="lineno">   95</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;....-&quot;</span>;</div>
+<div class="line"><span class="lineno">   96</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;5&#39;</span>:</div>
+<div class="line"><span class="lineno">   97</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;.....&quot;</span>;</div>
+<div class="line"><span class="lineno">   98</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;6&#39;</span>:</div>
+<div class="line"><span class="lineno">   99</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;-....&quot;</span>;</div>
+<div class="line"><span class="lineno">  100</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;7&#39;</span>:</div>
+<div class="line"><span class="lineno">  101</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;--...&quot;</span>;</div>
+<div class="line"><span class="lineno">  102</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;8&#39;</span>:</div>
+<div class="line"><span class="lineno">  103</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;---..&quot;</span>;</div>
+<div class="line"><span class="lineno">  104</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;9&#39;</span>:</div>
+<div class="line"><span class="lineno">  105</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;----.&quot;</span>;</div>
+<div class="line"><span class="lineno">  106</span>        <span class="keywordflow">case</span> <span class="charliteral">&#39;0&#39;</span>:</div>
+<div class="line"><span class="lineno">  107</span>            <span class="keywordflow">return</span> <span class="stringliteral">&quot;-----&quot;</span>;</div>
+<div class="line"><span class="lineno">  108</span>        <span class="keywordflow">default</span>:</div>
+<div class="line"><span class="lineno">  109</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Found invalid character: &quot;</span> &lt;&lt; c &lt;&lt; <span class="charliteral">&#39; &#39;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  110</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(0);</div>
+<div class="line"><span class="lineno">  111</span>    }</div>
+<div class="line"><span class="lineno">  112</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
 <div class="ttc" id="aexit_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a></div><div class="ttdeci">T exit(T... args)</div></div>
@@ -277,28 +277,28 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>new decrypted text </dd></dl>
-<div class="fragment"><div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>                                         {</div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>    <span class="comment">// Going through each character of text and converting it</span></div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>    <span class="comment">// back to normal representation.</span></div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> decrypted_text = <span class="stringliteral">&quot;&quot;</span>;  <span class="comment">// Empty string to store decrypted text</span></div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>    <span class="comment">// Spliting string (with delimiter = &quot; &quot;) and storing it</span></div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>    <span class="comment">// in vector</span></div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> pos_start = 0, pos_end = 0, delim_len = 1;</div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::string&gt;</a> splits;</div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    <span class="keywordflow">while</span> ((pos_end = text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/find.html">find</a>(<span class="charliteral">&#39; &#39;</span>, pos_start)) != std::string::npos) {</div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> token = text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(pos_start, pos_end - pos_start);</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>        pos_start = pos_end + delim_len;</div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>        splits.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(token);</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    }</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span> </div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>    <span class="comment">// Traversing through each morse code string</span></div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;s : splits) {</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>        <span class="comment">// Add corresponding character</span></div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>        decrypted_text += <a class="code hl_function" href="../../d8/d76/morse__code_8cpp.html#ac9f294b0dec08a4a11d477a32f9bd829">ciphers::morse::morse_to_char</a>(s);</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>    }</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span> </div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>    <span class="keywordflow">return</span> decrypted_text;  <span class="comment">// Returning decrypted text</span></div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  216</span>                                         {</div>
+<div class="line"><span class="lineno">  217</span>    <span class="comment">// Going through each character of text and converting it</span></div>
+<div class="line"><span class="lineno">  218</span>    <span class="comment">// back to normal representation.</span></div>
+<div class="line"><span class="lineno">  219</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> decrypted_text = <span class="stringliteral">&quot;&quot;</span>;  <span class="comment">// Empty string to store decrypted text</span></div>
+<div class="line"><span class="lineno">  220</span>    <span class="comment">// Spliting string (with delimiter = &quot; &quot;) and storing it</span></div>
+<div class="line"><span class="lineno">  221</span>    <span class="comment">// in vector</span></div>
+<div class="line"><span class="lineno">  222</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> pos_start = 0, pos_end = 0, delim_len = 1;</div>
+<div class="line"><span class="lineno">  223</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::string&gt;</a> splits;</div>
+<div class="line"><span class="lineno">  224</span>    <span class="keywordflow">while</span> ((pos_end = text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/find.html">find</a>(<span class="charliteral">&#39; &#39;</span>, pos_start)) != std::string::npos) {</div>
+<div class="line"><span class="lineno">  225</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> token = text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(pos_start, pos_end - pos_start);</div>
+<div class="line"><span class="lineno">  226</span>        pos_start = pos_end + delim_len;</div>
+<div class="line"><span class="lineno">  227</span>        splits.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(token);</div>
+<div class="line"><span class="lineno">  228</span>    }</div>
+<div class="line"><span class="lineno">  229</span> </div>
+<div class="line"><span class="lineno">  230</span>    <span class="comment">// Traversing through each morse code string</span></div>
+<div class="line"><span class="lineno">  231</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;s : splits) {</div>
+<div class="line"><span class="lineno">  232</span>        <span class="comment">// Add corresponding character</span></div>
+<div class="line"><span class="lineno">  233</span>        decrypted_text += <a class="code hl_function" href="../../d8/d76/morse__code_8cpp.html#ac9f294b0dec08a4a11d477a32f9bd829">ciphers::morse::morse_to_char</a>(s);</div>
+<div class="line"><span class="lineno">  234</span>    }</div>
+<div class="line"><span class="lineno">  235</span> </div>
+<div class="line"><span class="lineno">  236</span>    <span class="keywordflow">return</span> decrypted_text;  <span class="comment">// Returning decrypted text</span></div>
+<div class="line"><span class="lineno">  237</span>}</div>
 <div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
 <div class="ttc" id="afind_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/find.html">std::string::find</a></div><div class="ttdeci">T find(T... args)</div></div>
 <div class="ttc" id="amorse__code_8cpp_html_ac9f294b0dec08a4a11d477a32f9bd829"><div class="ttname"><a href="../../d8/d76/morse__code_8cpp.html#ac9f294b0dec08a4a11d477a32f9bd829">ciphers::morse::morse_to_char</a></div><div class="ttdeci">char morse_to_char(const std::string &amp;s)</div><div class="ttdef"><b>Definition:</b> morse_code.cpp:118</div></div>
@@ -337,15 +337,15 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>new encrypted text </dd></dl>
-<div class="fragment"><div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>                                         {</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> encrypted_text = <span class="stringliteral">&quot;&quot;</span>;  <span class="comment">// Empty string to store encrypted text</span></div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>    <span class="comment">// Going through each character of text and converting it</span></div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    <span class="comment">// to morse representation</span></div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">char</span> &amp;c : text) {</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>        encrypted_text += <a class="code hl_function" href="../../d8/d76/morse__code_8cpp.html#ab31773fd11555d21f70d6914138d9535">ciphers::morse::char_to_morse</a>(c) + <span class="stringliteral">&quot; &quot;</span>;</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    }</div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>    <span class="keywordflow">return</span> encrypted_text;  <span class="comment">// Returning encrypted text</span></div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  202</span>                                         {</div>
+<div class="line"><span class="lineno">  203</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> encrypted_text = <span class="stringliteral">&quot;&quot;</span>;  <span class="comment">// Empty string to store encrypted text</span></div>
+<div class="line"><span class="lineno">  204</span>    <span class="comment">// Going through each character of text and converting it</span></div>
+<div class="line"><span class="lineno">  205</span>    <span class="comment">// to morse representation</span></div>
+<div class="line"><span class="lineno">  206</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">char</span> &amp;c : text) {</div>
+<div class="line"><span class="lineno">  207</span>        encrypted_text += <a class="code hl_function" href="../../d8/d76/morse__code_8cpp.html#ab31773fd11555d21f70d6914138d9535">ciphers::morse::char_to_morse</a>(c) + <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">  208</span>    }</div>
+<div class="line"><span class="lineno">  209</span>    <span class="keywordflow">return</span> encrypted_text;  <span class="comment">// Returning encrypted text</span></div>
+<div class="line"><span class="lineno">  210</span>}</div>
 <div class="ttc" id="amorse__code_8cpp_html_ab31773fd11555d21f70d6914138d9535"><div class="ttname"><a href="../../d8/d76/morse__code_8cpp.html#ab31773fd11555d21f70d6914138d9535">ciphers::morse::char_to_morse</a></div><div class="ttdeci">std::string char_to_morse(const char &amp;c)</div><div class="ttdef"><b>Definition:</b> morse_code.cpp:33</div></div>
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@@ -374,11 +374,11 @@ Here is the call graph for this function:</div>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>           {</div>
-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>    <span class="comment">// Testing</span></div>
-<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>    <a class="code hl_function" href="../../d8/d76/morse__code_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
-<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  268</span>           {</div>
+<div class="line"><span class="lineno">  269</span>    <span class="comment">// Testing</span></div>
+<div class="line"><span class="lineno">  270</span>    <a class="code hl_function" href="../../d8/d76/morse__code_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
+<div class="line"><span class="lineno">  271</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  272</span>}</div>
 <div class="ttc" id="amorse__code_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d8/d76/morse__code_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Function to test above algorithm.</div><div class="ttdef"><b>Definition:</b> morse_code.cpp:245</div></div>
 </div><!-- fragment --><div class="dynheader">
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@@ -411,85 +411,85 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>corresponding character </dd></dl>
-<div class="fragment"><div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>                                       {</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    <span class="comment">// return corresponding character</span></div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;.-&quot;</span>) {</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;a&#39;</span>;</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-...&quot;</span>) {</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;b&#39;</span>;</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-.-.&quot;</span>) {</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;c&#39;</span>;</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-..&quot;</span>) {</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;d&#39;</span>;</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;.&quot;</span>) {</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;e&#39;</span>;</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;..-.&quot;</span>) {</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;f&#39;</span>;</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;--.&quot;</span>) {</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;g&#39;</span>;</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;....&quot;</span>) {</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;h&#39;</span>;</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;..&quot;</span>) {</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;i&#39;</span>;</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;.---&quot;</span>) {</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;j&#39;</span>;</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-.-&quot;</span>) {</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;k&#39;</span>;</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;.-..&quot;</span>) {</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;l&#39;</span>;</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;--&quot;</span>) {</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;m&#39;</span>;</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-.&quot;</span>) {</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;n&#39;</span>;</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;---&quot;</span>) {</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;o&#39;</span>;</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;.--.&quot;</span>) {</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;p&#39;</span>;</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;--.-&quot;</span>) {</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;q&#39;</span>;</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;.-.&quot;</span>) {</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;r&#39;</span>;</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;...&quot;</span>) {</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;s&#39;</span>;</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-&quot;</span>) {</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;t&#39;</span>;</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;..-&quot;</span>) {</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;u&#39;</span>;</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;...-&quot;</span>) {</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;v&#39;</span>;</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;.--&quot;</span>) {</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;w&#39;</span>;</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-..-&quot;</span>) {</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;x&#39;</span>;</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-.--&quot;</span>) {</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;y&#39;</span>;</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;--..&quot;</span>) {</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;z&#39;</span>;</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;.----&quot;</span>) {</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;1&#39;</span>;</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;..---&quot;</span>) {</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;2&#39;</span>;</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;...--&quot;</span>) {</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;3&#39;</span>;</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;....-&quot;</span>) {</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;4&#39;</span>;</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;.....&quot;</span>) {</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;5&#39;</span>;</div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-....&quot;</span>) {</div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;6&#39;</span>;</div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;--...&quot;</span>) {</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;7&#39;</span>;</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;---..&quot;</span>) {</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;8&#39;</span>;</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;----.&quot;</span>) {</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;9&#39;</span>;</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-----&quot;</span>) {</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;0&#39;</span>;</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Found invalid Morse code: &quot;</span> &lt;&lt; s &lt;&lt; <span class="charliteral">&#39; &#39;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(0);</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>    }</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  118</span>                                       {</div>
+<div class="line"><span class="lineno">  119</span>    <span class="comment">// return corresponding character</span></div>
+<div class="line"><span class="lineno">  120</span>    <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;.-&quot;</span>) {</div>
+<div class="line"><span class="lineno">  121</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;a&#39;</span>;</div>
+<div class="line"><span class="lineno">  122</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-...&quot;</span>) {</div>
+<div class="line"><span class="lineno">  123</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;b&#39;</span>;</div>
+<div class="line"><span class="lineno">  124</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-.-.&quot;</span>) {</div>
+<div class="line"><span class="lineno">  125</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;c&#39;</span>;</div>
+<div class="line"><span class="lineno">  126</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-..&quot;</span>) {</div>
+<div class="line"><span class="lineno">  127</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;d&#39;</span>;</div>
+<div class="line"><span class="lineno">  128</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;.&quot;</span>) {</div>
+<div class="line"><span class="lineno">  129</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;e&#39;</span>;</div>
+<div class="line"><span class="lineno">  130</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;..-.&quot;</span>) {</div>
+<div class="line"><span class="lineno">  131</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;f&#39;</span>;</div>
+<div class="line"><span class="lineno">  132</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;--.&quot;</span>) {</div>
+<div class="line"><span class="lineno">  133</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;g&#39;</span>;</div>
+<div class="line"><span class="lineno">  134</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;....&quot;</span>) {</div>
+<div class="line"><span class="lineno">  135</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;h&#39;</span>;</div>
+<div class="line"><span class="lineno">  136</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;..&quot;</span>) {</div>
+<div class="line"><span class="lineno">  137</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;i&#39;</span>;</div>
+<div class="line"><span class="lineno">  138</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;.---&quot;</span>) {</div>
+<div class="line"><span class="lineno">  139</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;j&#39;</span>;</div>
+<div class="line"><span class="lineno">  140</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-.-&quot;</span>) {</div>
+<div class="line"><span class="lineno">  141</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;k&#39;</span>;</div>
+<div class="line"><span class="lineno">  142</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;.-..&quot;</span>) {</div>
+<div class="line"><span class="lineno">  143</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;l&#39;</span>;</div>
+<div class="line"><span class="lineno">  144</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;--&quot;</span>) {</div>
+<div class="line"><span class="lineno">  145</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;m&#39;</span>;</div>
+<div class="line"><span class="lineno">  146</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-.&quot;</span>) {</div>
+<div class="line"><span class="lineno">  147</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;n&#39;</span>;</div>
+<div class="line"><span class="lineno">  148</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;---&quot;</span>) {</div>
+<div class="line"><span class="lineno">  149</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;o&#39;</span>;</div>
+<div class="line"><span class="lineno">  150</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;.--.&quot;</span>) {</div>
+<div class="line"><span class="lineno">  151</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;p&#39;</span>;</div>
+<div class="line"><span class="lineno">  152</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;--.-&quot;</span>) {</div>
+<div class="line"><span class="lineno">  153</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;q&#39;</span>;</div>
+<div class="line"><span class="lineno">  154</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;.-.&quot;</span>) {</div>
+<div class="line"><span class="lineno">  155</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;r&#39;</span>;</div>
+<div class="line"><span class="lineno">  156</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;...&quot;</span>) {</div>
+<div class="line"><span class="lineno">  157</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;s&#39;</span>;</div>
+<div class="line"><span class="lineno">  158</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-&quot;</span>) {</div>
+<div class="line"><span class="lineno">  159</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;t&#39;</span>;</div>
+<div class="line"><span class="lineno">  160</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;..-&quot;</span>) {</div>
+<div class="line"><span class="lineno">  161</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;u&#39;</span>;</div>
+<div class="line"><span class="lineno">  162</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;...-&quot;</span>) {</div>
+<div class="line"><span class="lineno">  163</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;v&#39;</span>;</div>
+<div class="line"><span class="lineno">  164</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;.--&quot;</span>) {</div>
+<div class="line"><span class="lineno">  165</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;w&#39;</span>;</div>
+<div class="line"><span class="lineno">  166</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-..-&quot;</span>) {</div>
+<div class="line"><span class="lineno">  167</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;x&#39;</span>;</div>
+<div class="line"><span class="lineno">  168</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-.--&quot;</span>) {</div>
+<div class="line"><span class="lineno">  169</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;y&#39;</span>;</div>
+<div class="line"><span class="lineno">  170</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;--..&quot;</span>) {</div>
+<div class="line"><span class="lineno">  171</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;z&#39;</span>;</div>
+<div class="line"><span class="lineno">  172</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;.----&quot;</span>) {</div>
+<div class="line"><span class="lineno">  173</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;1&#39;</span>;</div>
+<div class="line"><span class="lineno">  174</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;..---&quot;</span>) {</div>
+<div class="line"><span class="lineno">  175</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;2&#39;</span>;</div>
+<div class="line"><span class="lineno">  176</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;...--&quot;</span>) {</div>
+<div class="line"><span class="lineno">  177</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;3&#39;</span>;</div>
+<div class="line"><span class="lineno">  178</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;....-&quot;</span>) {</div>
+<div class="line"><span class="lineno">  179</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;4&#39;</span>;</div>
+<div class="line"><span class="lineno">  180</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;.....&quot;</span>) {</div>
+<div class="line"><span class="lineno">  181</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;5&#39;</span>;</div>
+<div class="line"><span class="lineno">  182</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-....&quot;</span>) {</div>
+<div class="line"><span class="lineno">  183</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;6&#39;</span>;</div>
+<div class="line"><span class="lineno">  184</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;--...&quot;</span>) {</div>
+<div class="line"><span class="lineno">  185</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;7&#39;</span>;</div>
+<div class="line"><span class="lineno">  186</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;---..&quot;</span>) {</div>
+<div class="line"><span class="lineno">  187</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;8&#39;</span>;</div>
+<div class="line"><span class="lineno">  188</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;----.&quot;</span>) {</div>
+<div class="line"><span class="lineno">  189</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;9&#39;</span>;</div>
+<div class="line"><span class="lineno">  190</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (s == <span class="stringliteral">&quot;-----&quot;</span>) {</div>
+<div class="line"><span class="lineno">  191</span>        <span class="keywordflow">return</span> <span class="charliteral">&#39;0&#39;</span>;</div>
+<div class="line"><span class="lineno">  192</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  193</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Found invalid Morse code: &quot;</span> &lt;&lt; s &lt;&lt; <span class="charliteral">&#39; &#39;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  194</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(0);</div>
+<div class="line"><span class="lineno">  195</span>    }</div>
+<div class="line"><span class="lineno">  196</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -524,24 +524,24 @@ Here is the call graph for this function:</div>
 
 <p>Function to test above algorithm. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>                   {</div>
-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>    <span class="comment">// Test 1</span></div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> text1 = <span class="stringliteral">&quot;01234567890&quot;</span>;</div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> encrypted1 = <a class="code hl_function" href="../../d8/d76/morse__code_8cpp.html#a0242e458904de8a242fcdaffe9e3ba1a">ciphers::morse::encrypt</a>(text1);</div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> decrypted1 = <a class="code hl_function" href="../../d8/d76/morse__code_8cpp.html#a15c66ec8cf4cef0a35c50cbab86965dc">ciphers::morse::decrypt</a>(encrypted1);</div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>    assert(text1 == decrypted1);</div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Original text : &quot;</span> &lt;&lt; text1 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Encrypted text : &quot;</span> &lt;&lt; encrypted1 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Decrypted text : &quot;</span> &lt;&lt; decrypted1 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>    <span class="comment">// Test 2</span></div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> text2 = <span class="stringliteral">&quot;abcdefghijklmnopqrstuvwxyz&quot;</span>;</div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> encrypted2 = <a class="code hl_function" href="../../d8/d76/morse__code_8cpp.html#a0242e458904de8a242fcdaffe9e3ba1a">ciphers::morse::encrypt</a>(text2);</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> decrypted2 = <a class="code hl_function" href="../../d8/d76/morse__code_8cpp.html#a15c66ec8cf4cef0a35c50cbab86965dc">ciphers::morse::decrypt</a>(encrypted2);</div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>    assert(text2 == decrypted2);</div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Original text : &quot;</span> &lt;&lt; text2 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Encrypted text : &quot;</span> &lt;&lt; encrypted2 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Decrypted text : &quot;</span> &lt;&lt; decrypted2 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  245</span>                   {</div>
+<div class="line"><span class="lineno">  246</span>    <span class="comment">// Test 1</span></div>
+<div class="line"><span class="lineno">  247</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> text1 = <span class="stringliteral">&quot;01234567890&quot;</span>;</div>
+<div class="line"><span class="lineno">  248</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> encrypted1 = <a class="code hl_function" href="../../d8/d76/morse__code_8cpp.html#a0242e458904de8a242fcdaffe9e3ba1a">ciphers::morse::encrypt</a>(text1);</div>
+<div class="line"><span class="lineno">  249</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> decrypted1 = <a class="code hl_function" href="../../d8/d76/morse__code_8cpp.html#a15c66ec8cf4cef0a35c50cbab86965dc">ciphers::morse::decrypt</a>(encrypted1);</div>
+<div class="line"><span class="lineno">  250</span>    assert(text1 == decrypted1);</div>
+<div class="line"><span class="lineno">  251</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Original text : &quot;</span> &lt;&lt; text1 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  252</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Encrypted text : &quot;</span> &lt;&lt; encrypted1 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  253</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Decrypted text : &quot;</span> &lt;&lt; decrypted1 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  254</span>    <span class="comment">// Test 2</span></div>
+<div class="line"><span class="lineno">  255</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> text2 = <span class="stringliteral">&quot;abcdefghijklmnopqrstuvwxyz&quot;</span>;</div>
+<div class="line"><span class="lineno">  256</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> encrypted2 = <a class="code hl_function" href="../../d8/d76/morse__code_8cpp.html#a0242e458904de8a242fcdaffe9e3ba1a">ciphers::morse::encrypt</a>(text2);</div>
+<div class="line"><span class="lineno">  257</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> decrypted2 = <a class="code hl_function" href="../../d8/d76/morse__code_8cpp.html#a15c66ec8cf4cef0a35c50cbab86965dc">ciphers::morse::decrypt</a>(encrypted2);</div>
+<div class="line"><span class="lineno">  258</span>    assert(text2 == decrypted2);</div>
+<div class="line"><span class="lineno">  259</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Original text : &quot;</span> &lt;&lt; text2 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  260</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Encrypted text : &quot;</span> &lt;&lt; encrypted2 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  261</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Decrypted text : &quot;</span> &lt;&lt; decrypted2 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  262</span>}</div>
 <div class="ttc" id="amorse__code_8cpp_html_a0242e458904de8a242fcdaffe9e3ba1a"><div class="ttname"><a href="../../d8/d76/morse__code_8cpp.html#a0242e458904de8a242fcdaffe9e3ba1a">ciphers::morse::encrypt</a></div><div class="ttdeci">std::string encrypt(const std::string &amp;text)</div><div class="ttdef"><b>Definition:</b> morse_code.cpp:202</div></div>
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+<div class="fragment"><div class="line"><span class="lineno">  137</span>                                                            {</div>
+<div class="line"><span class="lineno">  138</span>    <span class="comment">// If two vectors have different sizes</span></div>
+<div class="line"><span class="lineno">  139</span>    <span class="keywordflow">if</span> (A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() != B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) {</div>
+<div class="line"><span class="lineno">  140</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
+<div class="line"><span class="lineno">  141</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div>
+<div class="line"><span class="lineno">  142</span>            &lt;&lt; <span class="stringliteral">&quot;Can not equally shuffle two vectors with different sizes: &quot;</span>;</div>
+<div class="line"><span class="lineno">  143</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot; and &quot;</span> &lt;&lt; B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  144</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><span class="lineno">  145</span>    }</div>
+<div class="line"><span class="lineno">  146</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {  <span class="comment">// For every element in A and B</span></div>
+<div class="line"><span class="lineno">  147</span>        <span class="comment">// Genrating random index &lt; size of A and B</span></div>
+<div class="line"><span class="lineno">  148</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/system_clock/now.html">std::chrono::system_clock::now</a>().time_since_epoch().count());</div>
+<div class="line"><span class="lineno">  149</span>        <span class="keywordtype">size_t</span> random_index = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">  150</span>        <span class="comment">// Swap elements in both A and B with same random index</span></div>
+<div class="line"><span class="lineno">  151</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(A[i], A[random_index]);</div>
+<div class="line"><span class="lineno">  152</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(B[i], B[random_index]);</div>
+<div class="line"><span class="lineno">  153</span>    }</div>
+<div class="line"><span class="lineno">  154</span>    <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  155</span>}</div>
 <div class="ttc" id="anow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/system_clock/now.html">std::chrono::system_clock::now</a></div><div class="ttdeci">T now(T... args)</div></div>
 <div class="ttc" id="arand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a></div><div class="ttdeci">T rand(T... args)</div></div>
 <div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
@@ -414,18 +414,18 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>shape as pair </dd></dl>
-<div class="fragment"><div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>                                                                      {</div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>    <span class="keyword">const</span> <span class="keywordtype">size_t</span> sub_size = (*A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>()).size();</div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;a : A) {</div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>        <span class="comment">// If supplied vector don&#39;t have same shape in all rows</span></div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>        <span class="keywordflow">if</span> (a.size() != sub_size) {</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Supplied vector is not 2D Matrix&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>        }</div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>    }</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>    <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(A.size(), sub_size);  <span class="comment">// Return shape as pair</span></div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  247</span>                                                                      {</div>
+<div class="line"><span class="lineno">  248</span>    <span class="keyword">const</span> <span class="keywordtype">size_t</span> sub_size = (*A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>()).size();</div>
+<div class="line"><span class="lineno">  249</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;a : A) {</div>
+<div class="line"><span class="lineno">  250</span>        <span class="comment">// If supplied vector don&#39;t have same shape in all rows</span></div>
+<div class="line"><span class="lineno">  251</span>        <span class="keywordflow">if</span> (a.size() != sub_size) {</div>
+<div class="line"><span class="lineno">  252</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
+<div class="line"><span class="lineno">  253</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Supplied vector is not 2D Matrix&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  254</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><span class="lineno">  255</span>        }</div>
+<div class="line"><span class="lineno">  256</span>    }</div>
+<div class="line"><span class="lineno">  257</span>    <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(A.size(), sub_size);  <span class="comment">// Return shape as pair</span></div>
+<div class="line"><span class="lineno">  258</span>}</div>
 <div class="ttc" id="amake_pair_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a></div><div class="ttdeci">T make_pair(T... args)</div></div>
 </div><!-- fragment -->
 </div>
@@ -471,22 +471,22 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>new resultant vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00496" name="l00496"></a><span class="lineno">  496</span>                                        {</div>
-<div class="line"><a id="l00497" name="l00497"></a><span class="lineno">  497</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape_a = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(A);</div>
-<div class="line"><a id="l00498" name="l00498"></a><span class="lineno">  498</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape_b = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(B);</div>
-<div class="line"><a id="l00499" name="l00499"></a><span class="lineno">  499</span>    <span class="comment">// If vectors are not eligible for hadamard product</span></div>
-<div class="line"><a id="l00500" name="l00500"></a><span class="lineno">  500</span>    <span class="keywordflow">if</span> (shape_a.first != shape_b.first || shape_a.second != shape_b.second) {</div>
-<div class="line"><a id="l00501" name="l00501"></a><span class="lineno">  501</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
-<div class="line"><a id="l00502" name="l00502"></a><span class="lineno">  502</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Vectors have different shapes &quot;</span>;</div>
-<div class="line"><a id="l00503" name="l00503"></a><span class="lineno">  503</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; shape_a &lt;&lt; <span class="stringliteral">&quot; and &quot;</span> &lt;&lt; shape_b &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00504" name="l00504"></a><span class="lineno">  504</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
-<div class="line"><a id="l00505" name="l00505"></a><span class="lineno">  505</span>    }</div>
-<div class="line"><a id="l00506" name="l00506"></a><span class="lineno">  506</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;T&gt;</a>&gt; C;  <span class="comment">// Vector to store result</span></div>
-<div class="line"><a id="l00507" name="l00507"></a><span class="lineno">  507</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
-<div class="line"><a id="l00508" name="l00508"></a><span class="lineno">  508</span>        C.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(A[i] * B[i]);  <span class="comment">// Elementwise multiplication</span></div>
-<div class="line"><a id="l00509" name="l00509"></a><span class="lineno">  509</span>    }</div>
-<div class="line"><a id="l00510" name="l00510"></a><span class="lineno">  510</span>    <span class="keywordflow">return</span> C;  <span class="comment">// Return new resultant 2D vector</span></div>
-<div class="line"><a id="l00511" name="l00511"></a><span class="lineno">  511</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  496</span>                                        {</div>
+<div class="line"><span class="lineno">  497</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape_a = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(A);</div>
+<div class="line"><span class="lineno">  498</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape_b = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(B);</div>
+<div class="line"><span class="lineno">  499</span>    <span class="comment">// If vectors are not eligible for hadamard product</span></div>
+<div class="line"><span class="lineno">  500</span>    <span class="keywordflow">if</span> (shape_a.first != shape_b.first || shape_a.second != shape_b.second) {</div>
+<div class="line"><span class="lineno">  501</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
+<div class="line"><span class="lineno">  502</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Vectors have different shapes &quot;</span>;</div>
+<div class="line"><span class="lineno">  503</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; shape_a &lt;&lt; <span class="stringliteral">&quot; and &quot;</span> &lt;&lt; shape_b &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  504</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><span class="lineno">  505</span>    }</div>
+<div class="line"><span class="lineno">  506</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;T&gt;</a>&gt; C;  <span class="comment">// Vector to store result</span></div>
+<div class="line"><span class="lineno">  507</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
+<div class="line"><span class="lineno">  508</span>        C.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(A[i] * B[i]);  <span class="comment">// Elementwise multiplication</span></div>
+<div class="line"><span class="lineno">  509</span>    }</div>
+<div class="line"><span class="lineno">  510</span>    <span class="keywordflow">return</span> C;  <span class="comment">// Return new resultant 2D vector</span></div>
+<div class="line"><span class="lineno">  511</span>}</div>
 <div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -538,15 +538,15 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>new resultant vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>                                                                     {</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> B;      <span class="comment">// New 1D vector to store resultant vector</span></div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    B.resize(A.size() + 1);  <span class="comment">// Resizing it accordingly</span></div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; A.size(); i++) {  <span class="comment">// For every element in A</span></div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        B[i] = A[i];                         <span class="comment">// Copy element in B</span></div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    }</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    B[B.size() - 1] = ele;  <span class="comment">// Inserting new element in last position</span></div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    <span class="keywordflow">return</span> B;               <span class="comment">// Return resultant vector</span></div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   85</span>                                                                     {</div>
+<div class="line"><span class="lineno">   86</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> B;      <span class="comment">// New 1D vector to store resultant vector</span></div>
+<div class="line"><span class="lineno">   87</span>    B.resize(A.size() + 1);  <span class="comment">// Resizing it accordingly</span></div>
+<div class="line"><span class="lineno">   88</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; A.size(); i++) {  <span class="comment">// For every element in A</span></div>
+<div class="line"><span class="lineno">   89</span>        B[i] = A[i];                         <span class="comment">// Copy element in B</span></div>
+<div class="line"><span class="lineno">   90</span>    }</div>
+<div class="line"><span class="lineno">   91</span>    B[B.size() - 1] = ele;  <span class="comment">// Inserting new element in last position</span></div>
+<div class="line"><span class="lineno">   92</span>    <span class="keywordflow">return</span> B;               <span class="comment">// Return resultant vector</span></div>
+<div class="line"><span class="lineno">   93</span>}</div>
 <div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a></div></div>
 </div><!-- fragment -->
 </div>
@@ -591,48 +591,48 @@ template&lt;typename T &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>                                   {</div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>    <span class="keywordtype">size_t</span> num_samples = X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();  <span class="comment">// number of rows</span></div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>    <span class="comment">// size_t num_features = X[0].size();  // number of columns</span></div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>    <span class="keywordtype">size_t</span> num_out = W-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();  <span class="comment">// output matrix size</span></div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>    <span class="keywordtype">size_t</span> R = num_out &gt;&gt; 2, iter = 0;</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>    <span class="keywordtype">double</span> alpha = 1.f;</div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span> </div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; D(num_out);</div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; num_out; i++) D[i] = std::valarray&lt;double&gt;(num_out);</div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span> </div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>    <span class="keywordtype">double</span> dmin = 1.f;        <span class="comment">// average minimum distance of all samples</span></div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>    <span class="keywordtype">double</span> past_dmin = 1.f;   <span class="comment">// average minimum distance of all samples</span></div>
-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>    <span class="keywordtype">double</span> dmin_ratio = 1.f;  <span class="comment">// change per step</span></div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span> </div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>    <span class="comment">// Loop alpha from 1 to slpha_min</span></div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>    <span class="keywordflow">for</span> (; alpha &gt; 0 &amp;&amp; dmin_ratio &gt; 1e-5; alpha -= 1e-4, iter++) {</div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>        <span class="comment">// Loop for each sample pattern in the data set</span></div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> sample = 0; sample &lt; num_samples; sample++) {</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>            <span class="comment">// update weights for the current input pattern sample</span></div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>            dmin += <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ae868ad43698a1d69ba46ea3827d7d2c3">update_weights</a>(X[sample], W, &amp;D, alpha, R);</div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>        }</div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span> </div>
-<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>        <span class="comment">// every 100th iteration, reduce the neighborhood range</span></div>
-<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>        <span class="keywordflow">if</span> (iter % 300 == 0 &amp;&amp; R &gt; 1) {</div>
-<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span>            R--;</div>
-<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>        }</div>
-<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span> </div>
-<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>        dmin /= num_samples;</div>
-<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span> </div>
-<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span>        <span class="comment">// termination condition variable -&gt; % change in minimum distance</span></div>
-<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span>        dmin_ratio = (past_dmin - dmin) / past_dmin;</div>
-<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span>        <span class="keywordflow">if</span> (dmin_ratio &lt; 0) {</div>
-<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span>            dmin_ratio = 1.f;</div>
-<div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span>        }</div>
-<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span>        past_dmin = dmin;</div>
-<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span> </div>
-<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;iter: &quot;</span> &lt;&lt; iter &lt;&lt; <span class="stringliteral">&quot;\t alpha: &quot;</span> &lt;&lt; alpha &lt;&lt; <span class="stringliteral">&quot;\t R: &quot;</span> &lt;&lt; R</div>
-<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>                  &lt;&lt; <span class="stringliteral">&quot;\t d_min: &quot;</span> &lt;&lt; dmin_ratio &lt;&lt; <span class="stringliteral">&quot;\r&quot;</span>;</div>
-<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span>    }</div>
-<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span> </div>
-<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  271</span>                                   {</div>
+<div class="line"><span class="lineno">  272</span>    <span class="keywordtype">size_t</span> num_samples = X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();  <span class="comment">// number of rows</span></div>
+<div class="line"><span class="lineno">  273</span>    <span class="comment">// size_t num_features = X[0].size();  // number of columns</span></div>
+<div class="line"><span class="lineno">  274</span>    <span class="keywordtype">size_t</span> num_out = W-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();  <span class="comment">// output matrix size</span></div>
+<div class="line"><span class="lineno">  275</span>    <span class="keywordtype">size_t</span> R = num_out &gt;&gt; 2, iter = 0;</div>
+<div class="line"><span class="lineno">  276</span>    <span class="keywordtype">double</span> alpha = 1.f;</div>
+<div class="line"><span class="lineno">  277</span> </div>
+<div class="line"><span class="lineno">  278</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; D(num_out);</div>
+<div class="line"><span class="lineno">  279</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; num_out; i++) D[i] = std::valarray&lt;double&gt;(num_out);</div>
+<div class="line"><span class="lineno">  280</span> </div>
+<div class="line"><span class="lineno">  281</span>    <span class="keywordtype">double</span> dmin = 1.f;        <span class="comment">// average minimum distance of all samples</span></div>
+<div class="line"><span class="lineno">  282</span>    <span class="keywordtype">double</span> past_dmin = 1.f;   <span class="comment">// average minimum distance of all samples</span></div>
+<div class="line"><span class="lineno">  283</span>    <span class="keywordtype">double</span> dmin_ratio = 1.f;  <span class="comment">// change per step</span></div>
+<div class="line"><span class="lineno">  284</span> </div>
+<div class="line"><span class="lineno">  285</span>    <span class="comment">// Loop alpha from 1 to slpha_min</span></div>
+<div class="line"><span class="lineno">  286</span>    <span class="keywordflow">for</span> (; alpha &gt; 0 &amp;&amp; dmin_ratio &gt; 1e-5; alpha -= 1e-4, iter++) {</div>
+<div class="line"><span class="lineno">  287</span>        <span class="comment">// Loop for each sample pattern in the data set</span></div>
+<div class="line"><span class="lineno">  288</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> sample = 0; sample &lt; num_samples; sample++) {</div>
+<div class="line"><span class="lineno">  289</span>            <span class="comment">// update weights for the current input pattern sample</span></div>
+<div class="line"><span class="lineno">  290</span>            dmin += <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#ae868ad43698a1d69ba46ea3827d7d2c3">update_weights</a>(X[sample], W, &amp;D, alpha, R);</div>
+<div class="line"><span class="lineno">  291</span>        }</div>
+<div class="line"><span class="lineno">  292</span> </div>
+<div class="line"><span class="lineno">  293</span>        <span class="comment">// every 100th iteration, reduce the neighborhood range</span></div>
+<div class="line"><span class="lineno">  294</span>        <span class="keywordflow">if</span> (iter % 300 == 0 &amp;&amp; R &gt; 1) {</div>
+<div class="line"><span class="lineno">  295</span>            R--;</div>
+<div class="line"><span class="lineno">  296</span>        }</div>
+<div class="line"><span class="lineno">  297</span> </div>
+<div class="line"><span class="lineno">  298</span>        dmin /= num_samples;</div>
+<div class="line"><span class="lineno">  299</span> </div>
+<div class="line"><span class="lineno">  300</span>        <span class="comment">// termination condition variable -&gt; % change in minimum distance</span></div>
+<div class="line"><span class="lineno">  301</span>        dmin_ratio = (past_dmin - dmin) / past_dmin;</div>
+<div class="line"><span class="lineno">  302</span>        <span class="keywordflow">if</span> (dmin_ratio &lt; 0) {</div>
+<div class="line"><span class="lineno">  303</span>            dmin_ratio = 1.f;</div>
+<div class="line"><span class="lineno">  304</span>        }</div>
+<div class="line"><span class="lineno">  305</span>        past_dmin = dmin;</div>
+<div class="line"><span class="lineno">  306</span> </div>
+<div class="line"><span class="lineno">  307</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;iter: &quot;</span> &lt;&lt; iter &lt;&lt; <span class="stringliteral">&quot;\t alpha: &quot;</span> &lt;&lt; alpha &lt;&lt; <span class="stringliteral">&quot;\t R: &quot;</span> &lt;&lt; R</div>
+<div class="line"><span class="lineno">  308</span>                  &lt;&lt; <span class="stringliteral">&quot;\t d_min: &quot;</span> &lt;&lt; dmin_ratio &lt;&lt; <span class="stringliteral">&quot;\r&quot;</span>;</div>
+<div class="line"><span class="lineno">  309</span>    }</div>
+<div class="line"><span class="lineno">  310</span> </div>
+<div class="line"><span class="lineno">  311</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  312</span>}</div>
 <div class="ttc" id="anamespacemachine__learning_html_ae868ad43698a1d69ba46ea3827d7d2c3"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#ae868ad43698a1d69ba46ea3827d7d2c3">machine_learning::update_weights</a></div><div class="ttdeci">double update_weights(const std::valarray&lt; double &gt; &amp;X, std::vector&lt; std::vector&lt; std::valarray&lt; double &gt; &gt; &gt; *W, std::vector&lt; std::valarray&lt; double &gt; &gt; *D, double alpha, int R)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:200</div></div>
 </div><!-- fragment --><div class="dynheader">
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@@ -683,32 +683,32 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>                                          {</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>    <span class="keywordtype">int</span> num_samples = X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();  <span class="comment">// number of rows</span></div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>    <span class="comment">// int num_features = X[0].size();  // number of columns</span></div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>    <span class="keywordtype">int</span> num_out = W-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();  <span class="comment">// number of rows</span></div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>    <span class="keywordtype">int</span> R = num_out &gt;&gt; 2, iter = 0;</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>    <span class="keywordtype">double</span> alpha = 1.f;</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span> </div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> D(num_out);</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span> </div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>    <span class="comment">// Loop alpha from 1 to slpha_min</span></div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>    <span class="keywordflow">do</span> {</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>        <span class="comment">// Loop for each sample pattern in the data set</span></div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> sample = 0; sample &lt; num_samples; sample++) {</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>            <span class="comment">// update weights for the current input pattern sample</span></div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>            <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa6aac06ccf128b0a9c55c9ee1a8e5631">update_weights</a>(X[sample], W, &amp;D, alpha, R);</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>        }</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span> </div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>        <span class="comment">// every 10th iteration, reduce the neighborhood range</span></div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>        <span class="keywordflow">if</span> (iter % 10 == 0 &amp;&amp; R &gt; 1) {</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>            R--;</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>        }</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span> </div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>        alpha -= 0.01;</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>        iter++;</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>    } <span class="keywordflow">while</span> (alpha &gt; alpha_min);</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  151</span>                                          {</div>
+<div class="line"><span class="lineno">  152</span>    <span class="keywordtype">int</span> num_samples = X.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();  <span class="comment">// number of rows</span></div>
+<div class="line"><span class="lineno">  153</span>    <span class="comment">// int num_features = X[0].size();  // number of columns</span></div>
+<div class="line"><span class="lineno">  154</span>    <span class="keywordtype">int</span> num_out = W-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();  <span class="comment">// number of rows</span></div>
+<div class="line"><span class="lineno">  155</span>    <span class="keywordtype">int</span> R = num_out &gt;&gt; 2, iter = 0;</div>
+<div class="line"><span class="lineno">  156</span>    <span class="keywordtype">double</span> alpha = 1.f;</div>
+<div class="line"><span class="lineno">  157</span> </div>
+<div class="line"><span class="lineno">  158</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> D(num_out);</div>
+<div class="line"><span class="lineno">  159</span> </div>
+<div class="line"><span class="lineno">  160</span>    <span class="comment">// Loop alpha from 1 to slpha_min</span></div>
+<div class="line"><span class="lineno">  161</span>    <span class="keywordflow">do</span> {</div>
+<div class="line"><span class="lineno">  162</span>        <span class="comment">// Loop for each sample pattern in the data set</span></div>
+<div class="line"><span class="lineno">  163</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> sample = 0; sample &lt; num_samples; sample++) {</div>
+<div class="line"><span class="lineno">  164</span>            <span class="comment">// update weights for the current input pattern sample</span></div>
+<div class="line"><span class="lineno">  165</span>            <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa6aac06ccf128b0a9c55c9ee1a8e5631">update_weights</a>(X[sample], W, &amp;D, alpha, R);</div>
+<div class="line"><span class="lineno">  166</span>        }</div>
+<div class="line"><span class="lineno">  167</span> </div>
+<div class="line"><span class="lineno">  168</span>        <span class="comment">// every 10th iteration, reduce the neighborhood range</span></div>
+<div class="line"><span class="lineno">  169</span>        <span class="keywordflow">if</span> (iter % 10 == 0 &amp;&amp; R &gt; 1) {</div>
+<div class="line"><span class="lineno">  170</span>            R--;</div>
+<div class="line"><span class="lineno">  171</span>        }</div>
+<div class="line"><span class="lineno">  172</span> </div>
+<div class="line"><span class="lineno">  173</span>        alpha -= 0.01;</div>
+<div class="line"><span class="lineno">  174</span>        iter++;</div>
+<div class="line"><span class="lineno">  175</span>    } <span class="keywordflow">while</span> (alpha &gt; alpha_min);</div>
+<div class="line"><span class="lineno">  176</span>}</div>
 <div class="ttc" id="anamespacemachine__learning_html_aa6aac06ccf128b0a9c55c9ee1a8e5631"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#aa6aac06ccf128b0a9c55c9ee1a8e5631">machine_learning::update_weights</a></div><div class="ttdeci">void update_weights(const std::valarray&lt; double &gt; &amp;x, std::vector&lt; std::valarray&lt; double &gt; &gt; *W, std::valarray&lt; double &gt; *D, double alpha, int R)</div><div class="ttdef"><b>Definition:</b> kohonen_som_trace.cpp:103</div></div>
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@@ -767,34 +767,34 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>new scaled 3D vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>                   {</div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;T&gt;</a>&gt;&gt; B =</div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>        A;                               <span class="comment">// Copying into new vector B</span></div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(B[0]);  <span class="comment">// Storing shape of B&#39;s every element</span></div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>    <span class="comment">// As this function is used for scaling training data vector should be of</span></div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>    <span class="comment">// shape (1, X)</span></div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>    <span class="keywordflow">if</span> (shape.first != 1) {</div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>            &lt;&lt; <span class="stringliteral">&quot;Supplied vector is not supported for minmax scaling, shape: &quot;</span>;</div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; shape &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>    }</div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; shape.second; i++) {</div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>        T min = B[0][0][i], max = B[0][0][i];</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) {</div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>            <span class="comment">// Updating minimum and maximum values</span></div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>            min = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(min, B[j][0][i]);</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>            max = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(max, B[j][0][i]);</div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>        }</div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) {</div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>            <span class="comment">// Applying min-max scaler formula</span></div>
-<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>            B[j][0][i] =</div>
-<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>                ((B[j][0][i] - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a>) / (max - min)) * (high - low) + low;</div>
-<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span>        }</div>
-<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>    }</div>
-<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>    <span class="keywordflow">return</span> B;  <span class="comment">// Return new resultant 3D vector</span></div>
-<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  271</span>                   {</div>
+<div class="line"><span class="lineno">  272</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;T&gt;</a>&gt;&gt; B =</div>
+<div class="line"><span class="lineno">  273</span>        A;                               <span class="comment">// Copying into new vector B</span></div>
+<div class="line"><span class="lineno">  274</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(B[0]);  <span class="comment">// Storing shape of B&#39;s every element</span></div>
+<div class="line"><span class="lineno">  275</span>    <span class="comment">// As this function is used for scaling training data vector should be of</span></div>
+<div class="line"><span class="lineno">  276</span>    <span class="comment">// shape (1, X)</span></div>
+<div class="line"><span class="lineno">  277</span>    <span class="keywordflow">if</span> (shape.first != 1) {</div>
+<div class="line"><span class="lineno">  278</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
+<div class="line"><span class="lineno">  279</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div>
+<div class="line"><span class="lineno">  280</span>            &lt;&lt; <span class="stringliteral">&quot;Supplied vector is not supported for minmax scaling, shape: &quot;</span>;</div>
+<div class="line"><span class="lineno">  281</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; shape &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  282</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><span class="lineno">  283</span>    }</div>
+<div class="line"><span class="lineno">  284</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; shape.second; i++) {</div>
+<div class="line"><span class="lineno">  285</span>        T min = B[0][0][i], max = B[0][0][i];</div>
+<div class="line"><span class="lineno">  286</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) {</div>
+<div class="line"><span class="lineno">  287</span>            <span class="comment">// Updating minimum and maximum values</span></div>
+<div class="line"><span class="lineno">  288</span>            min = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(min, B[j][0][i]);</div>
+<div class="line"><span class="lineno">  289</span>            max = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(max, B[j][0][i]);</div>
+<div class="line"><span class="lineno">  290</span>        }</div>
+<div class="line"><span class="lineno">  291</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) {</div>
+<div class="line"><span class="lineno">  292</span>            <span class="comment">// Applying min-max scaler formula</span></div>
+<div class="line"><span class="lineno">  293</span>            B[j][0][i] =</div>
+<div class="line"><span class="lineno">  294</span>                ((B[j][0][i] - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a>) / (max - min)) * (high - low) + low;</div>
+<div class="line"><span class="lineno">  295</span>        }</div>
+<div class="line"><span class="lineno">  296</span>    }</div>
+<div class="line"><span class="lineno">  297</span>    <span class="keywordflow">return</span> B;  <span class="comment">// Return new resultant 3D vector</span></div>
+<div class="line"><span class="lineno">  298</span>}</div>
 <div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
 <div class="ttc" id="amin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a></div><div class="ttdeci">T min(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -847,30 +847,30 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>new resultant vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00461" name="l00461"></a><span class="lineno">  461</span>                                                                           {</div>
-<div class="line"><a id="l00462" name="l00462"></a><span class="lineno">  462</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape_a = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(A);</div>
-<div class="line"><a id="l00463" name="l00463"></a><span class="lineno">  463</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape_b = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(B);</div>
-<div class="line"><a id="l00464" name="l00464"></a><span class="lineno">  464</span>    <span class="comment">// If vectors are not eligible for multiplication</span></div>
-<div class="line"><a id="l00465" name="l00465"></a><span class="lineno">  465</span>    <span class="keywordflow">if</span> (shape_a.second != shape_b.first) {</div>
-<div class="line"><a id="l00466" name="l00466"></a><span class="lineno">  466</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
-<div class="line"><a id="l00467" name="l00467"></a><span class="lineno">  467</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Vectors are not eligible for multiplication &quot;</span>;</div>
-<div class="line"><a id="l00468" name="l00468"></a><span class="lineno">  468</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; shape_a &lt;&lt; <span class="stringliteral">&quot; and &quot;</span> &lt;&lt; shape_b &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00469" name="l00469"></a><span class="lineno">  469</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
-<div class="line"><a id="l00470" name="l00470"></a><span class="lineno">  470</span>    }</div>
-<div class="line"><a id="l00471" name="l00471"></a><span class="lineno">  471</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;T&gt;</a>&gt; C;  <span class="comment">// Vector to store result</span></div>
-<div class="line"><a id="l00472" name="l00472"></a><span class="lineno">  472</span>    <span class="comment">// Normal matrix multiplication</span></div>
-<div class="line"><a id="l00473" name="l00473"></a><span class="lineno">  473</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; shape_a.first; i++) {</div>
-<div class="line"><a id="l00474" name="l00474"></a><span class="lineno">  474</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> row;</div>
-<div class="line"><a id="l00475" name="l00475"></a><span class="lineno">  475</span>        row.resize(shape_b.second);</div>
-<div class="line"><a id="l00476" name="l00476"></a><span class="lineno">  476</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; shape_b.second; j++) {</div>
-<div class="line"><a id="l00477" name="l00477"></a><span class="lineno">  477</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> k = 0; k &lt; shape_a.second; k++) {</div>
-<div class="line"><a id="l00478" name="l00478"></a><span class="lineno">  478</span>                row[j] += A[i][k] * B[k][j];</div>
-<div class="line"><a id="l00479" name="l00479"></a><span class="lineno">  479</span>            }</div>
-<div class="line"><a id="l00480" name="l00480"></a><span class="lineno">  480</span>        }</div>
-<div class="line"><a id="l00481" name="l00481"></a><span class="lineno">  481</span>        C.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(row);</div>
-<div class="line"><a id="l00482" name="l00482"></a><span class="lineno">  482</span>    }</div>
-<div class="line"><a id="l00483" name="l00483"></a><span class="lineno">  483</span>    <span class="keywordflow">return</span> C;  <span class="comment">// Return new resultant 2D vector</span></div>
-<div class="line"><a id="l00484" name="l00484"></a><span class="lineno">  484</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  461</span>                                                                           {</div>
+<div class="line"><span class="lineno">  462</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape_a = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(A);</div>
+<div class="line"><span class="lineno">  463</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape_b = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(B);</div>
+<div class="line"><span class="lineno">  464</span>    <span class="comment">// If vectors are not eligible for multiplication</span></div>
+<div class="line"><span class="lineno">  465</span>    <span class="keywordflow">if</span> (shape_a.second != shape_b.first) {</div>
+<div class="line"><span class="lineno">  466</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
+<div class="line"><span class="lineno">  467</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Vectors are not eligible for multiplication &quot;</span>;</div>
+<div class="line"><span class="lineno">  468</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; shape_a &lt;&lt; <span class="stringliteral">&quot; and &quot;</span> &lt;&lt; shape_b &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  469</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><span class="lineno">  470</span>    }</div>
+<div class="line"><span class="lineno">  471</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;T&gt;</a>&gt; C;  <span class="comment">// Vector to store result</span></div>
+<div class="line"><span class="lineno">  472</span>    <span class="comment">// Normal matrix multiplication</span></div>
+<div class="line"><span class="lineno">  473</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; shape_a.first; i++) {</div>
+<div class="line"><span class="lineno">  474</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> row;</div>
+<div class="line"><span class="lineno">  475</span>        row.resize(shape_b.second);</div>
+<div class="line"><span class="lineno">  476</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; shape_b.second; j++) {</div>
+<div class="line"><span class="lineno">  477</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> k = 0; k &lt; shape_a.second; k++) {</div>
+<div class="line"><span class="lineno">  478</span>                row[j] += A[i][k] * B[k][j];</div>
+<div class="line"><span class="lineno">  479</span>            }</div>
+<div class="line"><span class="lineno">  480</span>        }</div>
+<div class="line"><span class="lineno">  481</span>        C.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(row);</div>
+<div class="line"><span class="lineno">  482</span>    }</div>
+<div class="line"><span class="lineno">  483</span>    <span class="keywordflow">return</span> C;  <span class="comment">// Return new resultant 2D vector</span></div>
+<div class="line"><span class="lineno">  484</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -921,14 +921,14 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>new resultant vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00348" name="l00348"></a><span class="lineno">  348</span>                                                      {</div>
-<div class="line"><a id="l00349" name="l00349"></a><span class="lineno">  349</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; B =</div>
-<div class="line"><a id="l00350" name="l00350"></a><span class="lineno">  350</span>        A;               <span class="comment">// New vector to store resultant vector</span></div>
-<div class="line"><a id="l00351" name="l00351"></a><span class="lineno">  351</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;b : B) {  <span class="comment">// For every row in vector</span></div>
-<div class="line"><a id="l00352" name="l00352"></a><span class="lineno">  352</span>        b = b * val;     <span class="comment">// Multiply row with scaler</span></div>
-<div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span>    }</div>
-<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span>    <span class="keywordflow">return</span> B;  <span class="comment">// Return new resultant 2D vector</span></div>
-<div class="line"><a id="l00355" name="l00355"></a><span class="lineno">  355</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  348</span>                                                      {</div>
+<div class="line"><span class="lineno">  349</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; B =</div>
+<div class="line"><span class="lineno">  350</span>        A;               <span class="comment">// New vector to store resultant vector</span></div>
+<div class="line"><span class="lineno">  351</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;b : B) {  <span class="comment">// For every row in vector</span></div>
+<div class="line"><span class="lineno">  352</span>        b = b * val;     <span class="comment">// Multiply row with scaler</span></div>
+<div class="line"><span class="lineno">  353</span>    }</div>
+<div class="line"><span class="lineno">  354</span>    <span class="keywordflow">return</span> B;  <span class="comment">// Return new resultant 2D vector</span></div>
+<div class="line"><span class="lineno">  355</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -973,22 +973,22 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>new resultant vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00408" name="l00408"></a><span class="lineno">  408</span>                                        {</div>
-<div class="line"><a id="l00409" name="l00409"></a><span class="lineno">  409</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape_a = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(A);</div>
-<div class="line"><a id="l00410" name="l00410"></a><span class="lineno">  410</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape_b = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(B);</div>
-<div class="line"><a id="l00411" name="l00411"></a><span class="lineno">  411</span>    <span class="comment">// If vectors don&#39;t have equal shape</span></div>
-<div class="line"><a id="l00412" name="l00412"></a><span class="lineno">  412</span>    <span class="keywordflow">if</span> (shape_a.first != shape_b.first || shape_a.second != shape_b.second) {</div>
-<div class="line"><a id="l00413" name="l00413"></a><span class="lineno">  413</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
-<div class="line"><a id="l00414" name="l00414"></a><span class="lineno">  414</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Supplied vectors have different shapes &quot;</span>;</div>
-<div class="line"><a id="l00415" name="l00415"></a><span class="lineno">  415</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; shape_a &lt;&lt; <span class="stringliteral">&quot; and &quot;</span> &lt;&lt; shape_b &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00416" name="l00416"></a><span class="lineno">  416</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
-<div class="line"><a id="l00417" name="l00417"></a><span class="lineno">  417</span>    }</div>
-<div class="line"><a id="l00418" name="l00418"></a><span class="lineno">  418</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;T&gt;</a>&gt; C;</div>
-<div class="line"><a id="l00419" name="l00419"></a><span class="lineno">  419</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {  <span class="comment">// For every row</span></div>
-<div class="line"><a id="l00420" name="l00420"></a><span class="lineno">  420</span>        C.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(A[i] + B[i]);            <span class="comment">// Elementwise addition</span></div>
-<div class="line"><a id="l00421" name="l00421"></a><span class="lineno">  421</span>    }</div>
-<div class="line"><a id="l00422" name="l00422"></a><span class="lineno">  422</span>    <span class="keywordflow">return</span> C;  <span class="comment">// Return new resultant 2D vector</span></div>
-<div class="line"><a id="l00423" name="l00423"></a><span class="lineno">  423</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  408</span>                                        {</div>
+<div class="line"><span class="lineno">  409</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape_a = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(A);</div>
+<div class="line"><span class="lineno">  410</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape_b = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(B);</div>
+<div class="line"><span class="lineno">  411</span>    <span class="comment">// If vectors don&#39;t have equal shape</span></div>
+<div class="line"><span class="lineno">  412</span>    <span class="keywordflow">if</span> (shape_a.first != shape_b.first || shape_a.second != shape_b.second) {</div>
+<div class="line"><span class="lineno">  413</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
+<div class="line"><span class="lineno">  414</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Supplied vectors have different shapes &quot;</span>;</div>
+<div class="line"><span class="lineno">  415</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; shape_a &lt;&lt; <span class="stringliteral">&quot; and &quot;</span> &lt;&lt; shape_b &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  416</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><span class="lineno">  417</span>    }</div>
+<div class="line"><span class="lineno">  418</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;T&gt;</a>&gt; C;</div>
+<div class="line"><span class="lineno">  419</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {  <span class="comment">// For every row</span></div>
+<div class="line"><span class="lineno">  420</span>        C.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(A[i] + B[i]);            <span class="comment">// Elementwise addition</span></div>
+<div class="line"><span class="lineno">  421</span>    }</div>
+<div class="line"><span class="lineno">  422</span>    <span class="keywordflow">return</span> C;  <span class="comment">// Return new resultant 2D vector</span></div>
+<div class="line"><span class="lineno">  423</span>}</div>
 </div><!-- fragment --><div class="dynheader">
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 <div class="dyncontent">
@@ -1039,22 +1039,22 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>new resultant vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00435" name="l00435"></a><span class="lineno">  435</span>                                        {</div>
-<div class="line"><a id="l00436" name="l00436"></a><span class="lineno">  436</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape_a = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(A);</div>
-<div class="line"><a id="l00437" name="l00437"></a><span class="lineno">  437</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape_b = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(B);</div>
-<div class="line"><a id="l00438" name="l00438"></a><span class="lineno">  438</span>    <span class="comment">// If vectors don&#39;t have equal shape</span></div>
-<div class="line"><a id="l00439" name="l00439"></a><span class="lineno">  439</span>    <span class="keywordflow">if</span> (shape_a.first != shape_b.first || shape_a.second != shape_b.second) {</div>
-<div class="line"><a id="l00440" name="l00440"></a><span class="lineno">  440</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
-<div class="line"><a id="l00441" name="l00441"></a><span class="lineno">  441</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Supplied vectors have different shapes &quot;</span>;</div>
-<div class="line"><a id="l00442" name="l00442"></a><span class="lineno">  442</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; shape_a &lt;&lt; <span class="stringliteral">&quot; and &quot;</span> &lt;&lt; shape_b &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00443" name="l00443"></a><span class="lineno">  443</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
-<div class="line"><a id="l00444" name="l00444"></a><span class="lineno">  444</span>    }</div>
-<div class="line"><a id="l00445" name="l00445"></a><span class="lineno">  445</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;T&gt;</a>&gt; C;         <span class="comment">// Vector to store result</span></div>
-<div class="line"><a id="l00446" name="l00446"></a><span class="lineno">  446</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {  <span class="comment">// For every row</span></div>
-<div class="line"><a id="l00447" name="l00447"></a><span class="lineno">  447</span>        C.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(A[i] - B[i]);            <span class="comment">// Elementwise substraction</span></div>
-<div class="line"><a id="l00448" name="l00448"></a><span class="lineno">  448</span>    }</div>
-<div class="line"><a id="l00449" name="l00449"></a><span class="lineno">  449</span>    <span class="keywordflow">return</span> C;  <span class="comment">// Return new resultant 2D vector</span></div>
-<div class="line"><a id="l00450" name="l00450"></a><span class="lineno">  450</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  435</span>                                        {</div>
+<div class="line"><span class="lineno">  436</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape_a = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(A);</div>
+<div class="line"><span class="lineno">  437</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape_b = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(B);</div>
+<div class="line"><span class="lineno">  438</span>    <span class="comment">// If vectors don&#39;t have equal shape</span></div>
+<div class="line"><span class="lineno">  439</span>    <span class="keywordflow">if</span> (shape_a.first != shape_b.first || shape_a.second != shape_b.second) {</div>
+<div class="line"><span class="lineno">  440</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
+<div class="line"><span class="lineno">  441</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Supplied vectors have different shapes &quot;</span>;</div>
+<div class="line"><span class="lineno">  442</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; shape_a &lt;&lt; <span class="stringliteral">&quot; and &quot;</span> &lt;&lt; shape_b &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  443</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><span class="lineno">  444</span>    }</div>
+<div class="line"><span class="lineno">  445</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;T&gt;</a>&gt; C;         <span class="comment">// Vector to store result</span></div>
+<div class="line"><span class="lineno">  446</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {  <span class="comment">// For every row</span></div>
+<div class="line"><span class="lineno">  447</span>        C.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(A[i] - B[i]);            <span class="comment">// Elementwise substraction</span></div>
+<div class="line"><span class="lineno">  448</span>    }</div>
+<div class="line"><span class="lineno">  449</span>    <span class="keywordflow">return</span> C;  <span class="comment">// Return new resultant 2D vector</span></div>
+<div class="line"><span class="lineno">  450</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -1105,14 +1105,14 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>new resultant vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00366" name="l00366"></a><span class="lineno">  366</span>                                                      {</div>
-<div class="line"><a id="l00367" name="l00367"></a><span class="lineno">  367</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; B =</div>
-<div class="line"><a id="l00368" name="l00368"></a><span class="lineno">  368</span>        A;               <span class="comment">// New vector to store resultant vector</span></div>
-<div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;b : B) {  <span class="comment">// For every row in vector</span></div>
-<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span>        b = b / val;     <span class="comment">// Divide row with scaler</span></div>
-<div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span>    }</div>
-<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span>    <span class="keywordflow">return</span> B;  <span class="comment">// Return new resultant 2D vector</span></div>
-<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  366</span>                                                      {</div>
+<div class="line"><span class="lineno">  367</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; B =</div>
+<div class="line"><span class="lineno">  368</span>        A;               <span class="comment">// New vector to store resultant vector</span></div>
+<div class="line"><span class="lineno">  369</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;b : B) {  <span class="comment">// For every row in vector</span></div>
+<div class="line"><span class="lineno">  370</span>        b = b / val;     <span class="comment">// Divide row with scaler</span></div>
+<div class="line"><span class="lineno">  371</span>    }</div>
+<div class="line"><span class="lineno">  372</span>    <span class="keywordflow">return</span> B;  <span class="comment">// Return new resultant 2D vector</span></div>
+<div class="line"><span class="lineno">  373</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1156,13 +1156,13 @@ template&lt;typename T &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>                                                                {</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    <span class="comment">// Setting output precision to 4 in case of floating point numbers</span></div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>    out.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/ios_base/precision.html">precision</a>(4);</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <span class="comment">// printing pair in the form (p, q)</span></div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;(&quot;</span> &lt;&lt; A.first &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; A.second &lt;&lt; <span class="stringliteral">&quot;)&quot;</span>;</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    <span class="keywordflow">return</span> out;</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   52</span>                                                                {</div>
+<div class="line"><span class="lineno">   53</span>    <span class="comment">// Setting output precision to 4 in case of floating point numbers</span></div>
+<div class="line"><span class="lineno">   54</span>    out.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/ios_base/precision.html">precision</a>(4);</div>
+<div class="line"><span class="lineno">   55</span>    <span class="comment">// printing pair in the form (p, q)</span></div>
+<div class="line"><span class="lineno">   56</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;(&quot;</span> &lt;&lt; A.first &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; A.second &lt;&lt; <span class="stringliteral">&quot;)&quot;</span>;</div>
+<div class="line"><span class="lineno">   57</span>    <span class="keywordflow">return</span> out;</div>
+<div class="line"><span class="lineno">   58</span>}</div>
 <div class="ttc" id="aprecision_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/ios_base/precision.html">std::ostream::precision</a></div><div class="ttdeci">T precision(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -1213,15 +1213,15 @@ template&lt;typename T &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>                                                                 {</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <span class="comment">// Setting output precision to 4 in case of floating point numbers</span></div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    out.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/ios_base/precision.html">precision</a>(4);</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;a : A) {   <span class="comment">// For every element in the vector.</span></div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; a &lt;&lt; <span class="charliteral">&#39; &#39;</span>;  <span class="comment">// Print element</span></div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    }</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    <span class="keywordflow">return</span> out;</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   67</span>                                                                 {</div>
+<div class="line"><span class="lineno">   68</span>    <span class="comment">// Setting output precision to 4 in case of floating point numbers</span></div>
+<div class="line"><span class="lineno">   69</span>    out.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/ios_base/precision.html">precision</a>(4);</div>
+<div class="line"><span class="lineno">   70</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;a : A) {   <span class="comment">// For every element in the vector.</span></div>
+<div class="line"><span class="lineno">   71</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; a &lt;&lt; <span class="charliteral">&#39; &#39;</span>;  <span class="comment">// Print element</span></div>
+<div class="line"><span class="lineno">   72</span>    }</div>
+<div class="line"><span class="lineno">   73</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   74</span>    <span class="keywordflow">return</span> out;</div>
+<div class="line"><span class="lineno">   75</span>}</div>
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@@ -1271,17 +1271,17 @@ template&lt;typename T &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>                                                             {</div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>    <span class="comment">// Setting output precision to 4 in case of floating point numbers</span></div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    out.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/ios_base/precision.html">precision</a>(4);</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;a : A) {       <span class="comment">// For each row in A</span></div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>        <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;x : a) {   <span class="comment">// For each element in row</span></div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; x &lt;&lt; <span class="charliteral">&#39; &#39;</span>;  <span class="comment">// print element</span></div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>        }</div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    }</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>    <span class="keywordflow">return</span> out;</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   33</span>                                                             {</div>
+<div class="line"><span class="lineno">   34</span>    <span class="comment">// Setting output precision to 4 in case of floating point numbers</span></div>
+<div class="line"><span class="lineno">   35</span>    out.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/ios_base/precision.html">precision</a>(4);</div>
+<div class="line"><span class="lineno">   36</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;a : A) {       <span class="comment">// For each row in A</span></div>
+<div class="line"><span class="lineno">   37</span>        <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;x : a) {   <span class="comment">// For each element in row</span></div>
+<div class="line"><span class="lineno">   38</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; x &lt;&lt; <span class="charliteral">&#39; &#39;</span>;  <span class="comment">// print element</span></div>
+<div class="line"><span class="lineno">   39</span>        }</div>
+<div class="line"><span class="lineno">   40</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   41</span>    }</div>
+<div class="line"><span class="lineno">   42</span>    <span class="keywordflow">return</span> out;</div>
+<div class="line"><span class="lineno">   43</span>}</div>
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@@ -1321,15 +1321,15 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>new resultant vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>                                                 {</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> B;      <span class="comment">// New 1D vector to store resultant vector</span></div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    B.resize(A.size() - 1);  <span class="comment">// Resizing it accordingly</span></div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; A.size() - 1;</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>         i++) {       <span class="comment">// For every (except last) element in A</span></div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>        B[i] = A[i];  <span class="comment">// Copy element in B</span></div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>    }</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    <span class="keywordflow">return</span> B;  <span class="comment">// Return resultant vector</span></div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  119</span>                                                 {</div>
+<div class="line"><span class="lineno">  120</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> B;      <span class="comment">// New 1D vector to store resultant vector</span></div>
+<div class="line"><span class="lineno">  121</span>    B.resize(A.size() - 1);  <span class="comment">// Resizing it accordingly</span></div>
+<div class="line"><span class="lineno">  122</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; A.size() - 1;</div>
+<div class="line"><span class="lineno">  123</span>         i++) {       <span class="comment">// For every (except last) element in A</span></div>
+<div class="line"><span class="lineno">  124</span>        B[i] = A[i];  <span class="comment">// Copy element in B</span></div>
+<div class="line"><span class="lineno">  125</span>    }</div>
+<div class="line"><span class="lineno">  126</span>    <span class="keywordflow">return</span> B;  <span class="comment">// Return resultant vector</span></div>
+<div class="line"><span class="lineno">  127</span>}</div>
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 </div>
 </div>
@@ -1363,15 +1363,15 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>new resultant vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>                                                  {</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> B;      <span class="comment">// New 1D vector to store resultant vector</span></div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    B.resize(A.size() - 1);  <span class="comment">// Resizing it accordingly</span></div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 1; i &lt; A.size();</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>         i++) {           <span class="comment">// // For every (except first) element in A</span></div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>        B[i - 1] = A[i];  <span class="comment">// Copy element in B with left shifted position</span></div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    }</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <span class="keywordflow">return</span> B;  <span class="comment">// Return resultant vector</span></div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  102</span>                                                  {</div>
+<div class="line"><span class="lineno">  103</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> B;      <span class="comment">// New 1D vector to store resultant vector</span></div>
+<div class="line"><span class="lineno">  104</span>    B.resize(A.size() - 1);  <span class="comment">// Resizing it accordingly</span></div>
+<div class="line"><span class="lineno">  105</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 1; i &lt; A.size();</div>
+<div class="line"><span class="lineno">  106</span>         i++) {           <span class="comment">// // For every (except first) element in A</span></div>
+<div class="line"><span class="lineno">  107</span>        B[i - 1] = A[i];  <span class="comment">// Copy element in B with left shifted position</span></div>
+<div class="line"><span class="lineno">  108</span>    }</div>
+<div class="line"><span class="lineno">  109</span>    <span class="keywordflow">return</span> B;  <span class="comment">// Return resultant vector</span></div>
+<div class="line"><span class="lineno">  110</span>}</div>
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 </div>
 </div>
@@ -1411,52 +1411,52 @@ template&lt;typename T &gt; </div>
 <dl class="section return"><dt>Returns</dt><dd>0 if all ok </dd>
 <dd>
 -1 if file creation failed </dd></dl>
-<div class="fragment"><div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>                                                                      {</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp(fname);</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <span class="keywordflow">if</span> (!fp) {  <span class="comment">// error with fopen</span></div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;File error (&quot;</span> &lt;&lt; fname &lt;&lt; <span class="stringliteral">&quot;): &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/strerror.html">std::strerror</a>(errno)</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>                  &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>        <span class="keywordflow">return</span> -1;</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>    }</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span> </div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    <span class="comment">// neighborhood range</span></div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> R = 1;</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span> </div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; W.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {         <span class="comment">// for each x</span></div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; W[0].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) {  <span class="comment">// for each y</span></div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>            <span class="keywordtype">double</span> distance = 0.f;</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span> </div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>            <span class="keywordtype">int</span> from_x = std::max&lt;int&gt;(0, i - R);</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>            <span class="keywordtype">int</span> to_x = std::min&lt;int&gt;(W.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(), i + R + 1);</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>            <span class="keywordtype">int</span> from_y = std::max&lt;int&gt;(0, j - R);</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>            <span class="keywordtype">int</span> to_y = std::min&lt;int&gt;(W[0].size(), j + R + 1);</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>            <span class="keywordtype">int</span> l = 0, m = 0;</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span><span class="preprocessor">#pragma omp parallel for reduction(+ : distance)</span></div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>            <span class="keywordflow">for</span> (l = from_x; l &lt; to_x; l++) {      <span class="comment">// scan neighborhoor in x</span></div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>                <span class="keywordflow">for</span> (m = from_y; m &lt; to_y; m++) {  <span class="comment">// scan neighborhood in y</span></div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>                    <span class="keyword">auto</span> d = W[i][j] - W[l][m];</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>                    <span class="keywordtype">double</span> d2 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(d, 2).sum();</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>                    distance += <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(d2);</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>                    <span class="comment">// distance += d2;</span></div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>                }</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>            }</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span> </div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a> /= R * R;          <span class="comment">// mean distance from neighbors</span></div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>            fp &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a>;             <span class="comment">// print the mean separation</span></div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>            <span class="keywordflow">if</span> (j &lt; W[0].size() - 1) {  <span class="comment">// if not the last column</span></div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>                fp &lt;&lt; <span class="charliteral">&#39;,&#39;</span>;              <span class="comment">// suffix comma</span></div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>            }</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>        }</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>        <span class="keywordflow">if</span> (i &lt; W.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() - 1) {  <span class="comment">// if not the last row</span></div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>            fp &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;          <span class="comment">// start a new line</span></div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>        }</div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>    }</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span> </div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>    fp.close();</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  143</span>                                                                      {</div>
+<div class="line"><span class="lineno">  144</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp(fname);</div>
+<div class="line"><span class="lineno">  145</span>    <span class="keywordflow">if</span> (!fp) {  <span class="comment">// error with fopen</span></div>
+<div class="line"><span class="lineno">  146</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;File error (&quot;</span> &lt;&lt; fname &lt;&lt; <span class="stringliteral">&quot;): &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/strerror.html">std::strerror</a>(errno)</div>
+<div class="line"><span class="lineno">  147</span>                  &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  148</span>        <span class="keywordflow">return</span> -1;</div>
+<div class="line"><span class="lineno">  149</span>    }</div>
+<div class="line"><span class="lineno">  150</span> </div>
+<div class="line"><span class="lineno">  151</span>    <span class="comment">// neighborhood range</span></div>
+<div class="line"><span class="lineno">  152</span>    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> R = 1;</div>
+<div class="line"><span class="lineno">  153</span> </div>
+<div class="line"><span class="lineno">  154</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; W.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {         <span class="comment">// for each x</span></div>
+<div class="line"><span class="lineno">  155</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; W[0].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) {  <span class="comment">// for each y</span></div>
+<div class="line"><span class="lineno">  156</span>            <span class="keywordtype">double</span> distance = 0.f;</div>
+<div class="line"><span class="lineno">  157</span> </div>
+<div class="line"><span class="lineno">  158</span>            <span class="keywordtype">int</span> from_x = std::max&lt;int&gt;(0, i - R);</div>
+<div class="line"><span class="lineno">  159</span>            <span class="keywordtype">int</span> to_x = std::min&lt;int&gt;(W.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(), i + R + 1);</div>
+<div class="line"><span class="lineno">  160</span>            <span class="keywordtype">int</span> from_y = std::max&lt;int&gt;(0, j - R);</div>
+<div class="line"><span class="lineno">  161</span>            <span class="keywordtype">int</span> to_y = std::min&lt;int&gt;(W[0].size(), j + R + 1);</div>
+<div class="line"><span class="lineno">  162</span>            <span class="keywordtype">int</span> l = 0, m = 0;</div>
+<div class="line"><span class="lineno">  163</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  164</span><span class="preprocessor">#pragma omp parallel for reduction(+ : distance)</span></div>
+<div class="line"><span class="lineno">  165</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  166</span>            <span class="keywordflow">for</span> (l = from_x; l &lt; to_x; l++) {      <span class="comment">// scan neighborhoor in x</span></div>
+<div class="line"><span class="lineno">  167</span>                <span class="keywordflow">for</span> (m = from_y; m &lt; to_y; m++) {  <span class="comment">// scan neighborhood in y</span></div>
+<div class="line"><span class="lineno">  168</span>                    <span class="keyword">auto</span> d = W[i][j] - W[l][m];</div>
+<div class="line"><span class="lineno">  169</span>                    <span class="keywordtype">double</span> d2 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(d, 2).sum();</div>
+<div class="line"><span class="lineno">  170</span>                    distance += <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(d2);</div>
+<div class="line"><span class="lineno">  171</span>                    <span class="comment">// distance += d2;</span></div>
+<div class="line"><span class="lineno">  172</span>                }</div>
+<div class="line"><span class="lineno">  173</span>            }</div>
+<div class="line"><span class="lineno">  174</span> </div>
+<div class="line"><span class="lineno">  175</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a> /= R * R;          <span class="comment">// mean distance from neighbors</span></div>
+<div class="line"><span class="lineno">  176</span>            fp &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a>;             <span class="comment">// print the mean separation</span></div>
+<div class="line"><span class="lineno">  177</span>            <span class="keywordflow">if</span> (j &lt; W[0].size() - 1) {  <span class="comment">// if not the last column</span></div>
+<div class="line"><span class="lineno">  178</span>                fp &lt;&lt; <span class="charliteral">&#39;,&#39;</span>;              <span class="comment">// suffix comma</span></div>
+<div class="line"><span class="lineno">  179</span>            }</div>
+<div class="line"><span class="lineno">  180</span>        }</div>
+<div class="line"><span class="lineno">  181</span>        <span class="keywordflow">if</span> (i &lt; W.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() - 1) {  <span class="comment">// if not the last row</span></div>
+<div class="line"><span class="lineno">  182</span>            fp &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;          <span class="comment">// start a new line</span></div>
+<div class="line"><span class="lineno">  183</span>        }</div>
+<div class="line"><span class="lineno">  184</span>    }</div>
+<div class="line"><span class="lineno">  185</span> </div>
+<div class="line"><span class="lineno">  186</span>    fp.close();</div>
+<div class="line"><span class="lineno">  187</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  188</span>}</div>
 <div class="ttc" id="abasic_ofstream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a></div></div>
 <div class="ttc" id="apow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a></div><div class="ttdeci">T pow(T... args)</div></div>
 <div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
@@ -1500,13 +1500,13 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>returns sum of all elements of 2D vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>                                          {</div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>    T cur_sum = 0;             <span class="comment">// Initially sum is zero</span></div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;a : A) {  <span class="comment">// For every row in A</span></div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>        cur_sum += a.sum();    <span class="comment">// Add sum of that row to current sum</span></div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>    }</div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>    <span class="keywordflow">return</span> cur_sum;  <span class="comment">// Return sum</span></div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  232</span>                                          {</div>
+<div class="line"><span class="lineno">  233</span>    T cur_sum = 0;             <span class="comment">// Initially sum is zero</span></div>
+<div class="line"><span class="lineno">  234</span>    <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;a : A) {  <span class="comment">// For every row in A</span></div>
+<div class="line"><span class="lineno">  235</span>        cur_sum += a.sum();    <span class="comment">// Add sum of that row to current sum</span></div>
+<div class="line"><span class="lineno">  236</span>    }</div>
+<div class="line"><span class="lineno">  237</span>    <span class="keywordflow">return</span> cur_sum;  <span class="comment">// Return sum</span></div>
+<div class="line"><span class="lineno">  238</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1540,20 +1540,20 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>new resultant vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00383" name="l00383"></a><span class="lineno">  383</span>                                        {</div>
-<div class="line"><a id="l00384" name="l00384"></a><span class="lineno">  384</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(A);  <span class="comment">// Current shape of vector</span></div>
-<div class="line"><a id="l00385" name="l00385"></a><span class="lineno">  385</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;T&gt;</a>&gt; B;  <span class="comment">// New vector to store result</span></div>
-<div class="line"><a id="l00386" name="l00386"></a><span class="lineno">  386</span>    <span class="comment">// Storing transpose values of A in B</span></div>
-<div class="line"><a id="l00387" name="l00387"></a><span class="lineno">  387</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; shape.second; j++) {</div>
-<div class="line"><a id="l00388" name="l00388"></a><span class="lineno">  388</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> row;</div>
-<div class="line"><a id="l00389" name="l00389"></a><span class="lineno">  389</span>        row.resize(shape.first);</div>
-<div class="line"><a id="l00390" name="l00390"></a><span class="lineno">  390</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; shape.first; i++) {</div>
-<div class="line"><a id="l00391" name="l00391"></a><span class="lineno">  391</span>            row[i] = A[i][j];</div>
-<div class="line"><a id="l00392" name="l00392"></a><span class="lineno">  392</span>        }</div>
-<div class="line"><a id="l00393" name="l00393"></a><span class="lineno">  393</span>        B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(row);</div>
-<div class="line"><a id="l00394" name="l00394"></a><span class="lineno">  394</span>    }</div>
-<div class="line"><a id="l00395" name="l00395"></a><span class="lineno">  395</span>    <span class="keywordflow">return</span> B;  <span class="comment">// Return new resultant 2D vector</span></div>
-<div class="line"><a id="l00396" name="l00396"></a><span class="lineno">  396</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  383</span>                                        {</div>
+<div class="line"><span class="lineno">  384</span>    <span class="keyword">const</span> <span class="keyword">auto</span> shape = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#aa4bbf61e65f8cd297255fa94b983d078">get_shape</a>(A);  <span class="comment">// Current shape of vector</span></div>
+<div class="line"><span class="lineno">  385</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;T&gt;</a>&gt; B;  <span class="comment">// New vector to store result</span></div>
+<div class="line"><span class="lineno">  386</span>    <span class="comment">// Storing transpose values of A in B</span></div>
+<div class="line"><span class="lineno">  387</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; shape.second; j++) {</div>
+<div class="line"><span class="lineno">  388</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> row;</div>
+<div class="line"><span class="lineno">  389</span>        row.resize(shape.first);</div>
+<div class="line"><span class="lineno">  390</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; shape.first; i++) {</div>
+<div class="line"><span class="lineno">  391</span>            row[i] = A[i][j];</div>
+<div class="line"><span class="lineno">  392</span>        }</div>
+<div class="line"><span class="lineno">  393</span>        B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(row);</div>
+<div class="line"><span class="lineno">  394</span>    }</div>
+<div class="line"><span class="lineno">  395</span>    <span class="keywordflow">return</span> B;  <span class="comment">// Return new resultant 2D vector</span></div>
+<div class="line"><span class="lineno">  396</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -1617,23 +1617,23 @@ template&lt;typename T &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>                                                                {</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>    A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/clear.html">clear</a>();  <span class="comment">// Making A empty</span></div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>    <span class="comment">// Uniform distribution in range [low, high]</span></div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random.html">std::default_random_engine</a> generator(</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/system_clock/now.html">std::chrono::system_clock::now</a>().time_since_epoch().count());</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/uniform_real_distribution.html">std::uniform_real_distribution&lt;T&gt;</a> distribution(low, high);</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; shape.first; i++) {  <span class="comment">// For every row</span></div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a></div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>            row;  <span class="comment">// Making empty row which will be inserted in vector</span></div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>        row.resize(shape.second);</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>        <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;r : row) {             <span class="comment">// For every element in row</span></div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>            r = distribution(generator);  <span class="comment">// copy random number</span></div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>        }</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>        A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(row);  <span class="comment">// Insert new row in vector</span></div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>    }</div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>    <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  168</span>                                                                {</div>
+<div class="line"><span class="lineno">  169</span>    A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/clear.html">clear</a>();  <span class="comment">// Making A empty</span></div>
+<div class="line"><span class="lineno">  170</span>    <span class="comment">// Uniform distribution in range [low, high]</span></div>
+<div class="line"><span class="lineno">  171</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random.html">std::default_random_engine</a> generator(</div>
+<div class="line"><span class="lineno">  172</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/system_clock/now.html">std::chrono::system_clock::now</a>().time_since_epoch().count());</div>
+<div class="line"><span class="lineno">  173</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/uniform_real_distribution.html">std::uniform_real_distribution&lt;T&gt;</a> distribution(low, high);</div>
+<div class="line"><span class="lineno">  174</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; shape.first; i++) {  <span class="comment">// For every row</span></div>
+<div class="line"><span class="lineno">  175</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a></div>
+<div class="line"><span class="lineno">  176</span>            row;  <span class="comment">// Making empty row which will be inserted in vector</span></div>
+<div class="line"><span class="lineno">  177</span>        row.resize(shape.second);</div>
+<div class="line"><span class="lineno">  178</span>        <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;r : row) {             <span class="comment">// For every element in row</span></div>
+<div class="line"><span class="lineno">  179</span>            r = distribution(generator);  <span class="comment">// copy random number</span></div>
+<div class="line"><span class="lineno">  180</span>        }</div>
+<div class="line"><span class="lineno">  181</span>        A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(row);  <span class="comment">// Insert new row in vector</span></div>
+<div class="line"><span class="lineno">  182</span>    }</div>
+<div class="line"><span class="lineno">  183</span>    <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  184</span>}</div>
 <div class="ttc" id="aclear_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/clear.html">std::vector::clear</a></div><div class="ttdeci">T clear(T... args)</div></div>
 <div class="ttc" id="arandom_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random.html">std::default_random_engine</a></div></div>
 <div class="ttc" id="auniform_real_distribution_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/uniform_real_distribution.html">std::uniform_real_distribution</a></div></div>
@@ -1686,17 +1686,17 @@ template&lt;typename T &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>                                                                      {</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>    A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/clear.html">clear</a>();  <span class="comment">// Making A empty</span></div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; shape.first; i++) {</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a></div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>            row;  <span class="comment">// Making empty row which will be inserted in vector</span></div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>        row.resize(shape.second);</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>        row[i] = T(1);     <span class="comment">// Insert 1 at ith position</span></div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>        A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(row);  <span class="comment">// Insert new row in vector</span></div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>    }</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>    <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  194</span>                                                                      {</div>
+<div class="line"><span class="lineno">  195</span>    A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/clear.html">clear</a>();  <span class="comment">// Making A empty</span></div>
+<div class="line"><span class="lineno">  196</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; shape.first; i++) {</div>
+<div class="line"><span class="lineno">  197</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a></div>
+<div class="line"><span class="lineno">  198</span>            row;  <span class="comment">// Making empty row which will be inserted in vector</span></div>
+<div class="line"><span class="lineno">  199</span>        row.resize(shape.second);</div>
+<div class="line"><span class="lineno">  200</span>        row[i] = T(1);     <span class="comment">// Insert 1 at ith position</span></div>
+<div class="line"><span class="lineno">  201</span>        A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(row);  <span class="comment">// Insert new row in vector</span></div>
+<div class="line"><span class="lineno">  202</span>    }</div>
+<div class="line"><span class="lineno">  203</span>    <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  204</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1754,41 +1754,41 @@ template&lt;typename T &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>                                                                 {</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    <span class="keywordtype">int</span> j = 0, k = 0;</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    <span class="keywordtype">int</span> num_out = W-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();  <span class="comment">// number of SOM output nodes</span></div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    <span class="comment">// int num_features = x.size();  // number of data features</span></div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span> </div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    <span class="comment">// step 1: for each output point</span></div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    <span class="keywordflow">for</span> (j = 0; j &lt; num_out; j++) {</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>        <span class="comment">// compute Euclidian distance of each output</span></div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>        <span class="comment">// point from the current sample</span></div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>        (*D)[j] = (((*W)[j] - x) * ((*W)[j] - x)).sum();</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    }</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span> </div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <span class="comment">// step 2:  get closest node i.e., node with snallest Euclidian distance to</span></div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    <span class="comment">// the current pattern</span></div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    <span class="keyword">auto</span> result = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min_element.html">std::min_element</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(*D), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(*D));</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <span class="comment">// double d_min = *result;</span></div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    <span class="keywordtype">int</span> d_min_idx = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">std::distance</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(*D), result);</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span> </div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    <span class="comment">// step 3a: get the neighborhood range</span></div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    <span class="keywordtype">int</span> from_node = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(0, d_min_idx - R);</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    <span class="keywordtype">int</span> to_node = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(num_out, d_min_idx + R + 1);</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span> </div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    <span class="comment">// step 3b: update the weights of nodes in the</span></div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    <span class="comment">// neighborhood</span></div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    <span class="keywordflow">for</span> (j = from_node; j &lt; to_node; j++) {</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>        <span class="comment">// update weights of nodes in the neighborhood</span></div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        (*W)[j] += alpha * (x - (*W)[j]);</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    }</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  105</span>                                                                 {</div>
+<div class="line"><span class="lineno">  106</span>    <span class="keywordtype">int</span> j = 0, k = 0;</div>
+<div class="line"><span class="lineno">  107</span>    <span class="keywordtype">int</span> num_out = W-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();  <span class="comment">// number of SOM output nodes</span></div>
+<div class="line"><span class="lineno">  108</span>    <span class="comment">// int num_features = x.size();  // number of data features</span></div>
+<div class="line"><span class="lineno">  109</span> </div>
+<div class="line"><span class="lineno">  110</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  111</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  112</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  113</span>    <span class="comment">// step 1: for each output point</span></div>
+<div class="line"><span class="lineno">  114</span>    <span class="keywordflow">for</span> (j = 0; j &lt; num_out; j++) {</div>
+<div class="line"><span class="lineno">  115</span>        <span class="comment">// compute Euclidian distance of each output</span></div>
+<div class="line"><span class="lineno">  116</span>        <span class="comment">// point from the current sample</span></div>
+<div class="line"><span class="lineno">  117</span>        (*D)[j] = (((*W)[j] - x) * ((*W)[j] - x)).sum();</div>
+<div class="line"><span class="lineno">  118</span>    }</div>
+<div class="line"><span class="lineno">  119</span> </div>
+<div class="line"><span class="lineno">  120</span>    <span class="comment">// step 2:  get closest node i.e., node with snallest Euclidian distance to</span></div>
+<div class="line"><span class="lineno">  121</span>    <span class="comment">// the current pattern</span></div>
+<div class="line"><span class="lineno">  122</span>    <span class="keyword">auto</span> result = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min_element.html">std::min_element</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(*D), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(*D));</div>
+<div class="line"><span class="lineno">  123</span>    <span class="comment">// double d_min = *result;</span></div>
+<div class="line"><span class="lineno">  124</span>    <span class="keywordtype">int</span> d_min_idx = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">std::distance</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(*D), result);</div>
+<div class="line"><span class="lineno">  125</span> </div>
+<div class="line"><span class="lineno">  126</span>    <span class="comment">// step 3a: get the neighborhood range</span></div>
+<div class="line"><span class="lineno">  127</span>    <span class="keywordtype">int</span> from_node = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(0, d_min_idx - R);</div>
+<div class="line"><span class="lineno">  128</span>    <span class="keywordtype">int</span> to_node = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(num_out, d_min_idx + R + 1);</div>
+<div class="line"><span class="lineno">  129</span> </div>
+<div class="line"><span class="lineno">  130</span>    <span class="comment">// step 3b: update the weights of nodes in the</span></div>
+<div class="line"><span class="lineno">  131</span>    <span class="comment">// neighborhood</span></div>
+<div class="line"><span class="lineno">  132</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  133</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  134</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  135</span>    <span class="keywordflow">for</span> (j = from_node; j &lt; to_node; j++) {</div>
+<div class="line"><span class="lineno">  136</span>        <span class="comment">// update weights of nodes in the neighborhood</span></div>
+<div class="line"><span class="lineno">  137</span>        (*W)[j] += alpha * (x - (*W)[j]);</div>
+<div class="line"><span class="lineno">  138</span>    }</div>
+<div class="line"><span class="lineno">  139</span>}</div>
 <div class="ttc" id="amin_element_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/min_element.html">std::min_element</a></div><div class="ttdeci">T min_element(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -1854,63 +1854,63 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>minimum distance of sample and trained weights </dd></dl>
-<div class="fragment"><div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>                             {</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>    <span class="keywordtype">int</span> x = 0, y = 0;</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    <span class="keywordtype">int</span> num_out_x = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(W-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());       <span class="comment">// output nodes - in X</span></div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    <span class="keywordtype">int</span> num_out_y = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(W[0][0].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());  <span class="comment">// output nodes - in Y</span></div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>    <span class="comment">// int num_features = static_cast&lt;int&gt;(W[0][0][0].size());  //  features =</span></div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    <span class="comment">// in Z</span></div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>    <span class="keywordtype">double</span> d_min = 0.f;</div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span> </div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>    <span class="comment">// step 1: for each output point</span></div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>    <span class="keywordflow">for</span> (x = 0; x &lt; num_out_x; x++) {</div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>        <span class="keywordflow">for</span> (y = 0; y &lt; num_out_y; y++) {</div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>            (*D)[x][y] = 0.f;</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>            <span class="comment">// compute Euclidian distance of each output</span></div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>            <span class="comment">// point from the current sample</span></div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>            <span class="keyword">auto</span> d = ((*W)[x][y] - X);</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>            (*D)[x][y] = (d * d).<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>();</div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>            (*D)[x][y] = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>((*D)[x][y]);</div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>        }</div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    }</div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span> </div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>    <span class="comment">// step 2:  get closest node i.e., node with snallest Euclidian distance</span></div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>    <span class="comment">// to the current pattern</span></div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    <span class="keywordtype">int</span> d_min_x = 0, d_min_y = 0;</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#ga60f9186ccb682724a8792a2bf81e9b9e">get_min_2d</a>(*D, &amp;d_min, &amp;d_min_x, &amp;d_min_y);</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span> </div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>    <span class="comment">// step 3a: get the neighborhood range</span></div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>    <span class="keywordtype">int</span> from_x = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(0, d_min_x - R);</div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>    <span class="keywordtype">int</span> to_x = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(num_out_x, d_min_x + R + 1);</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>    <span class="keywordtype">int</span> from_y = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(0, d_min_y - R);</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>    <span class="keywordtype">int</span> to_y = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(num_out_y, d_min_y + R + 1);</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span> </div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>    <span class="comment">// step 3b: update the weights of nodes in the</span></div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>    <span class="comment">// neighborhood</span></div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>    <span class="keywordflow">for</span> (x = from_x; x &lt; to_x; x++) {</div>
-<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>        <span class="keywordflow">for</span> (y = from_y; y &lt; to_y; y++) {</div>
-<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>            <span class="comment">/* you can enable the following normalization if needed.</span></div>
-<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span><span class="comment">   personally, I found it detrimental to convergence */</span></div>
-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>            <span class="comment">// const double s2pi = sqrt(2.f * M_PI);</span></div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>            <span class="comment">// double normalize = 1.f / (alpha * s2pi);</span></div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span> </div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>            <span class="comment">/* apply scaling inversely proportional to distance from the</span></div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span><span class="comment">               current node */</span></div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>            <span class="keywordtype">double</span> d2 =</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>                (d_min_x - x) * (d_min_x - x) + (d_min_y - y) * (d_min_y - y);</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>            <span class="keywordtype">double</span> scale_factor = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">std::exp</a>(-d2 / (2.f * alpha * alpha));</div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span> </div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>            (*W)[x][y] += (X - (*W)[x][y]) * alpha * scale_factor;</div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>        }</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>    }</div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>    <span class="keywordflow">return</span> d_min;</div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  203</span>                             {</div>
+<div class="line"><span class="lineno">  204</span>    <span class="keywordtype">int</span> x = 0, y = 0;</div>
+<div class="line"><span class="lineno">  205</span>    <span class="keywordtype">int</span> num_out_x = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(W-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());       <span class="comment">// output nodes - in X</span></div>
+<div class="line"><span class="lineno">  206</span>    <span class="keywordtype">int</span> num_out_y = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(W[0][0].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());  <span class="comment">// output nodes - in Y</span></div>
+<div class="line"><span class="lineno">  207</span>    <span class="comment">// int num_features = static_cast&lt;int&gt;(W[0][0][0].size());  //  features =</span></div>
+<div class="line"><span class="lineno">  208</span>    <span class="comment">// in Z</span></div>
+<div class="line"><span class="lineno">  209</span>    <span class="keywordtype">double</span> d_min = 0.f;</div>
+<div class="line"><span class="lineno">  210</span> </div>
+<div class="line"><span class="lineno">  211</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  212</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  213</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  214</span>    <span class="comment">// step 1: for each output point</span></div>
+<div class="line"><span class="lineno">  215</span>    <span class="keywordflow">for</span> (x = 0; x &lt; num_out_x; x++) {</div>
+<div class="line"><span class="lineno">  216</span>        <span class="keywordflow">for</span> (y = 0; y &lt; num_out_y; y++) {</div>
+<div class="line"><span class="lineno">  217</span>            (*D)[x][y] = 0.f;</div>
+<div class="line"><span class="lineno">  218</span>            <span class="comment">// compute Euclidian distance of each output</span></div>
+<div class="line"><span class="lineno">  219</span>            <span class="comment">// point from the current sample</span></div>
+<div class="line"><span class="lineno">  220</span>            <span class="keyword">auto</span> d = ((*W)[x][y] - X);</div>
+<div class="line"><span class="lineno">  221</span>            (*D)[x][y] = (d * d).<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>();</div>
+<div class="line"><span class="lineno">  222</span>            (*D)[x][y] = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>((*D)[x][y]);</div>
+<div class="line"><span class="lineno">  223</span>        }</div>
+<div class="line"><span class="lineno">  224</span>    }</div>
+<div class="line"><span class="lineno">  225</span> </div>
+<div class="line"><span class="lineno">  226</span>    <span class="comment">// step 2:  get closest node i.e., node with snallest Euclidian distance</span></div>
+<div class="line"><span class="lineno">  227</span>    <span class="comment">// to the current pattern</span></div>
+<div class="line"><span class="lineno">  228</span>    <span class="keywordtype">int</span> d_min_x = 0, d_min_y = 0;</div>
+<div class="line"><span class="lineno">  229</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#ga60f9186ccb682724a8792a2bf81e9b9e">get_min_2d</a>(*D, &amp;d_min, &amp;d_min_x, &amp;d_min_y);</div>
+<div class="line"><span class="lineno">  230</span> </div>
+<div class="line"><span class="lineno">  231</span>    <span class="comment">// step 3a: get the neighborhood range</span></div>
+<div class="line"><span class="lineno">  232</span>    <span class="keywordtype">int</span> from_x = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(0, d_min_x - R);</div>
+<div class="line"><span class="lineno">  233</span>    <span class="keywordtype">int</span> to_x = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(num_out_x, d_min_x + R + 1);</div>
+<div class="line"><span class="lineno">  234</span>    <span class="keywordtype">int</span> from_y = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(0, d_min_y - R);</div>
+<div class="line"><span class="lineno">  235</span>    <span class="keywordtype">int</span> to_y = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(num_out_y, d_min_y + R + 1);</div>
+<div class="line"><span class="lineno">  236</span> </div>
+<div class="line"><span class="lineno">  237</span>    <span class="comment">// step 3b: update the weights of nodes in the</span></div>
+<div class="line"><span class="lineno">  238</span>    <span class="comment">// neighborhood</span></div>
+<div class="line"><span class="lineno">  239</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  240</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  241</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  242</span>    <span class="keywordflow">for</span> (x = from_x; x &lt; to_x; x++) {</div>
+<div class="line"><span class="lineno">  243</span>        <span class="keywordflow">for</span> (y = from_y; y &lt; to_y; y++) {</div>
+<div class="line"><span class="lineno">  244</span>            <span class="comment">/* you can enable the following normalization if needed.</span></div>
+<div class="line"><span class="lineno">  245</span><span class="comment">   personally, I found it detrimental to convergence */</span></div>
+<div class="line"><span class="lineno">  246</span>            <span class="comment">// const double s2pi = sqrt(2.f * M_PI);</span></div>
+<div class="line"><span class="lineno">  247</span>            <span class="comment">// double normalize = 1.f / (alpha * s2pi);</span></div>
+<div class="line"><span class="lineno">  248</span> </div>
+<div class="line"><span class="lineno">  249</span>            <span class="comment">/* apply scaling inversely proportional to distance from the</span></div>
+<div class="line"><span class="lineno">  250</span><span class="comment">               current node */</span></div>
+<div class="line"><span class="lineno">  251</span>            <span class="keywordtype">double</span> d2 =</div>
+<div class="line"><span class="lineno">  252</span>                (d_min_x - x) * (d_min_x - x) + (d_min_y - y) * (d_min_y - y);</div>
+<div class="line"><span class="lineno">  253</span>            <span class="keywordtype">double</span> scale_factor = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">std::exp</a>(-d2 / (2.f * alpha * alpha));</div>
+<div class="line"><span class="lineno">  254</span> </div>
+<div class="line"><span class="lineno">  255</span>            (*W)[x][y] += (X - (*W)[x][y]) * alpha * scale_factor;</div>
+<div class="line"><span class="lineno">  256</span>        }</div>
+<div class="line"><span class="lineno">  257</span>    }</div>
+<div class="line"><span class="lineno">  258</span>    <span class="keywordflow">return</span> d_min;</div>
+<div class="line"><span class="lineno">  259</span>}</div>
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@@ -1963,16 +1963,16 @@ template&lt;typename T &gt; </div>
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-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  214</span>                                                                 {</div>
+<div class="line"><span class="lineno">  215</span>    A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/clear.html">clear</a>();  <span class="comment">// Making A empty</span></div>
+<div class="line"><span class="lineno">  216</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; shape.first; i++) {</div>
+<div class="line"><span class="lineno">  217</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a></div>
+<div class="line"><span class="lineno">  218</span>            row;  <span class="comment">// Making empty row which will be inserted in vector</span></div>
+<div class="line"><span class="lineno">  219</span>        row.resize(shape.second);  <span class="comment">// By default all elements are zero</span></div>
+<div class="line"><span class="lineno">  220</span>        A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(row);          <span class="comment">// Insert new row in vector</span></div>
+<div class="line"><span class="lineno">  221</span>    }</div>
+<div class="line"><span class="lineno">  222</span>    <span class="keywordflow">return</span>;</div>
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    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
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    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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+<!-- Generated by Doxygen 1.9.3 -->
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@@ -179,9 +179,9 @@ Algorithm</h3>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void* Pointer to the SHA-1 signature </dd></dl>
-<div class="fragment"><div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>                                     {</div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a5341431cef7fcfc33794326e1deb2425">hash_bs</a>(&amp;message[0], message.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>());</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  210</span>                                     {</div>
+<div class="line"><span class="lineno">  211</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a5341431cef7fcfc33794326e1deb2425">hash_bs</a>(&amp;message[0], message.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>());</div>
+<div class="line"><span class="lineno">  212</span>}</div>
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 <div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">std::string::size</a></div><div class="ttdeci">T size(T... args)</div></div>
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@@ -228,127 +228,127 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void* Pointer to the 160-bit signature </dd></dl>
-<div class="fragment"><div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>                                                         {</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    <span class="keyword">auto</span>* input = <span class="keyword">static_cast&lt;</span><span class="keyword">const </span>uint8_t*<span class="keyword">&gt;</span>(input_bs);</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span> </div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>    <span class="comment">// Step 0: The initial 160-bit state</span></div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    uint32_t h0 = 0x67452301, a = 0;</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    uint32_t h1 = 0xEFCDAB89, b = 0;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    uint32_t h2 = 0x98BADCFE, c = 0;</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    uint32_t h3 = 0x10325476, d = 0;</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    uint32_t h4 = 0xC3D2E1F0, e = 0;</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span> </div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    <span class="comment">// Step 1: Processing the bytestring</span></div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>    <span class="comment">// First compute the size the padded message will have</span></div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>    <span class="comment">// so it is possible to allocate the right amount of memory</span></div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    uint64_t padded_message_size = 0;</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    <span class="keywordflow">if</span> (input_size % 64 &lt; 56) {</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>        padded_message_size = input_size + 64 - (input_size % 64);</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>        padded_message_size = input_size + 128 - (input_size % 64);</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    }</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span> </div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <span class="comment">// Allocate the memory for the padded message</span></div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint8_t&gt;</a> padded_message(padded_message_size);</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span> </div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    <span class="comment">// Beginning of the padded message is the original message</span></div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/copy.html">std::copy</a>(input, input + input_size, padded_message.begin());</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span> </div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <span class="comment">// Afterwards comes a single 1 bit and then only zeroes</span></div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    padded_message[input_size] = 1 &lt;&lt; 7;  <span class="comment">// 10000000</span></div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <span class="keywordflow">for</span> (uint64_t i = input_size; i % 64 != 56; i++) {</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>        <span class="keywordflow">if</span> (i == input_size) {</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>            <span class="keywordflow">continue</span>;  <span class="comment">// pass first iteration</span></div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>        }</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>        padded_message[i] = 0;</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    }</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span> </div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    <span class="comment">// We then have to add the 64-bit size of the message in bits (hence the</span></div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    <span class="comment">// times 8) in the last 8 bytes</span></div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    uint64_t input_bitsize = input_size * 8;</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; 8; i++) {</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>        padded_message[padded_message_size - 8 + i] =</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>            (input_bitsize &gt;&gt; (56 - 8 * i)) &amp; 0xFF;</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    }</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span> </div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    <span class="comment">// Already allocate memory for blocks</span></div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;uint32_t, 80&gt;</a> blocks{};</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span> </div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    <span class="comment">// Rounds</span></div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    <span class="keywordflow">for</span> (uint64_t chunk = 0; chunk * 64 &lt; padded_message_size; chunk++) {</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>        <span class="comment">// First, build 16 32-bits blocks from the chunk</span></div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>        <span class="keywordflow">for</span> (uint8_t bid = 0; bid &lt; 16; bid++) {</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>            blocks[bid] = 0;</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span> </div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>            <span class="comment">// Having to build a 32-bit word from 4-bit words</span></div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>            <span class="comment">// Add each and shift them to the left</span></div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>            <span class="keywordflow">for</span> (uint8_t cid = 0; cid &lt; 4; cid++) {</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>                blocks[bid] = (blocks[bid] &lt;&lt; 8) +</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>                              padded_message[chunk * 64 + bid * 4 + cid];</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>            }</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span> </div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>            <span class="comment">// Extend the 16 32-bit words into 80 32-bit words</span></div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>            <span class="keywordflow">for</span> (uint8_t i = 16; i &lt; 80; i++) {</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>                blocks[i] =</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>                    <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#add2bf982d5dd64a45d13cba52c2b371d">leftRotate32bits</a>(blocks[i - 3] ^ blocks[i - 8] ^</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>                                         blocks[i - 14] ^ blocks[i - 16],</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>                                     1);</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>            }</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>        }</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span> </div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>        a = h0;</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>        b = h1;</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>        c = h2;</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>        d = h3;</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>        e = h4;</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span> </div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>        <span class="comment">// Main &quot;hashing&quot; loop</span></div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>        <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; 80; i++) {</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>            uint32_t F = 0, <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = 0;</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>            <span class="keywordflow">if</span> (i &lt; 20) {</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>                F = (b &amp; c) | ((~b) &amp; d);</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = 0x5A827999;</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (i &lt; 40) {</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>                F = b ^ c ^ d;</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = 0x6ED9EBA1;</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (i &lt; 60) {</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>                F = (b &amp; c) | (b &amp; d) | (c &amp; d);</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = 0x8F1BBCDC;</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>                F = b ^ c ^ d;</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = 0xCA62C1D6;</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>            }</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span> </div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>            <span class="comment">// Update the accumulators</span></div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>            uint32_t temp = <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#add2bf982d5dd64a45d13cba52c2b371d">leftRotate32bits</a>(a, 5) + F + e + <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> + blocks[i];</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>            e = d;</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>            d = c;</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>            c = <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#add2bf982d5dd64a45d13cba52c2b371d">leftRotate32bits</a>(b, 30);</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>            b = a;</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>            a = temp;</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>        }</div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>        <span class="comment">// Update the state with this chunk&#39;s hash</span></div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>        h0 += a;</div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>        h1 += b;</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>        h2 += c;</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>        h3 += d;</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>        h4 += e;</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>    }</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span> </div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>    <span class="comment">// Build signature from state</span></div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>    <span class="comment">// Note, any type could be used for the signature</span></div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>    <span class="comment">// uint8_t was used to make the 20 bytes obvious</span></div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>    <span class="keyword">auto</span>* sig = <span class="keyword">new</span> uint8_t[20];</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>    <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; 4; i++) {</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>        sig[i] = (h0 &gt;&gt; (24 - 8 * i)) &amp; 0xFF;</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>        sig[i + 4] = (h1 &gt;&gt; (24 - 8 * i)) &amp; 0xFF;</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>        sig[i + 8] = (h2 &gt;&gt; (24 - 8 * i)) &amp; 0xFF;</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>        sig[i + 12] = (h3 &gt;&gt; (24 - 8 * i)) &amp; 0xFF;</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>        sig[i + 16] = (h4 &gt;&gt; (24 - 8 * i)) &amp; 0xFF;</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    }</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span> </div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>    <span class="keywordflow">return</span> sig;</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   83</span>                                                         {</div>
+<div class="line"><span class="lineno">   84</span>    <span class="keyword">auto</span>* input = <span class="keyword">static_cast&lt;</span><span class="keyword">const </span>uint8_t*<span class="keyword">&gt;</span>(input_bs);</div>
+<div class="line"><span class="lineno">   85</span> </div>
+<div class="line"><span class="lineno">   86</span>    <span class="comment">// Step 0: The initial 160-bit state</span></div>
+<div class="line"><span class="lineno">   87</span>    uint32_t h0 = 0x67452301, a = 0;</div>
+<div class="line"><span class="lineno">   88</span>    uint32_t h1 = 0xEFCDAB89, b = 0;</div>
+<div class="line"><span class="lineno">   89</span>    uint32_t h2 = 0x98BADCFE, c = 0;</div>
+<div class="line"><span class="lineno">   90</span>    uint32_t h3 = 0x10325476, d = 0;</div>
+<div class="line"><span class="lineno">   91</span>    uint32_t h4 = 0xC3D2E1F0, e = 0;</div>
+<div class="line"><span class="lineno">   92</span> </div>
+<div class="line"><span class="lineno">   93</span>    <span class="comment">// Step 1: Processing the bytestring</span></div>
+<div class="line"><span class="lineno">   94</span>    <span class="comment">// First compute the size the padded message will have</span></div>
+<div class="line"><span class="lineno">   95</span>    <span class="comment">// so it is possible to allocate the right amount of memory</span></div>
+<div class="line"><span class="lineno">   96</span>    uint64_t padded_message_size = 0;</div>
+<div class="line"><span class="lineno">   97</span>    <span class="keywordflow">if</span> (input_size % 64 &lt; 56) {</div>
+<div class="line"><span class="lineno">   98</span>        padded_message_size = input_size + 64 - (input_size % 64);</div>
+<div class="line"><span class="lineno">   99</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  100</span>        padded_message_size = input_size + 128 - (input_size % 64);</div>
+<div class="line"><span class="lineno">  101</span>    }</div>
+<div class="line"><span class="lineno">  102</span> </div>
+<div class="line"><span class="lineno">  103</span>    <span class="comment">// Allocate the memory for the padded message</span></div>
+<div class="line"><span class="lineno">  104</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint8_t&gt;</a> padded_message(padded_message_size);</div>
+<div class="line"><span class="lineno">  105</span> </div>
+<div class="line"><span class="lineno">  106</span>    <span class="comment">// Beginning of the padded message is the original message</span></div>
+<div class="line"><span class="lineno">  107</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/copy.html">std::copy</a>(input, input + input_size, padded_message.begin());</div>
+<div class="line"><span class="lineno">  108</span> </div>
+<div class="line"><span class="lineno">  109</span>    <span class="comment">// Afterwards comes a single 1 bit and then only zeroes</span></div>
+<div class="line"><span class="lineno">  110</span>    padded_message[input_size] = 1 &lt;&lt; 7;  <span class="comment">// 10000000</span></div>
+<div class="line"><span class="lineno">  111</span>    <span class="keywordflow">for</span> (uint64_t i = input_size; i % 64 != 56; i++) {</div>
+<div class="line"><span class="lineno">  112</span>        <span class="keywordflow">if</span> (i == input_size) {</div>
+<div class="line"><span class="lineno">  113</span>            <span class="keywordflow">continue</span>;  <span class="comment">// pass first iteration</span></div>
+<div class="line"><span class="lineno">  114</span>        }</div>
+<div class="line"><span class="lineno">  115</span>        padded_message[i] = 0;</div>
+<div class="line"><span class="lineno">  116</span>    }</div>
+<div class="line"><span class="lineno">  117</span> </div>
+<div class="line"><span class="lineno">  118</span>    <span class="comment">// We then have to add the 64-bit size of the message in bits (hence the</span></div>
+<div class="line"><span class="lineno">  119</span>    <span class="comment">// times 8) in the last 8 bytes</span></div>
+<div class="line"><span class="lineno">  120</span>    uint64_t input_bitsize = input_size * 8;</div>
+<div class="line"><span class="lineno">  121</span>    <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; 8; i++) {</div>
+<div class="line"><span class="lineno">  122</span>        padded_message[padded_message_size - 8 + i] =</div>
+<div class="line"><span class="lineno">  123</span>            (input_bitsize &gt;&gt; (56 - 8 * i)) &amp; 0xFF;</div>
+<div class="line"><span class="lineno">  124</span>    }</div>
+<div class="line"><span class="lineno">  125</span> </div>
+<div class="line"><span class="lineno">  126</span>    <span class="comment">// Already allocate memory for blocks</span></div>
+<div class="line"><span class="lineno">  127</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;uint32_t, 80&gt;</a> blocks{};</div>
+<div class="line"><span class="lineno">  128</span> </div>
+<div class="line"><span class="lineno">  129</span>    <span class="comment">// Rounds</span></div>
+<div class="line"><span class="lineno">  130</span>    <span class="keywordflow">for</span> (uint64_t chunk = 0; chunk * 64 &lt; padded_message_size; chunk++) {</div>
+<div class="line"><span class="lineno">  131</span>        <span class="comment">// First, build 16 32-bits blocks from the chunk</span></div>
+<div class="line"><span class="lineno">  132</span>        <span class="keywordflow">for</span> (uint8_t bid = 0; bid &lt; 16; bid++) {</div>
+<div class="line"><span class="lineno">  133</span>            blocks[bid] = 0;</div>
+<div class="line"><span class="lineno">  134</span> </div>
+<div class="line"><span class="lineno">  135</span>            <span class="comment">// Having to build a 32-bit word from 4-bit words</span></div>
+<div class="line"><span class="lineno">  136</span>            <span class="comment">// Add each and shift them to the left</span></div>
+<div class="line"><span class="lineno">  137</span>            <span class="keywordflow">for</span> (uint8_t cid = 0; cid &lt; 4; cid++) {</div>
+<div class="line"><span class="lineno">  138</span>                blocks[bid] = (blocks[bid] &lt;&lt; 8) +</div>
+<div class="line"><span class="lineno">  139</span>                              padded_message[chunk * 64 + bid * 4 + cid];</div>
+<div class="line"><span class="lineno">  140</span>            }</div>
+<div class="line"><span class="lineno">  141</span> </div>
+<div class="line"><span class="lineno">  142</span>            <span class="comment">// Extend the 16 32-bit words into 80 32-bit words</span></div>
+<div class="line"><span class="lineno">  143</span>            <span class="keywordflow">for</span> (uint8_t i = 16; i &lt; 80; i++) {</div>
+<div class="line"><span class="lineno">  144</span>                blocks[i] =</div>
+<div class="line"><span class="lineno">  145</span>                    <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#add2bf982d5dd64a45d13cba52c2b371d">leftRotate32bits</a>(blocks[i - 3] ^ blocks[i - 8] ^</div>
+<div class="line"><span class="lineno">  146</span>                                         blocks[i - 14] ^ blocks[i - 16],</div>
+<div class="line"><span class="lineno">  147</span>                                     1);</div>
+<div class="line"><span class="lineno">  148</span>            }</div>
+<div class="line"><span class="lineno">  149</span>        }</div>
+<div class="line"><span class="lineno">  150</span> </div>
+<div class="line"><span class="lineno">  151</span>        a = h0;</div>
+<div class="line"><span class="lineno">  152</span>        b = h1;</div>
+<div class="line"><span class="lineno">  153</span>        c = h2;</div>
+<div class="line"><span class="lineno">  154</span>        d = h3;</div>
+<div class="line"><span class="lineno">  155</span>        e = h4;</div>
+<div class="line"><span class="lineno">  156</span> </div>
+<div class="line"><span class="lineno">  157</span>        <span class="comment">// Main &quot;hashing&quot; loop</span></div>
+<div class="line"><span class="lineno">  158</span>        <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; 80; i++) {</div>
+<div class="line"><span class="lineno">  159</span>            uint32_t F = 0, <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = 0;</div>
+<div class="line"><span class="lineno">  160</span>            <span class="keywordflow">if</span> (i &lt; 20) {</div>
+<div class="line"><span class="lineno">  161</span>                F = (b &amp; c) | ((~b) &amp; d);</div>
+<div class="line"><span class="lineno">  162</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = 0x5A827999;</div>
+<div class="line"><span class="lineno">  163</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (i &lt; 40) {</div>
+<div class="line"><span class="lineno">  164</span>                F = b ^ c ^ d;</div>
+<div class="line"><span class="lineno">  165</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = 0x6ED9EBA1;</div>
+<div class="line"><span class="lineno">  166</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (i &lt; 60) {</div>
+<div class="line"><span class="lineno">  167</span>                F = (b &amp; c) | (b &amp; d) | (c &amp; d);</div>
+<div class="line"><span class="lineno">  168</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = 0x8F1BBCDC;</div>
+<div class="line"><span class="lineno">  169</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  170</span>                F = b ^ c ^ d;</div>
+<div class="line"><span class="lineno">  171</span>                <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = 0xCA62C1D6;</div>
+<div class="line"><span class="lineno">  172</span>            }</div>
+<div class="line"><span class="lineno">  173</span> </div>
+<div class="line"><span class="lineno">  174</span>            <span class="comment">// Update the accumulators</span></div>
+<div class="line"><span class="lineno">  175</span>            uint32_t temp = <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#add2bf982d5dd64a45d13cba52c2b371d">leftRotate32bits</a>(a, 5) + F + e + <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> + blocks[i];</div>
+<div class="line"><span class="lineno">  176</span>            e = d;</div>
+<div class="line"><span class="lineno">  177</span>            d = c;</div>
+<div class="line"><span class="lineno">  178</span>            c = <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#add2bf982d5dd64a45d13cba52c2b371d">leftRotate32bits</a>(b, 30);</div>
+<div class="line"><span class="lineno">  179</span>            b = a;</div>
+<div class="line"><span class="lineno">  180</span>            a = temp;</div>
+<div class="line"><span class="lineno">  181</span>        }</div>
+<div class="line"><span class="lineno">  182</span>        <span class="comment">// Update the state with this chunk&#39;s hash</span></div>
+<div class="line"><span class="lineno">  183</span>        h0 += a;</div>
+<div class="line"><span class="lineno">  184</span>        h1 += b;</div>
+<div class="line"><span class="lineno">  185</span>        h2 += c;</div>
+<div class="line"><span class="lineno">  186</span>        h3 += d;</div>
+<div class="line"><span class="lineno">  187</span>        h4 += e;</div>
+<div class="line"><span class="lineno">  188</span>    }</div>
+<div class="line"><span class="lineno">  189</span> </div>
+<div class="line"><span class="lineno">  190</span>    <span class="comment">// Build signature from state</span></div>
+<div class="line"><span class="lineno">  191</span>    <span class="comment">// Note, any type could be used for the signature</span></div>
+<div class="line"><span class="lineno">  192</span>    <span class="comment">// uint8_t was used to make the 20 bytes obvious</span></div>
+<div class="line"><span class="lineno">  193</span>    <span class="keyword">auto</span>* sig = <span class="keyword">new</span> uint8_t[20];</div>
+<div class="line"><span class="lineno">  194</span>    <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; 4; i++) {</div>
+<div class="line"><span class="lineno">  195</span>        sig[i] = (h0 &gt;&gt; (24 - 8 * i)) &amp; 0xFF;</div>
+<div class="line"><span class="lineno">  196</span>        sig[i + 4] = (h1 &gt;&gt; (24 - 8 * i)) &amp; 0xFF;</div>
+<div class="line"><span class="lineno">  197</span>        sig[i + 8] = (h2 &gt;&gt; (24 - 8 * i)) &amp; 0xFF;</div>
+<div class="line"><span class="lineno">  198</span>        sig[i + 12] = (h3 &gt;&gt; (24 - 8 * i)) &amp; 0xFF;</div>
+<div class="line"><span class="lineno">  199</span>        sig[i + 16] = (h4 &gt;&gt; (24 - 8 * i)) &amp; 0xFF;</div>
+<div class="line"><span class="lineno">  200</span>    }</div>
+<div class="line"><span class="lineno">  201</span> </div>
+<div class="line"><span class="lineno">  202</span>    <span class="keywordflow">return</span> sig;</div>
+<div class="line"><span class="lineno">  203</span>}</div>
 <div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a2f67508d5f392b0321772169342c98ad"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">numerical_methods::simpson_method::g</a></div><div class="ttdeci">double g(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:115</div></div>
 <div class="ttc" id="acopy_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/copy.html">std::copy</a></div><div class="ttdeci">T copy(T... args)</div></div>
@@ -388,26 +388,26 @@ Here is the call graph for this function:</div>
 
 <p>Puts user in a loop where inputs can be given and SHA-1 hash will be computed and printed. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>                          {</div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>    <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> input;</div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter a message to be hashed (Ctrl-C to exit): &quot;</span></div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>                  &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/getline.html">std::getline</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>, input);</div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>        <span class="keywordtype">void</span>* sig = <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#a2397f2444a05e4d1487c67e215410d3c">hashing::sha1::hash</a>(input);</div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hash is: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#aada0803ef851d831b7a290a924e3c228">hashing::sha1::sig2hex</a>(sig) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span> </div>
-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>        <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Want to enter another message? (y/n) &quot;</span>;</div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/getline.html">std::getline</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>, input);</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>            <span class="keywordflow">if</span> (input.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/compare.html">compare</a>(<span class="stringliteral">&quot;y&quot;</span>) == 0) {</div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (input.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/compare.html">compare</a>(<span class="stringliteral">&quot;n&quot;</span>) == 0) {</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>                <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>            }</div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>        }</div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>    }</div>
-<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  274</span>                          {</div>
+<div class="line"><span class="lineno">  275</span>    <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
+<div class="line"><span class="lineno">  276</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> input;</div>
+<div class="line"><span class="lineno">  277</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter a message to be hashed (Ctrl-C to exit): &quot;</span></div>
+<div class="line"><span class="lineno">  278</span>                  &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  279</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/getline.html">std::getline</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>, input);</div>
+<div class="line"><span class="lineno">  280</span>        <span class="keywordtype">void</span>* sig = <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#a2397f2444a05e4d1487c67e215410d3c">hashing::sha1::hash</a>(input);</div>
+<div class="line"><span class="lineno">  281</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hash is: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#aada0803ef851d831b7a290a924e3c228">hashing::sha1::sig2hex</a>(sig) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  282</span> </div>
+<div class="line"><span class="lineno">  283</span>        <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
+<div class="line"><span class="lineno">  284</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Want to enter another message? (y/n) &quot;</span>;</div>
+<div class="line"><span class="lineno">  285</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/getline.html">std::getline</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>, input);</div>
+<div class="line"><span class="lineno">  286</span>            <span class="keywordflow">if</span> (input.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/compare.html">compare</a>(<span class="stringliteral">&quot;y&quot;</span>) == 0) {</div>
+<div class="line"><span class="lineno">  287</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  288</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (input.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/compare.html">compare</a>(<span class="stringliteral">&quot;n&quot;</span>) == 0) {</div>
+<div class="line"><span class="lineno">  289</span>                <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  290</span>            }</div>
+<div class="line"><span class="lineno">  291</span>        }</div>
+<div class="line"><span class="lineno">  292</span>    }</div>
+<div class="line"><span class="lineno">  293</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
@@ -460,9 +460,9 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>uint32_t The rotated integer </dd></dl>
-<div class="fragment"><div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>                                                        {</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <span class="keywordflow">return</span> (n &lt;&lt; rotate) | (n &gt;&gt; (32 - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/rotate.html">rotate</a>));</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   57</span>                                                        {</div>
+<div class="line"><span class="lineno">   58</span>    <span class="keywordflow">return</span> (n &lt;&lt; rotate) | (n &gt;&gt; (32 - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/rotate.html">rotate</a>));</div>
+<div class="line"><span class="lineno">   59</span>}</div>
 <div class="ttc" id="arotate_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/rotate.html">std::rotate</a></div><div class="ttdeci">T rotate(T... args)</div></div>
 </div><!-- fragment -->
 </div>
@@ -485,14 +485,14 @@ Here is the call graph for this function:</div>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>           {</div>
-<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span>    <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
-<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span> </div>
-<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span>    <span class="comment">// Launch interactive mode where user can input messages and see</span></div>
-<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span>    <span class="comment">// their hash</span></div>
-<div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span>    <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#ac9e1a11f44135b890dd10a00e73b5661">interactive</a>();</div>
-<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  299</span>           {</div>
+<div class="line"><span class="lineno">  300</span>    <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
+<div class="line"><span class="lineno">  301</span> </div>
+<div class="line"><span class="lineno">  302</span>    <span class="comment">// Launch interactive mode where user can input messages and see</span></div>
+<div class="line"><span class="lineno">  303</span>    <span class="comment">// their hash</span></div>
+<div class="line"><span class="lineno">  304</span>    <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#ac9e1a11f44135b890dd10a00e73b5661">interactive</a>();</div>
+<div class="line"><span class="lineno">  305</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  306</span>}</div>
 <div class="ttc" id="asha1_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d8/d7a/sha1_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations of well-known SHA-1 hashes.</div><div class="ttdef"><b>Definition:</b> sha1.cpp:220</div></div>
 <div class="ttc" id="asha1_8cpp_html_ac9e1a11f44135b890dd10a00e73b5661"><div class="ttname"><a href="../../d8/d7a/sha1_8cpp.html#ac9e1a11f44135b890dd10a00e73b5661">interactive</a></div><div class="ttdeci">static void interactive()</div><div class="ttdoc">Puts user in a loop where inputs can be given and SHA-1 hash will be computed and printed.</div><div class="ttdef"><b>Definition:</b> sha1.cpp:274</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -528,16 +528,16 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> The hex signature </dd></dl>
-<div class="fragment"><div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>                             {</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <span class="keyword">const</span> <span class="keywordtype">char</span>* hexChars = <span class="stringliteral">&quot;0123456789abcdef&quot;</span>;</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <span class="keyword">auto</span>* intsig = <span class="keyword">static_cast&lt;</span>uint8_t*<span class="keyword">&gt;</span>(sig);</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/hex.html">hex</a> = <span class="stringliteral">&quot;&quot;</span>;</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>    <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; 20; i++) {</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/hex.html">hex</a>.push_back(hexChars[(intsig[i] &gt;&gt; 4) &amp; 0xF]);</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/hex.html">hex</a>.push_back(hexChars[(intsig[i]) &amp; 0xF]);</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    }</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/hex.html">hex</a>;</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   66</span>                             {</div>
+<div class="line"><span class="lineno">   67</span>    <span class="keyword">const</span> <span class="keywordtype">char</span>* hexChars = <span class="stringliteral">&quot;0123456789abcdef&quot;</span>;</div>
+<div class="line"><span class="lineno">   68</span>    <span class="keyword">auto</span>* intsig = <span class="keyword">static_cast&lt;</span>uint8_t*<span class="keyword">&gt;</span>(sig);</div>
+<div class="line"><span class="lineno">   69</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/hex.html">hex</a> = <span class="stringliteral">&quot;&quot;</span>;</div>
+<div class="line"><span class="lineno">   70</span>    <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; 20; i++) {</div>
+<div class="line"><span class="lineno">   71</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/hex.html">hex</a>.push_back(hexChars[(intsig[i] &gt;&gt; 4) &amp; 0xF]);</div>
+<div class="line"><span class="lineno">   72</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/hex.html">hex</a>.push_back(hexChars[(intsig[i]) &amp; 0xF]);</div>
+<div class="line"><span class="lineno">   73</span>    }</div>
+<div class="line"><span class="lineno">   74</span>    <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/hex.html">hex</a>;</div>
+<div class="line"><span class="lineno">   75</span>}</div>
 <div class="ttc" id="ahex_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/hex.html">std::hex</a></div><div class="ttdeci">T hex(T... args)</div></div>
 </div><!-- fragment -->
 </div>
@@ -567,54 +567,54 @@ Here is the call graph for this function:</div>
 
 <p>Self-test implementations of well-known SHA-1 hashes. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>                   {</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>    <span class="comment">// Hashes empty string and stores signature</span></div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>    <span class="keywordtype">void</span>* sig = <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#a2397f2444a05e4d1487c67e215410d3c">hashing::sha1::hash</a>(<span class="stringliteral">&quot;&quot;</span>);</div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hashing empty string&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    <span class="comment">// Prints signature hex representation</span></div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#aada0803ef851d831b7a290a924e3c228">hashing::sha1::sig2hex</a>(sig) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>    <span class="comment">// Test with cassert wether sig is correct from expected value</span></div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>    assert(hashing::sha1::sig2hex(sig).<a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a>(</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>               <span class="stringliteral">&quot;da39a3ee5e6b4b0d3255bfef95601890afd80709&quot;</span>) == 0);</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span> </div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>    <span class="comment">// Hashes &quot;The quick brown fox jumps over the lazy dog&quot; and stores signature</span></div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>    <span class="keywordtype">void</span>* sig2 =</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>        <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#a2397f2444a05e4d1487c67e215410d3c">hashing::sha1::hash</a>(<span class="stringliteral">&quot;The quick brown fox jumps over the lazy dog&quot;</span>);</div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hashing The quick brown fox jumps over the lazy dog&quot;</span></div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>    <span class="comment">// Prints signature hex representation</span></div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#aada0803ef851d831b7a290a924e3c228">hashing::sha1::sig2hex</a>(sig2) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>    <span class="comment">// Test with cassert wether sig is correct from expected value</span></div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>    assert(hashing::sha1::sig2hex(sig2).<a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a>(</div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>               <span class="stringliteral">&quot;2fd4e1c67a2d28fced849ee1bb76e7391b93eb12&quot;</span>) == 0);</div>
-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span> </div>
-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>    <span class="comment">// Hashes &quot;The quick brown fox jumps over the lazy dog.&quot; (notice the</span></div>
-<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>    <span class="comment">// additional period) and stores signature</span></div>
-<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>    <span class="keywordtype">void</span>* sig3 =</div>
-<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>        <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#a2397f2444a05e4d1487c67e215410d3c">hashing::sha1::hash</a>(<span class="stringliteral">&quot;The quick brown fox jumps over the lazy dog.&quot;</span>);</div>
-<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hashing &quot;</span></div>
-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>                 <span class="stringliteral">&quot;The quick brown fox jumps over the lazy dog.&quot;</span></div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>    <span class="comment">// Prints signature hex representation</span></div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#aada0803ef851d831b7a290a924e3c228">hashing::sha1::sig2hex</a>(sig3) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>    <span class="comment">// Test with cassert wether sig is correct from expected value</span></div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>    assert(hashing::sha1::sig2hex(sig3).<a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a>(</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>               <span class="stringliteral">&quot;408d94384216f890ff7a0c3528e8bed1e0b01621&quot;</span>) == 0);</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span> </div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>    <span class="comment">// Hashes &quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789&quot;</span></div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>    <span class="comment">// and stores signature</span></div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>    <span class="keywordtype">void</span>* sig4 = <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#a2397f2444a05e4d1487c67e215410d3c">hashing::sha1::hash</a>(</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>        <span class="stringliteral">&quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789&quot;</span>);</div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>        &lt;&lt; <span class="stringliteral">&quot;Hashing &quot;</span></div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>           <span class="stringliteral">&quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789&quot;</span></div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>        &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>    <span class="comment">// Prints signature hex representation</span></div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#aada0803ef851d831b7a290a924e3c228">hashing::sha1::sig2hex</a>(sig4) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>    <span class="comment">// Test with cassert wether sig is correct from expected value</span></div>
-<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>    assert(hashing::sha1::sig2hex(sig4).<a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a>(</div>
-<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>               <span class="stringliteral">&quot;761c457bf73b14d27e9e9265c46f4b4dda11f940&quot;</span>) == 0);</div>
-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  220</span>                   {</div>
+<div class="line"><span class="lineno">  221</span>    <span class="comment">// Hashes empty string and stores signature</span></div>
+<div class="line"><span class="lineno">  222</span>    <span class="keywordtype">void</span>* sig = <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#a2397f2444a05e4d1487c67e215410d3c">hashing::sha1::hash</a>(<span class="stringliteral">&quot;&quot;</span>);</div>
+<div class="line"><span class="lineno">  223</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hashing empty string&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  224</span>    <span class="comment">// Prints signature hex representation</span></div>
+<div class="line"><span class="lineno">  225</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#aada0803ef851d831b7a290a924e3c228">hashing::sha1::sig2hex</a>(sig) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  226</span>    <span class="comment">// Test with cassert wether sig is correct from expected value</span></div>
+<div class="line"><span class="lineno">  227</span>    assert(hashing::sha1::sig2hex(sig).<a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a>(</div>
+<div class="line"><span class="lineno">  228</span>               <span class="stringliteral">&quot;da39a3ee5e6b4b0d3255bfef95601890afd80709&quot;</span>) == 0);</div>
+<div class="line"><span class="lineno">  229</span> </div>
+<div class="line"><span class="lineno">  230</span>    <span class="comment">// Hashes &quot;The quick brown fox jumps over the lazy dog&quot; and stores signature</span></div>
+<div class="line"><span class="lineno">  231</span>    <span class="keywordtype">void</span>* sig2 =</div>
+<div class="line"><span class="lineno">  232</span>        <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#a2397f2444a05e4d1487c67e215410d3c">hashing::sha1::hash</a>(<span class="stringliteral">&quot;The quick brown fox jumps over the lazy dog&quot;</span>);</div>
+<div class="line"><span class="lineno">  233</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hashing The quick brown fox jumps over the lazy dog&quot;</span></div>
+<div class="line"><span class="lineno">  234</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  235</span>    <span class="comment">// Prints signature hex representation</span></div>
+<div class="line"><span class="lineno">  236</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#aada0803ef851d831b7a290a924e3c228">hashing::sha1::sig2hex</a>(sig2) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  237</span>    <span class="comment">// Test with cassert wether sig is correct from expected value</span></div>
+<div class="line"><span class="lineno">  238</span>    assert(hashing::sha1::sig2hex(sig2).<a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a>(</div>
+<div class="line"><span class="lineno">  239</span>               <span class="stringliteral">&quot;2fd4e1c67a2d28fced849ee1bb76e7391b93eb12&quot;</span>) == 0);</div>
+<div class="line"><span class="lineno">  240</span> </div>
+<div class="line"><span class="lineno">  241</span>    <span class="comment">// Hashes &quot;The quick brown fox jumps over the lazy dog.&quot; (notice the</span></div>
+<div class="line"><span class="lineno">  242</span>    <span class="comment">// additional period) and stores signature</span></div>
+<div class="line"><span class="lineno">  243</span>    <span class="keywordtype">void</span>* sig3 =</div>
+<div class="line"><span class="lineno">  244</span>        <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#a2397f2444a05e4d1487c67e215410d3c">hashing::sha1::hash</a>(<span class="stringliteral">&quot;The quick brown fox jumps over the lazy dog.&quot;</span>);</div>
+<div class="line"><span class="lineno">  245</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hashing &quot;</span></div>
+<div class="line"><span class="lineno">  246</span>                 <span class="stringliteral">&quot;The quick brown fox jumps over the lazy dog.&quot;</span></div>
+<div class="line"><span class="lineno">  247</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  248</span>    <span class="comment">// Prints signature hex representation</span></div>
+<div class="line"><span class="lineno">  249</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#aada0803ef851d831b7a290a924e3c228">hashing::sha1::sig2hex</a>(sig3) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  250</span>    <span class="comment">// Test with cassert wether sig is correct from expected value</span></div>
+<div class="line"><span class="lineno">  251</span>    assert(hashing::sha1::sig2hex(sig3).<a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a>(</div>
+<div class="line"><span class="lineno">  252</span>               <span class="stringliteral">&quot;408d94384216f890ff7a0c3528e8bed1e0b01621&quot;</span>) == 0);</div>
+<div class="line"><span class="lineno">  253</span> </div>
+<div class="line"><span class="lineno">  254</span>    <span class="comment">// Hashes &quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789&quot;</span></div>
+<div class="line"><span class="lineno">  255</span>    <span class="comment">// and stores signature</span></div>
+<div class="line"><span class="lineno">  256</span>    <span class="keywordtype">void</span>* sig4 = <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#a2397f2444a05e4d1487c67e215410d3c">hashing::sha1::hash</a>(</div>
+<div class="line"><span class="lineno">  257</span>        <span class="stringliteral">&quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789&quot;</span>);</div>
+<div class="line"><span class="lineno">  258</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
+<div class="line"><span class="lineno">  259</span>        &lt;&lt; <span class="stringliteral">&quot;Hashing &quot;</span></div>
+<div class="line"><span class="lineno">  260</span>           <span class="stringliteral">&quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789&quot;</span></div>
+<div class="line"><span class="lineno">  261</span>        &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  262</span>    <span class="comment">// Prints signature hex representation</span></div>
+<div class="line"><span class="lineno">  263</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d8/d7a/sha1_8cpp.html#aada0803ef851d831b7a290a924e3c228">hashing::sha1::sig2hex</a>(sig4) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  264</span>    <span class="comment">// Test with cassert wether sig is correct from expected value</span></div>
+<div class="line"><span class="lineno">  265</span>    assert(hashing::sha1::sig2hex(sig4).<a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a>(</div>
+<div class="line"><span class="lineno">  266</span>               <span class="stringliteral">&quot;761c457bf73b14d27e9e9265c46f4b4dda11f940&quot;</span>) == 0);</div>
+<div class="line"><span class="lineno">  267</span>}</div>
 <div class="ttc" id="ashell__sort2_8cpp_html_a7eb77daed2cf1513f6d68c47a1c2db1c"><div class="ttname"><a href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a></div><div class="ttdeci">int compare(const void *a, const void *b)</div><div class="ttdef"><b>Definition:</b> shell_sort2.cpp:87</div></div>
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 Here is the call graph for this function:</div>
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 <div class="ttc" id="aclassoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list_html_a398d6cc927a2c8e4a156ae2806f48986"><div class="ttname"><a href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a398d6cc927a2c8e4a156ae2806f48986">operations_on_datastructures::circular_linked_list::CircularLinkedList::erase</a></div><div class="ttdeci">void erase()</div><div class="ttdef"><b>Definition:</b> circular_linked_list.cpp:126</div></div>
 <div class="ttc" id="aclassoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list_html_ac38565472a07d07f63ec0d2fd8a69d4d"><div class="ttname"><a href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ac38565472a07d07f63ec0d2fd8a69d4d">operations_on_datastructures::circular_linked_list::CircularLinkedList::insert</a></div><div class="ttdeci">void insert(const std::vector&lt; int64_t &gt; &amp;values)</div><div class="ttdoc">Inserts all the values from a vector into the Circular Linked List.</div><div class="ttdef"><b>Definition:</b> circular_linked_list.cpp:146</div></div>
 <div class="ttc" id="acopy_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/copy.html">std::copy</a></div><div class="ttdeci">T copy(T... args)</div></div>
@@ -277,12 +277,12 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>                                                             {</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>        <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a> = source.root;</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ab682f854f39582a20c9c4102f0482208">end</a> = source.end;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        source.root = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>        source.end = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   86</span>                                                             {</div>
+<div class="line"><span class="lineno">   87</span>        <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a> = source.root;</div>
+<div class="line"><span class="lineno">   88</span>        <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ab682f854f39582a20c9c4102f0482208">end</a> = source.end;</div>
+<div class="line"><span class="lineno">   89</span>        source.root = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">   90</span>        source.end = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">   91</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -310,7 +310,7 @@ Here is the call graph for this function:</div>
 </div><div class="memdoc">
 
 <p>Cleans up memory when destroyed. </p>
-<div class="fragment"><div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>{ <a class="code hl_function" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a398d6cc927a2c8e4a156ae2806f48986">erase</a>(); }</div>
+<div class="fragment"><div class="line"><span class="lineno">  122</span>{ <a class="code hl_function" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a398d6cc927a2c8e4a156ae2806f48986">erase</a>(); }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -344,19 +344,19 @@ Here is the call graph for this function:</div>
 </table>
 </div><div class="memdoc">
 <p >Iteratively frees each node in the Circular Linked List from the heap </p>
-<div class="fragment"><div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>                 {</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a> == <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>            <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>        }</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>* <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>;</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>        <span class="keywordflow">do</span> {</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>            <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>* temp = <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;next;</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>            <span class="keyword">delete</span> (temp);</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>        } <span class="keywordflow">while</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a> != <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>);</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>        <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a> = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ab682f854f39582a20c9c4102f0482208">end</a> = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  126</span>                 {</div>
+<div class="line"><span class="lineno">  127</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a> == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  128</span>            <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  129</span>        }</div>
+<div class="line"><span class="lineno">  130</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>* <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>;</div>
+<div class="line"><span class="lineno">  131</span>        <span class="keywordflow">do</span> {</div>
+<div class="line"><span class="lineno">  132</span>            <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>* temp = <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
+<div class="line"><span class="lineno">  133</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;next;</div>
+<div class="line"><span class="lineno">  134</span>            <span class="keyword">delete</span> (temp);</div>
+<div class="line"><span class="lineno">  135</span>        } <span class="keywordflow">while</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a> != <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>);</div>
+<div class="line"><span class="lineno">  136</span>        <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a> = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  137</span>        <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ab682f854f39582a20c9c4102f0482208">end</a> = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  138</span>    }</div>
 <div class="ttc" id="ahash__search_8cpp_html_a8ca8dcb494104d273679e219e53d0555"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a></div><div class="ttdeci">struct list node</div></div>
 </div><!-- fragment -->
 </div>
@@ -393,11 +393,11 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>                                                  {</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>        <span class="keywordflow">for</span> (int64_t value : <a class="code hl_function" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a53611ec1fef92eeeb875aea1bde1e4de">values</a>) {</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>            <a class="code hl_function" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ac38565472a07d07f63ec0d2fd8a69d4d">insert</a>(value);</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>        }</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  146</span>                                                  {</div>
+<div class="line"><span class="lineno">  147</span>        <span class="keywordflow">for</span> (int64_t value : <a class="code hl_function" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a53611ec1fef92eeeb875aea1bde1e4de">values</a>) {</div>
+<div class="line"><span class="lineno">  148</span>            <a class="code hl_function" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ac38565472a07d07f63ec0d2fd8a69d4d">insert</a>(value);</div>
+<div class="line"><span class="lineno">  149</span>        }</div>
+<div class="line"><span class="lineno">  150</span>    }</div>
 <div class="ttc" id="aclassoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list_html_a53611ec1fef92eeeb875aea1bde1e4de"><div class="ttname"><a href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a53611ec1fef92eeeb875aea1bde1e4de">operations_on_datastructures::circular_linked_list::CircularLinkedList::values</a></div><div class="ttdeci">std::vector&lt; int64_t &gt; values()</div><div class="ttdoc">Returns a std::vector of the values of the Circular Linked List.</div><div class="ttdef"><b>Definition:</b> circular_linked_list.cpp:214</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -440,10 +440,10 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>                              {</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>* <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>);</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>        <a class="code hl_function" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ac38565472a07d07f63ec0d2fd8a69d4d">insert</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>);</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  158</span>                              {</div>
+<div class="line"><span class="lineno">  159</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>* <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>);</div>
+<div class="line"><span class="lineno">  160</span>        <a class="code hl_function" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ac38565472a07d07f63ec0d2fd8a69d4d">insert</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>);</div>
+<div class="line"><span class="lineno">  161</span>    }</div>
 <div class="ttc" id="ahash__search_8cpp_html_a6e1a77282bc65ad359d753d25df23243"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a></div><div class="ttdeci">int data[MAX]</div><div class="ttdoc">test data</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:24</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -492,17 +492,17 @@ Here is the call graph for this function:</div>
 <p >&lt; Append node to the end</p>
 <p >&lt; Set the next value to the root</p>
 <p >&lt; Make end point to node</p>
-<div class="fragment"><div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>                            {</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a> == <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>            <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a> = <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;        <span class="comment">///&lt; Set node as the root</span></div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;next = <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>;  <span class="comment">///&lt; Point node to itself</span></div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>            <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ab682f854f39582a20c9c4102f0482208">end</a> = <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>;         <span class="comment">///&lt; Set the end to the root</span></div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>            <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ab682f854f39582a20c9c4102f0482208">end</a>-&gt;<a class="code hl_variable" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html#a7c867b8e1034a6f5da490c8b8c09cb77">next</a> = <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;   <span class="comment">///&lt; Append node to the end</span></div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;next = <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>;  <span class="comment">///&lt; Set the next value to the root</span></div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>            <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ab682f854f39582a20c9c4102f0482208">end</a> = <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;         <span class="comment">///&lt; Make end point to node</span></div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>        }</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  169</span>                            {</div>
+<div class="line"><span class="lineno">  170</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a> == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  171</span>            <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a> = <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;        <span class="comment">///&lt; Set node as the root</span></div>
+<div class="line"><span class="lineno">  172</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;next = <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>;  <span class="comment">///&lt; Point node to itself</span></div>
+<div class="line"><span class="lineno">  173</span>            <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ab682f854f39582a20c9c4102f0482208">end</a> = <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>;         <span class="comment">///&lt; Set the end to the root</span></div>
+<div class="line"><span class="lineno">  174</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  175</span>            <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ab682f854f39582a20c9c4102f0482208">end</a>-&gt;<a class="code hl_variable" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html#a7c867b8e1034a6f5da490c8b8c09cb77">next</a> = <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;   <span class="comment">///&lt; Append node to the end</span></div>
+<div class="line"><span class="lineno">  176</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;next = <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>;  <span class="comment">///&lt; Set the next value to the root</span></div>
+<div class="line"><span class="lineno">  177</span>            <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ab682f854f39582a20c9c4102f0482208">end</a> = <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;         <span class="comment">///&lt; Make end point to node</span></div>
+<div class="line"><span class="lineno">  178</span>        }</div>
+<div class="line"><span class="lineno">  179</span>    }</div>
 <div class="ttc" id="astructoperations__on__datastructures_1_1circular__linked__list_1_1_node_html_a7c867b8e1034a6f5da490c8b8c09cb77"><div class="ttname"><a href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html#a7c867b8e1034a6f5da490c8b8c09cb77">operations_on_datastructures::circular_linked_list::Node::next</a></div><div class="ttdeci">Node * next</div><div class="ttdoc">The Node's successor.</div><div class="ttdef"><b>Definition:</b> circular_linked_list.cpp:34</div></div>
 </div><!-- fragment -->
 </div>
@@ -539,13 +539,13 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>Reference to <a class="el" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html" title="A class that implements a Circular Linked List.">CircularLinkedList</a> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>                                                                       {</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a> = other.root;</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>        <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ab682f854f39582a20c9c4102f0482208">end</a> = other.end;</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>        other.root = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>        other.end = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  112</span>                                                                       {</div>
+<div class="line"><span class="lineno">  113</span>        <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a> = other.root;</div>
+<div class="line"><span class="lineno">  114</span>        <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ab682f854f39582a20c9c4102f0482208">end</a> = other.end;</div>
+<div class="line"><span class="lineno">  115</span>        other.root = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  116</span>        other.end = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  117</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  118</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -581,16 +581,16 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>Reference to <a class="el" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html" title="A class that implements a Circular Linked List.">CircularLinkedList</a> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>                                                                   {</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>        <a class="code hl_function" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a398d6cc927a2c8e4a156ae2806f48986">erase</a>();</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>        <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a> = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>* <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = other.root;</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>        <span class="keywordflow">while</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a> != <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>            <a class="code hl_function" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ac38565472a07d07f63ec0d2fd8a69d4d">insert</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;data);</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;next;</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>        }</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   97</span>                                                                   {</div>
+<div class="line"><span class="lineno">   98</span>        <a class="code hl_function" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a398d6cc927a2c8e4a156ae2806f48986">erase</a>();</div>
+<div class="line"><span class="lineno">   99</span>        <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a> = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  100</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>* <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = other.root;</div>
+<div class="line"><span class="lineno">  101</span>        <span class="keywordflow">while</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a> != <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  102</span>            <a class="code hl_function" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ac38565472a07d07f63ec0d2fd8a69d4d">insert</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;data);</div>
+<div class="line"><span class="lineno">  103</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;next;</div>
+<div class="line"><span class="lineno">  104</span>        }</div>
+<div class="line"><span class="lineno">  105</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  106</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -625,7 +625,7 @@ Here is the call graph for this function:</div>
 
 <p>Prints the values of the Circular Linked List, beginning from the root <a class="el" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html" title="A Node struct that represents a single Node in a Binary Tree.">Node</a>. </p>
 <p >Goes through each <a class="el" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html" title="A Node struct that represents a single Node in a Binary Tree.">Node</a> from the root and prints them out in order </p><dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>{ <a class="code hl_function" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ac341901e926b3fa3a796c64ca572f592">print</a>(<a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>); }</div>
+<div class="fragment"><div class="line"><span class="lineno">  187</span>{ <a class="code hl_function" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ac341901e926b3fa3a796c64ca572f592">print</a>(<a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>); }</div>
 <div class="ttc" id="aclassoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list_html_ac341901e926b3fa3a796c64ca572f592"><div class="ttname"><a href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#ac341901e926b3fa3a796c64ca572f592">operations_on_datastructures::circular_linked_list::CircularLinkedList::print</a></div><div class="ttdeci">void print()</div><div class="ttdoc">Prints the values of the Circular Linked List, beginning from the root Node.</div><div class="ttdef"><b>Definition:</b> circular_linked_list.cpp:187</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -668,18 +668,18 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>                           {</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>* temp = <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>;</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a> == <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Empty List!\n&quot;</span>;</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>            <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>        }</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>        <span class="keywordflow">do</span> {</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; temp-&gt;data &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>            temp = temp-&gt;next;</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>        } <span class="keywordflow">while</span> (temp != <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>);</div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  196</span>                           {</div>
+<div class="line"><span class="lineno">  197</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>* temp = <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>;</div>
+<div class="line"><span class="lineno">  198</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a> == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  199</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Empty List!\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  200</span>            <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  201</span>        }</div>
+<div class="line"><span class="lineno">  202</span>        <span class="keywordflow">do</span> {</div>
+<div class="line"><span class="lineno">  203</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; temp-&gt;data &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">  204</span>            temp = temp-&gt;next;</div>
+<div class="line"><span class="lineno">  205</span>        } <span class="keywordflow">while</span> (temp != <a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>);</div>
+<div class="line"><span class="lineno">  206</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  207</span>    }</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 </div><!-- fragment -->
 </div>
@@ -709,7 +709,7 @@ Here is the call graph for this function:</div>
 
 <p>Returns a <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> of the values of the Circular Linked List. </p>
 <p >Starting from the root <a class="el" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html" title="A Node struct that represents a single Node in a Binary Tree.">Node</a>, appends each value of the list to a <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> and returns it </p><dl class="section return"><dt>Returns</dt><dd>A <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> of the list's values </dd></dl>
-<div class="fragment"><div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a53611ec1fef92eeeb875aea1bde1e4de">values</a>(<a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>); }</div>
+<div class="fragment"><div class="line"><span class="lineno">  214</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a53611ec1fef92eeeb875aea1bde1e4de">values</a>(<a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a>); }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -752,20 +752,20 @@ Here is the call graph for this function:</div>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>A <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> of the list's values </dd></dl>
 <p >&lt; Return empty vector</p>
-<div class="fragment"><div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>                                          {</div>
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-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html#a5d5cebd6bc906c60763fc6be10cfdd13">root</a> == <span class="keyword">nullptr</span>) {</div>
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+<p>Functions for the [From the right, set the Kth bit in the binary representation of N] (<a href="https://practice.geeksforgeeks.org/problems/set-kth-bit3724/1/">https://practice.geeksforgeeks.org/problems/set-kth-bit3724/1/</a>) implementation.  
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-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;hash of &quot;</span> &lt;&lt; key &lt;&lt; <span class="stringliteral">&quot; is &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a4bde7a47f98dd1ad24c84038e2608527">hashFxn</a>(key) &lt;&lt; <span class="stringliteral">&quot; % &quot;</span></div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>              &lt;&lt; totalSize &lt;&lt; <span class="stringliteral">&quot; == &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a4bde7a47f98dd1ad24c84038e2608527">hashFxn</a>(key) % totalSize;</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>    <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a16d34fd3511626a83ab00665d7bc34d1">add</a>(key);</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;New table: &quot;</span>;</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>    <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#ad87b71d810901fab69c4ad9d4d0fa635">display</a>();</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  186</span>                      {</div>
+<div class="line"><span class="lineno">  187</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initial table: &quot;</span>;</div>
+<div class="line"><span class="lineno">  188</span>    <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#ad87b71d810901fab69c4ad9d4d0fa635">display</a>();</div>
+<div class="line"><span class="lineno">  189</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  190</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;hash of &quot;</span> &lt;&lt; key &lt;&lt; <span class="stringliteral">&quot; is &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a4bde7a47f98dd1ad24c84038e2608527">hashFxn</a>(key) &lt;&lt; <span class="stringliteral">&quot; % &quot;</span></div>
+<div class="line"><span class="lineno">  191</span>              &lt;&lt; totalSize &lt;&lt; <span class="stringliteral">&quot; == &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a4bde7a47f98dd1ad24c84038e2608527">hashFxn</a>(key) % totalSize;</div>
+<div class="line"><span class="lineno">  192</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  193</span>    <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a16d34fd3511626a83ab00665d7bc34d1">add</a>(key);</div>
+<div class="line"><span class="lineno">  194</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;New table: &quot;</span>;</div>
+<div class="line"><span class="lineno">  195</span>    <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#ad87b71d810901fab69c4ad9d4d0fa635">display</a>();</div>
+<div class="line"><span class="lineno">  196</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
 <div class="ttc" id="anamespacelinear__probing_html_a16d34fd3511626a83ab00665d7bc34d1"><div class="ttname"><a href="../../d8/d89/namespacelinear__probing.html#a16d34fd3511626a83ab00665d7bc34d1">linear_probing::add</a></div><div class="ttdeci">void add(int key)</div><div class="ttdef"><b>Definition:</b> linear_probing_hash_table.cpp:161</div></div>
@@ -262,20 +262,20 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Function to displays the table </p><dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
-<div class="fragment"><div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>               {</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; totalSize; i++) {</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>        <span class="keywordflow">if</span> (table[i].key == notPresent) {</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; Empty &quot;</span>;</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (table[i].key == tomb) {</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; Tomb &quot;</span>;</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; table[i].key;</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>        }</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    }</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  120</span>               {</div>
+<div class="line"><span class="lineno">  121</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; totalSize; i++) {</div>
+<div class="line"><span class="lineno">  122</span>        <span class="keywordflow">if</span> (table[i].key == notPresent) {</div>
+<div class="line"><span class="lineno">  123</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; Empty &quot;</span>;</div>
+<div class="line"><span class="lineno">  124</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (table[i].key == tomb) {</div>
+<div class="line"><span class="lineno">  125</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; Tomb &quot;</span>;</div>
+<div class="line"><span class="lineno">  126</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  127</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">  128</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; table[i].key;</div>
+<div class="line"><span class="lineno">  129</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">  130</span>        }</div>
+<div class="line"><span class="lineno">  131</span>    }</div>
+<div class="line"><span class="lineno">  132</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  133</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -309,10 +309,10 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>hash value of the key </dd></dl>
-<div class="fragment"><div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>                        {</div>
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-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <span class="keywordflow">return</span> hash(key);</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   46</span>                        {</div>
+<div class="line"><span class="lineno">   47</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/hash.html">std::hash&lt;int&gt;</a> hash;</div>
+<div class="line"><span class="lineno">   48</span>    <span class="keywordflow">return</span> hash(key);</div>
+<div class="line"><span class="lineno">   49</span>}</div>
 <div class="ttc" id="ahash_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/hash.html">std::hash</a></div></div>
 </div><!-- fragment -->
 </div>
@@ -349,43 +349,43 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>hash value of the key </dd></dl>
-<div class="fragment"><div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>                                         {</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    <span class="keywordtype">int</span> hash = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(<a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a4bde7a47f98dd1ad24c84038e2608527">hashFxn</a>(key));</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    <span class="keywordtype">int</span> i = 0;</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <a class="code hl_struct" href="../../db/d19/structlinear__probing_1_1_entry.html">Entry</a> entry;</div>
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-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        entry = table[index];</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        <span class="keywordflow">if</span> (searching) {</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>            <span class="keywordflow">if</span> (entry.<a class="code hl_variable" href="../../db/d19/structlinear__probing_1_1_entry.html#a4d84e90b73022083761f85f8586c4c2a">key</a> == notPresent) {</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>                <span class="keywordflow">return</span> notPresent;</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>            }</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>            <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a942fc8407b8001890ea26830cdcd9d77">searchingProber</a>(entry, key)) {</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Found key!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>                }</div>
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-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>            i++;</div>
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+<div class="fragment"><div class="line"><span class="lineno">   55</span>                                         {</div>
+<div class="line"><span class="lineno">   56</span>    <span class="keywordtype">int</span> hash = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(<a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a4bde7a47f98dd1ad24c84038e2608527">hashFxn</a>(key));</div>
+<div class="line"><span class="lineno">   57</span>    <span class="keywordtype">int</span> i = 0;</div>
+<div class="line"><span class="lineno">   58</span>    <a class="code hl_struct" href="../../db/d19/structlinear__probing_1_1_entry.html">Entry</a> entry;</div>
+<div class="line"><span class="lineno">   59</span>    <span class="keywordflow">do</span> {</div>
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+<div class="line"><span class="lineno">   61</span>        entry = table[index];</div>
+<div class="line"><span class="lineno">   62</span>        <span class="keywordflow">if</span> (searching) {</div>
+<div class="line"><span class="lineno">   63</span>            <span class="keywordflow">if</span> (entry.<a class="code hl_variable" href="../../db/d19/structlinear__probing_1_1_entry.html#a4d84e90b73022083761f85f8586c4c2a">key</a> == notPresent) {</div>
+<div class="line"><span class="lineno">   64</span>                <span class="keywordflow">return</span> notPresent;</div>
+<div class="line"><span class="lineno">   65</span>            }</div>
+<div class="line"><span class="lineno">   66</span>            <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a942fc8407b8001890ea26830cdcd9d77">searchingProber</a>(entry, key)) {</div>
+<div class="line"><span class="lineno">   67</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Found key!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   68</span>                <span class="keywordflow">return</span> index;</div>
+<div class="line"><span class="lineno">   69</span>            }</div>
+<div class="line"><span class="lineno">   70</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Found tombstone or equal hash, checking next&quot;</span></div>
+<div class="line"><span class="lineno">   71</span>                      &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   72</span>            i++;</div>
+<div class="line"><span class="lineno">   73</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   74</span>            <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a75d779938df7ebc68581d922b60a2541">putProber</a>(entry, key)) {</div>
+<div class="line"><span class="lineno">   75</span>                <span class="keywordflow">if</span> (!rehashing) {</div>
+<div class="line"><span class="lineno">   76</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Spot found!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   77</span>                }</div>
+<div class="line"><span class="lineno">   78</span>                <span class="keywordflow">return</span> index;</div>
+<div class="line"><span class="lineno">   79</span>            }</div>
+<div class="line"><span class="lineno">   80</span>            <span class="keywordflow">if</span> (!rehashing) {</div>
+<div class="line"><span class="lineno">   81</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Spot taken, looking at next&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   82</span>            }</div>
+<div class="line"><span class="lineno">   83</span>            i++;</div>
+<div class="line"><span class="lineno">   84</span>        }</div>
+<div class="line"><span class="lineno">   85</span>        <span class="keywordflow">if</span> (i == totalSize) {</div>
+<div class="line"><span class="lineno">   86</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Linear probe failed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   87</span>            <span class="keywordflow">return</span> notPresent;</div>
+<div class="line"><span class="lineno">   88</span>        }</div>
+<div class="line"><span class="lineno">   89</span>    } <span class="keywordflow">while</span> (entry.<a class="code hl_variable" href="../../db/d19/structlinear__probing_1_1_entry.html#a4d84e90b73022083761f85f8586c4c2a">key</a> != notPresent);</div>
+<div class="line"><span class="lineno">   90</span>    <span class="keywordflow">return</span> notPresent;</div>
+<div class="line"><span class="lineno">   91</span>}</div>
 <div class="ttc" id="anamespacelinear__probing_html_a75d779938df7ebc68581d922b60a2541"><div class="ttname"><a href="../../d8/d89/namespacelinear__probing.html#a75d779938df7ebc68581d922b60a2541">linear_probing::putProber</a></div><div class="ttdeci">bool putProber(const Entry &amp;entry, int key)</div><div class="ttdef"><b>Definition:</b> linear_probing_hash_table.cpp:98</div></div>
 <div class="ttc" id="anamespacelinear__probing_html_a942fc8407b8001890ea26830cdcd9d77"><div class="ttname"><a href="../../d8/d89/namespacelinear__probing.html#a942fc8407b8001890ea26830cdcd9d77">linear_probing::searchingProber</a></div><div class="ttdeci">bool searchingProber(const Entry &amp;entry, int key)</div><div class="ttdef"><b>Definition:</b> linear_probing_hash_table.cpp:110</div></div>
 <div class="ttc" id="astructlinear__probing_1_1_entry_html"><div class="ttname"><a href="../../db/d19/structlinear__probing_1_1_entry.html">linear_probing::Entry</a></div><div class="ttdef"><b>Definition:</b> linear_probing_hash_table.cpp:35</div></div>
@@ -432,12 +432,12 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>hash value of the key </dd></dl>
-<div class="fragment"><div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>                                            {</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>    <span class="keywordflow">if</span> (entry.<a class="code hl_variable" href="../../db/d19/structlinear__probing_1_1_entry.html#a4d84e90b73022083761f85f8586c4c2a">key</a> == notPresent || entry.<a class="code hl_variable" href="../../db/d19/structlinear__probing_1_1_entry.html#a4d84e90b73022083761f85f8586c4c2a">key</a> == tomb) {</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    }</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   98</span>                                            {</div>
+<div class="line"><span class="lineno">   99</span>    <span class="keywordflow">if</span> (entry.<a class="code hl_variable" href="../../db/d19/structlinear__probing_1_1_entry.html#a4d84e90b73022083761f85f8586c4c2a">key</a> == notPresent || entry.<a class="code hl_variable" href="../../db/d19/structlinear__probing_1_1_entry.html#a4d84e90b73022083761f85f8586c4c2a">key</a> == tomb) {</div>
+<div class="line"><span class="lineno">  100</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  101</span>    }</div>
+<div class="line"><span class="lineno">  102</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  103</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -456,25 +456,25 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Rehashes the table into a bigger table </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
-<div class="fragment"><div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>              {</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>    <span class="comment">// Necessary so wall of add info isn&#39;t printed all at once</span></div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>    rehashing = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    <span class="keywordtype">int</span> oldSize = totalSize;</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Entry&gt;</a> oldTable(table);</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    <span class="comment">// Really this should use the next prime number greater than totalSize *</span></div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    <span class="comment">// 2</span></div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    totalSize *= 2;</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    table = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Entry&gt;</a>(totalSize);</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; oldSize; i++) {</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>        <span class="keywordflow">if</span> (oldTable[i].key != -1 &amp;&amp; oldTable[i].key != notPresent) {</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>            size--;  <span class="comment">// Size stays the same (add increments size)</span></div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>            <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a16d34fd3511626a83ab00665d7bc34d1">add</a>(oldTable[i].key);</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>        }</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>    }</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>    <span class="comment">// delete[] oldTable;</span></div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>    rehashing = <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Table was rehashed, new size is: &quot;</span> &lt;&lt; totalSize &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  138</span>              {</div>
+<div class="line"><span class="lineno">  139</span>    <span class="comment">// Necessary so wall of add info isn&#39;t printed all at once</span></div>
+<div class="line"><span class="lineno">  140</span>    rehashing = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  141</span>    <span class="keywordtype">int</span> oldSize = totalSize;</div>
+<div class="line"><span class="lineno">  142</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Entry&gt;</a> oldTable(table);</div>
+<div class="line"><span class="lineno">  143</span>    <span class="comment">// Really this should use the next prime number greater than totalSize *</span></div>
+<div class="line"><span class="lineno">  144</span>    <span class="comment">// 2</span></div>
+<div class="line"><span class="lineno">  145</span>    totalSize *= 2;</div>
+<div class="line"><span class="lineno">  146</span>    table = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Entry&gt;</a>(totalSize);</div>
+<div class="line"><span class="lineno">  147</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; oldSize; i++) {</div>
+<div class="line"><span class="lineno">  148</span>        <span class="keywordflow">if</span> (oldTable[i].key != -1 &amp;&amp; oldTable[i].key != notPresent) {</div>
+<div class="line"><span class="lineno">  149</span>            size--;  <span class="comment">// Size stays the same (add increments size)</span></div>
+<div class="line"><span class="lineno">  150</span>            <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a16d34fd3511626a83ab00665d7bc34d1">add</a>(oldTable[i].key);</div>
+<div class="line"><span class="lineno">  151</span>        }</div>
+<div class="line"><span class="lineno">  152</span>    }</div>
+<div class="line"><span class="lineno">  153</span>    <span class="comment">// delete[] oldTable;</span></div>
+<div class="line"><span class="lineno">  154</span>    rehashing = <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  155</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Table was rehashed, new size is: &quot;</span> &lt;&lt; totalSize &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  156</span>}</div>
 <div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -506,17 +506,17 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>                          {</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initial table: &quot;</span>;</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>    <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#ad87b71d810901fab69c4ad9d4d0fa635">display</a>();</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;hash of &quot;</span> &lt;&lt; key &lt;&lt; <span class="stringliteral">&quot; is &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a4bde7a47f98dd1ad24c84038e2608527">hashFxn</a>(key) &lt;&lt; <span class="stringliteral">&quot; % &quot;</span></div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>              &lt;&lt; totalSize &lt;&lt; <span class="stringliteral">&quot; == &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a4bde7a47f98dd1ad24c84038e2608527">hashFxn</a>(key) % totalSize;</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#abcf8d033f8115f39f3c93cfb6cee0b28">remove</a>(key);</div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;New table: &quot;</span>;</div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>    <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#ad87b71d810901fab69c4ad9d4d0fa635">display</a>();</div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  201</span>                          {</div>
+<div class="line"><span class="lineno">  202</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initial table: &quot;</span>;</div>
+<div class="line"><span class="lineno">  203</span>    <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#ad87b71d810901fab69c4ad9d4d0fa635">display</a>();</div>
+<div class="line"><span class="lineno">  204</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  205</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;hash of &quot;</span> &lt;&lt; key &lt;&lt; <span class="stringliteral">&quot; is &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a4bde7a47f98dd1ad24c84038e2608527">hashFxn</a>(key) &lt;&lt; <span class="stringliteral">&quot; % &quot;</span></div>
+<div class="line"><span class="lineno">  206</span>              &lt;&lt; totalSize &lt;&lt; <span class="stringliteral">&quot; == &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#a4bde7a47f98dd1ad24c84038e2608527">hashFxn</a>(key) % totalSize;</div>
+<div class="line"><span class="lineno">  207</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  208</span>    <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#abcf8d033f8115f39f3c93cfb6cee0b28">remove</a>(key);</div>
+<div class="line"><span class="lineno">  209</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;New table: &quot;</span>;</div>
+<div class="line"><span class="lineno">  210</span>    <a class="code hl_function" href="../../d8/d89/namespacelinear__probing.html#ad87b71d810901fab69c4ad9d4d0fa635">display</a>();</div>
+<div class="line"><span class="lineno">  211</span>}</div>
 <div class="ttc" id="anamespacelinear__probing_html_abcf8d033f8115f39f3c93cfb6cee0b28"><div class="ttname"><a href="../../d8/d89/namespacelinear__probing.html#abcf8d033f8115f39f3c93cfb6cee0b28">linear_probing::remove</a></div><div class="ttdeci">void remove(int key)</div><div class="ttdef"><b>Definition:</b> linear_probing_hash_table.cpp:173</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -548,15 +548,15 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>                     {</div>
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+<div class="line"><span class="lineno">   77</span>    assert(struzik_search&lt;int&gt;(sorted_array, 7, 0) == <span class="keyword">nullptr</span>);</div>
+<div class="line"><span class="lineno">   78</span>    assert(struzik_search&lt;int&gt;(sorted_array, 7, 1000) == <span class="keyword">nullptr</span>);</div>
+<div class="line"><span class="lineno">   79</span>    assert(struzik_search&lt;int&gt;(sorted_array, 7, 50) == <span class="keyword">nullptr</span>);</div>
+<div class="line"><span class="lineno">   80</span>    assert(struzik_search&lt;int&gt;(sorted_array, 7, 7) == sorted_array);</div>
+<div class="line"><span class="lineno">   81</span>    <span class="comment">// TEST CASES</span></div>
+<div class="line"><span class="lineno">   82</span>    <span class="keyword">delete</span>[] sorted_array;</div>
+<div class="line"><span class="lineno">   83</span>    <span class="keywordflow">return</span> 0;</div>
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+<div class="line"><span class="lineno">   60</span>    uint32_t block_front(0), block_size = size == 0 ? 0 : 1;</div>
+<div class="line"><span class="lineno">   61</span>    <span class="keywordflow">while</span> (block_front != block_size) {</div>
+<div class="line"><span class="lineno">   62</span>        <span class="keywordflow">if</span> (*(array + block_size - 1) &lt; key) {</div>
+<div class="line"><span class="lineno">   63</span>            block_front = block_size;</div>
+<div class="line"><span class="lineno">   64</span>            (block_size * 2 - 1 &lt; size) ? (block_size *= 2) : block_size = size;</div>
+<div class="line"><span class="lineno">   65</span>            <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno">   66</span>        }</div>
+<div class="line"><span class="lineno">   67</span>        <span class="keywordflow">return</span> binary_s&lt;Type&gt;(array + block_front, (block_size - block_front),</div>
+<div class="line"><span class="lineno">   68</span>                              key);</div>
+<div class="line"><span class="lineno">   69</span>    }</div>
+<div class="line"><span class="lineno">   70</span>    <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">   71</span>}</div>
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-<p>Iterative version of Preorder, Postorder, and preorder <a href="https://en.wikipedia.org/wiki/Tree_traversal" target="_blank">Traversal of the Tree</a>  
+<p>Iterative version of Preorder, Postorder, and preorder [Traversal of the Tree] (<a href="https://en.wikipedia.org/wiki/Tree_traversal">https://en.wikipedia.org/wiki/Tree_traversal</a>)  
 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
 <code>#include &lt;cassert&gt;</code><br />
@@ -155,7 +155,7 @@ Functions</h2></td></tr>
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 </table>
 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
-<div class="textblock"><p >Iterative version of Preorder, Postorder, and preorder <a href="https://en.wikipedia.org/wiki/Tree_traversal" target="_blank">Traversal of the Tree</a> </p>
+<div class="textblock"><p >Iterative version of Preorder, Postorder, and preorder [Traversal of the Tree] (<a href="https://en.wikipedia.org/wiki/Tree_traversal">https://en.wikipedia.org/wiki/Tree_traversal</a>) </p>
 <dl class="section author"><dt>Author</dt><dd><a href="https://github.com/motasimmakki" target="_blank">Motasim</a></dd></dl>
 <h3><a class="anchor" id="autotoc_md91"></a>
 Iterative Preorder Traversal of a tree</h3>
@@ -186,57 +186,58 @@ Iterative Inorder Traversal of a tree</h3>
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
 <p >&lt; instace of BinaryTree, used to access its members functions.</p>
-<div class="fragment"><div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span>           {</div>
-<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span>    <span class="comment">// Creating a tree with the following structure,</span></div>
-<div class="line"><a id="l00355" name="l00355"></a><span class="lineno">  355</span>    <span class="comment">/*</span></div>
-<div class="line"><a id="l00356" name="l00356"></a><span class="lineno">  356</span><span class="comment">              1</span></div>
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-<div class="line"><a id="l00358" name="l00358"></a><span class="lineno">  358</span><span class="comment">           2     3</span></div>
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-<div class="line"><a id="l00360" name="l00360"></a><span class="lineno">  360</span><span class="comment">        4     5</span></div>
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-<div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span> </div>
-<div class="line"><a id="l00363" name="l00363"></a><span class="lineno">  363</span>    <a class="code hl_class" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html">others::iterative_tree_traversals::BinaryTree</a></div>
-<div class="line"><a id="l00364" name="l00364"></a><span class="lineno">  364</span>        binaryTree;  <span class="comment">///&lt; instace of BinaryTree, used to access its members</span><span class="comment"></span></div>
-<div class="line"><a id="l00365" name="l00365"></a><span class="lineno">  365</span><span class="comment">                     ///&lt; functions.</span></div>
-<div class="line"><a id="l00366" name="l00366"></a><span class="lineno">  366</span><span class="comment"></span>    <a class="code hl_struct" href="../../d2/d9a/structothers_1_1iterative__tree__traversals_1_1_node.html">others::iterative_tree_traversals::Node</a> *root = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a3078a5ccf45d6a7031dcf46e43de65b6">createNewNode</a>(1);</div>
-<div class="line"><a id="l00367" name="l00367"></a><span class="lineno">  367</span>    root-&gt;left = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a3078a5ccf45d6a7031dcf46e43de65b6">createNewNode</a>(2);</div>
-<div class="line"><a id="l00368" name="l00368"></a><span class="lineno">  368</span>    root-&gt;right = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a3078a5ccf45d6a7031dcf46e43de65b6">createNewNode</a>(3);</div>
-<div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span>    root-&gt;left-&gt;left = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a3078a5ccf45d6a7031dcf46e43de65b6">createNewNode</a>(4);</div>
-<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span>    root-&gt;left-&gt;right = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a3078a5ccf45d6a7031dcf46e43de65b6">createNewNode</a>(5);</div>
-<div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span> </div>
-<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n| Tests for positive data value |&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>    <a class="code hl_function" href="../../d8/d90/iterative__tree__traversals_8cpp.html#a21d922dbb5905993960c6a7f0ba71ac0">test1</a>(binaryTree, root);  <span class="comment">// run preorder-iterative test</span></div>
-<div class="line"><a id="l00374" name="l00374"></a><span class="lineno">  374</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPre-order test Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00375" name="l00375"></a><span class="lineno">  375</span> </div>
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-<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPost-order test Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span> </div>
-<div class="line"><a id="l00379" name="l00379"></a><span class="lineno">  379</span>    <a class="code hl_function" href="../../d8/d90/iterative__tree__traversals_8cpp.html#a425c4c8520991999ee6dbe13d99b87f4">test3</a>(binaryTree, root);  <span class="comment">// run inorder-iterative test</span></div>
-<div class="line"><a id="l00380" name="l00380"></a><span class="lineno">  380</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nIn-order test Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00381" name="l00381"></a><span class="lineno">  381</span> </div>
-<div class="line"><a id="l00382" name="l00382"></a><span class="lineno">  382</span>    <span class="comment">// Modifying tree for negative values.</span></div>
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-<div class="line"><a id="l00384" name="l00384"></a><span class="lineno">  384</span>    root-&gt;left-&gt;data = -2;</div>
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-<div class="line"><a id="l00387" name="l00387"></a><span class="lineno">  387</span>    root-&gt;left-&gt;right-&gt;data = -5;</div>
-<div class="line"><a id="l00388" name="l00388"></a><span class="lineno">  388</span> </div>
-<div class="line"><a id="l00389" name="l00389"></a><span class="lineno">  389</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n| Tests for negative data values |&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00390" name="l00390"></a><span class="lineno">  390</span>    <a class="code hl_function" href="../../d8/d90/iterative__tree__traversals_8cpp.html#a038b236fe900f7bb7e57164f5bed66c2">test4</a>(binaryTree, root);  <span class="comment">// run preorder-iterative test on negative values</span></div>
-<div class="line"><a id="l00391" name="l00391"></a><span class="lineno">  391</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPre-order test on-negative value Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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-<div class="line"><a id="l00394" name="l00394"></a><span class="lineno">  394</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPost-order test on-negative value Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><span class="lineno">  358</span><span class="comment">           2     3</span></div>
+<div class="line"><span class="lineno">  359</span><span class="comment">         /   \</span></div>
+<div class="line"><span class="lineno">  360</span><span class="comment">        4     5</span></div>
+<div class="line"><span class="lineno">  361</span><span class="comment">    */</span></div>
+<div class="line"><span class="lineno">  362</span> </div>
+<div class="line"><span class="lineno">  363</span>    <a class="code hl_class" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html">others::iterative_tree_traversals::BinaryTree</a></div>
+<div class="line"><span class="lineno">  364</span>        binaryTree;  <span class="comment">///&lt; instace of BinaryTree, used to access its members</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  365</span><span class="comment">                     ///&lt; functions.</span></div>
+<div class="line"><span class="lineno">  366</span><span class="comment"></span>    <a class="code hl_struct" href="../../d2/d9a/structothers_1_1iterative__tree__traversals_1_1_node.html">others::iterative_tree_traversals::Node</a> *root = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a3078a5ccf45d6a7031dcf46e43de65b6">createNewNode</a>(1);</div>
+<div class="line"><span class="lineno">  367</span>    root-&gt;left = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a3078a5ccf45d6a7031dcf46e43de65b6">createNewNode</a>(2);</div>
+<div class="line"><span class="lineno">  368</span>    root-&gt;right = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a3078a5ccf45d6a7031dcf46e43de65b6">createNewNode</a>(3);</div>
+<div class="line"><span class="lineno">  369</span>    root-&gt;left-&gt;left = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a3078a5ccf45d6a7031dcf46e43de65b6">createNewNode</a>(4);</div>
+<div class="line"><span class="lineno">  370</span>    root-&gt;left-&gt;right = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a3078a5ccf45d6a7031dcf46e43de65b6">createNewNode</a>(5);</div>
+<div class="line"><span class="lineno">  371</span> </div>
+<div class="line"><span class="lineno">  372</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n| Tests for positive data value |&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  373</span>    <a class="code hl_function" href="../../d8/d90/iterative__tree__traversals_8cpp.html#a21d922dbb5905993960c6a7f0ba71ac0">test1</a>(binaryTree, root);  <span class="comment">// run preorder-iterative test</span></div>
+<div class="line"><span class="lineno">  374</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPre-order test Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  375</span> </div>
+<div class="line"><span class="lineno">  376</span>    <a class="code hl_function" href="../../d8/d90/iterative__tree__traversals_8cpp.html#ac35ae2868441f8a11c965b87b2494f21">test2</a>(binaryTree, root);  <span class="comment">// run postorder-iterative test</span></div>
+<div class="line"><span class="lineno">  377</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPost-order test Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  378</span> </div>
+<div class="line"><span class="lineno">  379</span>    <a class="code hl_function" href="../../d8/d90/iterative__tree__traversals_8cpp.html#a425c4c8520991999ee6dbe13d99b87f4">test3</a>(binaryTree, root);  <span class="comment">// run inorder-iterative test</span></div>
+<div class="line"><span class="lineno">  380</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nIn-order test Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  381</span> </div>
+<div class="line"><span class="lineno">  382</span>    <span class="comment">// Modifying tree for negative values.</span></div>
+<div class="line"><span class="lineno">  383</span>    root-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a> = -1;</div>
+<div class="line"><span class="lineno">  384</span>    root-&gt;left-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a> = -2;</div>
+<div class="line"><span class="lineno">  385</span>    root-&gt;right-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a> = -3;</div>
+<div class="line"><span class="lineno">  386</span>    root-&gt;left-&gt;left-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a> = -4;</div>
+<div class="line"><span class="lineno">  387</span>    root-&gt;left-&gt;right-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a> = -5;</div>
+<div class="line"><span class="lineno">  388</span> </div>
+<div class="line"><span class="lineno">  389</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n| Tests for negative data values |&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  390</span>    <a class="code hl_function" href="../../d8/d90/iterative__tree__traversals_8cpp.html#a038b236fe900f7bb7e57164f5bed66c2">test4</a>(binaryTree, root);  <span class="comment">// run preorder-iterative test on negative values</span></div>
+<div class="line"><span class="lineno">  391</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPre-order test on-negative value Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  392</span> </div>
+<div class="line"><span class="lineno">  393</span>    <a class="code hl_function" href="../../d8/d90/iterative__tree__traversals_8cpp.html#aa9ef334cd7eb607f4eb8732566ea00b8">test5</a>(binaryTree, root);  <span class="comment">// run postorder-iterative test on negative values</span></div>
+<div class="line"><span class="lineno">  394</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPost-order test on-negative value Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  395</span> </div>
+<div class="line"><span class="lineno">  396</span>    <a class="code hl_function" href="../../d8/d90/iterative__tree__traversals_8cpp.html#af727f920064f2b8f484b589b60d49b89">test6</a>(binaryTree, root);  <span class="comment">// run inorder-iterative test on negative values</span></div>
+<div class="line"><span class="lineno">  397</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nIn-order test on-negative value Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  398</span> </div>
+<div class="line"><span class="lineno">  399</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  400</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aclassothers_1_1iterative__tree__traversals_1_1_binary_tree_html"><div class="ttname"><a href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html">others::iterative_tree_traversals::BinaryTree</a></div><div class="ttdoc">defines the functions associated with the binary tree</div><div class="ttdef"><b>Definition:</b> iterative_tree_traversals.cpp:67</div></div>
 <div class="ttc" id="aclassothers_1_1iterative__tree__traversals_1_1_binary_tree_html_a3078a5ccf45d6a7031dcf46e43de65b6"><div class="ttname"><a href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a3078a5ccf45d6a7031dcf46e43de65b6">others::iterative_tree_traversals::BinaryTree::createNewNode</a></div><div class="ttdeci">Node * createNewNode(int64_t)</div><div class="ttdoc">function that will create new node for insertion.</div><div class="ttdef"><b>Definition:</b> iterative_tree_traversals.cpp:88</div></div>
+<div class="ttc" id="adata_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/data.html">std::vector::data</a></div><div class="ttdeci">T data(T... args)</div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
 <div class="ttc" id="aiterative__tree__traversals_8cpp_html_a038b236fe900f7bb7e57164f5bed66c2"><div class="ttname"><a href="../../d8/d90/iterative__tree__traversals_8cpp.html#a038b236fe900f7bb7e57164f5bed66c2">test4</a></div><div class="ttdeci">static void test4(others::iterative_tree_traversals::BinaryTree binaryTree, others::iterative_tree_traversals::Node *root)</div><div class="ttdoc">Test the computed preorder with the actual preorder on negative value.</div><div class="ttdef"><b>Definition:</b> iterative_tree_traversals.cpp:272</div></div>
 <div class="ttc" id="aiterative__tree__traversals_8cpp_html_a21d922dbb5905993960c6a7f0ba71ac0"><div class="ttname"><a href="../../d8/d90/iterative__tree__traversals_8cpp.html#a21d922dbb5905993960c6a7f0ba71ac0">test1</a></div><div class="ttdeci">static void test1(others::iterative_tree_traversals::BinaryTree binaryTree, others::iterative_tree_traversals::Node *root)</div><div class="ttdoc">Test the computed preorder with the actual preorder.</div><div class="ttdef"><b>Definition:</b> iterative_tree_traversals.cpp:191</div></div>
@@ -291,29 +292,29 @@ Iterative Inorder Traversal of a tree</h3>
   </dd>
 </dl>
 <p >&lt; result stores the preorder traversal of the binary tree</p>
-<div class="fragment"><div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>                                                             {</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> actual_result{1, 2, 4, 5, 3};</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a></div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;  <span class="comment">///&lt; result stores the preorder traversal of the binary tree</span></div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span> </div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>    <span class="comment">// Calling preOrderIterative() function by passing a root node,</span></div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>    <span class="comment">// and storing the preorder traversal in result.</span></div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#ad4c6a8e67fb8267a65439b035666b5ae">preOrderIterative</a>(root);</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span> </div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>    <span class="comment">// Self-testing the result using `assert`</span></div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.size(); i++) {</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>        assert(actual_result[i] == result[i]);</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>    }</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span> </div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    <span class="comment">// Printing the result storing preorder.</span></div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPreOrder Traversal Is : &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i : result) {</div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;  &quot;</span>;</div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>    }</div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  192</span>                                                             {</div>
+<div class="line"><span class="lineno">  193</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> actual_result{1, 2, 4, 5, 3};</div>
+<div class="line"><span class="lineno">  194</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a></div>
+<div class="line"><span class="lineno">  195</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;  <span class="comment">///&lt; result stores the preorder traversal of the binary tree</span></div>
+<div class="line"><span class="lineno">  196</span> </div>
+<div class="line"><span class="lineno">  197</span>    <span class="comment">// Calling preOrderIterative() function by passing a root node,</span></div>
+<div class="line"><span class="lineno">  198</span>    <span class="comment">// and storing the preorder traversal in result.</span></div>
+<div class="line"><span class="lineno">  199</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#ad4c6a8e67fb8267a65439b035666b5ae">preOrderIterative</a>(root);</div>
+<div class="line"><span class="lineno">  200</span> </div>
+<div class="line"><span class="lineno">  201</span>    <span class="comment">// Self-testing the result using `assert`</span></div>
+<div class="line"><span class="lineno">  202</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.size(); i++) {</div>
+<div class="line"><span class="lineno">  203</span>        assert(actual_result[i] == result[i]);</div>
+<div class="line"><span class="lineno">  204</span>    }</div>
+<div class="line"><span class="lineno">  205</span> </div>
+<div class="line"><span class="lineno">  206</span>    <span class="comment">// Printing the result storing preorder.</span></div>
+<div class="line"><span class="lineno">  207</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPreOrder Traversal Is : &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  208</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i : result) {</div>
+<div class="line"><span class="lineno">  209</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;  &quot;</span>;</div>
+<div class="line"><span class="lineno">  210</span>    }</div>
+<div class="line"><span class="lineno">  211</span>}</div>
 <div class="ttc" id="aclassothers_1_1iterative__tree__traversals_1_1_binary_tree_html_ad4c6a8e67fb8267a65439b035666b5ae"><div class="ttname"><a href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#ad4c6a8e67fb8267a65439b035666b5ae">others::iterative_tree_traversals::BinaryTree::preOrderIterative</a></div><div class="ttdeci">std::vector&lt; int64_t &gt; preOrderIterative(Node *)</div><div class="ttdoc">preOrderIterative() function that will perform the preorder traversal iteratively,...</div><div class="ttdef"><b>Definition:</b> iterative_tree_traversals.cpp:102</div></div>
 <div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int64_t &gt;</a></div></div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -360,26 +361,26 @@ Iterative Inorder Traversal of a tree</h3>
   </dd>
 </dl>
 <p >&lt; result stores the postorder traversal of the binary tree.</p>
-<div class="fragment"><div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>                                                             {</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> actual_result{4, 5, 2, 3, 1};</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a></div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;  <span class="comment">///&lt; result stores the postorder traversal of the binary tree.</span></div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span> </div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    <span class="comment">// Calling postOrderIterative() function by passing a root node,</span></div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>    <span class="comment">// and storing the postorder traversal in result.</span></div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a636a07c90b7f312bb86d2ec104efca25">postOrderIterative</a>(root);</div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span> </div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    <span class="comment">// Self-testing the result using `assert`</span></div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.size(); i++) {</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>        assert(actual_result[i] == result[i]);</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>    }</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span> </div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>    <span class="comment">// Printing the result storing postorder.</span></div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPostOrder Traversal Is : &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i : result) {</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;  &quot;</span>;</div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>    }</div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  219</span>                                                             {</div>
+<div class="line"><span class="lineno">  220</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> actual_result{4, 5, 2, 3, 1};</div>
+<div class="line"><span class="lineno">  221</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a></div>
+<div class="line"><span class="lineno">  222</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;  <span class="comment">///&lt; result stores the postorder traversal of the binary tree.</span></div>
+<div class="line"><span class="lineno">  223</span> </div>
+<div class="line"><span class="lineno">  224</span>    <span class="comment">// Calling postOrderIterative() function by passing a root node,</span></div>
+<div class="line"><span class="lineno">  225</span>    <span class="comment">// and storing the postorder traversal in result.</span></div>
+<div class="line"><span class="lineno">  226</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a636a07c90b7f312bb86d2ec104efca25">postOrderIterative</a>(root);</div>
+<div class="line"><span class="lineno">  227</span> </div>
+<div class="line"><span class="lineno">  228</span>    <span class="comment">// Self-testing the result using `assert`</span></div>
+<div class="line"><span class="lineno">  229</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.size(); i++) {</div>
+<div class="line"><span class="lineno">  230</span>        assert(actual_result[i] == result[i]);</div>
+<div class="line"><span class="lineno">  231</span>    }</div>
+<div class="line"><span class="lineno">  232</span> </div>
+<div class="line"><span class="lineno">  233</span>    <span class="comment">// Printing the result storing postorder.</span></div>
+<div class="line"><span class="lineno">  234</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPostOrder Traversal Is : &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  235</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i : result) {</div>
+<div class="line"><span class="lineno">  236</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;  &quot;</span>;</div>
+<div class="line"><span class="lineno">  237</span>    }</div>
+<div class="line"><span class="lineno">  238</span>}</div>
 <div class="ttc" id="aclassothers_1_1iterative__tree__traversals_1_1_binary_tree_html_a636a07c90b7f312bb86d2ec104efca25"><div class="ttname"><a href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a636a07c90b7f312bb86d2ec104efca25">others::iterative_tree_traversals::BinaryTree::postOrderIterative</a></div><div class="ttdeci">std::vector&lt; int64_t &gt; postOrderIterative(Node *)</div><div class="ttdoc">postOrderIterative() function that will perform the postorder traversal iteratively,...</div><div class="ttdef"><b>Definition:</b> iterative_tree_traversals.cpp:132</div></div>
 </div><!-- fragment -->
 </div>
@@ -427,26 +428,26 @@ Iterative Inorder Traversal of a tree</h3>
   </dd>
 </dl>
 <p >&lt; result stores the inorder traversal of the binary tree.</p>
-<div class="fragment"><div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>                                                             {</div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> actual_result{4, 2, 5, 1, 3};</div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a></div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;  <span class="comment">///&lt; result stores the inorder traversal of the binary tree.</span></div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span> </div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>    <span class="comment">// Calling inOrderIterative() function by passing a root node,</span></div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>    <span class="comment">// and storing the inorder traversal in result.</span></div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a0c33f2c1a3a3deb486a1c33ee5239499">inOrderIterative</a>(root);</div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span> </div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>    <span class="comment">// Self-testing the result using `assert`</span></div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.size(); i++) {</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>        assert(actual_result[i] == result[i]);</div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>    }</div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span> </div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>    <span class="comment">// Printing the result storing inorder.</span></div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nInOrder Traversal Is : &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i : result) {</div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;  &quot;</span>;</div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>    }</div>
-<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  246</span>                                                             {</div>
+<div class="line"><span class="lineno">  247</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> actual_result{4, 2, 5, 1, 3};</div>
+<div class="line"><span class="lineno">  248</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a></div>
+<div class="line"><span class="lineno">  249</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;  <span class="comment">///&lt; result stores the inorder traversal of the binary tree.</span></div>
+<div class="line"><span class="lineno">  250</span> </div>
+<div class="line"><span class="lineno">  251</span>    <span class="comment">// Calling inOrderIterative() function by passing a root node,</span></div>
+<div class="line"><span class="lineno">  252</span>    <span class="comment">// and storing the inorder traversal in result.</span></div>
+<div class="line"><span class="lineno">  253</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a0c33f2c1a3a3deb486a1c33ee5239499">inOrderIterative</a>(root);</div>
+<div class="line"><span class="lineno">  254</span> </div>
+<div class="line"><span class="lineno">  255</span>    <span class="comment">// Self-testing the result using `assert`</span></div>
+<div class="line"><span class="lineno">  256</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.size(); i++) {</div>
+<div class="line"><span class="lineno">  257</span>        assert(actual_result[i] == result[i]);</div>
+<div class="line"><span class="lineno">  258</span>    }</div>
+<div class="line"><span class="lineno">  259</span> </div>
+<div class="line"><span class="lineno">  260</span>    <span class="comment">// Printing the result storing inorder.</span></div>
+<div class="line"><span class="lineno">  261</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nInOrder Traversal Is : &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  262</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i : result) {</div>
+<div class="line"><span class="lineno">  263</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;  &quot;</span>;</div>
+<div class="line"><span class="lineno">  264</span>    }</div>
+<div class="line"><span class="lineno">  265</span>}</div>
 <div class="ttc" id="aclassothers_1_1iterative__tree__traversals_1_1_binary_tree_html_a0c33f2c1a3a3deb486a1c33ee5239499"><div class="ttname"><a href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a0c33f2c1a3a3deb486a1c33ee5239499">others::iterative_tree_traversals::BinaryTree::inOrderIterative</a></div><div class="ttdeci">std::vector&lt; int64_t &gt; inOrderIterative(Node *)</div><div class="ttdoc">inOrderIterative() function that will perform the inorder traversal iteratively, and return the resul...</div><div class="ttdef"><b>Definition:</b> iterative_tree_traversals.cpp:164</div></div>
 </div><!-- fragment -->
 </div>
@@ -494,26 +495,26 @@ Iterative Inorder Traversal of a tree</h3>
   </dd>
 </dl>
 <p >&lt; result stores the preorder traversal of the binary tree</p>
-<div class="fragment"><div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>                                                             {</div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> actual_result{-1, -2, -4, -5, -3};</div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a></div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;  <span class="comment">///&lt; result stores the preorder traversal of the binary tree</span></div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span> </div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>    <span class="comment">// Calling preOrderIterative() function by passing a root node,</span></div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>    <span class="comment">// and storing the preorder traversal in result.</span></div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#ad4c6a8e67fb8267a65439b035666b5ae">preOrderIterative</a>(root);</div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span> </div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>    <span class="comment">// Self-testing the result using `assert`</span></div>
-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.size(); i++) {</div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>        assert(actual_result[i] == result[i]);</div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>    }</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span> </div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>    <span class="comment">// Printing the result storing preorder.</span></div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPreOrder Traversal Is : &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i : result) {</div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;  &quot;</span>;</div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>    }</div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  273</span>                                                             {</div>
+<div class="line"><span class="lineno">  274</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> actual_result{-1, -2, -4, -5, -3};</div>
+<div class="line"><span class="lineno">  275</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a></div>
+<div class="line"><span class="lineno">  276</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;  <span class="comment">///&lt; result stores the preorder traversal of the binary tree</span></div>
+<div class="line"><span class="lineno">  277</span> </div>
+<div class="line"><span class="lineno">  278</span>    <span class="comment">// Calling preOrderIterative() function by passing a root node,</span></div>
+<div class="line"><span class="lineno">  279</span>    <span class="comment">// and storing the preorder traversal in result.</span></div>
+<div class="line"><span class="lineno">  280</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#ad4c6a8e67fb8267a65439b035666b5ae">preOrderIterative</a>(root);</div>
+<div class="line"><span class="lineno">  281</span> </div>
+<div class="line"><span class="lineno">  282</span>    <span class="comment">// Self-testing the result using `assert`</span></div>
+<div class="line"><span class="lineno">  283</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.size(); i++) {</div>
+<div class="line"><span class="lineno">  284</span>        assert(actual_result[i] == result[i]);</div>
+<div class="line"><span class="lineno">  285</span>    }</div>
+<div class="line"><span class="lineno">  286</span> </div>
+<div class="line"><span class="lineno">  287</span>    <span class="comment">// Printing the result storing preorder.</span></div>
+<div class="line"><span class="lineno">  288</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPreOrder Traversal Is : &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  289</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i : result) {</div>
+<div class="line"><span class="lineno">  290</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;  &quot;</span>;</div>
+<div class="line"><span class="lineno">  291</span>    }</div>
+<div class="line"><span class="lineno">  292</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -560,26 +561,26 @@ Iterative Inorder Traversal of a tree</h3>
   </dd>
 </dl>
 <p >&lt; result stores the postorder traversal of the binary tree.</p>
-<div class="fragment"><div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span>                                                             {</div>
-<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> actual_result{-4, -5, -2, -3, -1};</div>
-<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a></div>
-<div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;  <span class="comment">///&lt; result stores the postorder traversal of the binary tree.</span></div>
-<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span> </div>
-<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>    <span class="comment">// Calling postOrderIterative() function by passing a root node,</span></div>
-<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>    <span class="comment">// and storing the postorder traversal in result.</span></div>
-<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a636a07c90b7f312bb86d2ec104efca25">postOrderIterative</a>(root);</div>
-<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span> </div>
-<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span>    <span class="comment">// Self-testing the result using `assert`</span></div>
-<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.size(); i++) {</div>
-<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>        assert(actual_result[i] == result[i]);</div>
-<div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span>    }</div>
-<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span> </div>
-<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span>    <span class="comment">// Printing the result storing postorder.</span></div>
-<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPostOrder Traversal Is : &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i : result) {</div>
-<div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;  &quot;</span>;</div>
-<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>    }</div>
-<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  301</span>                                                             {</div>
+<div class="line"><span class="lineno">  302</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> actual_result{-4, -5, -2, -3, -1};</div>
+<div class="line"><span class="lineno">  303</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a></div>
+<div class="line"><span class="lineno">  304</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;  <span class="comment">///&lt; result stores the postorder traversal of the binary tree.</span></div>
+<div class="line"><span class="lineno">  305</span> </div>
+<div class="line"><span class="lineno">  306</span>    <span class="comment">// Calling postOrderIterative() function by passing a root node,</span></div>
+<div class="line"><span class="lineno">  307</span>    <span class="comment">// and storing the postorder traversal in result.</span></div>
+<div class="line"><span class="lineno">  308</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a636a07c90b7f312bb86d2ec104efca25">postOrderIterative</a>(root);</div>
+<div class="line"><span class="lineno">  309</span> </div>
+<div class="line"><span class="lineno">  310</span>    <span class="comment">// Self-testing the result using `assert`</span></div>
+<div class="line"><span class="lineno">  311</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.size(); i++) {</div>
+<div class="line"><span class="lineno">  312</span>        assert(actual_result[i] == result[i]);</div>
+<div class="line"><span class="lineno">  313</span>    }</div>
+<div class="line"><span class="lineno">  314</span> </div>
+<div class="line"><span class="lineno">  315</span>    <span class="comment">// Printing the result storing postorder.</span></div>
+<div class="line"><span class="lineno">  316</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPostOrder Traversal Is : &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  317</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i : result) {</div>
+<div class="line"><span class="lineno">  318</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;  &quot;</span>;</div>
+<div class="line"><span class="lineno">  319</span>    }</div>
+<div class="line"><span class="lineno">  320</span>}</div>
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@@ -626,26 +627,26 @@ Iterative Inorder Traversal of a tree</h3>
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-<div class="line"><a id="l00329" name="l00329"></a><span class="lineno">  329</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> actual_result{-4, -2, -5, -1, -3};</div>
-<div class="line"><a id="l00330" name="l00330"></a><span class="lineno">  330</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a></div>
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-<div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span> </div>
-<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>    <span class="comment">// Calling inOrderIterative() function by passing a root node,</span></div>
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-<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span>    <span class="comment">// Self-testing the result using `assert`</span></div>
-<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.size(); i++) {</div>
-<div class="line"><a id="l00339" name="l00339"></a><span class="lineno">  339</span>        assert(actual_result[i] == result[i]);</div>
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-<div class="line"><a id="l00341" name="l00341"></a><span class="lineno">  341</span> </div>
-<div class="line"><a id="l00342" name="l00342"></a><span class="lineno">  342</span>    <span class="comment">// Printing the result storing inorder.</span></div>
-<div class="line"><a id="l00343" name="l00343"></a><span class="lineno">  343</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nInOrder Traversal Is : &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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-<div class="line"><a id="l00347" name="l00347"></a><span class="lineno">  347</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  328</span>                                                             {</div>
+<div class="line"><span class="lineno">  329</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> actual_result{-4, -2, -5, -1, -3};</div>
+<div class="line"><span class="lineno">  330</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a></div>
+<div class="line"><span class="lineno">  331</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;  <span class="comment">///&lt; result stores the inorder traversal of the binary tree.</span></div>
+<div class="line"><span class="lineno">  332</span> </div>
+<div class="line"><span class="lineno">  333</span>    <span class="comment">// Calling inOrderIterative() function by passing a root node,</span></div>
+<div class="line"><span class="lineno">  334</span>    <span class="comment">// and storing the inorder traversal in result.</span></div>
+<div class="line"><span class="lineno">  335</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = binaryTree.<a class="code hl_function" href="../../d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html#a0c33f2c1a3a3deb486a1c33ee5239499">inOrderIterative</a>(root);</div>
+<div class="line"><span class="lineno">  336</span> </div>
+<div class="line"><span class="lineno">  337</span>    <span class="comment">// Self-testing the result using `assert`</span></div>
+<div class="line"><span class="lineno">  338</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.size(); i++) {</div>
+<div class="line"><span class="lineno">  339</span>        assert(actual_result[i] == result[i]);</div>
+<div class="line"><span class="lineno">  340</span>    }</div>
+<div class="line"><span class="lineno">  341</span> </div>
+<div class="line"><span class="lineno">  342</span>    <span class="comment">// Printing the result storing inorder.</span></div>
+<div class="line"><span class="lineno">  343</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nInOrder Traversal Is : &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  344</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i : result) {</div>
+<div class="line"><span class="lineno">  345</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;  &quot;</span>;</div>
+<div class="line"><span class="lineno">  346</span>    }</div>
+<div class="line"><span class="lineno">  347</span>}</div>
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-<p>Various functions for vectors associated with &lt;a href="https://en.wikipedia.org/wiki/Multilayer_perceptron".  
+<p>Various functions for vectors associated with [NeuralNetwork (aka Multilayer Perceptron)] (<a href="https://en.wikipedia.org/wiki/Multilayer_perceptron">https://en.wikipedia.org/wiki/Multilayer_perceptron</a>).  
 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
 <code>#include &lt;chrono&gt;</code><br />
@@ -196,16 +196,15 @@ Functions</h2></td></tr>
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 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
-<div class="textblock"><p >Various functions for vectors associated with &lt;a href="https://en.wikipedia.org/wiki/Multilayer_perceptron". </p>
-<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/imdeep2905" target="_blank">Deep Raval</a></dd></dl>
-<p>target="_blank" &gt;NeuralNetwork (aka Multilayer Perceptron). </p>
+<div class="textblock"><p >Various functions for vectors associated with [NeuralNetwork (aka Multilayer Perceptron)] (<a href="https://en.wikipedia.org/wiki/Multilayer_perceptron">https://en.wikipedia.org/wiki/Multilayer_perceptron</a>). </p>
+<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/imdeep2905" target="_blank">Deep Raval</a> </dd></dl>
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+<div class="line"><span class="lineno">   93</span>    <span class="keyword">namespace </span><a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> = graph::disjoint_union;</div>
+<div class="line"><span class="lineno">   94</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; dsu::number_of_nodes;</div>
+<div class="line"><span class="lineno">   95</span>    dsu::parent.resize(dsu::number_of_nodes + 1);</div>
+<div class="line"><span class="lineno">   96</span>    dsu::connected_set_size.resize(dsu::number_of_nodes + 1);</div>
+<div class="line"><span class="lineno">   97</span>    dsu::make_set();</div>
+<div class="line"><span class="lineno">   98</span>    uint32_t edges = 0;</div>
+<div class="line"><span class="lineno">   99</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; edges;  <span class="comment">// no of edges in the graph</span></div>
+<div class="line"><span class="lineno">  100</span>    <span class="keywordflow">while</span> (edges--) {</div>
+<div class="line"><span class="lineno">  101</span>        int64_t node_a = 0, node_b = 0;</div>
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+<div class="line"><span class="lineno">  103</span>        dsu::union_sets(node_a, node_b);</div>
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-<div class="fragment"><div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>                                              {</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    node1 = <a class="code hl_function" href="../../d8/d99/connected__components__with__dsu_8cpp.html#a469384d8a4197a9b24482ce7c321a85e">find_set</a>(node1);  <span class="comment">// find the parent of node1</span></div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    node2 = <a class="code hl_function" href="../../d8/d99/connected__components__with__dsu_8cpp.html#a469384d8a4197a9b24482ce7c321a85e">find_set</a>(node2);  <span class="comment">// find the parent of node2</span></div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span> </div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <span class="comment">// If parents of both nodes are not same, combine them</span></div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <span class="keywordflow">if</span> (node1 != node2) {</div>
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-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        }</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        parent[node2] = node1;  <span class="comment">// make node1 as parent of node2.</span></div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>        connected_set_size[node1] +=</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>            connected_set_size[node2];  <span class="comment">// sum the size of both as they combined</span></div>
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-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   62</span>                                              {</div>
+<div class="line"><span class="lineno">   63</span>    node1 = <a class="code hl_function" href="../../d8/d99/connected__components__with__dsu_8cpp.html#a469384d8a4197a9b24482ce7c321a85e">find_set</a>(node1);  <span class="comment">// find the parent of node1</span></div>
+<div class="line"><span class="lineno">   64</span>    node2 = <a class="code hl_function" href="../../d8/d99/connected__components__with__dsu_8cpp.html#a469384d8a4197a9b24482ce7c321a85e">find_set</a>(node2);  <span class="comment">// find the parent of node2</span></div>
+<div class="line"><span class="lineno">   65</span> </div>
+<div class="line"><span class="lineno">   66</span>    <span class="comment">// If parents of both nodes are not same, combine them</span></div>
+<div class="line"><span class="lineno">   67</span>    <span class="keywordflow">if</span> (node1 != node2) {</div>
+<div class="line"><span class="lineno">   68</span>        <span class="keywordflow">if</span> (connected_set_size[node1] &lt; connected_set_size[node2]) {</div>
+<div class="line"><span class="lineno">   69</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(node1, node2);  <span class="comment">// swap both components</span></div>
+<div class="line"><span class="lineno">   70</span>        }</div>
+<div class="line"><span class="lineno">   71</span>        parent[node2] = node1;  <span class="comment">// make node1 as parent of node2.</span></div>
+<div class="line"><span class="lineno">   72</span>        connected_set_size[node1] +=</div>
+<div class="line"><span class="lineno">   73</span>            connected_set_size[node2];  <span class="comment">// sum the size of both as they combined</span></div>
+<div class="line"><span class="lineno">   74</span>    }</div>
+<div class="line"><span class="lineno">   75</span>}</div>
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@@ -168,11 +168,11 @@ Functions</h2></td></tr>
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-<div class="fragment"><div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>                                       {</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>    <a class="code hl_function" href="../../d8/d9a/fast__fourier__transform_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">//  run self-test implementations</span></div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>             <span class="comment">//  with 2 defined test cases</span></div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  162</span>                                       {</div>
+<div class="line"><span class="lineno">  163</span>    <a class="code hl_function" href="../../d8/d9a/fast__fourier__transform_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">//  run self-test implementations</span></div>
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+<div class="line"><span class="lineno">  165</span>    <span class="keywordflow">return</span> 0;</div>
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 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -216,55 +216,55 @@ Here is the call graph for this function:</div>
 <p >Temporary variable used to delete memory location of o2</p>
 <p >Comparing for both real and imaginary values for test case 1</p>
 <p >Comparing for both real and imaginary values for test case 2</p>
-<div class="fragment"><div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>                   {</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <span class="comment">/* descriptions of the following test */</span></div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span> </div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    <span class="keyword">auto</span> *t1 = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[2];  <span class="comment">/// Test case 1</span></div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    <span class="keyword">auto</span> *t2 = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[4];  <span class="comment">/// Test case 2</span></div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span> </div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    t1[0] = {1, 0};</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    t1[1] = {2, 0};</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    t2[0] = {1, 0};</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    t2[1] = {2, 0};</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    t2[2] = {3, 0};</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    t2[3] = {4, 0};</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span> </div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    uint8_t n1 = 2;</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    uint8_t n2 = 4;</div>
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-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        {3, 0}, {-1, 0}};  <span class="comment">/// True Answer for test case 1</span></div>
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-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>        {10, 0}, {-2, -2}, {-2, 0}, {-2, 2}};  <span class="comment">/// True Answer for test case 2</span></div>
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-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>               (r1[i].imag() - o1-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>() &lt;</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>                0.000000000001));  <span class="comment">/// Comparing for both real and imaginary</span><span class="comment"></span></div>
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+<div class="fragment"><div class="line"><span class="lineno">  104</span>                   {</div>
+<div class="line"><span class="lineno">  105</span>    <span class="comment">/* descriptions of the following test */</span></div>
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+<div class="line"><span class="lineno">  107</span>    <span class="keyword">auto</span> *t1 = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[2];  <span class="comment">/// Test case 1</span></div>
+<div class="line"><span class="lineno">  108</span>    <span class="keyword">auto</span> *t2 = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[4];  <span class="comment">/// Test case 2</span></div>
+<div class="line"><span class="lineno">  109</span> </div>
+<div class="line"><span class="lineno">  110</span>    t1[0] = {1, 0};</div>
+<div class="line"><span class="lineno">  111</span>    t1[1] = {2, 0};</div>
+<div class="line"><span class="lineno">  112</span>    t2[0] = {1, 0};</div>
+<div class="line"><span class="lineno">  113</span>    t2[1] = {2, 0};</div>
+<div class="line"><span class="lineno">  114</span>    t2[2] = {3, 0};</div>
+<div class="line"><span class="lineno">  115</span>    t2[3] = {4, 0};</div>
+<div class="line"><span class="lineno">  116</span> </div>
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+<div class="line"><span class="lineno">  120</span>        {3, 0}, {-1, 0}};  <span class="comment">/// True Answer for test case 1</span></div>
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+<div class="line"><span class="lineno">  123</span>        {10, 0}, {-2, -2}, {-2, 0}, {-2, 2}};  <span class="comment">/// True Answer for test case 2</span></div>
+<div class="line"><span class="lineno">  124</span> </div>
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+<div class="line"><span class="lineno">  126</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *t3 =</div>
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+<div class="line"><span class="lineno">  132</span>        assert((r1[i].real() - o1-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>() &lt; 0.000000000001) &amp;&amp;</div>
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+<div class="line"><span class="lineno">  135</span><span class="comment">                                   /// values for test case 1</span></div>
+<div class="line"><span class="lineno">  136</span><span class="comment"></span>        o1++;</div>
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+<div class="line"><span class="lineno">  140</span>        assert((r2[i].real() - o2-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>() &lt; 0.000000000001) &amp;&amp;</div>
+<div class="line"><span class="lineno">  141</span>               (r2[i].imag() - o2-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>() &lt;</div>
+<div class="line"><span class="lineno">  142</span>                0.000000000001));  <span class="comment">/// Comparing for both real and imaginary</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  143</span><span class="comment">                                   /// values for test case 2</span></div>
+<div class="line"><span class="lineno">  144</span><span class="comment"></span>        o2++;</div>
+<div class="line"><span class="lineno">  145</span>    }</div>
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@@ -170,23 +170,23 @@ Functions</h2></td></tr>
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 <dl class="section return"><dt>Returns</dt><dd>binomial coefficient for n and k </dd></dl>
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-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    <span class="keywordflow">if</span> (k == 0)</div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>        <span class="keywordflow">return</span> 1;</div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span> </div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    <span class="keywordtype">size_t</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = 1;</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>    <span class="keywordflow">for</span> (int32_t i = 1; i &lt;= <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>; ++i) {</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> *= n - <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> + i;</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> /= i;</div>
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-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   32</span>                                       {</div>
+<div class="line"><span class="lineno">   33</span>    <span class="comment">// basic cases</span></div>
+<div class="line"><span class="lineno">   34</span>    <span class="keywordflow">if</span> (k &gt; (n / 2))</div>
+<div class="line"><span class="lineno">   35</span>        <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> = n - <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>;</div>
+<div class="line"><span class="lineno">   36</span>    <span class="keywordflow">if</span> (k == 1)</div>
+<div class="line"><span class="lineno">   37</span>        <span class="keywordflow">return</span> n;</div>
+<div class="line"><span class="lineno">   38</span>    <span class="keywordflow">if</span> (k == 0)</div>
+<div class="line"><span class="lineno">   39</span>        <span class="keywordflow">return</span> 1;</div>
+<div class="line"><span class="lineno">   40</span> </div>
+<div class="line"><span class="lineno">   41</span>    <span class="keywordtype">size_t</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = 1;</div>
+<div class="line"><span class="lineno">   42</span>    <span class="keywordflow">for</span> (int32_t i = 1; i &lt;= <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>; ++i) {</div>
+<div class="line"><span class="lineno">   43</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> *= n - <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> + i;</div>
+<div class="line"><span class="lineno">   44</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> /= i;</div>
+<div class="line"><span class="lineno">   45</span>    }</div>
+<div class="line"><span class="lineno">   46</span> </div>
+<div class="line"><span class="lineno">   47</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">   48</span>}</div>
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+<div class="line"><span class="lineno">   88</span>    int32_t <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">atoi</a>(argv[2]);</div>
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+<div class="line"><span class="lineno">   91</span>    <span class="keywordflow">return</span> 0;</div>
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@@ -286,22 +286,22 @@ Here is the call graph for this function:</div>
 
 <p>Test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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+<div class="line"><span class="lineno">   57</span>    <span class="comment">// tests for calculate function</span></div>
+<div class="line"><span class="lineno">   58</span>    assert(math::binomial::calculate(1, 1) == 1);</div>
+<div class="line"><span class="lineno">   59</span>    assert(math::binomial::calculate(57, 57) == 1);</div>
+<div class="line"><span class="lineno">   60</span>    assert(math::binomial::calculate(6, 3) == 20);</div>
+<div class="line"><span class="lineno">   61</span>    assert(math::binomial::calculate(10, 5) == 252);</div>
+<div class="line"><span class="lineno">   62</span>    assert(math::binomial::calculate(20, 10) == 184756);</div>
+<div class="line"><span class="lineno">   63</span>    assert(math::binomial::calculate(30, 15) == 155117520);</div>
+<div class="line"><span class="lineno">   64</span>    assert(math::binomial::calculate(40, 20) == 137846528820);</div>
+<div class="line"><span class="lineno">   65</span>    assert(math::binomial::calculate(50, 25) == 126410606437752);</div>
+<div class="line"><span class="lineno">   66</span>    assert(math::binomial::calculate(60, 30) == 118264581564861424);</div>
+<div class="line"><span class="lineno">   67</span>    assert(math::binomial::calculate(62, 31) == 465428353255261088);</div>
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+<div class="line"><span class="lineno">   69</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;[+] Binomial coefficients calculate test completed&quot;</span></div>
+<div class="line"><span class="lineno">   70</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   71</span>}</div>
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 <div class="ttc" id="abinary__insertion__sort_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d8/dcc/binary__insertion__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition:</b> binary_insertion_sort.cpp:104</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -222,47 +222,47 @@ Here is the call graph for this function:</div>
 
 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>                   {</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <span class="comment">/* descriptions of the following test */</span></div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    <span class="comment">/* 1st test:</span></div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span><span class="comment">       [5, -3, -1, -2, 7] returns [-3, -2, -1, 5, 7] */</span></div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr1({5, -3, -1, -2, 7});</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test... &quot;</span>;</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a5f4bc75cca6dd8294af2d0e328006c68">sorting::insertionSort_binsrch</a>(arr1);</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr1), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr1)));</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span> </div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    <span class="comment">/* 2nd test:</span></div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span><span class="comment">       [12, 26, 15, 91, 32, 54, 41] returns [12, 15, 26, 32, 41, 54, 91] */</span></div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr2({12, 26, 15, 91, 32, 54, 41});</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test... &quot;</span>;</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a5f4bc75cca6dd8294af2d0e328006c68">sorting::insertionSort_binsrch</a>(arr2);</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr2), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr2)));</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span> </div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    <span class="comment">/* 3rd test:</span></div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span><span class="comment">       [7.1, -2.5, -4.0, -2.1, 5.7] returns [-4.0, -2.5, -2.1, 5.7, 7.1] */</span></div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> arr3({7.1, -2.5, -4.0, -2.1, 5.7});</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3rd test... &quot;</span>;</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a5f4bc75cca6dd8294af2d0e328006c68">sorting::insertionSort_binsrch</a>(arr3);</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr3), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr3)));</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span> </div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    <span class="comment">/* 4th test:</span></div>
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-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> arr4({12.8, -3.7, -20.7, -7.1, 2.2});</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4th test... &quot;</span>;</div>
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-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr4), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr4)));</div>
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-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  104</span>                   {</div>
+<div class="line"><span class="lineno">  105</span>    <span class="comment">/* descriptions of the following test */</span></div>
+<div class="line"><span class="lineno">  106</span>    <span class="comment">/* 1st test:</span></div>
+<div class="line"><span class="lineno">  107</span><span class="comment">       [5, -3, -1, -2, 7] returns [-3, -2, -1, 5, 7] */</span></div>
+<div class="line"><span class="lineno">  108</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr1({5, -3, -1, -2, 7});</div>
+<div class="line"><span class="lineno">  109</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test... &quot;</span>;</div>
+<div class="line"><span class="lineno">  110</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a5f4bc75cca6dd8294af2d0e328006c68">sorting::insertionSort_binsrch</a>(arr1);</div>
+<div class="line"><span class="lineno">  111</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr1), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr1)));</div>
+<div class="line"><span class="lineno">  112</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  113</span> </div>
+<div class="line"><span class="lineno">  114</span>    <span class="comment">/* 2nd test:</span></div>
+<div class="line"><span class="lineno">  115</span><span class="comment">       [12, 26, 15, 91, 32, 54, 41] returns [12, 15, 26, 32, 41, 54, 91] */</span></div>
+<div class="line"><span class="lineno">  116</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr2({12, 26, 15, 91, 32, 54, 41});</div>
+<div class="line"><span class="lineno">  117</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test... &quot;</span>;</div>
+<div class="line"><span class="lineno">  118</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a5f4bc75cca6dd8294af2d0e328006c68">sorting::insertionSort_binsrch</a>(arr2);</div>
+<div class="line"><span class="lineno">  119</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr2), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr2)));</div>
+<div class="line"><span class="lineno">  120</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  121</span> </div>
+<div class="line"><span class="lineno">  122</span>    <span class="comment">/* 3rd test:</span></div>
+<div class="line"><span class="lineno">  123</span><span class="comment">       [7.1, -2.5, -4.0, -2.1, 5.7] returns [-4.0, -2.5, -2.1, 5.7, 7.1] */</span></div>
+<div class="line"><span class="lineno">  124</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> arr3({7.1, -2.5, -4.0, -2.1, 5.7});</div>
+<div class="line"><span class="lineno">  125</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3rd test... &quot;</span>;</div>
+<div class="line"><span class="lineno">  126</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a5f4bc75cca6dd8294af2d0e328006c68">sorting::insertionSort_binsrch</a>(arr3);</div>
+<div class="line"><span class="lineno">  127</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr3), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr3)));</div>
+<div class="line"><span class="lineno">  128</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  129</span> </div>
+<div class="line"><span class="lineno">  130</span>    <span class="comment">/* 4th test:</span></div>
+<div class="line"><span class="lineno">  131</span><span class="comment">       [12.8, -3.7, -20.7, -7.1, 2.2] returns [-20.7, -7.1, -3.7, 2.2, 12.8] */</span></div>
+<div class="line"><span class="lineno">  132</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> arr4({12.8, -3.7, -20.7, -7.1, 2.2});</div>
+<div class="line"><span class="lineno">  133</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4th test... &quot;</span>;</div>
+<div class="line"><span class="lineno">  134</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a5f4bc75cca6dd8294af2d0e328006c68">sorting::insertionSort_binsrch</a>(arr4);</div>
+<div class="line"><span class="lineno">  135</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr4), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr4)));</div>
+<div class="line"><span class="lineno">  136</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  137</span>}</div>
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 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
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 <p >Test function </p><dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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+<div class="line"><span class="lineno">   38</span>    assert(<a class="code hl_function" href="../../d8/dd5/check__factorial_8cpp.html#a814eea122b9c241c2b7c1ab760a3eca2">is_factorial</a>(50) == <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">   39</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
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+<div class="line"><span class="lineno">   42</span>    assert(<a class="code hl_function" href="../../d8/dd5/check__factorial_8cpp.html#a814eea122b9c241c2b7c1ab760a3eca2">is_factorial</a>(720) == <span class="keyword">true</span>);</div>
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+<div class="line"><span class="lineno">   44</span> </div>
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+<div class="line"><span class="lineno">   46</span>    assert(<a class="code hl_function" href="../../d8/dd5/check__factorial_8cpp.html#a814eea122b9c241c2b7c1ab760a3eca2">is_factorial</a>(0) == <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">   47</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
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+<div class="line"><span class="lineno">   50</span>    assert(<a class="code hl_function" href="../../d8/dd5/check__factorial_8cpp.html#a814eea122b9c241c2b7c1ab760a3eca2">is_factorial</a>(479001600) == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">   51</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
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+<div class="line"><span class="lineno">   54</span>    assert(<a class="code hl_function" href="../../d8/dd5/check__factorial_8cpp.html#a814eea122b9c241c2b7c1ab760a3eca2">is_factorial</a>(-24) == <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">   55</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
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 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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@@ -244,7 +244,7 @@ Here is the call graph for this function:</div>
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@@ -142,20 +142,20 @@ Space Complexity : \(O(N)\)</p>
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 <div class="ttc" id="adata__structures_2sparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:47</div></div>
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 <div class="ttc" id="asieve__of__eratosthenes_8cpp_html_a7eebd5e7686a8db363f937b2f30d3818"><div class="ttname"><a href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a7eebd5e7686a8db363f937b2f30d3818">sieve</a></div><div class="ttdeci">std::vector&lt; bool &gt; sieve(uint32_t N)</div><div class="ttdef"><b>Definition:</b> sieve_of_eratosthenes.cpp:26</div></div>
 <div class="ttc" id="asieve__of__eratosthenes_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdef"><b>Definition:</b> sieve_of_eratosthenes.cpp:56</div></div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
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-<div class="fragment"><div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>                                                        {</div>
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-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../db/d93/check__prime_8cpp.html#aa18b3517017d99bb4024853bddba5532">is_prime</a>[i]) {</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="charliteral">&#39; &#39;</span>;</div>
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-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   44</span>                                                        {</div>
+<div class="line"><span class="lineno">   45</span>    <span class="keywordflow">for</span> (uint32_t i = 2; i &lt;= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
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+<div class="line"><span class="lineno">   47</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="charliteral">&#39; &#39;</span>;</div>
+<div class="line"><span class="lineno">   48</span>        }</div>
+<div class="line"><span class="lineno">   49</span>    }</div>
+<div class="line"><span class="lineno">   50</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   51</span>}</div>
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-<div class="fragment"><div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>                                  {</div>
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-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>            <span class="keywordflow">for</span> (uint32_t j = i * i; j &lt;= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; j += i) {</div>
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+<div class="line"><span class="lineno">   58</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>{<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>};</div>
+<div class="line"><span class="lineno">   59</span>  assert(<a class="code hl_function" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a7eebd5e7686a8db363f937b2f30d3818">sieve</a>(10) == <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>);</div>
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@@ -165,14 +165,14 @@ Functions</h2></td></tr>
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 <p >Create and return a new <a class="el" href="../../db/d8b/struct_node.html">Node</a> </p>
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-<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *nn = <span class="keyword">new</span> <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>();</div>
-<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>    nn-&gt;data = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
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-<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   21</span>                           {</div>
+<div class="line"><span class="lineno">   22</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *nn = <span class="keyword">new</span> <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>();</div>
+<div class="line"><span class="lineno">   23</span>    nn-&gt;data = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
+<div class="line"><span class="lineno">   24</span>    nn-&gt;height = 0;</div>
+<div class="line"><span class="lineno">   25</span>    nn-&gt;left = NULL;</div>
+<div class="line"><span class="lineno">   26</span>    nn-&gt;right = NULL;</div>
+<div class="line"><span class="lineno">   27</span>    <span class="keywordflow">return</span> nn;</div>
+<div class="line"><span class="lineno">   28</span>}</div>
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 <p >Balanced Deletion </p>
-<div class="fragment"><div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>                                      {</div>
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-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   88</span>                                      {</div>
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+<div class="line"><span class="lineno">   93</span>    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (key &gt; root-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a>)</div>
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+<div class="line"><span class="lineno">   95</span> </div>
+<div class="line"><span class="lineno">   96</span>    <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   97</span>        <span class="comment">// Node to be deleted is leaf node or have only one Child</span></div>
+<div class="line"><span class="lineno">   98</span>        <span class="keywordflow">if</span> (!root-&gt;right) {</div>
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+<div class="line"><span class="lineno">  100</span>            <span class="keyword">delete</span> (root);</div>
+<div class="line"><span class="lineno">  101</span>            root = NULL;</div>
+<div class="line"><span class="lineno">  102</span>            <span class="keywordflow">return</span> temp;</div>
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+<div class="line"><span class="lineno">  109</span>        <span class="comment">// Node to be deleted have both left and right subtrees</span></div>
+<div class="line"><span class="lineno">  110</span>        <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *temp = <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#a5fa160a678a34dd51c0aea1c0c00ed5e">minValue</a>(root-&gt;right);</div>
+<div class="line"><span class="lineno">  111</span>        root-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a> = temp-&gt;data;</div>
+<div class="line"><span class="lineno">  112</span>        root-&gt;right = <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#a9977e004a42fade067836b295a0aa7c1">deleteNode</a>(root-&gt;right, temp-&gt;data);</div>
+<div class="line"><span class="lineno">  113</span>    }</div>
+<div class="line"><span class="lineno">  114</span>    <span class="comment">// Balancing Tree after deletion</span></div>
+<div class="line"><span class="lineno">  115</span>    <span class="keywordflow">return</span> root;</div>
+<div class="line"><span class="lineno">  116</span>}</div>
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+<div class="ttc" id="adata_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/data.html">std::vector::data</a></div><div class="ttdeci">T data(T... args)</div></div>
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 <p >Returns difference between height of left and right subtree </p>
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+<div class="fragment"><div class="line"><span class="lineno">   38</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>(root-&gt;left) - <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>(root-&gt;right); }</div>
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 <p >Returns height of tree </p>
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 <div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
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 <p >Balanced Insertion </p>
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-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    <span class="keywordflow">else</span></div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>        root-&gt;right = <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#a2473fe7416332495b2678ebe89652e4b">insert</a>(root-&gt;right, item);</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    <span class="keywordtype">int</span> b = <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#aaa457ffec24c9643f2768e7a65e96546">getBalance</a>(root);</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    <span class="keywordflow">if</span> (b &gt; 1) {</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#aaa457ffec24c9643f2768e7a65e96546">getBalance</a>(root-&gt;left) &lt; 0)</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>            root-&gt;left = <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#a473eee1803e4e44a54d685e4b0eef5a6">leftRotate</a>(root-&gt;left);  <span class="comment">// Left-Right Case</span></div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#adfc1d482a564c041756719667b955b8c">rightRotate</a>(root);                 <span class="comment">// Left-Left Case</span></div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (b &lt; -1) {</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#aaa457ffec24c9643f2768e7a65e96546">getBalance</a>(root-&gt;right) &gt; 0)</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>            root-&gt;right = <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#adfc1d482a564c041756719667b955b8c">rightRotate</a>(root-&gt;right);  <span class="comment">// Right-Left Case</span></div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#a473eee1803e4e44a54d685e4b0eef5a6">leftRotate</a>(root);                     <span class="comment">// Right-Right Case</span></div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    }</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    <span class="keywordflow">return</span> root;</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   66</span>                                   {</div>
+<div class="line"><span class="lineno">   67</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *nn = <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#a48d897353aeb6a721dbc6b6c57e035e6">createNode</a>(item);</div>
+<div class="line"><span class="lineno">   68</span>    <span class="keywordflow">if</span> (root == NULL)</div>
+<div class="line"><span class="lineno">   69</span>        <span class="keywordflow">return</span> nn;</div>
+<div class="line"><span class="lineno">   70</span>    <span class="keywordflow">if</span> (item &lt; root-&gt;<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>)</div>
+<div class="line"><span class="lineno">   71</span>        root-&gt;left = <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#a2473fe7416332495b2678ebe89652e4b">insert</a>(root-&gt;left, item);</div>
+<div class="line"><span class="lineno">   72</span>    <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">   73</span>        root-&gt;right = <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#a2473fe7416332495b2678ebe89652e4b">insert</a>(root-&gt;right, item);</div>
+<div class="line"><span class="lineno">   74</span>    <span class="keywordtype">int</span> b = <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#aaa457ffec24c9643f2768e7a65e96546">getBalance</a>(root);</div>
+<div class="line"><span class="lineno">   75</span>    <span class="keywordflow">if</span> (b &gt; 1) {</div>
+<div class="line"><span class="lineno">   76</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#aaa457ffec24c9643f2768e7a65e96546">getBalance</a>(root-&gt;left) &lt; 0)</div>
+<div class="line"><span class="lineno">   77</span>            root-&gt;left = <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#a473eee1803e4e44a54d685e4b0eef5a6">leftRotate</a>(root-&gt;left);  <span class="comment">// Left-Right Case</span></div>
+<div class="line"><span class="lineno">   78</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#adfc1d482a564c041756719667b955b8c">rightRotate</a>(root);                 <span class="comment">// Left-Left Case</span></div>
+<div class="line"><span class="lineno">   79</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (b &lt; -1) {</div>
+<div class="line"><span class="lineno">   80</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#aaa457ffec24c9643f2768e7a65e96546">getBalance</a>(root-&gt;right) &gt; 0)</div>
+<div class="line"><span class="lineno">   81</span>            root-&gt;right = <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#adfc1d482a564c041756719667b955b8c">rightRotate</a>(root-&gt;right);  <span class="comment">// Right-Left Case</span></div>
+<div class="line"><span class="lineno">   82</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#a473eee1803e4e44a54d685e4b0eef5a6">leftRotate</a>(root);                     <span class="comment">// Right-Right Case</span></div>
+<div class="line"><span class="lineno">   83</span>    }</div>
+<div class="line"><span class="lineno">   84</span>    <span class="keywordflow">return</span> root;</div>
+<div class="line"><span class="lineno">   85</span>}</div>
 <div class="ttc" id="aavltree_8cpp_html_a2473fe7416332495b2678ebe89652e4b"><div class="ttname"><a href="../../d8/dee/avltree_8cpp.html#a2473fe7416332495b2678ebe89652e4b">insert</a></div><div class="ttdeci">node * insert(node *root, int item)</div><div class="ttdef"><b>Definition:</b> avltree.cpp:66</div></div>
 <div class="ttc" id="aavltree_8cpp_html_a473eee1803e4e44a54d685e4b0eef5a6"><div class="ttname"><a href="../../d8/dee/avltree_8cpp.html#a473eee1803e4e44a54d685e4b0eef5a6">leftRotate</a></div><div class="ttdeci">node * leftRotate(node *root)</div><div class="ttdef"><b>Definition:</b> avltree.cpp:50</div></div>
 <div class="ttc" id="aavltree_8cpp_html_a48d897353aeb6a721dbc6b6c57e035e6"><div class="ttname"><a href="../../d8/dee/avltree_8cpp.html#a48d897353aeb6a721dbc6b6c57e035e6">createNode</a></div><div class="ttdeci">node * createNode(int data)</div><div class="ttdef"><b>Definition:</b> avltree.cpp:21</div></div>
@@ -355,13 +356,13 @@ Functions</h2></td></tr>
       </table>
 </div><div class="memdoc">
 <p >Returns <a class="el" href="../../db/d8b/struct_node.html">Node</a> after Left Rotation </p>
-<div class="fragment"><div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>                             {</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *t = root-&gt;right;</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *u = t-&gt;left;</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    t-&gt;left = root;</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>    root-&gt;right = u;</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <span class="keywordflow">return</span> t;</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   50</span>                             {</div>
+<div class="line"><span class="lineno">   51</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *t = root-&gt;right;</div>
+<div class="line"><span class="lineno">   52</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *u = t-&gt;left;</div>
+<div class="line"><span class="lineno">   53</span>    t-&gt;left = root;</div>
+<div class="line"><span class="lineno">   54</span>    root-&gt;right = u;</div>
+<div class="line"><span class="lineno">   55</span>    <span class="keywordflow">return</span> t;</div>
+<div class="line"><span class="lineno">   56</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -381,19 +382,19 @@ Functions</h2></td></tr>
       </table>
 </div><div class="memdoc">
 <p >LevelOrder (Breadth First Search) </p>
-<div class="fragment"><div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>                            {</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue&lt;node *&gt;</a> q;</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    q.push(root);</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    <span class="keywordflow">while</span> (!q.empty()) {</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>        root = q.front();</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; root-&gt;data &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>        q.pop();</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>        <span class="keywordflow">if</span> (root-&gt;left)</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>            q.push(root-&gt;left);</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>        <span class="keywordflow">if</span> (root-&gt;right)</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>            q.push(root-&gt;right);</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    }</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  119</span>                            {</div>
+<div class="line"><span class="lineno">  120</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue&lt;node *&gt;</a> q;</div>
+<div class="line"><span class="lineno">  121</span>    q.push(root);</div>
+<div class="line"><span class="lineno">  122</span>    <span class="keywordflow">while</span> (!q.empty()) {</div>
+<div class="line"><span class="lineno">  123</span>        root = q.front();</div>
+<div class="line"><span class="lineno">  124</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; root-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a> &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">  125</span>        q.pop();</div>
+<div class="line"><span class="lineno">  126</span>        <span class="keywordflow">if</span> (root-&gt;left)</div>
+<div class="line"><span class="lineno">  127</span>            q.push(root-&gt;left);</div>
+<div class="line"><span class="lineno">  128</span>        <span class="keywordflow">if</span> (root-&gt;right)</div>
+<div class="line"><span class="lineno">  129</span>            q.push(root-&gt;right);</div>
+<div class="line"><span class="lineno">  130</span>    }</div>
+<div class="line"><span class="lineno">  131</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aqueue_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue</a></div></div>
 </div><!-- fragment -->
@@ -415,21 +416,21 @@ Functions</h2></td></tr>
       </table>
 </div><div class="memdoc">
 <p >Main function </p>
-<div class="fragment"><div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>           {</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    <span class="comment">// Testing AVL Tree</span></div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *root = NULL;</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    <span class="keywordtype">int</span> i;</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    <span class="keywordflow">for</span> (i = 1; i &lt;= 7; i++) root = <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#a2473fe7416332495b2678ebe89652e4b">insert</a>(root, i);</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;LevelOrder: &quot;</span>;</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>    <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae197eb50188fb761346952b9b5f6be59">levelOrder</a>(root);</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    root = <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#a9977e004a42fade067836b295a0aa7c1">deleteNode</a>(root, 1);  <span class="comment">// Deleting key with value 1</span></div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nLevelOrder: &quot;</span>;</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae197eb50188fb761346952b9b5f6be59">levelOrder</a>(root);</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    root = <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#a9977e004a42fade067836b295a0aa7c1">deleteNode</a>(root, 4);  <span class="comment">// Deletin key with value 4</span></div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nLevelOrder: &quot;</span>;</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae197eb50188fb761346952b9b5f6be59">levelOrder</a>(root);</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  134</span>           {</div>
+<div class="line"><span class="lineno">  135</span>    <span class="comment">// Testing AVL Tree</span></div>
+<div class="line"><span class="lineno">  136</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> *root = NULL;</div>
+<div class="line"><span class="lineno">  137</span>    <span class="keywordtype">int</span> i;</div>
+<div class="line"><span class="lineno">  138</span>    <span class="keywordflow">for</span> (i = 1; i &lt;= 7; i++) root = <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#a2473fe7416332495b2678ebe89652e4b">insert</a>(root, i);</div>
+<div class="line"><span class="lineno">  139</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;LevelOrder: &quot;</span>;</div>
+<div class="line"><span class="lineno">  140</span>    <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae197eb50188fb761346952b9b5f6be59">levelOrder</a>(root);</div>
+<div class="line"><span class="lineno">  141</span>    root = <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#a9977e004a42fade067836b295a0aa7c1">deleteNode</a>(root, 1);  <span class="comment">// Deleting key with value 1</span></div>
+<div class="line"><span class="lineno">  142</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nLevelOrder: &quot;</span>;</div>
+<div class="line"><span class="lineno">  143</span>    <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae197eb50188fb761346952b9b5f6be59">levelOrder</a>(root);</div>
+<div class="line"><span class="lineno">  144</span>    root = <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#a9977e004a42fade067836b295a0aa7c1">deleteNode</a>(root, 4);  <span class="comment">// Deletin key with value 4</span></div>
+<div class="line"><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nLevelOrder: &quot;</span>;</div>
+<div class="line"><span class="lineno">  146</span>    <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae197eb50188fb761346952b9b5f6be59">levelOrder</a>(root);</div>
+<div class="line"><span class="lineno">  147</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  148</span>}</div>
 <div class="ttc" id="aavltree_8cpp_html_ae197eb50188fb761346952b9b5f6be59"><div class="ttname"><a href="../../d8/dee/avltree_8cpp.html#ae197eb50188fb761346952b9b5f6be59">levelOrder</a></div><div class="ttdeci">void levelOrder(node *root)</div><div class="ttdef"><b>Definition:</b> avltree.cpp:119</div></div>
 </div><!-- fragment -->
 </div>
@@ -450,11 +451,11 @@ Functions</h2></td></tr>
       </table>
 </div><div class="memdoc">
 <p >Returns node with minimum value in the tree </p>
-<div class="fragment"><div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>                           {</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <span class="keywordflow">if</span> (root-&gt;left == NULL)</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        <span class="keywordflow">return</span> root;</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#a5fa160a678a34dd51c0aea1c0c00ed5e">minValue</a>(root-&gt;left);</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   59</span>                           {</div>
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-<p>Implementation of Linear <a href="https://www.geeksforgeeks.org/array-implementation-of-queue-simple/" target="_blank">Queue using array</a>.  
+<p>Implementation of Linear [<a class="el" href="../../dc/db5/struct_queue.html">Queue</a> using array] (<a href="https://www.geeksforgeeks.org/array-implementation-of-queue-simple/">https://www.geeksforgeeks.org/array-implementation-of-queue-simple/</a>).  
 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;array&gt;</code><br />
 <code>#include &lt;iostream&gt;</code><br />
@@ -122,7 +122,7 @@ Namespaces</h2></td></tr>
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 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
-<div class="textblock"><p >Implementation of Linear <a href="https://www.geeksforgeeks.org/array-implementation-of-queue-simple/" target="_blank">Queue using array</a>. </p>
+<div class="textblock"><p >Implementation of Linear [<a class="el" href="../../dc/db5/struct_queue.html">Queue</a> using array] (<a href="https://www.geeksforgeeks.org/array-implementation-of-queue-simple/">https://www.geeksforgeeks.org/array-implementation-of-queue-simple/</a>). </p>
 <p >The Linear <a class="el" href="../../dc/db5/struct_queue.html">Queue</a> is a data structure used for holding a sequence of values, which can be added to the end line (enqueue), removed from head of line (dequeue) and displayed. </p>
 <h3><a class="anchor" id="autotoc_md41"></a>
 Algorithm</h3>
@@ -166,35 +166,35 @@ Algorithm</h3>
 
 <p>Main function. </p>
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 /* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
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@@ -154,21 +154,21 @@ Functions</h2></td></tr>
 <dl class="section return"><dt>Returns</dt><dd>Index where the pattern starts in the text </dd>
 <dd>
 -1 if the pattern was not found. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>                                                                 {</div>
-<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>    <span class="keywordtype">size_t</span> pat_l = pattern.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>();</div>
-<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>    <span class="keywordtype">size_t</span> txt_l = text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>();</div>
-<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span>    <span class="keywordtype">int</span> index = -1;</div>
-<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>    <span class="keywordflow">if</span> (pat_l &lt;= txt_l) {</div>
-<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; txt_l - pat_l + 1; i++) {</div>
-<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s = text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(i, pat_l);</div>
-<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>            <span class="keywordflow">if</span> (s == pattern) {</div>
-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>                index = i;</div>
-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>            }</div>
-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>        }</div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>    }</div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>    <span class="keywordflow">return</span> index;</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   21</span>                                                                 {</div>
+<div class="line"><span class="lineno">   22</span>    <span class="keywordtype">size_t</span> pat_l = pattern.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>();</div>
+<div class="line"><span class="lineno">   23</span>    <span class="keywordtype">size_t</span> txt_l = text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>();</div>
+<div class="line"><span class="lineno">   24</span>    <span class="keywordtype">int</span> index = -1;</div>
+<div class="line"><span class="lineno">   25</span>    <span class="keywordflow">if</span> (pat_l &lt;= txt_l) {</div>
+<div class="line"><span class="lineno">   26</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; txt_l - pat_l + 1; i++) {</div>
+<div class="line"><span class="lineno">   27</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s = text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(i, pat_l);</div>
+<div class="line"><span class="lineno">   28</span>            <span class="keywordflow">if</span> (s == pattern) {</div>
+<div class="line"><span class="lineno">   29</span>                index = i;</div>
+<div class="line"><span class="lineno">   30</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">   31</span>            }</div>
+<div class="line"><span class="lineno">   32</span>        }</div>
+<div class="line"><span class="lineno">   33</span>    }</div>
+<div class="line"><span class="lineno">   34</span>    <span class="keywordflow">return</span> index;</div>
+<div class="line"><span class="lineno">   35</span>}</div>
 <div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
 <div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">std::string::length</a></div><div class="ttdeci">T length(T... args)</div></div>
 <div class="ttc" id="asubstr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">std::string::substr</a></div><div class="ttdeci">T substr(T... args)</div></div>
@@ -243,19 +243,19 @@ Here is the call graph for this function:</div>
 <dd>
 <code>false</code> if pattern was not found </dd></dl>
 <dl class="section note"><dt>Note</dt><dd>can this be replaced by <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/compare.html">std::string::compare</a>? </dd></dl>
-<div class="fragment"><div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>                                                                {</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>    <span class="keywordflow">if</span> (end1 - start1 != end2 - start2) {</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    }</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <span class="keywordflow">while</span> (start1 &lt;= end1 &amp;&amp; start2 &lt;= end2) {</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="keywordflow">if</span> (str1[start1] != str2[start2]) {</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        }</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        start1++;</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        start2++;</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    }</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   61</span>                                                                {</div>
+<div class="line"><span class="lineno">   62</span>    <span class="keywordflow">if</span> (end1 - start1 != end2 - start2) {</div>
+<div class="line"><span class="lineno">   63</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   64</span>    }</div>
+<div class="line"><span class="lineno">   65</span>    <span class="keywordflow">while</span> (start1 &lt;= end1 &amp;&amp; start2 &lt;= end2) {</div>
+<div class="line"><span class="lineno">   66</span>        <span class="keywordflow">if</span> (str1[start1] != str2[start2]) {</div>
+<div class="line"><span class="lineno">   67</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   68</span>        }</div>
+<div class="line"><span class="lineno">   69</span>        start1++;</div>
+<div class="line"><span class="lineno">   70</span>        start2++;</div>
+<div class="line"><span class="lineno">   71</span>    }</div>
+<div class="line"><span class="lineno">   72</span>    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   73</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -292,13 +292,13 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>hash integer </dd></dl>
-<div class="fragment"><div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>                                               {</div>
-<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>    int64_t result = 0;</div>
-<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
-<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>        result += (int64_t)(s[i] * (int64_t)pow(<a class="code hl_define" href="../../d6/dce/rabin__karp_8cpp.html#ac4add2a227a10511e0128d63952030e8">PRIME</a>, i));</div>
-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>    }</div>
-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>    <span class="keywordflow">return</span> result;</div>
-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   25</span>                                               {</div>
+<div class="line"><span class="lineno">   26</span>    int64_t result = 0;</div>
+<div class="line"><span class="lineno">   27</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
+<div class="line"><span class="lineno">   28</span>        result += (int64_t)(s[i] * (int64_t)pow(<a class="code hl_define" href="../../d6/dce/rabin__karp_8cpp.html#ac4add2a227a10511e0128d63952030e8">PRIME</a>, i));</div>
+<div class="line"><span class="lineno">   29</span>    }</div>
+<div class="line"><span class="lineno">   30</span>    <span class="keywordflow">return</span> result;</div>
+<div class="line"><span class="lineno">   31</span>}</div>
 <div class="ttc" id="arabin__karp_8cpp_html_ac4add2a227a10511e0128d63952030e8"><div class="ttname"><a href="../../d6/dce/rabin__karp_8cpp.html#ac4add2a227a10511e0128d63952030e8">PRIME</a></div><div class="ttdeci">#define PRIME</div><div class="ttdoc">Prime modulus for hash functions.</div><div class="ttdef"><b>Definition:</b> rabin_karp.cpp:16</div></div>
 </div><!-- fragment -->
 </div>
@@ -325,22 +325,22 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>the partial match table as a vector array </dd></dl>
-<div class="fragment"><div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>                                                         {</div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>    <span class="keywordtype">int</span> pattern_length = pattern.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> failure(pattern_length + 1);</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>    failure[0] = -1;</div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    <span class="keywordtype">int</span> j = -1;</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span> </div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; pattern_length; i++) {</div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>        <span class="keywordflow">while</span> (j != -1 &amp;&amp; pattern[j] != pattern[i]) {</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>            j = failure[j];</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>        }</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>        j++;</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>        failure[i + 1] = j;</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>    }</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>    <span class="keywordflow">return</span> failure;</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>}</div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="fragment"><div class="line"><span class="lineno">   33</span>                                                         {</div>
+<div class="line"><span class="lineno">   34</span>    <span class="keywordtype">int</span> pattern_length = pattern.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   35</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> failure(pattern_length + 1);</div>
+<div class="line"><span class="lineno">   36</span>    failure[0] = -1;</div>
+<div class="line"><span class="lineno">   37</span>    <span class="keywordtype">int</span> j = -1;</div>
+<div class="line"><span class="lineno">   38</span> </div>
+<div class="line"><span class="lineno">   39</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; pattern_length; i++) {</div>
+<div class="line"><span class="lineno">   40</span>        <span class="keywordflow">while</span> (j != -1 &amp;&amp; pattern[j] != pattern[i]) {</div>
+<div class="line"><span class="lineno">   41</span>            j = failure[j];</div>
+<div class="line"><span class="lineno">   42</span>        }</div>
+<div class="line"><span class="lineno">   43</span>        j++;</div>
+<div class="line"><span class="lineno">   44</span>        failure[i + 1] = j;</div>
+<div class="line"><span class="lineno">   45</span>    }</div>
+<div class="line"><span class="lineno">   46</span>    <span class="keywordflow">return</span> failure;</div>
+<div class="line"><span class="lineno">   47</span>}</div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int &gt;</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -385,21 +385,21 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if pattern was found </dd>
 <dd>
 <code>false</code> if pattern was not found </dd></dl>
-<div class="fragment"><div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>                                                          {</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    <span class="keywordtype">int</span> text_length = text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>(), pattern_length = pattern.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> failure = <a class="code hl_function" href="../../d9/d03/namespacestring__search.html#a996573527312d5255e1495b879e8a34f">getFailureArray</a>(pattern);</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span> </div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <span class="keywordtype">int</span> k = 0;</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; text_length; j++) {</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        <span class="keywordflow">while</span> (k != -1 &amp;&amp; pattern[k] != text[j]) {</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>            k = failure[k];</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        }</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        k++;</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="keywordflow">if</span> (k == pattern_length)</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    }</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   56</span>                                                          {</div>
+<div class="line"><span class="lineno">   57</span>    <span class="keywordtype">int</span> text_length = text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>(), pattern_length = pattern.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   58</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> failure = <a class="code hl_function" href="../../d9/d03/namespacestring__search.html#a996573527312d5255e1495b879e8a34f">getFailureArray</a>(pattern);</div>
+<div class="line"><span class="lineno">   59</span> </div>
+<div class="line"><span class="lineno">   60</span>    <span class="keywordtype">int</span> k = 0;</div>
+<div class="line"><span class="lineno">   61</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; text_length; j++) {</div>
+<div class="line"><span class="lineno">   62</span>        <span class="keywordflow">while</span> (k != -1 &amp;&amp; pattern[k] != text[j]) {</div>
+<div class="line"><span class="lineno">   63</span>            k = failure[k];</div>
+<div class="line"><span class="lineno">   64</span>        }</div>
+<div class="line"><span class="lineno">   65</span>        k++;</div>
+<div class="line"><span class="lineno">   66</span>        <span class="keywordflow">if</span> (k == pattern_length)</div>
+<div class="line"><span class="lineno">   67</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   68</span>    }</div>
+<div class="line"><span class="lineno">   69</span>    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   70</span>}</div>
 <div class="ttc" id="anamespacestring__search_html_a996573527312d5255e1495b879e8a34f"><div class="ttname"><a href="../../d9/d03/namespacestring__search.html#a996573527312d5255e1495b879e8a34f">string_search::getFailureArray</a></div><div class="ttdeci">std::vector&lt; int &gt; getFailureArray(const std::string &amp;pattern)</div><div class="ttdef"><b>Definition:</b> knuth_morris_pratt.cpp:33</div></div>
 </div><!-- fragment --><div class="dynheader">
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@@ -445,22 +445,22 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd>index of first occurrence of pattern </dd>
 <dd>
 -1 if pattern not found </dd></dl>
-<div class="fragment"><div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>                                                           {</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    int64_t pat_hash = <a class="code hl_function" href="../../d9/d03/namespacestring__search.html#a8fb0bc932ba8b582c9f4c71338d050f8">create_hash</a>(pat, pat.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>());</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    int64_t str_hash = <a class="code hl_function" href="../../d9/d03/namespacestring__search.html#a8fb0bc932ba8b582c9f4c71338d050f8">create_hash</a>(str, pat.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>());</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= str.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - pat.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>(); ++i) {</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>        <span class="keywordflow">if</span> (pat_hash == str_hash &amp;&amp;</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>            <a class="code hl_function" href="../../d9/d03/namespacestring__search.html#aebe07cea289a13142503d98be7df11fd">check_if_equal</a>(str, pat, i, i + pat.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - 1, 0,</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>                           pat.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - 1)) {</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>            <span class="keywordflow">return</span> i;</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>        }</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>        <span class="keywordflow">if</span> (i &lt; str.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - pat.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>()) {</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>            str_hash =</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>                <a class="code hl_function" href="../../d9/d03/namespacestring__search.html#aed769d565b705a9b3e0eb1ec74088893">recalculate_hash</a>(str, i, i + pat.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>(), str_hash, pat.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>());</div>
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-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    <span class="keywordflow">return</span> -1;  <span class="comment">// return -1 if given pattern not found</span></div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   83</span>                                                           {</div>
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+<div class="line"><span class="lineno">   85</span>    int64_t str_hash = <a class="code hl_function" href="../../d9/d03/namespacestring__search.html#a8fb0bc932ba8b582c9f4c71338d050f8">create_hash</a>(str, pat.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>());</div>
+<div class="line"><span class="lineno">   86</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= str.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - pat.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>(); ++i) {</div>
+<div class="line"><span class="lineno">   87</span>        <span class="keywordflow">if</span> (pat_hash == str_hash &amp;&amp;</div>
+<div class="line"><span class="lineno">   88</span>            <a class="code hl_function" href="../../d9/d03/namespacestring__search.html#aebe07cea289a13142503d98be7df11fd">check_if_equal</a>(str, pat, i, i + pat.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - 1, 0,</div>
+<div class="line"><span class="lineno">   89</span>                           pat.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - 1)) {</div>
+<div class="line"><span class="lineno">   90</span>            <span class="keywordflow">return</span> i;</div>
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+<div class="line"><span class="lineno">   93</span>            str_hash =</div>
+<div class="line"><span class="lineno">   94</span>                <a class="code hl_function" href="../../d9/d03/namespacestring__search.html#aed769d565b705a9b3e0eb1ec74088893">recalculate_hash</a>(str, i, i + pat.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>(), str_hash, pat.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>());</div>
+<div class="line"><span class="lineno">   95</span>        }</div>
+<div class="line"><span class="lineno">   96</span>    }</div>
+<div class="line"><span class="lineno">   97</span>    <span class="keywordflow">return</span> -1;  <span class="comment">// return -1 if given pattern not found</span></div>
+<div class="line"><span class="lineno">   98</span>}</div>
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 <div class="ttc" id="anamespacestring__search_html_aed769d565b705a9b3e0eb1ec74088893"><div class="ttname"><a href="../../d9/d03/namespacestring__search.html#aed769d565b705a9b3e0eb1ec74088893">string_search::recalculate_hash</a></div><div class="ttdeci">int64_t recalculate_hash(const std::string &amp;s, int old_index, int new_index, int64_t old_hash, int patLength)</div><div class="ttdef"><b>Definition:</b> rabin_karp.cpp:42</div></div>
@@ -527,12 +527,12 @@ Here is the call graph for this function:</div>
   </dd>
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-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   43</span>                                                          {</div>
+<div class="line"><span class="lineno">   44</span>    int64_t new_hash = old_hash - s[old_index];</div>
+<div class="line"><span class="lineno">   45</span>    new_hash /= <a class="code hl_define" href="../../d6/dce/rabin__karp_8cpp.html#ac4add2a227a10511e0128d63952030e8">PRIME</a>;</div>
+<div class="line"><span class="lineno">   46</span>    new_hash += (int64_t)(s[new_index] * (int64_t)pow(<a class="code hl_define" href="../../d6/dce/rabin__karp_8cpp.html#ac4add2a227a10511e0128d63952030e8">PRIME</a>, patLength - 1));</div>
+<div class="line"><span class="lineno">   47</span>    <span class="keywordflow">return</span> new_hash;</div>
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+<div class="line"><span class="lineno">  133</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/stack.html">std::stack&lt;Node *&gt;</a></div>
+<div class="line"><span class="lineno">  134</span>        <a class="code hl_variable" href="../../dc/dc5/paranthesis__matching_8cpp.html#aa37d24a036d239b3b528f13b9de880c7">stack</a>;  <span class="comment">///&lt; is used to find and traverse the child nodes.</span></div>
+<div class="line"><span class="lineno">  135</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;  <span class="comment">///&lt; List of values, sorted in post-order.</span></div>
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+<div class="line"><span class="lineno">  137</span>    <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a5705c3926dcf5fd3f9c964467a50b81d">push</a>(root);</div>
+<div class="line"><span class="lineno">  138</span> </div>
+<div class="line"><span class="lineno">  139</span>    <span class="keywordflow">while</span> (!<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.empty()) {</div>
+<div class="line"><span class="lineno">  140</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.push_back(<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a21c0bb6ce7dcfe445cc12031977ea344">top</a>()-&gt;data);</div>
+<div class="line"><span class="lineno">  141</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *current = <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a21c0bb6ce7dcfe445cc12031977ea344">top</a>();</div>
+<div class="line"><span class="lineno">  142</span>        <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a6cd4b95d5de00d41b2491392338384dc">pop</a>();</div>
+<div class="line"><span class="lineno">  143</span> </div>
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+<div class="line"><span class="lineno">  146</span>        }</div>
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-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;  <span class="comment">///&lt; list of values, sorted in pre-order.</span></div>
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+<div class="line"><span class="lineno">  103</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/stack.html">std::stack&lt;Node *&gt;</a></div>
+<div class="line"><span class="lineno">  104</span>        <a class="code hl_variable" href="../../dc/dc5/paranthesis__matching_8cpp.html#aa37d24a036d239b3b528f13b9de880c7">stack</a>;  <span class="comment">///&lt; is used to find and traverse the child nodes.</span></div>
+<div class="line"><span class="lineno">  105</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;  <span class="comment">///&lt; list of values, sorted in pre-order.</span></div>
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+<div class="line"><span class="lineno">  107</span>    <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a5705c3926dcf5fd3f9c964467a50b81d">push</a>(root);</div>
+<div class="line"><span class="lineno">  108</span> </div>
+<div class="line"><span class="lineno">  109</span>    <span class="keywordflow">while</span> (!<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.empty()) {</div>
+<div class="line"><span class="lineno">  110</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.push_back(<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a21c0bb6ce7dcfe445cc12031977ea344">top</a>()-&gt;data);</div>
+<div class="line"><span class="lineno">  111</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *current = <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a21c0bb6ce7dcfe445cc12031977ea344">top</a>();</div>
+<div class="line"><span class="lineno">  112</span>        <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a6cd4b95d5de00d41b2491392338384dc">pop</a>();</div>
+<div class="line"><span class="lineno">  113</span> </div>
+<div class="line"><span class="lineno">  114</span>        <span class="keywordflow">if</span> (current-&gt;right) {</div>
+<div class="line"><span class="lineno">  115</span>            <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a5705c3926dcf5fd3f9c964467a50b81d">push</a>(current-&gt;right);</div>
+<div class="line"><span class="lineno">  116</span>        }</div>
+<div class="line"><span class="lineno">  117</span>        <span class="keywordflow">if</span> (current-&gt;left) {</div>
+<div class="line"><span class="lineno">  118</span>            <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a5705c3926dcf5fd3f9c964467a50b81d">push</a>(current-&gt;left);</div>
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+<div class="line"><span class="lineno">  121</span> </div>
+<div class="line"><span class="lineno">  122</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
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+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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diff --git a/d9/d21/namespacewave__sort.html b/d9/d21/namespacewave__sort.html
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+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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diff --git a/d9/d23/classgraph_1_1_lowest_common_ancestor.html b/d9/d23/classgraph_1_1_lowest_common_ancestor.html
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@@ -41,7 +41,7 @@ MathJax.Hub.Config({
 </table>
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+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d1/d71/classgraph_1_1_lowest_common_ancestor__coll__graph.svg" width="395" height="424"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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@@ -163,14 +163,14 @@ Protected Member Functions</h2></td></tr>
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-<div class="fragment"><div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>                                                           : tree(tree_) {</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>        <a class="code hl_function" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a42589cc39d6bbff6c997152f1b96e356">populate_up</a>();</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  151</span>                                                           : tree(tree_) {</div>
+<div class="line"><span class="lineno">  152</span>        <a class="code hl_function" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a42589cc39d6bbff6c997152f1b96e356">populate_up</a>();</div>
+<div class="line"><span class="lineno">  153</span>    }</div>
 <div class="ttc" id="aclassgraph_1_1_lowest_common_ancestor_html_a42589cc39d6bbff6c997152f1b96e356"><div class="ttname"><a href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a42589cc39d6bbff6c997152f1b96e356">graph::LowestCommonAncestor::populate_up</a></div><div class="ttdeci">void populate_up()</div><div class="ttdef"><b>Definition:</b> lowest_common_ancestor.cpp:212</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
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+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d9/d23/classgraph_1_1_lowest_common_ancestor_a80825a4fd4c41860b689d253dd2c8e93_cgraph.svg" width="100%" height="416"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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@@ -220,39 +220,39 @@ Here is the call graph for this function:</div>
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 <dl class="section return"><dt>Returns</dt><dd>index of the vertex which is the lowet common ancestor of u and v </dd></dl>
-<div class="fragment"><div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>                                                   {</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>        <span class="comment">// Ensure u is the deeper (higher level) of the two vertices</span></div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>        <span class="keywordflow">if</span> (tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[v] &gt; tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[u]) {</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(u, v);</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>        }</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span> </div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>        <span class="comment">// &quot;Lift&quot; u to the same level as v.</span></div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>        <span class="keywordtype">int</span> level_diff = tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[u] - tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[v];</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; (1 &lt;&lt; i) &lt;= level_diff; ++i) {</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>            <span class="keywordflow">if</span> (level_diff &amp; (1 &lt;&lt; i)) {</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>                u = <a class="code hl_variable" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[u][i];</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>            }</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>        }</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>        assert(tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[u] == tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[v]);</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span> </div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>        <span class="keywordflow">if</span> (u == v) {</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>            <span class="keywordflow">return</span> u;</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>        }</div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span> </div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>        <span class="comment">// &quot;Lift&quot; u and v to their 2^i th ancestor if they are different</span></div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(<a class="code hl_variable" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[u].size()) - 1; i &gt;= 0; --i) {</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[u][i] != <a class="code hl_variable" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[v][i]) {</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>                u = <a class="code hl_variable" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[u][i];</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>                v = <a class="code hl_variable" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[v][i];</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>            }</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>        }</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span> </div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>        <span class="comment">// As we regressed u an v such that they cannot further be lifted so</span></div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>        <span class="comment">// that their ancestor would be different, the only logical</span></div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>        <span class="comment">// consequence is that their parent is the sought answer.</span></div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>        assert(<a class="code hl_variable" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[u][0] == <a class="code hl_variable" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[v][0]);</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[u][0];</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  164</span>                                                   {</div>
+<div class="line"><span class="lineno">  165</span>        <span class="comment">// Ensure u is the deeper (higher level) of the two vertices</span></div>
+<div class="line"><span class="lineno">  166</span>        <span class="keywordflow">if</span> (tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[v] &gt; tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[u]) {</div>
+<div class="line"><span class="lineno">  167</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(u, v);</div>
+<div class="line"><span class="lineno">  168</span>        }</div>
+<div class="line"><span class="lineno">  169</span> </div>
+<div class="line"><span class="lineno">  170</span>        <span class="comment">// &quot;Lift&quot; u to the same level as v.</span></div>
+<div class="line"><span class="lineno">  171</span>        <span class="keywordtype">int</span> level_diff = tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[u] - tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[v];</div>
+<div class="line"><span class="lineno">  172</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; (1 &lt;&lt; i) &lt;= level_diff; ++i) {</div>
+<div class="line"><span class="lineno">  173</span>            <span class="keywordflow">if</span> (level_diff &amp; (1 &lt;&lt; i)) {</div>
+<div class="line"><span class="lineno">  174</span>                u = <a class="code hl_variable" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[u][i];</div>
+<div class="line"><span class="lineno">  175</span>            }</div>
+<div class="line"><span class="lineno">  176</span>        }</div>
+<div class="line"><span class="lineno">  177</span>        assert(tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[u] == tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[v]);</div>
+<div class="line"><span class="lineno">  178</span> </div>
+<div class="line"><span class="lineno">  179</span>        <span class="keywordflow">if</span> (u == v) {</div>
+<div class="line"><span class="lineno">  180</span>            <span class="keywordflow">return</span> u;</div>
+<div class="line"><span class="lineno">  181</span>        }</div>
+<div class="line"><span class="lineno">  182</span> </div>
+<div class="line"><span class="lineno">  183</span>        <span class="comment">// &quot;Lift&quot; u and v to their 2^i th ancestor if they are different</span></div>
+<div class="line"><span class="lineno">  184</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(<a class="code hl_variable" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[u].size()) - 1; i &gt;= 0; --i) {</div>
+<div class="line"><span class="lineno">  185</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[u][i] != <a class="code hl_variable" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[v][i]) {</div>
+<div class="line"><span class="lineno">  186</span>                u = <a class="code hl_variable" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[u][i];</div>
+<div class="line"><span class="lineno">  187</span>                v = <a class="code hl_variable" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[v][i];</div>
+<div class="line"><span class="lineno">  188</span>            }</div>
+<div class="line"><span class="lineno">  189</span>        }</div>
+<div class="line"><span class="lineno">  190</span> </div>
+<div class="line"><span class="lineno">  191</span>        <span class="comment">// As we regressed u an v such that they cannot further be lifted so</span></div>
+<div class="line"><span class="lineno">  192</span>        <span class="comment">// that their ancestor would be different, the only logical</span></div>
+<div class="line"><span class="lineno">  193</span>        <span class="comment">// consequence is that their parent is the sought answer.</span></div>
+<div class="line"><span class="lineno">  194</span>        assert(<a class="code hl_variable" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[u][0] == <a class="code hl_variable" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[v][0]);</div>
+<div class="line"><span class="lineno">  195</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[u][0];</div>
+<div class="line"><span class="lineno">  196</span>    }</div>
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+<div class="line"><span class="lineno">  220</span>                <span class="comment">// = 2^level th ancestor of 2^level th ancestor of vertex =</span></div>
+<div class="line"><span class="lineno">  221</span>                <span class="comment">// = 2^level th ancestor of up[vertex][level]</span></div>
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 <p >Compute factorial of a given number </p>
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+<div class="fragment"><div class="line"><span class="lineno">   30</span>                      {</div>
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+<div class="line"><span class="lineno">   32</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = x - 1; i &gt; 0; i--) {</div>
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+<div class="line"><span class="lineno">   38</span>    }</div>
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 <p >main function </p>
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-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <span class="keywordtype">double</span> rate, expected;</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    rate = <a class="code hl_function" href="../../d9/d24/poisson__dist_8cpp.html#ac217ab9a06291f360d816700a6958ca8">poisson_rate</a>(3, 1);</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Poisson rate : &quot;</span> &lt;&lt; rate &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span> </div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>    expected = <a class="code hl_function" href="../../d9/d24/poisson__dist_8cpp.html#ad0aa718023ce802dd5899f0e03a7ac71">poisson_expected</a>(rate, 2);</div>
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+<div class="line"><span class="lineno">   69</span> </div>
+<div class="line"><span class="lineno">   70</span>    expected = <a class="code hl_function" href="../../d9/d24/poisson__dist_8cpp.html#ad0aa718023ce802dd5899f0e03a7ac71">poisson_expected</a>(rate, 2);</div>
+<div class="line"><span class="lineno">   71</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Poisson expected : &quot;</span> &lt;&lt; expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><span class="lineno">   73</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Poisson 0 successes : &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d9/d24/poisson__dist_8cpp.html#a69a136b32707bdc7950fb9057b5fa1e1">poisson_x_successes</a>(expected, 0)</div>
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+<div class="line"><span class="lineno">   76</span>              &lt;&lt; <a class="code hl_function" href="../../d9/d24/poisson__dist_8cpp.html#ad9c9e74079278ca10e3b97a8d5391c9a">poisson_range_successes</a>(expected, 0, 8) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   77</span> </div>
+<div class="line"><span class="lineno">   78</span>    <span class="keywordflow">return</span> 0;</div>
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 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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 <div class="ttc" id="apoisson__dist_8cpp_html_a69a136b32707bdc7950fb9057b5fa1e1"><div class="ttname"><a href="../../d9/d24/poisson__dist_8cpp.html#a69a136b32707bdc7950fb9057b5fa1e1">poisson_x_successes</a></div><div class="ttdeci">double poisson_x_successes(double expected, double x)</div><div class="ttdef"><b>Definition:</b> poisson_dist.cpp:46</div></div>
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 <p >calculate the expected value over a time e.g rate of 2.5 over 10 mins = 2.5 x 10 = 25 </p>
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+<div class="fragment"><div class="line"><span class="lineno">   25</span>{ <span class="keywordflow">return</span> rate * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">time</a>; }</div>
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 <p >probability of a success in range for Poisson dist (inclusive, inclusive) </p><p class="formulaDsp">
 \[P = \sum_i p(\mu,i)\]
 </p>
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+<div class="line"><span class="lineno">   56</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = <a class="code hl_function" href="../../dc/db5/text__search_8cpp.html#a3f8975d227cd0e58f298b380c5dac0d9">lower</a>; i &lt;= upper; i++) {</div>
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 </div><!-- fragment --><div class="dynheader">
@@ -313,9 +313,9 @@ Here is the call graph for this function:</div>
 <p >poisson rate:<br  />
 calculate the events per unit time<br  />
 e.g 5 dollars every 2 mins = 5 / 2 = 2.5 </p>
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-<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span>}</div>
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 </div><!-- fragment -->
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@@ -347,9 +347,9 @@ e.g 5 dollars every 2 mins = 5 / 2 = 2.5 </p>
 <p >Find the probability of x successes in a Poisson dist. </p><p class="formulaDsp">
 \[p(\mu,x) = \frac{\mu^x e^{-\mu}}{x!}\]
 </p>
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+ <div class="fragment"><div class="line"><span class="lineno">   46</span>                                                      {</div>
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@@ -368,7 +368,7 @@ Here is the call graph for this function:</div>
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@@ -158,10 +158,10 @@ Functions</h2></td></tr>
 
 <p>Main function. </p>
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@@ -224,24 +224,24 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>minimum number of coins </dd></dl>
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-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>        <span class="keywordflow">if</span> (n - coins[i] &gt;= 0) {  <span class="comment">// if after subtracting the current</span></div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>                                  <span class="comment">// denomination is it greater than 0 or not</span></div>
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 <p>Test implementations. </p>
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-<div class="fragment"><div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>                                       {</div>
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 Here is the call graph for this function:</div>
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 <p >True Answer for test case 2</p>
 <p >Comparing for both real and imaginary values for test case 1</p>
 <p >Comparing for both real and imaginary values for test case 2</p>
-<div class="fragment"><div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>                   {</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <span class="comment">/* descriptions of the following test */</span></div>
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-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <span class="keyword">auto</span> *t1 = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[2];  <span class="comment">/// Test case 1</span></div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <span class="keyword">auto</span> *t2 = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[4];  <span class="comment">/// Test case 2</span></div>
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-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    t1[1] = {-1, 0};</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    t2[0] = {10, 0};</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    t2[1] = {-2, -2};</div>
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-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    t2[3] = {-2, 2};</div>
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-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    uint8_t n2 = 4;</div>
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-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>        {1, 0}, {2, 0}};  <span class="comment">/// True Answer for test case 1</span></div>
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-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        {1, 0}, {2, 0}, {3, 0}, {4, 0}};  <span class="comment">/// True Answer for test case 2</span></div>
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+<div class="fragment"><div class="line"><span class="lineno">  100</span>                   {</div>
+<div class="line"><span class="lineno">  101</span>    <span class="comment">/* descriptions of the following test */</span></div>
+<div class="line"><span class="lineno">  102</span> </div>
+<div class="line"><span class="lineno">  103</span>    <span class="keyword">auto</span> *t1 = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[2];  <span class="comment">/// Test case 1</span></div>
+<div class="line"><span class="lineno">  104</span>    <span class="keyword">auto</span> *t2 = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[4];  <span class="comment">/// Test case 2</span></div>
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+<div class="line"><span class="lineno">  106</span>    t1[0] = {3, 0};</div>
+<div class="line"><span class="lineno">  107</span>    t1[1] = {-1, 0};</div>
+<div class="line"><span class="lineno">  108</span>    t2[0] = {10, 0};</div>
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+<div class="line"><span class="lineno">  110</span>    t2[2] = {-2, 0};</div>
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+<div class="line"><span class="lineno">  112</span> </div>
+<div class="line"><span class="lineno">  113</span>    uint8_t n1 = 2;</div>
+<div class="line"><span class="lineno">  114</span>    uint8_t n2 = 4;</div>
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+<div class="line"><span class="lineno">  116</span>        {1, 0}, {2, 0}};  <span class="comment">/// True Answer for test case 1</span></div>
+<div class="line"><span class="lineno">  117</span> </div>
+<div class="line"><span class="lineno">  118</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::complex&lt;double&gt;</a>&gt; r2 = {</div>
+<div class="line"><span class="lineno">  119</span>        {1, 0}, {2, 0}, {3, 0}, {4, 0}};  <span class="comment">/// True Answer for test case 2</span></div>
+<div class="line"><span class="lineno">  120</span> </div>
+<div class="line"><span class="lineno">  121</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *o1 =</div>
+<div class="line"><span class="lineno">  122</span>        <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">numerical_methods::InverseFastFourierTransform</a>(t1, n1);</div>
+<div class="line"><span class="lineno">  123</span> </div>
+<div class="line"><span class="lineno">  124</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *o2 =</div>
+<div class="line"><span class="lineno">  125</span>        <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">numerical_methods::InverseFastFourierTransform</a>(t2, n2);</div>
+<div class="line"><span class="lineno">  126</span> </div>
+<div class="line"><span class="lineno">  127</span>    <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; n1; i++) {</div>
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+<div class="line"><span class="lineno">  129</span>               (r1[i].imag() - o1[i].imag() &lt;</div>
+<div class="line"><span class="lineno">  130</span>                0.000000000001));  <span class="comment">/// Comparing for both real and imaginary</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  131</span><span class="comment">                                   /// values for test case 1</span></div>
+<div class="line"><span class="lineno">  132</span><span class="comment"></span>    }</div>
+<div class="line"><span class="lineno">  133</span> </div>
+<div class="line"><span class="lineno">  134</span>    <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; n2; i++) {</div>
+<div class="line"><span class="lineno">  135</span>        assert((r2[i].real() - o2[i].real() &lt; 0.000000000001) &amp;&amp;</div>
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-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span> </div>
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-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    assert(<a class="code hl_function" href="../../dd/d47/namespacemath.html#a8d8e81a7cd59644b311ef9adb268f5f0">math::magic_number</a>(479001600) == <span class="keyword">false</span>);</div>
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-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   51</span>                    {</div>
+<div class="line"><span class="lineno">   52</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1:\t n=60\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   53</span>    assert(<a class="code hl_function" href="../../dd/d47/namespacemath.html#a8d8e81a7cd59644b311ef9adb268f5f0">math::magic_number</a>(60) == <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">   54</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   55</span> </div>
+<div class="line"><span class="lineno">   56</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2:\t n=730\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   57</span>    assert(<a class="code hl_function" href="../../dd/d47/namespacemath.html#a8d8e81a7cd59644b311ef9adb268f5f0">math::magic_number</a>(730) == <span class="keyword">true</span>);</div>
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+<div class="line"><span class="lineno">   59</span> </div>
+<div class="line"><span class="lineno">   60</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3:\t n=0\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   61</span>    assert(<a class="code hl_function" href="../../dd/d47/namespacemath.html#a8d8e81a7cd59644b311ef9adb268f5f0">math::magic_number</a>(0) == <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">   62</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   63</span> </div>
+<div class="line"><span class="lineno">   64</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 4:\t n=479001600\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   65</span>    assert(<a class="code hl_function" href="../../dd/d47/namespacemath.html#a8d8e81a7cd59644b311ef9adb268f5f0">math::magic_number</a>(479001600) == <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">   66</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   67</span> </div>
+<div class="line"><span class="lineno">   68</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 5:\t n=-35\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   69</span>    assert(<a class="code hl_function" href="../../dd/d47/namespacemath.html#a8d8e81a7cd59644b311ef9adb268f5f0">math::magic_number</a>(-35) == <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">   70</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   71</span>}</div>
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@@ -224,7 +224,7 @@ Here is the call graph for this function:</div>
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-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
+  <td id="projectalign">
    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
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    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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+<!-- Generated by Doxygen 1.9.3 -->
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@@ -192,9 +192,9 @@ The compiled code is much slower when compiled with MS Visual C++ 2019 than with
   </dd>
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 <dl class="section return"><dt>Returns</dt><dd>time difference in seconds </dd></dl>
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-<div class="line"><a id="l00453" name="l00453"></a><span class="lineno">  453</span>    <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(end_t - start_t) / CLOCKS_PER_SEC;</div>
-<div class="line"><a id="l00454" name="l00454"></a><span class="lineno">  454</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  452</span>                                                      {</div>
+<div class="line"><span class="lineno">  453</span>    <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(end_t - start_t) / CLOCKS_PER_SEC;</div>
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@@ -224,38 +224,38 @@ The compiled code is much slower when compiled with MS Visual C++ 2019 than with
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-<div class="line"><a id="l00458" name="l00458"></a><span class="lineno">  458</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00459" name="l00459"></a><span class="lineno">  459</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Using OpenMP based parallelization\n&quot;</span>;</div>
-<div class="line"><a id="l00460" name="l00460"></a><span class="lineno">  460</span><span class="preprocessor">#else</span></div>
-<div class="line"><a id="l00461" name="l00461"></a><span class="lineno">  461</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;NOT using OpenMP based parallelization\n&quot;</span>;</div>
-<div class="line"><a id="l00462" name="l00462"></a><span class="lineno">  462</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00463" name="l00463"></a><span class="lineno">  463</span> </div>
-<div class="line"><a id="l00464" name="l00464"></a><span class="lineno">  464</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
-<div class="line"><a id="l00465" name="l00465"></a><span class="lineno">  465</span> </div>
-<div class="line"><a id="l00466" name="l00466"></a><span class="lineno">  466</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start_clk = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00467" name="l00467"></a><span class="lineno">  467</span>    <a class="code hl_function" href="../../d9/d49/kohonen__som__trace_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
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+<div class="line"><span class="lineno">  460</span><span class="preprocessor">#else</span></div>
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+<div class="line"><span class="lineno">  470</span>              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
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+<div class="line"><span class="lineno">  472</span>    start_clk = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  473</span>    <a class="code hl_function" href="../../d9/d49/kohonen__som__trace_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
+<div class="line"><span class="lineno">  474</span>    end_clk = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  475</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 completed in &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d9/d49/kohonen__som__trace_8cpp.html#a2256c10b16edba377b64a44b6c656908">get_clock_diff</a>(start_clk, end_clk)</div>
+<div class="line"><span class="lineno">  476</span>              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  477</span> </div>
+<div class="line"><span class="lineno">  478</span>    start_clk = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  479</span>    <a class="code hl_function" href="../../d9/d49/kohonen__som__trace_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>();</div>
+<div class="line"><span class="lineno">  480</span>    end_clk = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">  481</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 completed in &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d9/d49/kohonen__som__trace_8cpp.html#a2256c10b16edba377b64a44b6c656908">get_clock_diff</a>(start_clk, end_clk)</div>
+<div class="line"><span class="lineno">  482</span>              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  483</span> </div>
+<div class="line"><span class="lineno">  484</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
+<div class="line"><span class="lineno">  485</span>        &lt;&lt; <span class="stringliteral">&quot;(Note: Calculated times include: creating test sets, training &quot;</span></div>
+<div class="line"><span class="lineno">  486</span>           <span class="stringliteral">&quot;model and writing files to disk.)\n\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  487</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  488</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aclock_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a></div><div class="ttdeci">T clock(T... args)</div></div>
 <div class="ttc" id="aclock_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a></div></div>
@@ -299,43 +299,43 @@ Here is the call graph for this function:</div>
 <div class="line">     &quot;w12.csv&quot; title &quot;w2&quot;</div>
 </div><!-- fragment --><p> <img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/machine_learning/kohonen/test1.svg" alt="Sample execution
 output" style="pointer-events: none;" class="inline"/> </p>
-<div class="fragment"><div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>             {</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>    <span class="keywordtype">int</span> j = 0, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 500;</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>    <span class="keywordtype">int</span> features = 2;</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>    <span class="keywordtype">int</span> num_out = 50;</div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; W(num_out);</div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>        <span class="comment">// loop till max(N, num_out)</span></div>
-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>        <span class="keywordflow">if</span> (i &lt; N) {  <span class="comment">// only add new arrays if i &lt; N</span></div>
-<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>            X[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
-<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>        }</div>
-<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
-<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>            W[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span> </div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>            <span class="keywordflow">for</span> (j = 0; j &lt; features; j++) {</div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>                <span class="comment">// preallocate with random initial weights</span></div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>                W[i][j] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-1, 1);</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>            }</div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>        }</div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>    }</div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span> </div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>    <a class="code hl_function" href="../../d9/d49/kohonen__som__trace_8cpp.html#ae571600aa42a81bc14a4a602ea5ff00d">test_circle</a>(&amp;X);  <span class="comment">// create test data around circumference of a circle</span></div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a>(<span class="stringliteral">&quot;test1.csv&quot;</span>, X);    <span class="comment">// save test data points</span></div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a>(<span class="stringliteral">&quot;w11.csv&quot;</span>, W);      <span class="comment">// save initial random weights</span></div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a042f435bca0839e721fc1574a61e8da3">kohonen_som_tracer</a>(X, &amp;W, 0.1);  <span class="comment">// train the SOM</span></div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a>(<span class="stringliteral">&quot;w12.csv&quot;</span>, W);      <span class="comment">// save the resultant weights</span></div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  233</span>             {</div>
+<div class="line"><span class="lineno">  234</span>    <span class="keywordtype">int</span> j = 0, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 500;</div>
+<div class="line"><span class="lineno">  235</span>    <span class="keywordtype">int</span> features = 2;</div>
+<div class="line"><span class="lineno">  236</span>    <span class="keywordtype">int</span> num_out = 50;</div>
+<div class="line"><span class="lineno">  237</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
+<div class="line"><span class="lineno">  238</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; W(num_out);</div>
+<div class="line"><span class="lineno">  239</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
+<div class="line"><span class="lineno">  240</span>        <span class="comment">// loop till max(N, num_out)</span></div>
+<div class="line"><span class="lineno">  241</span>        <span class="keywordflow">if</span> (i &lt; N) {  <span class="comment">// only add new arrays if i &lt; N</span></div>
+<div class="line"><span class="lineno">  242</span>            X[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><span class="lineno">  243</span>        }</div>
+<div class="line"><span class="lineno">  244</span>        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
+<div class="line"><span class="lineno">  245</span>            W[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><span class="lineno">  246</span> </div>
+<div class="line"><span class="lineno">  247</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  248</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  249</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  250</span>            <span class="keywordflow">for</span> (j = 0; j &lt; features; j++) {</div>
+<div class="line"><span class="lineno">  251</span>                <span class="comment">// preallocate with random initial weights</span></div>
+<div class="line"><span class="lineno">  252</span>                W[i][j] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-1, 1);</div>
+<div class="line"><span class="lineno">  253</span>            }</div>
+<div class="line"><span class="lineno">  254</span>        }</div>
+<div class="line"><span class="lineno">  255</span>    }</div>
+<div class="line"><span class="lineno">  256</span> </div>
+<div class="line"><span class="lineno">  257</span>    <a class="code hl_function" href="../../d9/d49/kohonen__som__trace_8cpp.html#ae571600aa42a81bc14a4a602ea5ff00d">test_circle</a>(&amp;X);  <span class="comment">// create test data around circumference of a circle</span></div>
+<div class="line"><span class="lineno">  258</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a>(<span class="stringliteral">&quot;test1.csv&quot;</span>, X);    <span class="comment">// save test data points</span></div>
+<div class="line"><span class="lineno">  259</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a>(<span class="stringliteral">&quot;w11.csv&quot;</span>, W);      <span class="comment">// save initial random weights</span></div>
+<div class="line"><span class="lineno">  260</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a042f435bca0839e721fc1574a61e8da3">kohonen_som_tracer</a>(X, &amp;W, 0.1);  <span class="comment">// train the SOM</span></div>
+<div class="line"><span class="lineno">  261</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a>(<span class="stringliteral">&quot;w12.csv&quot;</span>, W);      <span class="comment">// save the resultant weights</span></div>
+<div class="line"><span class="lineno">  262</span>}</div>
 <div class="ttc" id="adata__structures_2sparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:47</div></div>
 <div class="ttc" id="agroup__machine__learning_html_gae0208548f8b393528e5db01717e88e67"><div class="ttname"><a href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a></div><div class="ttdeci">int save_nd_data(const char *fname, const std::vector&lt; std::valarray&lt; double &gt; &gt; &amp;X)</div><div class="ttdef"><b>Definition:</b> kohonen_som_trace.cpp:58</div></div>
 <div class="ttc" id="agroup__machine__learning_html_gaf5ce14f026d6d231bef29161bac2b485"><div class="ttname"><a href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a></div><div class="ttdeci">double _random(double a, double b)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:53</div></div>
 <div class="ttc" id="akohonen__som__trace_8cpp_html_ae571600aa42a81bc14a4a602ea5ff00d"><div class="ttname"><a href="../../d9/d49/kohonen__som__trace_8cpp.html#ae571600aa42a81bc14a4a602ea5ff00d">test_circle</a></div><div class="ttdeci">void test_circle(std::vector&lt; std::valarray&lt; double &gt; &gt; *data)</div><div class="ttdef"><b>Definition:</b> kohonen_som_trace.cpp:196</div></div>
 <div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
 <div class="ttc" id="anamespacemachine__learning_html_a042f435bca0839e721fc1574a61e8da3"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a042f435bca0839e721fc1574a61e8da3">machine_learning::kohonen_som_tracer</a></div><div class="ttdeci">void kohonen_som_tracer(const std::vector&lt; std::valarray&lt; double &gt; &gt; &amp;X, std::vector&lt; std::valarray&lt; double &gt; &gt; *W, double alpha_min)</div><div class="ttdef"><b>Definition:</b> kohonen_som_trace.cpp:149</div></div>
-<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a></div></div>
+<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt; double &gt;</a></div></div>
 <div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -371,36 +371,36 @@ Here is the call graph for this function:</div>
 <div class="line">     &quot;w22.csv&quot; title &quot;w2&quot;</div>
 </div><!-- fragment --><p> <img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/machine_learning/kohonen/test2.svg" alt="Sample execution
 output" style="pointer-events: none;" class="inline"/> </p>
-<div class="fragment"><div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span>             {</div>
-<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>    <span class="keywordtype">int</span> j = 0, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 500;</div>
-<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span>    <span class="keywordtype">int</span> features = 2;</div>
-<div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span>    <span class="keywordtype">int</span> num_out = 20;</div>
-<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
-<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; W(num_out);</div>
-<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
-<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>        <span class="comment">// loop till max(N, num_out)</span></div>
-<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>        <span class="keywordflow">if</span> (i &lt; N) {  <span class="comment">// only add new arrays if i &lt; N</span></div>
-<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>            X[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
-<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span>        }</div>
-<div class="line"><a id="l00326" name="l00326"></a><span class="lineno">  326</span>        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
-<div class="line"><a id="l00327" name="l00327"></a><span class="lineno">  327</span>            W[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
-<div class="line"><a id="l00328" name="l00328"></a><span class="lineno">  328</span> </div>
-<div class="line"><a id="l00329" name="l00329"></a><span class="lineno">  329</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00330" name="l00330"></a><span class="lineno">  330</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00331" name="l00331"></a><span class="lineno">  331</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span>            <span class="keywordflow">for</span> (j = 0; j &lt; features; j++) {</div>
-<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>                <span class="comment">// preallocate with random initial weights</span></div>
-<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span>                W[i][j] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-1, 1);</div>
-<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span>            }</div>
-<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span>        }</div>
-<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span>    }</div>
-<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span> </div>
-<div class="line"><a id="l00339" name="l00339"></a><span class="lineno">  339</span>    <a class="code hl_function" href="../../d9/d49/kohonen__som__trace_8cpp.html#a53082f2e5bacec40266499da4547309a">test_lamniscate</a>(&amp;X);              <span class="comment">// create test data around the lamniscate</span></div>
-<div class="line"><a id="l00340" name="l00340"></a><span class="lineno">  340</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a>(<span class="stringliteral">&quot;test2.csv&quot;</span>, X);     <span class="comment">// save test data points</span></div>
-<div class="line"><a id="l00341" name="l00341"></a><span class="lineno">  341</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a>(<span class="stringliteral">&quot;w21.csv&quot;</span>, W);       <span class="comment">// save initial random weights</span></div>
-<div class="line"><a id="l00342" name="l00342"></a><span class="lineno">  342</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a042f435bca0839e721fc1574a61e8da3">kohonen_som_tracer</a>(X, &amp;W, 0.01);  <span class="comment">// train the SOM</span></div>
-<div class="line"><a id="l00343" name="l00343"></a><span class="lineno">  343</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a>(<span class="stringliteral">&quot;w22.csv&quot;</span>, W);       <span class="comment">// save the resultant weights</span></div>
-<div class="line"><a id="l00344" name="l00344"></a><span class="lineno">  344</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  315</span>             {</div>
+<div class="line"><span class="lineno">  316</span>    <span class="keywordtype">int</span> j = 0, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 500;</div>
+<div class="line"><span class="lineno">  317</span>    <span class="keywordtype">int</span> features = 2;</div>
+<div class="line"><span class="lineno">  318</span>    <span class="keywordtype">int</span> num_out = 20;</div>
+<div class="line"><span class="lineno">  319</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
+<div class="line"><span class="lineno">  320</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; W(num_out);</div>
+<div class="line"><span class="lineno">  321</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
+<div class="line"><span class="lineno">  322</span>        <span class="comment">// loop till max(N, num_out)</span></div>
+<div class="line"><span class="lineno">  323</span>        <span class="keywordflow">if</span> (i &lt; N) {  <span class="comment">// only add new arrays if i &lt; N</span></div>
+<div class="line"><span class="lineno">  324</span>            X[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><span class="lineno">  325</span>        }</div>
+<div class="line"><span class="lineno">  326</span>        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
+<div class="line"><span class="lineno">  327</span>            W[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><span class="lineno">  328</span> </div>
+<div class="line"><span class="lineno">  329</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  330</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  331</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  332</span>            <span class="keywordflow">for</span> (j = 0; j &lt; features; j++) {</div>
+<div class="line"><span class="lineno">  333</span>                <span class="comment">// preallocate with random initial weights</span></div>
+<div class="line"><span class="lineno">  334</span>                W[i][j] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-1, 1);</div>
+<div class="line"><span class="lineno">  335</span>            }</div>
+<div class="line"><span class="lineno">  336</span>        }</div>
+<div class="line"><span class="lineno">  337</span>    }</div>
+<div class="line"><span class="lineno">  338</span> </div>
+<div class="line"><span class="lineno">  339</span>    <a class="code hl_function" href="../../d9/d49/kohonen__som__trace_8cpp.html#a53082f2e5bacec40266499da4547309a">test_lamniscate</a>(&amp;X);              <span class="comment">// create test data around the lamniscate</span></div>
+<div class="line"><span class="lineno">  340</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a>(<span class="stringliteral">&quot;test2.csv&quot;</span>, X);     <span class="comment">// save test data points</span></div>
+<div class="line"><span class="lineno">  341</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a>(<span class="stringliteral">&quot;w21.csv&quot;</span>, W);       <span class="comment">// save initial random weights</span></div>
+<div class="line"><span class="lineno">  342</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a042f435bca0839e721fc1574a61e8da3">kohonen_som_tracer</a>(X, &amp;W, 0.01);  <span class="comment">// train the SOM</span></div>
+<div class="line"><span class="lineno">  343</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a>(<span class="stringliteral">&quot;w22.csv&quot;</span>, W);       <span class="comment">// save the resultant weights</span></div>
+<div class="line"><span class="lineno">  344</span>}</div>
 <div class="ttc" id="akohonen__som__trace_8cpp_html_a53082f2e5bacec40266499da4547309a"><div class="ttname"><a href="../../d9/d49/kohonen__som__trace_8cpp.html#a53082f2e5bacec40266499da4547309a">test_lamniscate</a></div><div class="ttdeci">void test_lamniscate(std::vector&lt; std::valarray&lt; double &gt; &gt; *data)</div><div class="ttdef"><b>Definition:</b> kohonen_som_trace.cpp:277</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -436,36 +436,36 @@ Here is the call graph for this function:</div>
 <div class="line">     &quot;w32.csv&quot; title &quot;w2&quot;</div>
 </div><!-- fragment --><p> <img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/machine_learning/kohonen/test3.svg" alt="Sample execution
 output" style="pointer-events: none;" class="inline"/> </p>
-<div class="fragment"><div class="line"><a id="l00414" name="l00414"></a><span class="lineno">  414</span>             {</div>
-<div class="line"><a id="l00415" name="l00415"></a><span class="lineno">  415</span>    <span class="keywordtype">int</span> j = 0, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 200;</div>
-<div class="line"><a id="l00416" name="l00416"></a><span class="lineno">  416</span>    <span class="keywordtype">int</span> features = 3;</div>
-<div class="line"><a id="l00417" name="l00417"></a><span class="lineno">  417</span>    <span class="keywordtype">int</span> num_out = 20;</div>
-<div class="line"><a id="l00418" name="l00418"></a><span class="lineno">  418</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
-<div class="line"><a id="l00419" name="l00419"></a><span class="lineno">  419</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; W(num_out);</div>
-<div class="line"><a id="l00420" name="l00420"></a><span class="lineno">  420</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
-<div class="line"><a id="l00421" name="l00421"></a><span class="lineno">  421</span>        <span class="comment">// loop till max(N, num_out)</span></div>
-<div class="line"><a id="l00422" name="l00422"></a><span class="lineno">  422</span>        <span class="keywordflow">if</span> (i &lt; N) {  <span class="comment">// only add new arrays if i &lt; N</span></div>
-<div class="line"><a id="l00423" name="l00423"></a><span class="lineno">  423</span>            X[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
-<div class="line"><a id="l00424" name="l00424"></a><span class="lineno">  424</span>        }</div>
-<div class="line"><a id="l00425" name="l00425"></a><span class="lineno">  425</span>        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
-<div class="line"><a id="l00426" name="l00426"></a><span class="lineno">  426</span>            W[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
-<div class="line"><a id="l00427" name="l00427"></a><span class="lineno">  427</span> </div>
-<div class="line"><a id="l00428" name="l00428"></a><span class="lineno">  428</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00429" name="l00429"></a><span class="lineno">  429</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00430" name="l00430"></a><span class="lineno">  430</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00431" name="l00431"></a><span class="lineno">  431</span>            <span class="keywordflow">for</span> (j = 0; j &lt; features; j++) {</div>
-<div class="line"><a id="l00432" name="l00432"></a><span class="lineno">  432</span>                <span class="comment">// preallocate with random initial weights</span></div>
-<div class="line"><a id="l00433" name="l00433"></a><span class="lineno">  433</span>                W[i][j] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-1, 1);</div>
-<div class="line"><a id="l00434" name="l00434"></a><span class="lineno">  434</span>            }</div>
-<div class="line"><a id="l00435" name="l00435"></a><span class="lineno">  435</span>        }</div>
-<div class="line"><a id="l00436" name="l00436"></a><span class="lineno">  436</span>    }</div>
-<div class="line"><a id="l00437" name="l00437"></a><span class="lineno">  437</span> </div>
-<div class="line"><a id="l00438" name="l00438"></a><span class="lineno">  438</span>    <a class="code hl_function" href="../../d9/d49/kohonen__som__trace_8cpp.html#a7154fe319e6033485a8a6cd6f0d8932d">test_3d_classes</a>(&amp;X);              <span class="comment">// create test data around the lamniscate</span></div>
-<div class="line"><a id="l00439" name="l00439"></a><span class="lineno">  439</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a>(<span class="stringliteral">&quot;test3.csv&quot;</span>, X);     <span class="comment">// save test data points</span></div>
-<div class="line"><a id="l00440" name="l00440"></a><span class="lineno">  440</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a>(<span class="stringliteral">&quot;w31.csv&quot;</span>, W);       <span class="comment">// save initial random weights</span></div>
-<div class="line"><a id="l00441" name="l00441"></a><span class="lineno">  441</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a042f435bca0839e721fc1574a61e8da3">kohonen_som_tracer</a>(X, &amp;W, 0.01);  <span class="comment">// train the SOM</span></div>
-<div class="line"><a id="l00442" name="l00442"></a><span class="lineno">  442</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a>(<span class="stringliteral">&quot;w32.csv&quot;</span>, W);       <span class="comment">// save the resultant weights</span></div>
-<div class="line"><a id="l00443" name="l00443"></a><span class="lineno">  443</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  414</span>             {</div>
+<div class="line"><span class="lineno">  415</span>    <span class="keywordtype">int</span> j = 0, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 200;</div>
+<div class="line"><span class="lineno">  416</span>    <span class="keywordtype">int</span> features = 3;</div>
+<div class="line"><span class="lineno">  417</span>    <span class="keywordtype">int</span> num_out = 20;</div>
+<div class="line"><span class="lineno">  418</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
+<div class="line"><span class="lineno">  419</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; W(num_out);</div>
+<div class="line"><span class="lineno">  420</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
+<div class="line"><span class="lineno">  421</span>        <span class="comment">// loop till max(N, num_out)</span></div>
+<div class="line"><span class="lineno">  422</span>        <span class="keywordflow">if</span> (i &lt; N) {  <span class="comment">// only add new arrays if i &lt; N</span></div>
+<div class="line"><span class="lineno">  423</span>            X[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><span class="lineno">  424</span>        }</div>
+<div class="line"><span class="lineno">  425</span>        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
+<div class="line"><span class="lineno">  426</span>            W[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><span class="lineno">  427</span> </div>
+<div class="line"><span class="lineno">  428</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  429</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  430</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  431</span>            <span class="keywordflow">for</span> (j = 0; j &lt; features; j++) {</div>
+<div class="line"><span class="lineno">  432</span>                <span class="comment">// preallocate with random initial weights</span></div>
+<div class="line"><span class="lineno">  433</span>                W[i][j] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-1, 1);</div>
+<div class="line"><span class="lineno">  434</span>            }</div>
+<div class="line"><span class="lineno">  435</span>        }</div>
+<div class="line"><span class="lineno">  436</span>    }</div>
+<div class="line"><span class="lineno">  437</span> </div>
+<div class="line"><span class="lineno">  438</span>    <a class="code hl_function" href="../../d9/d49/kohonen__som__trace_8cpp.html#a7154fe319e6033485a8a6cd6f0d8932d">test_3d_classes</a>(&amp;X);              <span class="comment">// create test data around the lamniscate</span></div>
+<div class="line"><span class="lineno">  439</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a>(<span class="stringliteral">&quot;test3.csv&quot;</span>, X);     <span class="comment">// save test data points</span></div>
+<div class="line"><span class="lineno">  440</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a>(<span class="stringliteral">&quot;w31.csv&quot;</span>, W);       <span class="comment">// save initial random weights</span></div>
+<div class="line"><span class="lineno">  441</span>    <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a042f435bca0839e721fc1574a61e8da3">kohonen_som_tracer</a>(X, &amp;W, 0.01);  <span class="comment">// train the SOM</span></div>
+<div class="line"><span class="lineno">  442</span>    <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gae0208548f8b393528e5db01717e88e67">save_nd_data</a>(<span class="stringliteral">&quot;w32.csv&quot;</span>, W);       <span class="comment">// save the resultant weights</span></div>
+<div class="line"><span class="lineno">  443</span>}</div>
 <div class="ttc" id="akohonen__som__trace_8cpp_html_a7154fe319e6033485a8a6cd6f0d8932d"><div class="ttname"><a href="../../d9/d49/kohonen__som__trace_8cpp.html#a7154fe319e6033485a8a6cd6f0d8932d">test_3d_classes</a></div><div class="ttdeci">void test_3d_classes(std::vector&lt; std::valarray&lt; double &gt; &gt; *data)</div><div class="ttdef"><b>Definition:</b> kohonen_som_trace.cpp:359</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -507,41 +507,41 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00359" name="l00359"></a><span class="lineno">  359</span>                                                           {</div>
-<div class="line"><a id="l00360" name="l00360"></a><span class="lineno">  360</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
-<div class="line"><a id="l00361" name="l00361"></a><span class="lineno">  361</span>    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.1;  <span class="comment">// radius of cluster</span></div>
-<div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span>    <span class="keywordtype">int</span> i = 0;</div>
-<div class="line"><a id="l00363" name="l00363"></a><span class="lineno">  363</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> num_classes = 8;</div>
-<div class="line"><a id="l00364" name="l00364"></a><span class="lineno">  364</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;const std::array&lt;double, 3&gt;</a>, num_classes&gt; centres = {</div>
-<div class="line"><a id="l00365" name="l00365"></a><span class="lineno">  365</span>        <span class="comment">// centres of each class cluster</span></div>
-<div class="line"><a id="l00366" name="l00366"></a><span class="lineno">  366</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, .5, .5}),    <span class="comment">// centre of class 0</span></div>
-<div class="line"><a id="l00367" name="l00367"></a><span class="lineno">  367</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, .5, -.5}),   <span class="comment">// centre of class 1</span></div>
-<div class="line"><a id="l00368" name="l00368"></a><span class="lineno">  368</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, -.5, .5}),   <span class="comment">// centre of class 2</span></div>
-<div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, -.5, -.5}),  <span class="comment">// centre of class 3</span></div>
-<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({-.5, .5, .5}),   <span class="comment">// centre of class 4</span></div>
-<div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({-.5, .5, -.5}),  <span class="comment">// centre of class 5</span></div>
-<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({-.5, -.5, .5}),  <span class="comment">// centre of class 6</span></div>
-<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({-.5, -.5, -.5})  <span class="comment">// centre of class 7</span></div>
-<div class="line"><a id="l00374" name="l00374"></a><span class="lineno">  374</span>    };</div>
-<div class="line"><a id="l00375" name="l00375"></a><span class="lineno">  375</span> </div>
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-<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00379" name="l00379"></a><span class="lineno">  379</span>    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
-<div class="line"><a id="l00380" name="l00380"></a><span class="lineno">  380</span>        <span class="keywordtype">int</span> cls =</div>
-<div class="line"><a id="l00381" name="l00381"></a><span class="lineno">  381</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % num_classes;  <span class="comment">// select a random class for the point</span></div>
-<div class="line"><a id="l00382" name="l00382"></a><span class="lineno">  382</span> </div>
-<div class="line"><a id="l00383" name="l00383"></a><span class="lineno">  383</span>        <span class="comment">// create random coordinates (x,y,z) around the centre of the class</span></div>
-<div class="line"><a id="l00384" name="l00384"></a><span class="lineno">  384</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][0] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][0] - R, centres[cls][0] + R);</div>
-<div class="line"><a id="l00385" name="l00385"></a><span class="lineno">  385</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][1] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][1] - R, centres[cls][1] + R);</div>
-<div class="line"><a id="l00386" name="l00386"></a><span class="lineno">  386</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][2] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][2] - R, centres[cls][2] + R);</div>
-<div class="line"><a id="l00387" name="l00387"></a><span class="lineno">  387</span> </div>
-<div class="line"><a id="l00388" name="l00388"></a><span class="lineno">  388</span>        <span class="comment">/* The follosing can also be used</span></div>
-<div class="line"><a id="l00389" name="l00389"></a><span class="lineno">  389</span><span class="comment">        for (int j = 0; j &lt; 3; j++)</span></div>
-<div class="line"><a id="l00390" name="l00390"></a><span class="lineno">  390</span><span class="comment">            data[0][i][j] = _random(centres[cls][j] - R, centres[cls][j] + R);</span></div>
-<div class="line"><a id="l00391" name="l00391"></a><span class="lineno">  391</span><span class="comment">        */</span></div>
-<div class="line"><a id="l00392" name="l00392"></a><span class="lineno">  392</span>    }</div>
-<div class="line"><a id="l00393" name="l00393"></a><span class="lineno">  393</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  359</span>                                                           {</div>
+<div class="line"><span class="lineno">  360</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
+<div class="line"><span class="lineno">  361</span>    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.1;  <span class="comment">// radius of cluster</span></div>
+<div class="line"><span class="lineno">  362</span>    <span class="keywordtype">int</span> i = 0;</div>
+<div class="line"><span class="lineno">  363</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> num_classes = 8;</div>
+<div class="line"><span class="lineno">  364</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;const std::array&lt;double, 3&gt;</a>, num_classes&gt; centres = {</div>
+<div class="line"><span class="lineno">  365</span>        <span class="comment">// centres of each class cluster</span></div>
+<div class="line"><span class="lineno">  366</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, .5, .5}),    <span class="comment">// centre of class 0</span></div>
+<div class="line"><span class="lineno">  367</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, .5, -.5}),   <span class="comment">// centre of class 1</span></div>
+<div class="line"><span class="lineno">  368</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, -.5, .5}),   <span class="comment">// centre of class 2</span></div>
+<div class="line"><span class="lineno">  369</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({.5, -.5, -.5}),  <span class="comment">// centre of class 3</span></div>
+<div class="line"><span class="lineno">  370</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({-.5, .5, .5}),   <span class="comment">// centre of class 4</span></div>
+<div class="line"><span class="lineno">  371</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({-.5, .5, -.5}),  <span class="comment">// centre of class 5</span></div>
+<div class="line"><span class="lineno">  372</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({-.5, -.5, .5}),  <span class="comment">// centre of class 6</span></div>
+<div class="line"><span class="lineno">  373</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a>({-.5, -.5, -.5})  <span class="comment">// centre of class 7</span></div>
+<div class="line"><span class="lineno">  374</span>    };</div>
+<div class="line"><span class="lineno">  375</span> </div>
+<div class="line"><span class="lineno">  376</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  377</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  378</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  379</span>    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
+<div class="line"><span class="lineno">  380</span>        <span class="keywordtype">int</span> cls =</div>
+<div class="line"><span class="lineno">  381</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % num_classes;  <span class="comment">// select a random class for the point</span></div>
+<div class="line"><span class="lineno">  382</span> </div>
+<div class="line"><span class="lineno">  383</span>        <span class="comment">// create random coordinates (x,y,z) around the centre of the class</span></div>
+<div class="line"><span class="lineno">  384</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][0] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][0] - R, centres[cls][0] + R);</div>
+<div class="line"><span class="lineno">  385</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][1] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][1] - R, centres[cls][1] + R);</div>
+<div class="line"><span class="lineno">  386</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][2] = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][2] - R, centres[cls][2] + R);</div>
+<div class="line"><span class="lineno">  387</span> </div>
+<div class="line"><span class="lineno">  388</span>        <span class="comment">/* The follosing can also be used</span></div>
+<div class="line"><span class="lineno">  389</span><span class="comment">        for (int j = 0; j &lt; 3; j++)</span></div>
+<div class="line"><span class="lineno">  390</span><span class="comment">            data[0][i][j] = _random(centres[cls][j] - R, centres[cls][j] + R);</span></div>
+<div class="line"><span class="lineno">  391</span><span class="comment">        */</span></div>
+<div class="line"><span class="lineno">  392</span>    }</div>
+<div class="line"><span class="lineno">  393</span>}</div>
 <div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
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 <div class="ttc" id="arand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a></div><div class="ttdeci">T rand(T... args)</div></div>
@@ -578,23 +578,23 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
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-<div class="fragment"><div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>                                                       {</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.75, dr = 0.3;</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>    <span class="keywordtype">double</span> a_t = 0., b_t = 2.f * M_PI;  <span class="comment">// theta random between 0 and 2*pi</span></div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    <span class="keywordtype">double</span> a_r = R - dr, b_r = R + dr;  <span class="comment">// radius random between R-dr and R+dr</span></div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>    <span class="keywordtype">int</span> i = 0;</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span> </div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>        <span class="keywordtype">double</span> r = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(a_r, b_r);      <span class="comment">// random radius</span></div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>        <span class="keywordtype">double</span> theta = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(a_t, b_t);  <span class="comment">// random theta</span></div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][0] = r * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">cos</a>(theta);    <span class="comment">// convert from polar to cartesian</span></div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][1] = r * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">sin</a>(theta);</div>
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-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  196</span>                                                       {</div>
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+<div class="line"><span class="lineno">  198</span>    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.75, dr = 0.3;</div>
+<div class="line"><span class="lineno">  199</span>    <span class="keywordtype">double</span> a_t = 0., b_t = 2.f * M_PI;  <span class="comment">// theta random between 0 and 2*pi</span></div>
+<div class="line"><span class="lineno">  200</span>    <span class="keywordtype">double</span> a_r = R - dr, b_r = R + dr;  <span class="comment">// radius random between R-dr and R+dr</span></div>
+<div class="line"><span class="lineno">  201</span>    <span class="keywordtype">int</span> i = 0;</div>
+<div class="line"><span class="lineno">  202</span> </div>
+<div class="line"><span class="lineno">  203</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  204</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">  205</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  206</span>    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
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+<div class="line"><span class="lineno">  208</span>        <span class="keywordtype">double</span> theta = <a class="code hl_function" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(a_t, b_t);  <span class="comment">// random theta</span></div>
+<div class="line"><span class="lineno">  209</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][0] = r * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">cos</a>(theta);    <span class="comment">// convert from polar to cartesian</span></div>
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+<div class="line"><span class="lineno">  139</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Median: &quot;</span>;            <span class="comment">// Median defination: https://en.wikipedia.org/wiki/Median</span></div>
+<div class="line"><span class="lineno">  140</span>    <span class="keywordtype">int</span> x = <a class="code hl_function" href="../../d9/d69/median__search_8cpp.html#a868847218f694e78bf433a0ff7648bae">search::median_search::median_of_medians</a>(a,  (n - 1) / 2);</div>
+<div class="line"><span class="lineno">  141</span>    <span class="keywordflow">if</span>(n % 2 == 0){</div>
+<div class="line"><span class="lineno">  142</span>        <span class="keywordtype">int</span> y = <a class="code hl_function" href="../../d9/d69/median__search_8cpp.html#a868847218f694e78bf433a0ff7648bae">search::median_search::median_of_medians</a>(a, n / 2);</div>
+<div class="line"><span class="lineno">  143</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; (float(x) + float(y))/2.0;</div>
+<div class="line"><span class="lineno">  144</span>    }</div>
+<div class="line"><span class="lineno">  145</span>    <span class="keywordflow">else</span>{</div>
+<div class="line"><span class="lineno">  146</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; x;</div>
+<div class="line"><span class="lineno">  147</span>    }</div>
+<div class="line"><span class="lineno">  148</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nTo find i-th smallest element &quot;</span>;</div>
+<div class="line"><span class="lineno">  149</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEnter i: &quot;</span>;</div>
+<div class="line"><span class="lineno">  150</span>    <span class="keywordtype">int</span> idx = 0;</div>
+<div class="line"><span class="lineno">  151</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; idx;</div>
+<div class="line"><span class="lineno">  152</span>    idx--;</div>
+<div class="line"><span class="lineno">  153</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; idx + 1&lt;&lt; <span class="stringliteral">&quot;-th smallest element: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d9/d69/median__search_8cpp.html#a868847218f694e78bf433a0ff7648bae">search::median_search::median_of_medians</a>(a, idx) &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;</div>
+<div class="line"><span class="lineno">  154</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  155</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="amedian__search_8cpp_html_a868847218f694e78bf433a0ff7648bae"><div class="ttname"><a href="../../d9/d69/median__search_8cpp.html#a868847218f694e78bf433a0ff7648bae">search::median_search::median_of_medians</a></div><div class="ttdeci">int median_of_medians(const std::vector&lt; int &gt; &amp;A, const int &amp;idx)</div><div class="ttdef"><b>Definition:</b> median_search.cpp:62</div></div>
 <div class="ttc" id="amedian__search_8cpp_html_ae1a3968e7947464bee7714f6d43b7002"><div class="ttname"><a href="../../d9/d69/median__search_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a></div><div class="ttdeci">void test()</div><div class="ttdef"><b>Definition:</b> median_search.cpp:107</div></div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int &gt;</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -227,45 +227,45 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>corresponding element which we want to search. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>                                                                {</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    <span class="keywordtype">int</span> pivot = 0;                  <span class="comment">// initialized with zero</span></div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> a(A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>());</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> m;</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <span class="keywordtype">int</span> r = a.size();</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i &lt; r; i += 5){</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/sort.html">std::sort</a>(a.begin() + i, a.begin() + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(r, i + 5));</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        <span class="keywordtype">int</span> mid = (i + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(r, i + 5)) / 2;</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        m.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(a[mid]);</div>
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-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    <span class="keywordtype">int</span> sz = int(m.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <span class="keywordflow">if</span>(sz &lt;= 5){</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/sort.html">std::sort</a>(m.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), m.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>());</div>
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-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> high;</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i &lt; r; i++){</div>
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-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    <span class="keywordflow">else</span>{</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>        <span class="keywordflow">return</span> pivot;</div>
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-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   62</span>                                                                {</div>
+<div class="line"><span class="lineno">   63</span>    <span class="keywordtype">int</span> pivot = 0;                  <span class="comment">// initialized with zero</span></div>
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+<div class="line"><span class="lineno">   65</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> m;</div>
+<div class="line"><span class="lineno">   66</span>    <span class="keywordtype">int</span> r = a.size();</div>
+<div class="line"><span class="lineno">   67</span>    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i &lt; r; i += 5){</div>
+<div class="line"><span class="lineno">   68</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/sort.html">std::sort</a>(a.begin() + i, a.begin() + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(r, i + 5));</div>
+<div class="line"><span class="lineno">   69</span>        <span class="keywordtype">int</span> mid = (i + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(r, i + 5)) / 2;</div>
+<div class="line"><span class="lineno">   70</span>        m.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(a[mid]);</div>
+<div class="line"><span class="lineno">   71</span>    }</div>
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+<div class="line"><span class="lineno">   73</span>    <span class="keywordflow">if</span>(sz &lt;= 5){</div>
+<div class="line"><span class="lineno">   74</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/sort.html">std::sort</a>(m.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), m.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>());</div>
+<div class="line"><span class="lineno">   75</span>        pivot = m[(sz- 1) / 2];</div>
+<div class="line"><span class="lineno">   76</span>    }</div>
+<div class="line"><span class="lineno">   77</span>    <span class="keywordflow">else</span>{</div>
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+<div class="line"><span class="lineno">   79</span>    }</div>
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+<div class="line"><span class="lineno">   81</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> high;</div>
+<div class="line"><span class="lineno">   82</span>    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i &lt; r; i++){</div>
+<div class="line"><span class="lineno">   83</span>        <span class="keywordflow">if</span>(a[i] &lt; pivot){</div>
+<div class="line"><span class="lineno">   84</span>            low.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(a[i]);</div>
+<div class="line"><span class="lineno">   85</span>        }</div>
+<div class="line"><span class="lineno">   86</span>        <span class="keywordflow">else</span> <span class="keywordflow">if</span>(a[i] &gt; pivot){</div>
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+<div class="line"><span class="lineno">   88</span>        }</div>
+<div class="line"><span class="lineno">   89</span>    }</div>
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+<div class="line"><span class="lineno">   91</span>    <span class="keywordflow">if</span>(idx &lt; k){</div>
+<div class="line"><span class="lineno">   92</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/d69/median__search_8cpp.html#a868847218f694e78bf433a0ff7648bae">median_of_medians</a>(low, idx);</div>
+<div class="line"><span class="lineno">   93</span>    }</div>
+<div class="line"><span class="lineno">   94</span>    <span class="keywordflow">else</span> <span class="keywordflow">if</span>(idx &gt; k){</div>
+<div class="line"><span class="lineno">   95</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/d69/median__search_8cpp.html#a868847218f694e78bf433a0ff7648bae">median_of_medians</a>(high, idx-k-1);</div>
+<div class="line"><span class="lineno">   96</span>    }</div>
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+<div class="line"><span class="lineno">   98</span>        <span class="keywordflow">return</span> pivot;</div>
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 <div class="ttc" id="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/begin.html">std::vector::begin</a></div><div class="ttdeci">T begin(T... args)</div></div>
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 <div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/end.html">std::vector::end</a></div><div class="ttdeci">T end(T... args)</div></div>
@@ -297,23 +297,23 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Function to test above algorithm </p>
-<div class="fragment"><div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>           {</div>
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-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    assert(A[6] == search::median_search::median_of_medians(A, i));     <span class="comment">// A[6]  = 43, is the fourth smallest element.</span></div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;test case:1 passed\n&quot;</span>;</div>
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@@ -146,16 +146,16 @@ Functions</h2></td></tr>
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 <dl class="section return"><dt>Returns</dt><dd>n-th element of the Fbinacci's sequence </dd></dl>
-<div class="fragment"><div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span>                               {</div>
-<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span>    <span class="comment">/* If the input is 0 or 1 just return the same</span></div>
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-<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>        <span class="keywordflow">return</span> n;</div>
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-<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>    <span class="comment">/* Add the last 2 values of the sequence to get next */</span></div>
-<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci</a>(n - 1) + <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci</a>(n - 2);</div>
-<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   19</span>                               {</div>
+<div class="line"><span class="lineno">   20</span>    <span class="comment">/* If the input is 0 or 1 just return the same</span></div>
+<div class="line"><span class="lineno">   21</span><span class="comment">       This will set the first 2 values of the sequence */</span></div>
+<div class="line"><span class="lineno">   22</span>    <span class="keywordflow">if</span> (n &lt;= 1) {</div>
+<div class="line"><span class="lineno">   23</span>        <span class="keywordflow">return</span> n;</div>
+<div class="line"><span class="lineno">   24</span>    }</div>
+<div class="line"><span class="lineno">   25</span> </div>
+<div class="line"><span class="lineno">   26</span>    <span class="comment">/* Add the last 2 values of the sequence to get next */</span></div>
+<div class="line"><span class="lineno">   27</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci</a>(n - 1) + <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci</a>(n - 2);</div>
+<div class="line"><span class="lineno">   28</span>}</div>
 <div class="ttc" id="afibonacci_8cpp_html_aaf94f3212385cff0a5f19ff6b0cce8e7"><div class="ttname"><a href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci</a></div><div class="ttdeci">uint64_t fibonacci(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci.cpp:19</div></div>
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 Here is the call graph for this function:</div>
@@ -183,13 +183,13 @@ Here is the call graph for this function:</div>
 </div><div class="memdoc">
 
 <p>Main function. </p>
-<div class="fragment"><div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>           {</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
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-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>}</div>
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+<div class="line"><span class="lineno">   63</span>    <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
+<div class="line"><span class="lineno">   64</span>    <span class="keywordtype">int</span> n = 0;</div>
+<div class="line"><span class="lineno">   65</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
+<div class="line"><span class="lineno">   66</span>    assert(n &gt;= 0);</div>
+<div class="line"><span class="lineno">   67</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;F(&quot;</span> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot;)= &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci</a>(n) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   68</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
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 <p >Function for testing the <a class="el" href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci()</a> function with a few test cases and assert statement. </p><dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>                   {</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>    uint64_t test_case_1 = <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci</a>(0);</div>
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-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span> </div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    uint64_t test_case_2 = <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci</a>(1);</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    assert(test_case_2 == 1);</div>
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-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span> </div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    uint64_t test_case_3 = <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci</a>(2);</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>    assert(test_case_3 == 1);</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 3!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span> </div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    uint64_t test_case_4 = <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci</a>(3);</div>
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-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span> </div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    uint64_t test_case_5 = <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci</a>(4);</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    assert(test_case_5 == 3);</div>
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-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span> </div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    uint64_t test_case_6 = <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci</a>(15);</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    assert(test_case_6 == 610);</div>
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-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   35</span>                   {</div>
+<div class="line"><span class="lineno">   36</span>    uint64_t test_case_1 = <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci</a>(0);</div>
+<div class="line"><span class="lineno">   37</span>    assert(test_case_1 == 0);</div>
+<div class="line"><span class="lineno">   38</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 1!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   39</span> </div>
+<div class="line"><span class="lineno">   40</span>    uint64_t test_case_2 = <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci</a>(1);</div>
+<div class="line"><span class="lineno">   41</span>    assert(test_case_2 == 1);</div>
+<div class="line"><span class="lineno">   42</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 2!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   43</span> </div>
+<div class="line"><span class="lineno">   44</span>    uint64_t test_case_3 = <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci</a>(2);</div>
+<div class="line"><span class="lineno">   45</span>    assert(test_case_3 == 1);</div>
+<div class="line"><span class="lineno">   46</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 3!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   47</span> </div>
+<div class="line"><span class="lineno">   48</span>    uint64_t test_case_4 = <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci</a>(3);</div>
+<div class="line"><span class="lineno">   49</span>    assert(test_case_4 == 2);</div>
+<div class="line"><span class="lineno">   50</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 4!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   51</span> </div>
+<div class="line"><span class="lineno">   52</span>    uint64_t test_case_5 = <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci</a>(4);</div>
+<div class="line"><span class="lineno">   53</span>    assert(test_case_5 == 3);</div>
+<div class="line"><span class="lineno">   54</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 5!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   55</span> </div>
+<div class="line"><span class="lineno">   56</span>    uint64_t test_case_6 = <a class="code hl_function" href="../../d9/d89/fibonacci_8cpp.html#aaf94f3212385cff0a5f19ff6b0cce8e7">fibonacci</a>(15);</div>
+<div class="line"><span class="lineno">   57</span>    assert(test_case_6 == 610);</div>
+<div class="line"><span class="lineno">   58</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 6!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   59</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
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   <ul>
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+<div class="line"><span class="lineno">  135</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the size of Hash Table. = &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  136</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; mod;</div>
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+<div class="line"><span class="lineno">  138</span>    <a class="code hl_class" href="../../dd/d1c/classhash__chain.html">hash_chain</a> mychain(mod);</div>
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+<div class="line"><span class="lineno">  142</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  143</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;PLEASE CHOOSE -&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><span class="lineno">  145</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2. Find element.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  146</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3. Generate Hash.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  147</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4. Display Hash table.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  148</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;5. Exit.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  149</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; c;</div>
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+<div class="line"><span class="lineno">  152</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter element to add = &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  153</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; x;</div>
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+<div class="line"><span class="lineno">  157</span>                <span class="keywordflow">break</span>;</div>
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+<div class="line"><span class="lineno">  163</span>                <span class="keywordflow">break</span>;</div>
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+<div class="line"><span class="lineno">  167</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hash of &quot;</span> &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot; is = &quot;</span> &lt;&lt; mychain.hash(x)</div>
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+ <tr id="projectrow">
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+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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+ <tr id="projectrow">
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+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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@@ -30,8 +30,8 @@ MathJax.Hub.Config({
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- <tr style="height: 56px;">
-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
+  <td id="projectalign">
    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
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@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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diff --git a/d9/dde/classbinary__search__tree.html b/d9/dde/classbinary__search__tree.html
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+ <tr id="projectrow">
+  <td id="projectalign">
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@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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+<!-- Generated by Doxygen 1.9.3 -->
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@@ -105,7 +105,7 @@ $(document).ready(function(){initNavTree('d9/dde/classbinary__search__tree.html'
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+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d3/da6/classbinary__search__tree__coll__graph.svg" width="339" height="171"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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+          <td class="memname"><a class="el" href="../../d9/dde/classbinary__search__tree.html">binary_search_tree</a>&lt; T &gt;<a class="el" href="../../d9/dde/classbinary__search__tree.html">::binary_search_tree</a> </td>
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@@ -218,10 +218,10 @@ template&lt;class T &gt; </div>
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 <p>Construct a new Binary Search Tree object. </p>
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-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>        <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a> = <span class="keyword">nullptr</span>;</div>
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-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  246</span>                         {</div>
+<div class="line"><span class="lineno">  247</span>        <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a> = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  248</span>        <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#a07ba32ce1a2af6e357600ac8c8e98dbc">size_</a> = 0;</div>
+<div class="line"><span class="lineno">  249</span>    }</div>
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 <div class="ttc" id="aclassbinary__search__tree_html_aa08f65f6f3bfcb14f8c3d1e65305ae50"><div class="ttname"><a href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">binary_search_tree::root_</a></div><div class="ttdeci">std::unique_ptr&lt; bst_node &gt; root_</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:41</div></div>
 </div><!-- fragment -->
@@ -275,19 +275,19 @@ template&lt;class T &gt; </div>
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-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#aa4f84b2eec9b9201af1840868ddb5fb2">contains</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right, value);</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>        } <span class="keywordflow">else</span> {</div>
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-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  176</span>                                                          {</div>
+<div class="line"><span class="lineno">  177</span>        <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>) {</div>
+<div class="line"><span class="lineno">  178</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  179</span>        }</div>
+<div class="line"><span class="lineno">  180</span> </div>
+<div class="line"><span class="lineno">  181</span>        <span class="keywordflow">if</span> (value &lt; node-&gt;value) {</div>
+<div class="line"><span class="lineno">  182</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#aa4f84b2eec9b9201af1840868ddb5fb2">contains</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left, value);</div>
+<div class="line"><span class="lineno">  183</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (value &gt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;value) {</div>
+<div class="line"><span class="lineno">  184</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#aa4f84b2eec9b9201af1840868ddb5fb2">contains</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right, value);</div>
+<div class="line"><span class="lineno">  185</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  186</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  187</span>        }</div>
+<div class="line"><span class="lineno">  188</span>    }</div>
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 <div class="ttc" id="astructnode_html"><div class="ttname"><a href="../../d5/da1/structnode.html">node</a></div><div class="ttdef"><b>Definition:</b> avltree.cpp:13</div></div>
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@@ -335,7 +335,7 @@ template&lt;class T &gt; </div>
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 <dd>
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+<div class="fragment"><div class="line"><span class="lineno">  288</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#aa4f84b2eec9b9201af1840868ddb5fb2">contains</a>(<a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>, value); }</div>
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@@ -392,15 +392,15 @@ template&lt;class T &gt; </div>
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-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>            ret_value = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;value;</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   52</span>                                                               {</div>
+<div class="line"><span class="lineno">   53</span>        <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>) {</div>
+<div class="line"><span class="lineno">   54</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   55</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right) {</div>
+<div class="line"><span class="lineno">   56</span>            ret_value = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;value;</div>
+<div class="line"><span class="lineno">   57</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   58</span>        }</div>
+<div class="line"><span class="lineno">   59</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a75f897af6aa732a9901454401c869bcb">find_max</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right, ret_value);</div>
+<div class="line"><span class="lineno">   60</span>    }</div>
 <div class="ttc" id="aclassbinary__search__tree_html_a75f897af6aa732a9901454401c869bcb"><div class="ttname"><a href="../../d9/dde/classbinary__search__tree.html#a75f897af6aa732a9901454401c869bcb">binary_search_tree::find_max</a></div><div class="ttdeci">bool find_max(std::unique_ptr&lt; bst_node &gt; &amp;node, T &amp;ret_value)</div><div class="ttdoc">Recursive function to find the maximum value in the BST.</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:52</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -447,7 +447,7 @@ template&lt;class T &gt; </div>
 <dl class="section return"><dt>Returns</dt><dd>true If maximum value was successfully found. </dd>
 <dd>
 false Otherwise. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a75f897af6aa732a9901454401c869bcb">find_max</a>(<a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>, ret_value); }</div>
+<div class="fragment"><div class="line"><span class="lineno">  306</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a75f897af6aa732a9901454401c869bcb">find_max</a>(<a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>, ret_value); }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -504,16 +504,16 @@ template&lt;class T &gt; </div>
 <dl class="section return"><dt>Returns</dt><dd>true If the minimum value was successfully found. </dd>
 <dd>
 false Otherwise. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>                                                               {</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>) {</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left) {</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>            ret_value = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;value;</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        }</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span> </div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af9a2c7c187a7ca3142c77ce342ef3153">find_min</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left, ret_value);</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   70</span>                                                               {</div>
+<div class="line"><span class="lineno">   71</span>        <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>) {</div>
+<div class="line"><span class="lineno">   72</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   73</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left) {</div>
+<div class="line"><span class="lineno">   74</span>            ret_value = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;value;</div>
+<div class="line"><span class="lineno">   75</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   76</span>        }</div>
+<div class="line"><span class="lineno">   77</span> </div>
+<div class="line"><span class="lineno">   78</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af9a2c7c187a7ca3142c77ce342ef3153">find_min</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left, ret_value);</div>
+<div class="line"><span class="lineno">   79</span>    }</div>
 <div class="ttc" id="aclassbinary__search__tree_html_af9a2c7c187a7ca3142c77ce342ef3153"><div class="ttname"><a href="../../d9/dde/classbinary__search__tree.html#af9a2c7c187a7ca3142c77ce342ef3153">binary_search_tree::find_min</a></div><div class="ttdeci">bool find_min(std::unique_ptr&lt; bst_node &gt; &amp;node, T &amp;ret_value)</div><div class="ttdoc">Recursive function to find the minimum value in the BST.</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:70</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -560,7 +560,7 @@ template&lt;class T &gt; </div>
 <dl class="section return"><dt>Returns</dt><dd>true If minimum value was successfully found. </dd>
 <dd>
 false Otherwise. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af9a2c7c187a7ca3142c77ce342ef3153">find_min</a>(<a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>, ret_value); }</div>
+<div class="fragment"><div class="line"><span class="lineno">  297</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af9a2c7c187a7ca3142c77ce342ef3153">find_min</a>(<a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>, ret_value); }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -597,12 +597,12 @@ template&lt;class T &gt; </div>
 
 <p>Get all values of the BST in in-order order. </p>
 <dl class="section return"><dt>Returns</dt><dd>std::vector&lt;T&gt; List of values, sorted in in-order order. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>                                        {</div>
-<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>        <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a2fcf37549bd002c174a45b0b4203c2bd">traverse_inorder</a>([&amp;](T node_value) { <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.push_back(node_value); },</div>
-<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>                         <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>);</div>
-<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  320</span>                                        {</div>
+<div class="line"><span class="lineno">  321</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  322</span>        <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a2fcf37549bd002c174a45b0b4203c2bd">traverse_inorder</a>([&amp;](T node_value) { <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.push_back(node_value); },</div>
+<div class="line"><span class="lineno">  323</span>                         <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>);</div>
+<div class="line"><span class="lineno">  324</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  325</span>    }</div>
 <div class="ttc" id="aclassbinary__search__tree_html_a2fcf37549bd002c174a45b0b4203c2bd"><div class="ttname"><a href="../../d9/dde/classbinary__search__tree.html#a2fcf37549bd002c174a45b0b4203c2bd">binary_search_tree::traverse_inorder</a></div><div class="ttdeci">void traverse_inorder(std::function&lt; void(T)&gt; callback, std::unique_ptr&lt; bst_node &gt; &amp;node)</div><div class="ttdoc">Recursive function to traverse the tree in in-order order.</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:196</div></div>
 <div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
 <div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
@@ -642,12 +642,12 @@ template&lt;class T &gt; </div>
 
 <p>Get all values of the BST in post-order order. </p>
 <dl class="section return"><dt>Returns</dt><dd>std::vector&lt;T&gt; List of values, sorted in post-order order. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00344" name="l00344"></a><span class="lineno">  344</span>                                          {</div>
-<div class="line"><a id="l00345" name="l00345"></a><span class="lineno">  345</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00346" name="l00346"></a><span class="lineno">  346</span>        <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a87c0a35845d27e0f6fc1f4eaa0333362">traverse_postorder</a>([&amp;](T node_value) { <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.push_back(node_value); },</div>
-<div class="line"><a id="l00347" name="l00347"></a><span class="lineno">  347</span>                           <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>);</div>
-<div class="line"><a id="l00348" name="l00348"></a><span class="lineno">  348</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00349" name="l00349"></a><span class="lineno">  349</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  344</span>                                          {</div>
+<div class="line"><span class="lineno">  345</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  346</span>        <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a87c0a35845d27e0f6fc1f4eaa0333362">traverse_postorder</a>([&amp;](T node_value) { <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.push_back(node_value); },</div>
+<div class="line"><span class="lineno">  347</span>                           <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>);</div>
+<div class="line"><span class="lineno">  348</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  349</span>    }</div>
 <div class="ttc" id="aclassbinary__search__tree_html_a87c0a35845d27e0f6fc1f4eaa0333362"><div class="ttname"><a href="../../d9/dde/classbinary__search__tree.html#a87c0a35845d27e0f6fc1f4eaa0333362">binary_search_tree::traverse_postorder</a></div><div class="ttdeci">void traverse_postorder(std::function&lt; void(T)&gt; callback, std::unique_ptr&lt; bst_node &gt; &amp;node)</div><div class="ttdoc">Recursive function to traverse the tree in post-order order.</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:230</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -685,12 +685,12 @@ template&lt;class T &gt; </div>
 
 <p>Get all values of the BST in pre-order order. </p>
 <dl class="section return"><dt>Returns</dt><dd>std::vector&lt;T&gt; List of values, sorted in pre-order order. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span>                                         {</div>
-<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span>        <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#ab81edd415324d372632c42dc7dbcb9e1">traverse_preorder</a>([&amp;](T node_value) { <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.push_back(node_value); },</div>
-<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span>                          <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>);</div>
-<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  332</span>                                         {</div>
+<div class="line"><span class="lineno">  333</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  334</span>        <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#ab81edd415324d372632c42dc7dbcb9e1">traverse_preorder</a>([&amp;](T node_value) { <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.push_back(node_value); },</div>
+<div class="line"><span class="lineno">  335</span>                          <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>);</div>
+<div class="line"><span class="lineno">  336</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  337</span>    }</div>
 <div class="ttc" id="aclassbinary__search__tree_html_ab81edd415324d372632c42dc7dbcb9e1"><div class="ttname"><a href="../../d9/dde/classbinary__search__tree.html#ab81edd415324d372632c42dc7dbcb9e1">binary_search_tree::traverse_preorder</a></div><div class="ttdeci">void traverse_preorder(std::function&lt; void(T)&gt; callback, std::unique_ptr&lt; bst_node &gt; &amp;node)</div><div class="ttdoc">Recursive function to traverse the tree in pre-order order.</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:213</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -748,31 +748,31 @@ template&lt;class T &gt; </div>
 <dl class="section return"><dt>Returns</dt><dd>true If the insert operation was successful. </dd>
 <dd>
 false Otherwise. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>                                                            {</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a> == <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> &amp;&amp; !<a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>) {</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>            <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/unique_ptr.html">std::unique_ptr&lt;bst_node&gt;</a>(<span class="keyword">new</span> bst_node(new_value));</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>        }</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span> </div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>        <span class="keywordflow">if</span> (new_value &lt; node-&gt;value) {</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>            <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left) {</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>                <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/unique_ptr.html">std::unique_ptr&lt;bst_node&gt;</a>(<span class="keyword">new</span> bst_node(new_value));</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>                <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left, new_value);</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>            }</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (new_value &gt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;value) {</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>            <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right) {</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>                <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right =</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/unique_ptr.html">std::unique_ptr&lt;bst_node&gt;</a>(<span class="keyword">new</span> bst_node(new_value));</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>                <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right, new_value);</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>            }</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>        }</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   89</span>                                                            {</div>
+<div class="line"><span class="lineno">   90</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a> == <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> &amp;&amp; !<a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>) {</div>
+<div class="line"><span class="lineno">   91</span>            <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/unique_ptr.html">std::unique_ptr&lt;bst_node&gt;</a>(<span class="keyword">new</span> bst_node(new_value));</div>
+<div class="line"><span class="lineno">   92</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   93</span>        }</div>
+<div class="line"><span class="lineno">   94</span> </div>
+<div class="line"><span class="lineno">   95</span>        <span class="keywordflow">if</span> (new_value &lt; node-&gt;value) {</div>
+<div class="line"><span class="lineno">   96</span>            <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left) {</div>
+<div class="line"><span class="lineno">   97</span>                <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/unique_ptr.html">std::unique_ptr&lt;bst_node&gt;</a>(<span class="keyword">new</span> bst_node(new_value));</div>
+<div class="line"><span class="lineno">   98</span>                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   99</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  100</span>                <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left, new_value);</div>
+<div class="line"><span class="lineno">  101</span>            }</div>
+<div class="line"><span class="lineno">  102</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (new_value &gt; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;value) {</div>
+<div class="line"><span class="lineno">  103</span>            <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right) {</div>
+<div class="line"><span class="lineno">  104</span>                <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right =</div>
+<div class="line"><span class="lineno">  105</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/unique_ptr.html">std::unique_ptr&lt;bst_node&gt;</a>(<span class="keyword">new</span> bst_node(new_value));</div>
+<div class="line"><span class="lineno">  106</span>                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  107</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  108</span>                <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right, new_value);</div>
+<div class="line"><span class="lineno">  109</span>            }</div>
+<div class="line"><span class="lineno">  110</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  111</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  112</span>        }</div>
+<div class="line"><span class="lineno">  113</span>    }</div>
 <div class="ttc" id="aclassbinary__search__tree_html_a9d1e7e10efa74d741bf48cf032df3778"><div class="ttname"><a href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">binary_search_tree::insert</a></div><div class="ttdeci">bool insert(std::unique_ptr&lt; bst_node &gt; &amp;node, T new_value)</div><div class="ttdoc">Recursive function to insert a value into the BST.</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:89</div></div>
 <div class="ttc" id="aunique_ptr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/memory/unique_ptr.html">std::unique_ptr</a></div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -820,13 +820,13 @@ template&lt;class T &gt; </div>
 <dl class="section return"><dt>Returns</dt><dd>true If the insertion was successful. </dd>
 <dd>
 false Otherwise. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>                             {</div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>        <span class="keywordtype">bool</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(<a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>, new_value);</div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>        <span class="keywordflow">if</span> (result) {</div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>            <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#a07ba32ce1a2af6e357600ac8c8e98dbc">size_</a>++;</div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>        }</div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  258</span>                             {</div>
+<div class="line"><span class="lineno">  259</span>        <span class="keywordtype">bool</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(<a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>, new_value);</div>
+<div class="line"><span class="lineno">  260</span>        <span class="keywordflow">if</span> (result) {</div>
+<div class="line"><span class="lineno">  261</span>            <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#a07ba32ce1a2af6e357600ac8c8e98dbc">size_</a>++;</div>
+<div class="line"><span class="lineno">  262</span>        }</div>
+<div class="line"><span class="lineno">  263</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  264</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -890,48 +890,48 @@ template&lt;class T &gt; </div>
 <dl class="section return"><dt>Returns</dt><dd>true If the removal operation was successful. </dd>
 <dd>
 false Otherwise. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>                                                           {</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>        <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>) {</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>        }</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span> </div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>        <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;value == rm_value) {</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>            <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left &amp;&amp; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right) {</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>                T successor_node_value{};</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>                <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a75f897af6aa732a9901454401c869bcb">find_max</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left, successor_node_value);</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>                <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">remove</a>(<a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>, <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>, successor_node_value);</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>                <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;value = successor_node_value;</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left || <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right) {</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/unique_ptr.html">std::unique_ptr&lt;bst_node&gt;</a>&amp; non_null =</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>                    (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left ? <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left : <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right);</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span> </div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>                <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a> == <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>) {</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>                    <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(non_null);</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>                } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (rm_value &lt; parent-&gt;value) {</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>                    parent-&gt;left = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(non_null);</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>                } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>                    parent-&gt;right = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(non_null);</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>                }</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span> </div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>                <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a> == <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>) {</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>                    <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>.reset(<span class="keyword">nullptr</span>);</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>                } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (rm_value &lt; parent-&gt;value) {</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>                    parent-&gt;left.reset(<span class="keyword">nullptr</span>);</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>                } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>                    parent-&gt;right.reset(<span class="keyword">nullptr</span>);</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>                }</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span> </div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>            }</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (rm_value &lt; node-&gt;value) {</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">remove</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left, rm_value);</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">remove</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right, rm_value);</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>        }</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  125</span>                                                           {</div>
+<div class="line"><span class="lineno">  126</span>        <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>) {</div>
+<div class="line"><span class="lineno">  127</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  128</span>        }</div>
+<div class="line"><span class="lineno">  129</span> </div>
+<div class="line"><span class="lineno">  130</span>        <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;value == rm_value) {</div>
+<div class="line"><span class="lineno">  131</span>            <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left &amp;&amp; <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right) {</div>
+<div class="line"><span class="lineno">  132</span>                T successor_node_value{};</div>
+<div class="line"><span class="lineno">  133</span>                <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a75f897af6aa732a9901454401c869bcb">find_max</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left, successor_node_value);</div>
+<div class="line"><span class="lineno">  134</span>                <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">remove</a>(<a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>, <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>, successor_node_value);</div>
+<div class="line"><span class="lineno">  135</span>                <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;value = successor_node_value;</div>
+<div class="line"><span class="lineno">  136</span>                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  137</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left || <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right) {</div>
+<div class="line"><span class="lineno">  138</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/unique_ptr.html">std::unique_ptr&lt;bst_node&gt;</a>&amp; non_null =</div>
+<div class="line"><span class="lineno">  139</span>                    (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left ? <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left : <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right);</div>
+<div class="line"><span class="lineno">  140</span> </div>
+<div class="line"><span class="lineno">  141</span>                <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a> == <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>) {</div>
+<div class="line"><span class="lineno">  142</span>                    <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(non_null);</div>
+<div class="line"><span class="lineno">  143</span>                } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (rm_value &lt; parent-&gt;value) {</div>
+<div class="line"><span class="lineno">  144</span>                    parent-&gt;left = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(non_null);</div>
+<div class="line"><span class="lineno">  145</span>                } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  146</span>                    parent-&gt;right = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(non_null);</div>
+<div class="line"><span class="lineno">  147</span>                }</div>
+<div class="line"><span class="lineno">  148</span> </div>
+<div class="line"><span class="lineno">  149</span>                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  150</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  151</span>                <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a> == <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>) {</div>
+<div class="line"><span class="lineno">  152</span>                    <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>.reset(<span class="keyword">nullptr</span>);</div>
+<div class="line"><span class="lineno">  153</span>                } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (rm_value &lt; parent-&gt;value) {</div>
+<div class="line"><span class="lineno">  154</span>                    parent-&gt;left.reset(<span class="keyword">nullptr</span>);</div>
+<div class="line"><span class="lineno">  155</span>                } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  156</span>                    parent-&gt;right.reset(<span class="keyword">nullptr</span>);</div>
+<div class="line"><span class="lineno">  157</span>                }</div>
+<div class="line"><span class="lineno">  158</span> </div>
+<div class="line"><span class="lineno">  159</span>                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  160</span>            }</div>
+<div class="line"><span class="lineno">  161</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (rm_value &lt; node-&gt;value) {</div>
+<div class="line"><span class="lineno">  162</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">remove</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left, rm_value);</div>
+<div class="line"><span class="lineno">  163</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  164</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">remove</a>(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right, rm_value);</div>
+<div class="line"><span class="lineno">  165</span>        }</div>
+<div class="line"><span class="lineno">  166</span>    }</div>
 <div class="ttc" id="aclassbinary__search__tree_html_af4a865ce5244608819b169fc78a41153"><div class="ttname"><a href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">binary_search_tree::remove</a></div><div class="ttdeci">bool remove(std::unique_ptr&lt; bst_node &gt; &amp;parent, std::unique_ptr&lt; bst_node &gt; &amp;node, T rm_value)</div><div class="ttdoc">Recursive function to remove a value from the BST.</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:124</div></div>
 <div class="ttc" id="amove_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a></div><div class="ttdeci">T move(T... args)</div></div>
 </div><!-- fragment -->
@@ -973,13 +973,13 @@ template&lt;class T &gt; </div>
 <dl class="section return"><dt>Returns</dt><dd>true If the removal was successful. </dd>
 <dd>
 false Otherwise. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>                            {</div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>        <span class="keywordtype">bool</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">remove</a>(<a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>, <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>, rm_value);</div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>        <span class="keywordflow">if</span> (result) {</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>            <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#a07ba32ce1a2af6e357600ac8c8e98dbc">size_</a>--;</div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>        }</div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  273</span>                            {</div>
+<div class="line"><span class="lineno">  274</span>        <span class="keywordtype">bool</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">remove</a>(<a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>, <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#aa08f65f6f3bfcb14f8c3d1e65305ae50">root_</a>, rm_value);</div>
+<div class="line"><span class="lineno">  275</span>        <span class="keywordflow">if</span> (result) {</div>
+<div class="line"><span class="lineno">  276</span>            <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#a07ba32ce1a2af6e357600ac8c8e98dbc">size_</a>--;</div>
+<div class="line"><span class="lineno">  277</span>        }</div>
+<div class="line"><span class="lineno">  278</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  279</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -1016,7 +1016,7 @@ template&lt;class T &gt; </div>
 
 <p>Get the number of values in the BST. </p>
 <dl class="section return"><dt>Returns</dt><dd><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> Number of values in the BST. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#a07ba32ce1a2af6e357600ac8c8e98dbc">size_</a>; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  313</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d9/dde/classbinary__search__tree.html#a07ba32ce1a2af6e357600ac8c8e98dbc">size_</a>; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1064,15 +1064,15 @@ template&lt;class T &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>                                                         {</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>        <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>) {</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>            <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>        }</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span> </div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>        <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a2fcf37549bd002c174a45b0b4203c2bd">traverse_inorder</a>(callback, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left);</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>        callback(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;value);</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>        <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a2fcf37549bd002c174a45b0b4203c2bd">traverse_inorder</a>(callback, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right);</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  197</span>                                                         {</div>
+<div class="line"><span class="lineno">  198</span>        <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>) {</div>
+<div class="line"><span class="lineno">  199</span>            <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  200</span>        }</div>
+<div class="line"><span class="lineno">  201</span> </div>
+<div class="line"><span class="lineno">  202</span>        <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a2fcf37549bd002c174a45b0b4203c2bd">traverse_inorder</a>(callback, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left);</div>
+<div class="line"><span class="lineno">  203</span>        callback(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;value);</div>
+<div class="line"><span class="lineno">  204</span>        <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a2fcf37549bd002c174a45b0b4203c2bd">traverse_inorder</a>(callback, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right);</div>
+<div class="line"><span class="lineno">  205</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -1126,15 +1126,15 @@ template&lt;class T &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>                                                           {</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>        <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>) {</div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>            <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>        }</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span> </div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>        <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a87c0a35845d27e0f6fc1f4eaa0333362">traverse_postorder</a>(callback, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left);</div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>        <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a87c0a35845d27e0f6fc1f4eaa0333362">traverse_postorder</a>(callback, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right);</div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>        callback(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;value);</div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  231</span>                                                           {</div>
+<div class="line"><span class="lineno">  232</span>        <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>) {</div>
+<div class="line"><span class="lineno">  233</span>            <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  234</span>        }</div>
+<div class="line"><span class="lineno">  235</span> </div>
+<div class="line"><span class="lineno">  236</span>        <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a87c0a35845d27e0f6fc1f4eaa0333362">traverse_postorder</a>(callback, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left);</div>
+<div class="line"><span class="lineno">  237</span>        <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a87c0a35845d27e0f6fc1f4eaa0333362">traverse_postorder</a>(callback, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right);</div>
+<div class="line"><span class="lineno">  238</span>        callback(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;value);</div>
+<div class="line"><span class="lineno">  239</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -1188,15 +1188,15 @@ template&lt;class T &gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>                                                          {</div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>        <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>) {</div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>            <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>        }</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span> </div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>        callback(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;value);</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>        <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#ab81edd415324d372632c42dc7dbcb9e1">traverse_preorder</a>(callback, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left);</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>        <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#ab81edd415324d372632c42dc7dbcb9e1">traverse_preorder</a>(callback, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right);</div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  214</span>                                                          {</div>
+<div class="line"><span class="lineno">  215</span>        <span class="keywordflow">if</span> (!<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>) {</div>
+<div class="line"><span class="lineno">  216</span>            <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">  217</span>        }</div>
+<div class="line"><span class="lineno">  218</span> </div>
+<div class="line"><span class="lineno">  219</span>        callback(<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;value);</div>
+<div class="line"><span class="lineno">  220</span>        <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#ab81edd415324d372632c42dc7dbcb9e1">traverse_preorder</a>(callback, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left);</div>
+<div class="line"><span class="lineno">  221</span>        <a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#ab81edd415324d372632c42dc7dbcb9e1">traverse_preorder</a>(callback, <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right);</div>
+<div class="line"><span class="lineno">  222</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -1266,7 +1266,7 @@ template&lt;class T &gt; </div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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     <li class="navelem"><a class="el" href="../../d9/dde/classbinary__search__tree.html">binary_search_tree</a></li>
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@@ -164,17 +164,17 @@ Functions</h2></td></tr>
 <p >&lt; Check if both elements are same</p>
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+<div class="line"><span class="lineno">   92</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initialized arr = {}\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   93</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected result: {}\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   94</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> arr = {};</div>
+<div class="line"><span class="lineno">   95</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> res = <a class="code hl_function" href="../../da/d6d/namespaceoperations__on__datastructures.html#afce39cf843989a39811a49ebe29dd6d8">shift_left</a>(arr, 2);</div>
+<div class="line"><span class="lineno">   96</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> expected = {};</div>
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+<div class="line"><span class="lineno">  108</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected result: {}\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  109</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> arr = {1, 2, 3, 4, 5};</div>
+<div class="line"><span class="lineno">  110</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> res = <a class="code hl_function" href="../../da/d6d/namespaceoperations__on__datastructures.html#afce39cf843989a39811a49ebe29dd6d8">shift_left</a>(arr, 7);  <span class="comment">///&lt; 7 &gt; 5</span></div>
+<div class="line"><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> expected = {};</div>
+<div class="line"><span class="lineno">  112</span>    assert(res == expected);</div>
+<div class="line"><span class="lineno">  113</span>    <a class="code hl_function" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a235843bdf82d2a6cc8596ae8fd3b8df9">print</a>(res);  <span class="comment">///&lt; Should print empty newline</span></div>
+<div class="line"><span class="lineno">  114</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED!\n\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  115</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -333,25 +333,25 @@ Here is the call graph for this function:</div>
 <p >&lt; Should print 4 6</p>
 <p >&lt; Check if result is correct</p>
 <p >&lt; Should print 2 3 4 6 7</p>
-<div class="fragment"><div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>             {</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST CASE 4\n&quot;</span>;</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initialized arr = {2, 4, ..., 420}\n&quot;</span>;</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected result: {4, 6, ..., 420, 2}\n&quot;</span>;</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> arr;</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt;= 210; i++) {</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>        arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(i * 2);</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    }</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    <a class="code hl_function" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a235843bdf82d2a6cc8596ae8fd3b8df9">print</a>(arr);</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> res = <a class="code hl_function" href="../../da/d6d/namespaceoperations__on__datastructures.html#afce39cf843989a39811a49ebe29dd6d8">shift_left</a>(arr, 1);</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> expected;</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt; 210; i++) {</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>        expected.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(arr[i]);</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    }</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    expected.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(2);</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    assert(res == expected);</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    <a class="code hl_function" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a235843bdf82d2a6cc8596ae8fd3b8df9">print</a>(res);  <span class="comment">///&lt; Should print {4, 6, ..., 420, 2}</span></div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED!\n\n&quot;</span>;</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  120</span>             {</div>
+<div class="line"><span class="lineno">  121</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST CASE 4\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  122</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initialized arr = {2, 4, ..., 420}\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  123</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected result: {4, 6, ..., 420, 2}\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  124</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> arr;</div>
+<div class="line"><span class="lineno">  125</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt;= 210; i++) {</div>
+<div class="line"><span class="lineno">  126</span>        arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(i * 2);</div>
+<div class="line"><span class="lineno">  127</span>    }</div>
+<div class="line"><span class="lineno">  128</span>    <a class="code hl_function" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a235843bdf82d2a6cc8596ae8fd3b8df9">print</a>(arr);</div>
+<div class="line"><span class="lineno">  129</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> res = <a class="code hl_function" href="../../da/d6d/namespaceoperations__on__datastructures.html#afce39cf843989a39811a49ebe29dd6d8">shift_left</a>(arr, 1);</div>
+<div class="line"><span class="lineno">  130</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> expected;</div>
+<div class="line"><span class="lineno">  131</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt; 210; i++) {</div>
+<div class="line"><span class="lineno">  132</span>        expected.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(arr[i]);</div>
+<div class="line"><span class="lineno">  133</span>    }</div>
+<div class="line"><span class="lineno">  134</span>    expected.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(2);</div>
+<div class="line"><span class="lineno">  135</span>    assert(res == expected);</div>
+<div class="line"><span class="lineno">  136</span>    <a class="code hl_function" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a235843bdf82d2a6cc8596ae8fd3b8df9">print</a>(res);  <span class="comment">///&lt; Should print {4, 6, ..., 420, 2}</span></div>
+<div class="line"><span class="lineno">  137</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED!\n\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  138</span>}</div>
 <div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -392,16 +392,16 @@ Here is the call graph for this function:</div>
 <p >&lt; Should print 2 3 4</p>
 <p >&lt; Check if result is correct</p>
 <p >&lt; Should print 1 2 3 4 5 6 7 9</p>
-<div class="fragment"><div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>             {</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST CASE 5\n&quot;</span>;</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initialized arr = {1, 2, 3, 4, 5}\n&quot;</span>;</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected result: {1, 2, 3, 4, 5}\n&quot;</span>;</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> arr = {1, 2, 3, 4, 5};</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> res = <a class="code hl_function" href="../../da/d6d/namespaceoperations__on__datastructures.html#afce39cf843989a39811a49ebe29dd6d8">shift_left</a>(arr, 0);</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>    assert(res == arr);</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    <a class="code hl_function" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a235843bdf82d2a6cc8596ae8fd3b8df9">print</a>(res);  <span class="comment">///&lt; Should print 1 2 3 4 5</span></div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED!\n\n&quot;</span>;</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  143</span>             {</div>
+<div class="line"><span class="lineno">  144</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST CASE 5\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initialized arr = {1, 2, 3, 4, 5}\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  146</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected result: {1, 2, 3, 4, 5}\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  147</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> arr = {1, 2, 3, 4, 5};</div>
+<div class="line"><span class="lineno">  148</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> res = <a class="code hl_function" href="../../da/d6d/namespaceoperations__on__datastructures.html#afce39cf843989a39811a49ebe29dd6d8">shift_left</a>(arr, 0);</div>
+<div class="line"><span class="lineno">  149</span>    assert(res == arr);</div>
+<div class="line"><span class="lineno">  150</span>    <a class="code hl_function" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a235843bdf82d2a6cc8596ae8fd3b8df9">print</a>(res);  <span class="comment">///&lt; Should print 1 2 3 4 5</span></div>
+<div class="line"><span class="lineno">  151</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED!\n\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  152</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -440,21 +440,21 @@ Here is the call graph for this function:</div>
 <p >&lt; Sort vector b</p>
 <p >&lt; Check if result is correct</p>
 <p >&lt; Should print 1 2 3 4 5 6 7 8 9 11</p>
-<div class="fragment"><div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>             {</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST CASE 6\n&quot;</span>;</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Intialized a = {1, 3, 3, 2, 5, 9, 4, 7, 3, 2} &quot;</span>;</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;b = {11, 3, 7, 8, 6}\n&quot;</span>;</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected result: {3, 7}\n&quot;</span>;</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> a = {1, 3, 3, 2, 5, 9, 4, 7, 3, 2};</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> b = {11, 3, 7, 8, 6};</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/sort.html">std::sort</a>(a.begin(), a.end());  <span class="comment">///&lt; Sort vector a</span></div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/sort.html">std::sort</a>(b.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), b.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>());  <span class="comment">///&lt; Sort vector b</span></div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../da/d6d/namespaceoperations__on__datastructures.html#adaf9a06f0c236c2d95c97e441ea2d12e">get_intersection</a>(a, b);</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> expected = {3, 7};</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>    assert(result == expected);  <span class="comment">///&lt; Check if result is correct</span></div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>    <a class="code hl_function" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a235843bdf82d2a6cc8596ae8fd3b8df9">print</a>(result);               <span class="comment">///&lt; Should print 3 7</span></div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED!\n\n&quot;</span>;</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  166</span>             {</div>
+<div class="line"><span class="lineno">  167</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST CASE 6\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  168</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Intialized a = {1, 3, 3, 2, 5, 9, 4, 7, 3, 2} &quot;</span>;</div>
+<div class="line"><span class="lineno">  169</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;b = {11, 3, 7, 8, 6}\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  170</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected result: {3, 7}\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  171</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> a = {1, 3, 3, 2, 5, 9, 4, 7, 3, 2};</div>
+<div class="line"><span class="lineno">  172</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> b = {11, 3, 7, 8, 6};</div>
+<div class="line"><span class="lineno">  173</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/sort.html">std::sort</a>(a.begin(), a.end());  <span class="comment">///&lt; Sort vector a</span></div>
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-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span><span class="comment">        /// Find next gap</span></div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span><span class="comment"></span>        gap = <a class="code hl_function" href="../../d9/dfd/comb__sort_8cpp.html#aede08143e63105faba10e9ee8e745fd5">FindNextGap</a>(gap);</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span> </div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        swapped = <span class="keyword">false</span>;</div>
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-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span><span class="comment">        /// Compare all elements with current gap</span></div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span><span class="comment"></span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = l; i &lt; r - gap; ++i) {</div>
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-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>                swapped = <span class="keyword">true</span>;</div>
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+<div class="fragment"><div class="line"><span class="lineno">   42</span>                                      {<span class="comment"></span></div>
+<div class="line"><span class="lineno">   43</span><span class="comment">    /**</span></div>
+<div class="line"><span class="lineno">   44</span><span class="comment">     *</span></div>
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+<div class="line"><span class="lineno">   46</span><span class="comment">     * the size of the array that is n and which is equal to r in this</span></div>
+<div class="line"><span class="lineno">   47</span><span class="comment">     * case so to avoid passing an extra parameter n that is the size of</span></div>
+<div class="line"><span class="lineno">   48</span><span class="comment">     * the array we are using r to initialize the initial gap.</span></div>
+<div class="line"><span class="lineno">   49</span><span class="comment">     *</span></div>
+<div class="line"><span class="lineno">   50</span><span class="comment">     */</span></div>
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+<div class="line"><span class="lineno">   52</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   53</span><span class="comment">    /// Initialize swapped as true to make sure that loop runs</span></div>
+<div class="line"><span class="lineno">   54</span><span class="comment"></span>    <span class="keywordtype">bool</span> swapped = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   55</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   56</span><span class="comment">    /// Keep running until gap = 1 or none elements were swapped</span></div>
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+<div class="line"><span class="lineno">   58</span><span class="comment">        /// Find next gap</span></div>
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+<div class="line"><span class="lineno">   60</span> </div>
+<div class="line"><span class="lineno">   61</span>        swapped = <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   62</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   63</span><span class="comment">        /// Compare all elements with current gap</span></div>
+<div class="line"><span class="lineno">   64</span><span class="comment"></span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = l; i &lt; r - gap; ++i) {</div>
+<div class="line"><span class="lineno">   65</span>            <span class="keywordflow">if</span> (arr[i] &gt; arr[i + gap]) {</div>
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+<div class="line"><span class="lineno">   67</span>                swapped = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   68</span>            }</div>
+<div class="line"><span class="lineno">   69</span>        }</div>
+<div class="line"><span class="lineno">   70</span>    }</div>
+<div class="line"><span class="lineno">   71</span>}</div>
 <div class="ttc" id="acomb__sort_8cpp_html_aede08143e63105faba10e9ee8e745fd5"><div class="ttname"><a href="../../d9/dfd/comb__sort_8cpp.html#aede08143e63105faba10e9ee8e745fd5">FindNextGap</a></div><div class="ttdeci">int FindNextGap(int gap)</div><div class="ttdef"><b>Definition:</b> comb_sort.cpp:29</div></div>
 <div class="ttc" id="aswap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a></div><div class="ttdeci">T swap(T... args)</div></div>
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@@ -236,11 +236,11 @@ Here is the call graph for this function:</div>
   </dd>
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 <dl class="section return"><dt>Returns</dt><dd>new gap </dd></dl>
-<div class="fragment"><div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>                         {</div>
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+<div class="fragment"><div class="line"><span class="lineno">   29</span>                         {</div>
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+<div class="line"><span class="lineno">   33</span>}</div>
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 Here is the call graph for this function:</div>
@@ -269,20 +269,20 @@ Here is the call graph for this function:</div>
 <p >Main function </p>
 <p >Running predefined tests</p>
 <p >For user interaction</p>
-<div class="fragment"><div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>           {<span class="comment"></span></div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span><span class="comment">    /// Running predefined tests</span></div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span><span class="comment"></span>    <a class="code hl_function" href="../../d9/dfd/comb__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
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-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span><span class="comment">    /// For user interaction</span></div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span><span class="comment"></span>    <span class="keywordtype">int</span> n;</div>
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-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>    <span class="keywordtype">int</span> *arr = <span class="keyword">new</span> <span class="keywordtype">int</span>[n];</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) std::cin &gt;&gt; arr[i];</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    <a class="code hl_function" href="../../d9/dfd/comb__sort_8cpp.html#a0f4e7569090083fb53d5cdeaf0e2974f">CombSort</a>(arr, 0, n);</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; arr[i] &lt;&lt; <span class="charliteral">&#39; &#39;</span>;</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>    <span class="keyword">delete</span>[] arr;</div>
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-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   88</span>           {<span class="comment"></span></div>
+<div class="line"><span class="lineno">   89</span><span class="comment">    /// Running predefined tests</span></div>
+<div class="line"><span class="lineno">   90</span><span class="comment"></span>    <a class="code hl_function" href="../../d9/dfd/comb__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
+<div class="line"><span class="lineno">   91</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   92</span><span class="comment">    /// For user interaction</span></div>
+<div class="line"><span class="lineno">   93</span><span class="comment"></span>    <span class="keywordtype">int</span> n;</div>
+<div class="line"><span class="lineno">   94</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
+<div class="line"><span class="lineno">   95</span>    <span class="keywordtype">int</span> *arr = <span class="keyword">new</span> <span class="keywordtype">int</span>[n];</div>
+<div class="line"><span class="lineno">   96</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) std::cin &gt;&gt; arr[i];</div>
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 <p >Test 1</p>
 <p >Test 2</p>
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+<div class="line"><span class="lineno">   74</span><span class="comment">    /// Test 1</span></div>
+<div class="line"><span class="lineno">   75</span><span class="comment"></span>    <span class="keywordtype">int</span> arr1[10] = {34, 56, 6, 23, 76, 34, 76, 343, 4, 76};</div>
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+<div class="line"><span class="lineno">   77</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(arr1, arr1 + 10));</div>
+<div class="line"><span class="lineno">   78</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 passed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   79</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   80</span><span class="comment">    /// Test 2</span></div>
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-<div class="line"><a id="l00437" name="l00437"></a><span class="lineno">  437</span> </div>
-<div class="line"><a id="l00438" name="l00438"></a><span class="lineno">  438</span>        <span class="comment">// Before starting the AyStartSearch, initialize the set and maps</span></div>
-<div class="line"><a id="l00439" name="l00439"></a><span class="lineno">  439</span>        open_list.emplace(Initial);</div>
-<div class="line"><a id="l00440" name="l00440"></a><span class="lineno">  440</span>        parent_of[Initial] = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00441" name="l00441"></a><span class="lineno">  441</span>        g_score[Initial] = 0;</div>
-<div class="line"><a id="l00442" name="l00442"></a><span class="lineno">  442</span> </div>
-<div class="line"><a id="l00443" name="l00443"></a><span class="lineno">  443</span>        <span class="keywordflow">while</span> (!open_list.empty()) {</div>
-<div class="line"><a id="l00444" name="l00444"></a><span class="lineno">  444</span>            <span class="comment">// Iterator for state having having lowest f_score.</span></div>
-<div class="line"><a id="l00445" name="l00445"></a><span class="lineno">  445</span>            <span class="keyword">typename</span> SetOfPuzzleInfo::iterator it_low_f_score;</div>
-<div class="line"><a id="l00446" name="l00446"></a><span class="lineno">  446</span>            uint32_t min_f_score = 1e9;</div>
-<div class="line"><a id="l00447" name="l00447"></a><span class="lineno">  447</span>            <span class="keywordflow">for</span> (<span class="keyword">auto</span> iter = open_list.begin(); iter != open_list.end();</div>
-<div class="line"><a id="l00448" name="l00448"></a><span class="lineno">  448</span>                 ++iter) {</div>
-<div class="line"><a id="l00449" name="l00449"></a><span class="lineno">  449</span>                <span class="comment">// f score here is evaluated by g score (depth) and h score</span></div>
-<div class="line"><a id="l00450" name="l00450"></a><span class="lineno">  450</span>                <span class="comment">// (distance between current state and final state)</span></div>
-<div class="line"><a id="l00451" name="l00451"></a><span class="lineno">  451</span>                uint32_t f_score = (*iter)-&gt;heuristic_value + (*iter)-&gt;depth;</div>
-<div class="line"><a id="l00452" name="l00452"></a><span class="lineno">  452</span>                <span class="keywordflow">if</span> (f_score &lt; min_f_score) {</div>
-<div class="line"><a id="l00453" name="l00453"></a><span class="lineno">  453</span>                    min_f_score = f_score;</div>
-<div class="line"><a id="l00454" name="l00454"></a><span class="lineno">  454</span>                    it_low_f_score = iter;</div>
-<div class="line"><a id="l00455" name="l00455"></a><span class="lineno">  455</span>                }</div>
-<div class="line"><a id="l00456" name="l00456"></a><span class="lineno">  456</span>            }</div>
-<div class="line"><a id="l00457" name="l00457"></a><span class="lineno">  457</span> </div>
-<div class="line"><a id="l00458" name="l00458"></a><span class="lineno">  458</span>            <span class="comment">// current_state, stores lowest f score so far for this state.</span></div>
-<div class="line"><a id="l00459" name="l00459"></a><span class="lineno">  459</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Info&gt;</a> current_state = *it_low_f_score;</div>
-<div class="line"><a id="l00460" name="l00460"></a><span class="lineno">  460</span> </div>
-<div class="line"><a id="l00461" name="l00461"></a><span class="lineno">  461</span>            <span class="comment">// if this current state is equal to final, return</span></div>
-<div class="line"><a id="l00462" name="l00462"></a><span class="lineno">  462</span>            <span class="keywordflow">if</span> (*(current_state-&gt;state) == *(Final-&gt;state)) {</div>
-<div class="line"><a id="l00463" name="l00463"></a><span class="lineno">  463</span>                <span class="keywordflow">return</span> <a class="code hl_function" href="../../da/d02/classmachine__learning_1_1aystar__search_1_1_ay_star_search.html#a0a26aa9ad3d73707370d9fe83707aca4">Solution</a>(current_state, parent_of);</div>
-<div class="line"><a id="l00464" name="l00464"></a><span class="lineno">  464</span>            }</div>
-<div class="line"><a id="l00465" name="l00465"></a><span class="lineno">  465</span>            <span class="comment">// else remove from open list as visited.</span></div>
-<div class="line"><a id="l00466" name="l00466"></a><span class="lineno">  466</span>            open_list.erase(it_low_f_score);</div>
-<div class="line"><a id="l00467" name="l00467"></a><span class="lineno">  467</span>            <span class="comment">// if current_state has exceeded the allowed depth, skip</span></div>
-<div class="line"><a id="l00468" name="l00468"></a><span class="lineno">  468</span>            <span class="comment">// neighbor checking</span></div>
-<div class="line"><a id="l00469" name="l00469"></a><span class="lineno">  469</span>            <span class="keywordflow">if</span> (current_state-&gt;depth &gt;= permissible_depth) {</div>
-<div class="line"><a id="l00470" name="l00470"></a><span class="lineno">  470</span>                <span class="keywordflow">continue</span>;</div>
-<div class="line"><a id="l00471" name="l00471"></a><span class="lineno">  471</span>            }</div>
-<div class="line"><a id="l00472" name="l00472"></a><span class="lineno">  472</span>            <span class="comment">// Generate all possible moves (neighbors) given the current</span></div>
-<div class="line"><a id="l00473" name="l00473"></a><span class="lineno">  473</span>            <span class="comment">// state</span></div>
-<div class="line"><a id="l00474" name="l00474"></a><span class="lineno">  474</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Puzzle&gt;</a> total_possible_moves =</div>
-<div class="line"><a id="l00475" name="l00475"></a><span class="lineno">  475</span>                current_state-&gt;state-&gt;generate_possible_moves();</div>
-<div class="line"><a id="l00476" name="l00476"></a><span class="lineno">  476</span> </div>
-<div class="line"><a id="l00477" name="l00477"></a><span class="lineno">  477</span>            <span class="keywordflow">for</span> (Puzzle &amp;neighbor : total_possible_moves) {</div>
-<div class="line"><a id="l00478" name="l00478"></a><span class="lineno">  478</span>                <span class="comment">// calculate score of neighbors with respect to</span></div>
-<div class="line"><a id="l00479" name="l00479"></a><span class="lineno">  479</span>                <span class="comment">// current_state</span></div>
-<div class="line"><a id="l00480" name="l00480"></a><span class="lineno">  480</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Info&gt;</a> Neighbor = std::make_shared&lt;Info&gt;(</div>
-<div class="line"><a id="l00481" name="l00481"></a><span class="lineno">  481</span>                    neighbor, dist(neighbor, *(Final-&gt;state)),</div>
-<div class="line"><a id="l00482" name="l00482"></a><span class="lineno">  482</span>                    current_state-&gt;depth + 1U);</div>
-<div class="line"><a id="l00483" name="l00483"></a><span class="lineno">  483</span>                uint32_t temp_g_score = Neighbor-&gt;depth;</div>
-<div class="line"><a id="l00484" name="l00484"></a><span class="lineno">  484</span> </div>
-<div class="line"><a id="l00485" name="l00485"></a><span class="lineno">  485</span>                <span class="comment">// Check whether this state is explored.</span></div>
-<div class="line"><a id="l00486" name="l00486"></a><span class="lineno">  486</span>                <span class="comment">// If this state is discovered at greater depth, then discard,</span></div>
-<div class="line"><a id="l00487" name="l00487"></a><span class="lineno">  487</span>                <span class="comment">// else remove from closed list and explore the node</span></div>
-<div class="line"><a id="l00488" name="l00488"></a><span class="lineno">  488</span>                <span class="keyword">auto</span> closed_list_iter = closed_list.find(Neighbor);</div>
-<div class="line"><a id="l00489" name="l00489"></a><span class="lineno">  489</span>                <span class="keywordflow">if</span> (closed_list_iter != closed_list.end()) {</div>
-<div class="line"><a id="l00490" name="l00490"></a><span class="lineno">  490</span>                    <span class="comment">// 1. If state in closed list has higher depth, then remove</span></div>
-<div class="line"><a id="l00491" name="l00491"></a><span class="lineno">  491</span>                    <span class="comment">// from list since we have found better option,</span></div>
-<div class="line"><a id="l00492" name="l00492"></a><span class="lineno">  492</span>                    <span class="comment">// 2. Else don&#39;t explore this state.</span></div>
-<div class="line"><a id="l00493" name="l00493"></a><span class="lineno">  493</span>                    <span class="keywordflow">if</span> (Neighbor-&gt;depth &lt; (*closed_list_iter)-&gt;depth) {</div>
-<div class="line"><a id="l00494" name="l00494"></a><span class="lineno">  494</span>                        closed_list.erase(closed_list_iter);</div>
-<div class="line"><a id="l00495" name="l00495"></a><span class="lineno">  495</span>                    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00496" name="l00496"></a><span class="lineno">  496</span>                        <span class="keywordflow">continue</span>;</div>
-<div class="line"><a id="l00497" name="l00497"></a><span class="lineno">  497</span>                    }</div>
-<div class="line"><a id="l00498" name="l00498"></a><span class="lineno">  498</span>                }</div>
-<div class="line"><a id="l00499" name="l00499"></a><span class="lineno">  499</span>                <span class="keyword">auto</span> neighbor_g_score_iter = g_score.find(Neighbor);</div>
-<div class="line"><a id="l00500" name="l00500"></a><span class="lineno">  500</span>                <span class="comment">// if the neighbor is already created and has minimum</span></div>
-<div class="line"><a id="l00501" name="l00501"></a><span class="lineno">  501</span>                <span class="comment">// g_score, then update g_score and f_score else insert new</span></div>
-<div class="line"><a id="l00502" name="l00502"></a><span class="lineno">  502</span>                <span class="keywordflow">if</span> (neighbor_g_score_iter != g_score.end()) {</div>
-<div class="line"><a id="l00503" name="l00503"></a><span class="lineno">  503</span>                    <span class="keywordflow">if</span> (neighbor_g_score_iter-&gt;second &gt; temp_g_score) {</div>
-<div class="line"><a id="l00504" name="l00504"></a><span class="lineno">  504</span>                        neighbor_g_score_iter-&gt;second = temp_g_score;</div>
-<div class="line"><a id="l00505" name="l00505"></a><span class="lineno">  505</span>                        parent_of[Neighbor] = current_state;</div>
-<div class="line"><a id="l00506" name="l00506"></a><span class="lineno">  506</span>                    }</div>
-<div class="line"><a id="l00507" name="l00507"></a><span class="lineno">  507</span>                } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00508" name="l00508"></a><span class="lineno">  508</span>                    g_score[Neighbor] = temp_g_score;</div>
-<div class="line"><a id="l00509" name="l00509"></a><span class="lineno">  509</span>                    parent_of[Neighbor] = current_state;</div>
-<div class="line"><a id="l00510" name="l00510"></a><span class="lineno">  510</span>                }</div>
-<div class="line"><a id="l00511" name="l00511"></a><span class="lineno">  511</span>                <span class="comment">// If this is a new state, insert into open_list</span></div>
-<div class="line"><a id="l00512" name="l00512"></a><span class="lineno">  512</span>                <span class="comment">// else update if the this state has better g score than</span></div>
-<div class="line"><a id="l00513" name="l00513"></a><span class="lineno">  513</span>                <span class="comment">// existing one.</span></div>
-<div class="line"><a id="l00514" name="l00514"></a><span class="lineno">  514</span>                <span class="keyword">auto</span> iter = open_list.find(Neighbor);</div>
-<div class="line"><a id="l00515" name="l00515"></a><span class="lineno">  515</span>                <span class="keywordflow">if</span> (iter == open_list.end()) {</div>
-<div class="line"><a id="l00516" name="l00516"></a><span class="lineno">  516</span>                    open_list.emplace(Neighbor);</div>
-<div class="line"><a id="l00517" name="l00517"></a><span class="lineno">  517</span>                } <span class="keywordflow">else</span> <span class="keywordflow">if</span> ((*iter)-&gt;depth &gt; Neighbor-&gt;depth) {</div>
-<div class="line"><a id="l00518" name="l00518"></a><span class="lineno">  518</span>                    (*iter)-&gt;depth = Neighbor-&gt;depth;</div>
-<div class="line"><a id="l00519" name="l00519"></a><span class="lineno">  519</span>                }</div>
-<div class="line"><a id="l00520" name="l00520"></a><span class="lineno">  520</span>            }</div>
-<div class="line"><a id="l00521" name="l00521"></a><span class="lineno">  521</span>            closed_list.emplace(current_state);</div>
-<div class="line"><a id="l00522" name="l00522"></a><span class="lineno">  522</span>        }</div>
-<div class="line"><a id="l00523" name="l00523"></a><span class="lineno">  523</span>        <span class="comment">// Cannot find the solution, return empty vector</span></div>
-<div class="line"><a id="l00524" name="l00524"></a><span class="lineno">  524</span>        <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Puzzle&gt;</a>(0);</div>
-<div class="line"><a id="l00525" name="l00525"></a><span class="lineno">  525</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  431</span>                                               {</div>
+<div class="line"><span class="lineno">  432</span>        MapOfPuzzleInfoWithPuzzleInfo</div>
+<div class="line"><span class="lineno">  433</span>            parent_of;                       <span class="comment">/// Stores the parent of the states</span></div>
+<div class="line"><span class="lineno">  434</span>        MapOfPuzzleInfoWithInteger g_score;  <span class="comment">/// Stores the g_score</span></div>
+<div class="line"><span class="lineno">  435</span>        SetOfPuzzleInfo open_list;           <span class="comment">/// Stores the list to explore</span></div>
+<div class="line"><span class="lineno">  436</span>        SetOfPuzzleInfo closed_list;  <span class="comment">/// Stores the list that are explored</span></div>
+<div class="line"><span class="lineno">  437</span> </div>
+<div class="line"><span class="lineno">  438</span>        <span class="comment">// Before starting the AyStartSearch, initialize the set and maps</span></div>
+<div class="line"><span class="lineno">  439</span>        open_list.emplace(Initial);</div>
+<div class="line"><span class="lineno">  440</span>        parent_of[Initial] = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  441</span>        g_score[Initial] = 0;</div>
+<div class="line"><span class="lineno">  442</span> </div>
+<div class="line"><span class="lineno">  443</span>        <span class="keywordflow">while</span> (!open_list.empty()) {</div>
+<div class="line"><span class="lineno">  444</span>            <span class="comment">// Iterator for state having having lowest f_score.</span></div>
+<div class="line"><span class="lineno">  445</span>            <span class="keyword">typename</span> SetOfPuzzleInfo::iterator it_low_f_score;</div>
+<div class="line"><span class="lineno">  446</span>            uint32_t min_f_score = 1e9;</div>
+<div class="line"><span class="lineno">  447</span>            <span class="keywordflow">for</span> (<span class="keyword">auto</span> iter = open_list.begin(); iter != open_list.end();</div>
+<div class="line"><span class="lineno">  448</span>                 ++iter) {</div>
+<div class="line"><span class="lineno">  449</span>                <span class="comment">// f score here is evaluated by g score (depth) and h score</span></div>
+<div class="line"><span class="lineno">  450</span>                <span class="comment">// (distance between current state and final state)</span></div>
+<div class="line"><span class="lineno">  451</span>                uint32_t f_score = (*iter)-&gt;heuristic_value + (*iter)-&gt;depth;</div>
+<div class="line"><span class="lineno">  452</span>                <span class="keywordflow">if</span> (f_score &lt; min_f_score) {</div>
+<div class="line"><span class="lineno">  453</span>                    min_f_score = f_score;</div>
+<div class="line"><span class="lineno">  454</span>                    it_low_f_score = iter;</div>
+<div class="line"><span class="lineno">  455</span>                }</div>
+<div class="line"><span class="lineno">  456</span>            }</div>
+<div class="line"><span class="lineno">  457</span> </div>
+<div class="line"><span class="lineno">  458</span>            <span class="comment">// current_state, stores lowest f score so far for this state.</span></div>
+<div class="line"><span class="lineno">  459</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Info&gt;</a> current_state = *it_low_f_score;</div>
+<div class="line"><span class="lineno">  460</span> </div>
+<div class="line"><span class="lineno">  461</span>            <span class="comment">// if this current state is equal to final, return</span></div>
+<div class="line"><span class="lineno">  462</span>            <span class="keywordflow">if</span> (*(current_state-&gt;state) == *(Final-&gt;state)) {</div>
+<div class="line"><span class="lineno">  463</span>                <span class="keywordflow">return</span> <a class="code hl_function" href="../../da/d02/classmachine__learning_1_1aystar__search_1_1_ay_star_search.html#a0a26aa9ad3d73707370d9fe83707aca4">Solution</a>(current_state, parent_of);</div>
+<div class="line"><span class="lineno">  464</span>            }</div>
+<div class="line"><span class="lineno">  465</span>            <span class="comment">// else remove from open list as visited.</span></div>
+<div class="line"><span class="lineno">  466</span>            open_list.erase(it_low_f_score);</div>
+<div class="line"><span class="lineno">  467</span>            <span class="comment">// if current_state has exceeded the allowed depth, skip</span></div>
+<div class="line"><span class="lineno">  468</span>            <span class="comment">// neighbor checking</span></div>
+<div class="line"><span class="lineno">  469</span>            <span class="keywordflow">if</span> (current_state-&gt;depth &gt;= permissible_depth) {</div>
+<div class="line"><span class="lineno">  470</span>                <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno">  471</span>            }</div>
+<div class="line"><span class="lineno">  472</span>            <span class="comment">// Generate all possible moves (neighbors) given the current</span></div>
+<div class="line"><span class="lineno">  473</span>            <span class="comment">// state</span></div>
+<div class="line"><span class="lineno">  474</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Puzzle&gt;</a> total_possible_moves =</div>
+<div class="line"><span class="lineno">  475</span>                current_state-&gt;state-&gt;generate_possible_moves();</div>
+<div class="line"><span class="lineno">  476</span> </div>
+<div class="line"><span class="lineno">  477</span>            <span class="keywordflow">for</span> (Puzzle &amp;neighbor : total_possible_moves) {</div>
+<div class="line"><span class="lineno">  478</span>                <span class="comment">// calculate score of neighbors with respect to</span></div>
+<div class="line"><span class="lineno">  479</span>                <span class="comment">// current_state</span></div>
+<div class="line"><span class="lineno">  480</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Info&gt;</a> Neighbor = std::make_shared&lt;Info&gt;(</div>
+<div class="line"><span class="lineno">  481</span>                    neighbor, dist(neighbor, *(Final-&gt;state)),</div>
+<div class="line"><span class="lineno">  482</span>                    current_state-&gt;depth + 1U);</div>
+<div class="line"><span class="lineno">  483</span>                uint32_t temp_g_score = Neighbor-&gt;depth;</div>
+<div class="line"><span class="lineno">  484</span> </div>
+<div class="line"><span class="lineno">  485</span>                <span class="comment">// Check whether this state is explored.</span></div>
+<div class="line"><span class="lineno">  486</span>                <span class="comment">// If this state is discovered at greater depth, then discard,</span></div>
+<div class="line"><span class="lineno">  487</span>                <span class="comment">// else remove from closed list and explore the node</span></div>
+<div class="line"><span class="lineno">  488</span>                <span class="keyword">auto</span> closed_list_iter = closed_list.find(Neighbor);</div>
+<div class="line"><span class="lineno">  489</span>                <span class="keywordflow">if</span> (closed_list_iter != closed_list.end()) {</div>
+<div class="line"><span class="lineno">  490</span>                    <span class="comment">// 1. If state in closed list has higher depth, then remove</span></div>
+<div class="line"><span class="lineno">  491</span>                    <span class="comment">// from list since we have found better option,</span></div>
+<div class="line"><span class="lineno">  492</span>                    <span class="comment">// 2. Else don&#39;t explore this state.</span></div>
+<div class="line"><span class="lineno">  493</span>                    <span class="keywordflow">if</span> (Neighbor-&gt;depth &lt; (*closed_list_iter)-&gt;depth) {</div>
+<div class="line"><span class="lineno">  494</span>                        closed_list.erase(closed_list_iter);</div>
+<div class="line"><span class="lineno">  495</span>                    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  496</span>                        <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno">  497</span>                    }</div>
+<div class="line"><span class="lineno">  498</span>                }</div>
+<div class="line"><span class="lineno">  499</span>                <span class="keyword">auto</span> neighbor_g_score_iter = g_score.find(Neighbor);</div>
+<div class="line"><span class="lineno">  500</span>                <span class="comment">// if the neighbor is already created and has minimum</span></div>
+<div class="line"><span class="lineno">  501</span>                <span class="comment">// g_score, then update g_score and f_score else insert new</span></div>
+<div class="line"><span class="lineno">  502</span>                <span class="keywordflow">if</span> (neighbor_g_score_iter != g_score.end()) {</div>
+<div class="line"><span class="lineno">  503</span>                    <span class="keywordflow">if</span> (neighbor_g_score_iter-&gt;second &gt; temp_g_score) {</div>
+<div class="line"><span class="lineno">  504</span>                        neighbor_g_score_iter-&gt;second = temp_g_score;</div>
+<div class="line"><span class="lineno">  505</span>                        parent_of[Neighbor] = current_state;</div>
+<div class="line"><span class="lineno">  506</span>                    }</div>
+<div class="line"><span class="lineno">  507</span>                } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  508</span>                    g_score[Neighbor] = temp_g_score;</div>
+<div class="line"><span class="lineno">  509</span>                    parent_of[Neighbor] = current_state;</div>
+<div class="line"><span class="lineno">  510</span>                }</div>
+<div class="line"><span class="lineno">  511</span>                <span class="comment">// If this is a new state, insert into open_list</span></div>
+<div class="line"><span class="lineno">  512</span>                <span class="comment">// else update if the this state has better g score than</span></div>
+<div class="line"><span class="lineno">  513</span>                <span class="comment">// existing one.</span></div>
+<div class="line"><span class="lineno">  514</span>                <span class="keyword">auto</span> iter = open_list.find(Neighbor);</div>
+<div class="line"><span class="lineno">  515</span>                <span class="keywordflow">if</span> (iter == open_list.end()) {</div>
+<div class="line"><span class="lineno">  516</span>                    open_list.emplace(Neighbor);</div>
+<div class="line"><span class="lineno">  517</span>                } <span class="keywordflow">else</span> <span class="keywordflow">if</span> ((*iter)-&gt;depth &gt; Neighbor-&gt;depth) {</div>
+<div class="line"><span class="lineno">  518</span>                    (*iter)-&gt;depth = Neighbor-&gt;depth;</div>
+<div class="line"><span class="lineno">  519</span>                }</div>
+<div class="line"><span class="lineno">  520</span>            }</div>
+<div class="line"><span class="lineno">  521</span>            closed_list.emplace(current_state);</div>
+<div class="line"><span class="lineno">  522</span>        }</div>
+<div class="line"><span class="lineno">  523</span>        <span class="comment">// Cannot find the solution, return empty vector</span></div>
+<div class="line"><span class="lineno">  524</span>        <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Puzzle&gt;</a>(0);</div>
+<div class="line"><span class="lineno">  525</span>    }</div>
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 <div class="ttc" id="ashared_ptr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr</a></div></div>
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@@ -384,7 +390,7 @@ template&lt;typename Puzzle &gt; </div>
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       <table class="memname">
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-          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; Puzzle &gt; <a class="el" href="../../da/d02/classmachine__learning_1_1aystar__search_1_1_ay_star_search.html">machine_learning::aystar_search::AyStarSearch</a>&lt; Puzzle &gt;::<a class="el" href="../../dd/d4f/class_solution.html">Solution</a> </td>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; Puzzle &gt; <a class="el" href="../../da/d02/classmachine__learning_1_1aystar__search_1_1_ay_star_search.html">machine_learning::aystar_search::AyStarSearch</a>&lt; Puzzle &gt;<a class="el" href="../../dd/d4f/class_solution.html">::Solution</a> </td>
           <td>(</td>
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           <td class="paramname"><em>FinalState</em>, </td>
@@ -417,20 +423,20 @@ template&lt;typename Puzzle &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>the list of moves denoting moves from final state to initial state (in reverse) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00407" name="l00407"></a><span class="lineno">  407</span>                                                        {</div>
-<div class="line"><a id="l00408" name="l00408"></a><span class="lineno">  408</span>        <span class="comment">//  Useful for traversing from final state to current state.</span></div>
-<div class="line"><a id="l00409" name="l00409"></a><span class="lineno">  409</span>        <span class="keyword">auto</span> current_state = FinalState;</div>
-<div class="line"><a id="l00410" name="l00410"></a><span class="lineno">  410</span>        <span class="comment">/*</span></div>
-<div class="line"><a id="l00411" name="l00411"></a><span class="lineno">  411</span><span class="comment">         * For storing the solution tree starting from initial state to</span></div>
-<div class="line"><a id="l00412" name="l00412"></a><span class="lineno">  412</span><span class="comment">         * final state</span></div>
-<div class="line"><a id="l00413" name="l00413"></a><span class="lineno">  413</span><span class="comment">         */</span></div>
-<div class="line"><a id="l00414" name="l00414"></a><span class="lineno">  414</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Puzzle&gt;</a> answer;</div>
-<div class="line"><a id="l00415" name="l00415"></a><span class="lineno">  415</span>        <span class="keywordflow">while</span> (current_state != <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00416" name="l00416"></a><span class="lineno">  416</span>            answer.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/emplace_back.html">emplace_back</a>(*current_state-&gt;state);</div>
-<div class="line"><a id="l00417" name="l00417"></a><span class="lineno">  417</span>            current_state = parent_of.find(current_state)-&gt;second;</div>
-<div class="line"><a id="l00418" name="l00418"></a><span class="lineno">  418</span>        }</div>
-<div class="line"><a id="l00419" name="l00419"></a><span class="lineno">  419</span>        <span class="keywordflow">return</span> answer;</div>
-<div class="line"><a id="l00420" name="l00420"></a><span class="lineno">  420</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  407</span>                                                        {</div>
+<div class="line"><span class="lineno">  408</span>        <span class="comment">//  Useful for traversing from final state to current state.</span></div>
+<div class="line"><span class="lineno">  409</span>        <span class="keyword">auto</span> current_state = FinalState;</div>
+<div class="line"><span class="lineno">  410</span>        <span class="comment">/*</span></div>
+<div class="line"><span class="lineno">  411</span><span class="comment">         * For storing the solution tree starting from initial state to</span></div>
+<div class="line"><span class="lineno">  412</span><span class="comment">         * final state</span></div>
+<div class="line"><span class="lineno">  413</span><span class="comment">         */</span></div>
+<div class="line"><span class="lineno">  414</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Puzzle&gt;</a> answer;</div>
+<div class="line"><span class="lineno">  415</span>        <span class="keywordflow">while</span> (current_state != <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  416</span>            answer.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/emplace_back.html">emplace_back</a>(*current_state-&gt;state);</div>
+<div class="line"><span class="lineno">  417</span>            current_state = parent_of.find(current_state)-&gt;second;</div>
+<div class="line"><span class="lineno">  418</span>        }</div>
+<div class="line"><span class="lineno">  419</span>        <span class="keywordflow">return</span> answer;</div>
+<div class="line"><span class="lineno">  420</span>    }</div>
 <div class="ttc" id="aemplace_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/emplace_back.html">std::vector::emplace_back</a></div><div class="ttdeci">T emplace_back(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -450,7 +456,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../d8/d77/namespacemachine__learning.html">machine_learning</a></li><li class="navelem"><b>aystar_search</b></li><li class="navelem"><a class="el" href="../../da/d02/classmachine__learning_1_1aystar__search_1_1_ay_star_search.html">AyStarSearch</a></li>
-    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.2 </li>
+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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 <p>The standard deviation of a geometrically distributed random variable X. </p>
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@@ -506,7 +506,7 @@ Here is the call graph for this function:</div>
 
 <p>The variance of a geometrically distributed random variable X. </p>
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 <p >&lt; represents minimum value over the range [g, r - pow(2,g) + 1]</p>
 <p >&lt; represents minimum value over the whole range [l,r]</p>
-<div class="fragment"><div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>                                        {</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        int64_t <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = <a class="code hl_variable" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#a6cf72f93b1551f0d943c585b4f173be3">LOG</a>[r - <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> + 1];  <span class="comment">///&lt; smallest power of 2 covering [l,r]</span></div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>        int64_t x = <a class="code hl_variable" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#ad36b9a20fed47b068e407008c04e9f81">ST</a>[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a>];  <span class="comment">///&lt; represents minimum value over the range</span><span class="comment"></span></div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span><span class="comment">                               ///&lt; [g,l]</span></div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span><span class="comment"></span>        int64_t y =</div>
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-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span><span class="comment">                                      ///&lt; range [g, r - pow(2,g) + 1]</span></div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span><span class="comment"></span> </div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>        <span class="keywordflow">return</span> (<a class="code hl_variable" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#ab78620742305a35ff2f8d61179f47d3e">A</a>[x] &lt;= <a class="code hl_variable" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#ab78620742305a35ff2f8d61179f47d3e">A</a>[y] ? x : y);  <span class="comment">///&lt; represents minimum value over</span><span class="comment"></span></div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span><span class="comment">                                        ///&lt; the whole range [l,r]</span></div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span><span class="comment"></span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  109</span>                                        {</div>
+<div class="line"><span class="lineno">  110</span>        int64_t <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = <a class="code hl_variable" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#a6cf72f93b1551f0d943c585b4f173be3">LOG</a>[r - <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> + 1];  <span class="comment">///&lt; smallest power of 2 covering [l,r]</span></div>
+<div class="line"><span class="lineno">  111</span>        int64_t x = <a class="code hl_variable" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#ad36b9a20fed47b068e407008c04e9f81">ST</a>[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a>];  <span class="comment">///&lt; represents minimum value over the range</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  112</span><span class="comment">                               ///&lt; [g,l]</span></div>
+<div class="line"><span class="lineno">  113</span><span class="comment"></span>        int64_t y =</div>
+<div class="line"><span class="lineno">  114</span>            <a class="code hl_variable" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#ad36b9a20fed47b068e407008c04e9f81">ST</a>[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>][r - (1 &lt;&lt; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>) + 1];  <span class="comment">///&lt; represents minimum value over the</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  115</span><span class="comment">                                      ///&lt; range [g, r - pow(2,g) + 1]</span></div>
+<div class="line"><span class="lineno">  116</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  117</span>        <span class="keywordflow">return</span> (<a class="code hl_variable" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#ab78620742305a35ff2f8d61179f47d3e">A</a>[x] &lt;= <a class="code hl_variable" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#ab78620742305a35ff2f8d61179f47d3e">A</a>[y] ? x : y);  <span class="comment">///&lt; represents minimum value over</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  118</span><span class="comment">                                        ///&lt; the whole range [l,r]</span></div>
+<div class="line"><span class="lineno">  119</span><span class="comment"></span>    }</div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a2f67508d5f392b0321772169342c98ad"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">numerical_methods::simpson_method::g</a></div><div class="ttdeci">double g(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:115</div></div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a6d8df83a6f26ce24a75d3b358b7f5b8a"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">numerical_methods::simpson_method::l</a></div><div class="ttdeci">double l(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:119</div></div>
 <div class="ttc" id="astructdata__structures_1_1sparse__table_1_1_sparse__table_html_a6cf72f93b1551f0d943c585b4f173be3"><div class="ttname"><a href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#a6cf72f93b1551f0d943c585b4f173be3">data_structures::sparse_table::Sparse_table::LOG</a></div><div class="ttdeci">std::array&lt; int64_t, N &gt; LOG</div><div class="ttdoc">where floor(log2(i)) are precomputed.</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:59</div></div>
@@ -216,7 +222,7 @@ size_t&#160;</td><td class="memItemRight" valign="bottom"><b>n</b> = 0</td></tr>
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     <li class="navelem"><a class="el" href="../../d5/d3c/namespacedata__structures.html">data_structures</a></li><li class="navelem"><b>sparse_table</b></li><li class="navelem"><a class="el" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html">Sparse_table</a></li>
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@@ -176,10 +176,10 @@ Functions</h2></td></tr>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>           {</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>    <a class="code hl_function" href="../../da/d39/volume_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  235</span>           {</div>
+<div class="line"><span class="lineno">  236</span>    <a class="code hl_function" href="../../da/d39/volume_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
+<div class="line"><span class="lineno">  237</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  238</span>}</div>
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 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -215,124 +215,124 @@ Here is the call graph for this function:</div>
 
 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>                   {</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    <span class="comment">// Input variables</span></div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    uint32_t int_length = 0; <span class="comment">// 32 bit integer length input</span></div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    uint32_t int_width = 0;  <span class="comment">// 32 bit integer width input</span></div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    uint32_t int_base = 0;   <span class="comment">// 32 bit integer base input</span></div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    uint32_t int_height = 0; <span class="comment">// 32 bit integer height input</span></div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    uint32_t int_depth = 0;  <span class="comment">// 32 bit integer depth input</span></div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span> </div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <span class="keywordtype">double</span> double_radius = NAN; <span class="comment">// double radius input</span></div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    <span class="keywordtype">double</span> double_height = NAN; <span class="comment">// double height input</span></div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span> </div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <span class="comment">// Output variables</span></div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    uint32_t int_expected = 0; <span class="comment">// 32 bit integer expected output</span></div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>    uint32_t int_volume = 0;   <span class="comment">// 32 bit integer output</span></div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span> </div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    <span class="keywordtype">double</span> double_expected = NAN; <span class="comment">// double expected output</span></div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    <span class="keywordtype">double</span> double_volume = NAN;   <span class="comment">// double output</span></div>
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-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    <span class="comment">// 1st test</span></div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    int_length = 5;</div>
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-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span> </div>
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-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Width: &quot;</span> &lt;&lt; int_width &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Height: &quot;</span> &lt;&lt; int_height &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; int_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; int_volume &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>    assert(int_volume == int_expected);</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span> </div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    <span class="comment">// 3rd test</span></div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>    double_radius = 5;</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>    double_height = 7;</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>    double_expected = 183.16666666666666;  <span class="comment">// truncated to 14 decimal places</span></div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>    double_volume = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a3fe35440c27758ecc2287e08217d63a7">math::cone_volume</a>(double_radius, double_height);</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span> </div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;VOLUME OF A CONE&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Radius: &quot;</span> &lt;&lt; double_radius &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Height: &quot;</span> &lt;&lt; double_height &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; double_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; double_volume &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>    assert(double_volume == double_expected);</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span> </div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>    <span class="comment">// 4th test</span></div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>    int_base = 3;</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>    int_height = 4;</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>    int_depth = 5;</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>    int_expected = 30;</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>    int_volume = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a2d704a7b72a6b2db8b76c8581b577b2c">math::triangle_prism_volume</a>(int_base, int_height, int_depth);</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span> </div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;VOLUME OF A TRIANGULAR PRISM&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Base: &quot;</span> &lt;&lt; int_base &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Height: &quot;</span> &lt;&lt; int_height &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Depth: &quot;</span> &lt;&lt; int_depth &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; int_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; int_volume &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>    assert(int_volume == int_expected);</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span> </div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>    <span class="comment">// 5th test</span></div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>    int_length = 10;</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>    int_width = 3;</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>    int_height = 5;</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>    int_expected = 50;</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>    int_volume = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a94db02b3c9e55a69ac1696f30e2f761c">math::pyramid_volume</a>(int_length, int_width, int_height);</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span> </div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;VOLUME OF A PYRAMID&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Length: &quot;</span> &lt;&lt; int_length &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Width: &quot;</span> &lt;&lt; int_width &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Height: &quot;</span> &lt;&lt; int_height &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; int_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; int_volume &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>    assert(int_volume == int_expected);</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span> </div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>    <span class="comment">// 6th test</span></div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    double_radius = 3;</div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    double_expected = 113.04;</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>    double_volume = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a34d66a77c19ce9b8b3a3d14352b34551">math::sphere_volume</a>(double_radius);</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span> </div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;VOLUME OF A SPHERE&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Radius: &quot;</span> &lt;&lt; double_radius &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; double_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; double_volume &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>    assert(double_volume == double_expected);</div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span> </div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>    <span class="comment">// 7th test</span></div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>    double_radius = 5;</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>    double_height = 2;</div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>    double_expected = 157;</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>    double_volume = <a class="code hl_function" href="../../dd/d47/namespacemath.html#abde24398be43538c62e4a496968e60ca">math::cylinder_volume</a>(double_radius, double_height);</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span> </div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;VOLUME OF A CYLINDER&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Radius: &quot;</span> &lt;&lt; double_radius &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Height: &quot;</span> &lt;&lt; double_height &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; double_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; double_volume &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>    assert(double_volume == double_expected);</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  112</span>                   {</div>
+<div class="line"><span class="lineno">  113</span>    <span class="comment">// Input variables</span></div>
+<div class="line"><span class="lineno">  114</span>    uint32_t int_length = 0; <span class="comment">// 32 bit integer length input</span></div>
+<div class="line"><span class="lineno">  115</span>    uint32_t int_width = 0;  <span class="comment">// 32 bit integer width input</span></div>
+<div class="line"><span class="lineno">  116</span>    uint32_t int_base = 0;   <span class="comment">// 32 bit integer base input</span></div>
+<div class="line"><span class="lineno">  117</span>    uint32_t int_height = 0; <span class="comment">// 32 bit integer height input</span></div>
+<div class="line"><span class="lineno">  118</span>    uint32_t int_depth = 0;  <span class="comment">// 32 bit integer depth input</span></div>
+<div class="line"><span class="lineno">  119</span> </div>
+<div class="line"><span class="lineno">  120</span>    <span class="keywordtype">double</span> double_radius = NAN; <span class="comment">// double radius input</span></div>
+<div class="line"><span class="lineno">  121</span>    <span class="keywordtype">double</span> double_height = NAN; <span class="comment">// double height input</span></div>
+<div class="line"><span class="lineno">  122</span> </div>
+<div class="line"><span class="lineno">  123</span>    <span class="comment">// Output variables</span></div>
+<div class="line"><span class="lineno">  124</span>    uint32_t int_expected = 0; <span class="comment">// 32 bit integer expected output</span></div>
+<div class="line"><span class="lineno">  125</span>    uint32_t int_volume = 0;   <span class="comment">// 32 bit integer output</span></div>
+<div class="line"><span class="lineno">  126</span> </div>
+<div class="line"><span class="lineno">  127</span>    <span class="keywordtype">double</span> double_expected = NAN; <span class="comment">// double expected output</span></div>
+<div class="line"><span class="lineno">  128</span>    <span class="keywordtype">double</span> double_volume = NAN;   <span class="comment">// double output</span></div>
+<div class="line"><span class="lineno">  129</span> </div>
+<div class="line"><span class="lineno">  130</span>    <span class="comment">// 1st test</span></div>
+<div class="line"><span class="lineno">  131</span>    int_length = 5;</div>
+<div class="line"><span class="lineno">  132</span>    int_expected = 125;</div>
+<div class="line"><span class="lineno">  133</span>    int_volume = <a class="code hl_function" href="../../dd/d47/namespacemath.html#ae413098478fa38acaac887b7654f0725">math::cube_volume</a>(int_length);</div>
+<div class="line"><span class="lineno">  134</span> </div>
+<div class="line"><span class="lineno">  135</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;VOLUME OF A CUBE&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  136</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Length: &quot;</span> &lt;&lt; int_length &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  137</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; int_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  138</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; int_volume &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  139</span>    assert(int_volume == int_expected);</div>
+<div class="line"><span class="lineno">  140</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  141</span> </div>
+<div class="line"><span class="lineno">  142</span>    <span class="comment">// 2nd test</span></div>
+<div class="line"><span class="lineno">  143</span>    int_length = 4;</div>
+<div class="line"><span class="lineno">  144</span>    int_width = 3;</div>
+<div class="line"><span class="lineno">  145</span>    int_height = 5;</div>
+<div class="line"><span class="lineno">  146</span>    int_expected = 60;</div>
+<div class="line"><span class="lineno">  147</span>    int_volume = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a3fdc74c24697ec5bb5c3698c96117c12">math::rect_prism_volume</a>(int_length, int_width, int_height);</div>
+<div class="line"><span class="lineno">  148</span> </div>
+<div class="line"><span class="lineno">  149</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;VOLUME OF A RECTANGULAR PRISM&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  150</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Length: &quot;</span> &lt;&lt; int_length &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  151</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Width: &quot;</span> &lt;&lt; int_width &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  152</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Height: &quot;</span> &lt;&lt; int_height &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  153</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; int_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  154</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; int_volume &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  155</span>    assert(int_volume == int_expected);</div>
+<div class="line"><span class="lineno">  156</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  157</span> </div>
+<div class="line"><span class="lineno">  158</span>    <span class="comment">// 3rd test</span></div>
+<div class="line"><span class="lineno">  159</span>    double_radius = 5;</div>
+<div class="line"><span class="lineno">  160</span>    double_height = 7;</div>
+<div class="line"><span class="lineno">  161</span>    double_expected = 183.16666666666666;  <span class="comment">// truncated to 14 decimal places</span></div>
+<div class="line"><span class="lineno">  162</span>    double_volume = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a3fe35440c27758ecc2287e08217d63a7">math::cone_volume</a>(double_radius, double_height);</div>
+<div class="line"><span class="lineno">  163</span> </div>
+<div class="line"><span class="lineno">  164</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;VOLUME OF A CONE&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  165</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Radius: &quot;</span> &lt;&lt; double_radius &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  166</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Height: &quot;</span> &lt;&lt; double_height &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  167</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; double_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  168</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; double_volume &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  169</span>    assert(double_volume == double_expected);</div>
+<div class="line"><span class="lineno">  170</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  171</span> </div>
+<div class="line"><span class="lineno">  172</span>    <span class="comment">// 4th test</span></div>
+<div class="line"><span class="lineno">  173</span>    int_base = 3;</div>
+<div class="line"><span class="lineno">  174</span>    int_height = 4;</div>
+<div class="line"><span class="lineno">  175</span>    int_depth = 5;</div>
+<div class="line"><span class="lineno">  176</span>    int_expected = 30;</div>
+<div class="line"><span class="lineno">  177</span>    int_volume = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a2d704a7b72a6b2db8b76c8581b577b2c">math::triangle_prism_volume</a>(int_base, int_height, int_depth);</div>
+<div class="line"><span class="lineno">  178</span> </div>
+<div class="line"><span class="lineno">  179</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;VOLUME OF A TRIANGULAR PRISM&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  180</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Base: &quot;</span> &lt;&lt; int_base &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  181</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Height: &quot;</span> &lt;&lt; int_height &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  182</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Depth: &quot;</span> &lt;&lt; int_depth &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  183</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; int_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  184</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; int_volume &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  185</span>    assert(int_volume == int_expected);</div>
+<div class="line"><span class="lineno">  186</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  187</span> </div>
+<div class="line"><span class="lineno">  188</span>    <span class="comment">// 5th test</span></div>
+<div class="line"><span class="lineno">  189</span>    int_length = 10;</div>
+<div class="line"><span class="lineno">  190</span>    int_width = 3;</div>
+<div class="line"><span class="lineno">  191</span>    int_height = 5;</div>
+<div class="line"><span class="lineno">  192</span>    int_expected = 50;</div>
+<div class="line"><span class="lineno">  193</span>    int_volume = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a94db02b3c9e55a69ac1696f30e2f761c">math::pyramid_volume</a>(int_length, int_width, int_height);</div>
+<div class="line"><span class="lineno">  194</span> </div>
+<div class="line"><span class="lineno">  195</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;VOLUME OF A PYRAMID&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  196</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Length: &quot;</span> &lt;&lt; int_length &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  197</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Width: &quot;</span> &lt;&lt; int_width &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  198</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Height: &quot;</span> &lt;&lt; int_height &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  199</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; int_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  200</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; int_volume &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  201</span>    assert(int_volume == int_expected);</div>
+<div class="line"><span class="lineno">  202</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  203</span> </div>
+<div class="line"><span class="lineno">  204</span>    <span class="comment">// 6th test</span></div>
+<div class="line"><span class="lineno">  205</span>    double_radius = 3;</div>
+<div class="line"><span class="lineno">  206</span>    double_expected = 113.04;</div>
+<div class="line"><span class="lineno">  207</span>    double_volume = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a34d66a77c19ce9b8b3a3d14352b34551">math::sphere_volume</a>(double_radius);</div>
+<div class="line"><span class="lineno">  208</span> </div>
+<div class="line"><span class="lineno">  209</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;VOLUME OF A SPHERE&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    }</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    <span class="keywordflow">return</span> traversed_path;</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   87</span>                                                                                {<span class="comment"></span></div>
+<div class="line"><span class="lineno">   88</span><span class="comment">    /// checked[i] stores the status of each node</span></div>
+<div class="line"><span class="lineno">   89</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a> checked(<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.size(), <a class="code hl_variable" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#afb80b42b42381658a12a57a975ecd0c7">WHITE</a>), traversed_path;</div>
+<div class="line"><span class="lineno">   90</span> </div>
+<div class="line"><span class="lineno">   91</span>    checked[start] = <a class="code hl_variable" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#a43e30173f12330e85cce6239a277527e">GREY</a>;</div>
+<div class="line"><span class="lineno">   92</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/stack.html">std::stack&lt;size_t&gt;</a> <a class="code hl_variable" href="../../dc/dc5/paranthesis__matching_8cpp.html#aa37d24a036d239b3b528f13b9de880c7">stack</a>;</div>
+<div class="line"><span class="lineno">   93</span>    <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a5705c3926dcf5fd3f9c964467a50b81d">push</a>(start);</div>
+<div class="line"><span class="lineno">   94</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   95</span><span class="comment">    /// while stack is not empty we keep exploring the node on top of stack</span></div>
+<div class="line"><span class="lineno">   96</span><span class="comment"></span>    <span class="keywordflow">while</span> (!<a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.empty()) {</div>
+<div class="line"><span class="lineno">   97</span>        <span class="keywordtype">int</span> act = <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a21c0bb6ce7dcfe445cc12031977ea344">top</a>();</div>
+<div class="line"><span class="lineno">   98</span>        <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a6cd4b95d5de00d41b2491392338384dc">pop</a>();</div>
+<div class="line"><span class="lineno">   99</span> </div>
+<div class="line"><span class="lineno">  100</span>        <span class="keywordflow">if</span> (checked[act] == <a class="code hl_variable" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#a43e30173f12330e85cce6239a277527e">GREY</a>) {<span class="comment"></span></div>
+<div class="line"><span class="lineno">  101</span><span class="comment">            /// push the node to the final result vector</span></div>
+<div class="line"><span class="lineno">  102</span><span class="comment"></span>            traversed_path.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(act + 1);</div>
+<div class="line"><span class="lineno">  103</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  104</span><span class="comment">            /// exploring the neighbours of the current node</span></div>
+<div class="line"><span class="lineno">  105</span><span class="comment"></span>            <span class="keywordflow">for</span> (<span class="keyword">auto</span> it : <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>[act]) {</div>
+<div class="line"><span class="lineno">  106</span>                <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a5705c3926dcf5fd3f9c964467a50b81d">push</a>(it);</div>
+<div class="line"><span class="lineno">  107</span>                <span class="keywordflow">if</span> (checked[it] != <a class="code hl_variable" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#a7f1cd94cf4da32933e8551cb3577e18b">BLACK</a>) {</div>
+<div class="line"><span class="lineno">  108</span>                    checked[it] = <a class="code hl_variable" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#a43e30173f12330e85cce6239a277527e">GREY</a>;</div>
+<div class="line"><span class="lineno">  109</span>                }</div>
+<div class="line"><span class="lineno">  110</span>            }</div>
+<div class="line"><span class="lineno">  111</span>            checked[act] = <a class="code hl_variable" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#a7f1cd94cf4da32933e8551cb3577e18b">BLACK</a>;  <span class="comment">/// Node has been explored</span></div>
+<div class="line"><span class="lineno">  112</span>        }</div>
+<div class="line"><span class="lineno">  113</span>    }</div>
+<div class="line"><span class="lineno">  114</span>    <span class="keywordflow">return</span> traversed_path;</div>
+<div class="line"><span class="lineno">  115</span>}</div>
 <div class="ttc" id="aclassstack_html"><div class="ttname"><a href="../../d1/dc2/classstack.html">stack</a></div><div class="ttdef"><b>Definition:</b> stack.h:26</div></div>
 <div class="ttc" id="aclassstack_html_a21c0bb6ce7dcfe445cc12031977ea344"><div class="ttname"><a href="../../d1/dc2/classstack.html#a21c0bb6ce7dcfe445cc12031977ea344">stack::top</a></div><div class="ttdeci">Type top()</div><div class="ttdef"><b>Definition:</b> stack.h:93</div></div>
 <div class="ttc" id="aclassstack_html_a5705c3926dcf5fd3f9c964467a50b81d"><div class="ttname"><a href="../../d1/dc2/classstack.html#a5705c3926dcf5fd3f9c964467a50b81d">stack::push</a></div><div class="ttdeci">void push(Type item)</div><div class="ttdef"><b>Definition:</b> stack.h:83</div></div>
@@ -342,41 +342,41 @@ Here is the call graph for this function:</div>
 <p >taking input for the edges</p>
 <p >taking input for the starting position</p>
 <p >Printing the order of traversal</p>
-<div class="fragment"><div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>           {</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>();  <span class="comment">// execute the tests</span></div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span> </div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>    <span class="keywordtype">size_t</span> vertices = 0, edges = 0, start_pos = 1;</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a> traversal;</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span> </div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the Vertices : &quot;</span>;</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; vertices;</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the Edges : &quot;</span>;</div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; edges;</div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span><span class="comment"></span> </div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span><span class="comment">    /// creating a graph</span></div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;size_t&gt;</a> &gt; adj(vertices, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a>());</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span><span class="comment"></span> </div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span><span class="comment">    /// taking input for the edges</span></div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the vertices which have edges between them : &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>    <span class="keywordflow">while</span> (edges--) {</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>        <span class="keywordtype">size_t</span> u = 0, v = 0;</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; u &gt;&gt; v;</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>        <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;adj, u, v);</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>    }</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span><span class="comment"></span> </div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span><span class="comment">    /// taking input for the starting position</span></div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the starting vertex [1,n]: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; start_pos;</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>    start_pos -= 1;</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>    traversal = <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#a5738da9f508f6a9e87f123c9fb6f2ea9">graph::depth_first_search::dfs</a>(adj, start_pos);</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span><span class="comment"></span> </div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span><span class="comment">    /// Printing the order of traversal</span></div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span><span class="comment"></span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> x : traversal) {</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; x &lt;&lt; <span class="charliteral">&#39; &#39;</span>;</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>    }</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span> </div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  173</span>           {</div>
+<div class="line"><span class="lineno">  174</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>();  <span class="comment">// execute the tests</span></div>
+<div class="line"><span class="lineno">  175</span> </div>
+<div class="line"><span class="lineno">  176</span>    <span class="keywordtype">size_t</span> vertices = 0, edges = 0, start_pos = 1;</div>
+<div class="line"><span class="lineno">  177</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a> traversal;</div>
+<div class="line"><span class="lineno">  178</span> </div>
+<div class="line"><span class="lineno">  179</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the Vertices : &quot;</span>;</div>
+<div class="line"><span class="lineno">  180</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; vertices;</div>
+<div class="line"><span class="lineno">  181</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the Edges : &quot;</span>;</div>
+<div class="line"><span class="lineno">  182</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; edges;</div>
+<div class="line"><span class="lineno">  183</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  184</span><span class="comment">    /// creating a graph</span></div>
+<div class="line"><span class="lineno">  185</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;size_t&gt;</a> &gt; adj(vertices, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a>());</div>
+<div class="line"><span class="lineno">  186</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  187</span><span class="comment">    /// taking input for the edges</span></div>
+<div class="line"><span class="lineno">  188</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the vertices which have edges between them : &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  189</span>    <span class="keywordflow">while</span> (edges--) {</div>
+<div class="line"><span class="lineno">  190</span>        <span class="keywordtype">size_t</span> u = 0, v = 0;</div>
+<div class="line"><span class="lineno">  191</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; u &gt;&gt; v;</div>
+<div class="line"><span class="lineno">  192</span>        <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;adj, u, v);</div>
+<div class="line"><span class="lineno">  193</span>    }</div>
+<div class="line"><span class="lineno">  194</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  195</span><span class="comment">    /// taking input for the starting position</span></div>
+<div class="line"><span class="lineno">  196</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the starting vertex [1,n]: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  197</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; start_pos;</div>
+<div class="line"><span class="lineno">  198</span>    start_pos -= 1;</div>
+<div class="line"><span class="lineno">  199</span>    traversal = <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#a5738da9f508f6a9e87f123c9fb6f2ea9">graph::depth_first_search::dfs</a>(adj, start_pos);</div>
+<div class="line"><span class="lineno">  200</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  201</span><span class="comment">    /// Printing the order of traversal</span></div>
+<div class="line"><span class="lineno">  202</span><span class="comment"></span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> x : traversal) {</div>
+<div class="line"><span class="lineno">  203</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; x &lt;&lt; <span class="charliteral">&#39; &#39;</span>;</div>
+<div class="line"><span class="lineno">  204</span>    }</div>
+<div class="line"><span class="lineno">  205</span> </div>
+<div class="line"><span class="lineno">  206</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  207</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="adepth__first__search__with__stack_8cpp_html_a483bb8ccf42aaf7375a83e91490eda1e"><div class="ttname"><a href="../../da/d4b/depth__first__search__with__stack_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a></div><div class="ttdeci">static void tests()</div><div class="ttdef"><b>Definition:</b> depth_first_search_with_stack.cpp:123</div></div>
@@ -421,51 +421,51 @@ Here is the call graph for this function:</div>
 <p >for the above sample data, this is the expected output</p>
 <p >Test 3</p>
 <p >for the above sample data, this is the expected output</p>
-<div class="fragment"><div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>                    {</div>
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-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span><span class="comment"></span> </div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span><span class="comment">    /// Test 1</span></div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Case 1: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    start_pos = 1;</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;size_t&gt;</a> &gt; g1(3, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a>());</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span> </div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g1, 1, 2);</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g1, 2, 3);</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g1, 3, 1);</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span> </div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a> expected1 {1, 2, 3}; <span class="comment">/// for the above sample data, this is the expected output</span></div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    assert(graph::depth_first_search::dfs(g1, start_pos - 1) == expected1);</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span><span class="comment"></span> </div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span><span class="comment">    /// Test 2</span></div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Case 2: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    start_pos = 1;</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;size_t&gt;</a> &gt; g2(4, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a>());</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span> </div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g2, 1, 2);</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g2, 1, 3);</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g2, 2, 4);</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g2, 4, 1);</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span> </div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a> expected2 {1, 3, 2, 4}; <span class="comment">/// for the above sample data, this is the expected output</span></div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    assert(graph::depth_first_search::dfs(g2, start_pos - 1) == expected2);</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span><span class="comment"></span> </div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span><span class="comment">    /// Test 3</span></div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Case 3: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>    start_pos = 2;</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;size_t&gt;</a> &gt; g3(4, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a>());</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span> </div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g3, 1, 2);</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g3, 1, 3);</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g3, 2, 4);</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g3, 4, 1);</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span> </div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a> expected3 {2, 4, 1, 3}; <span class="comment">/// for the above sample data, this is the expected output</span></div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>    assert(graph::depth_first_search::dfs(g3, start_pos - 1) == expected3);</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span> </div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  123</span>                    {</div>
+<div class="line"><span class="lineno">  124</span>    <span class="keywordtype">size_t</span> start_pos;</div>
+<div class="line"><span class="lineno">  125</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  126</span><span class="comment">    /// Test 1</span></div>
+<div class="line"><span class="lineno">  127</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Case 1: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  128</span>    start_pos = 1;</div>
+<div class="line"><span class="lineno">  129</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;size_t&gt;</a> &gt; g1(3, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a>());</div>
+<div class="line"><span class="lineno">  130</span> </div>
+<div class="line"><span class="lineno">  131</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g1, 1, 2);</div>
+<div class="line"><span class="lineno">  132</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g1, 2, 3);</div>
+<div class="line"><span class="lineno">  133</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g1, 3, 1);</div>
+<div class="line"><span class="lineno">  134</span> </div>
+<div class="line"><span class="lineno">  135</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a> expected1 {1, 2, 3}; <span class="comment">/// for the above sample data, this is the expected output</span></div>
+<div class="line"><span class="lineno">  136</span>    assert(graph::depth_first_search::dfs(g1, start_pos - 1) == expected1);</div>
+<div class="line"><span class="lineno">  137</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  138</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  139</span><span class="comment">    /// Test 2</span></div>
+<div class="line"><span class="lineno">  140</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Case 2: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  141</span>    start_pos = 1;</div>
+<div class="line"><span class="lineno">  142</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;size_t&gt;</a> &gt; g2(4, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a>());</div>
+<div class="line"><span class="lineno">  143</span> </div>
+<div class="line"><span class="lineno">  144</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g2, 1, 2);</div>
+<div class="line"><span class="lineno">  145</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g2, 1, 3);</div>
+<div class="line"><span class="lineno">  146</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g2, 2, 4);</div>
+<div class="line"><span class="lineno">  147</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g2, 4, 1);</div>
+<div class="line"><span class="lineno">  148</span> </div>
+<div class="line"><span class="lineno">  149</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a> expected2 {1, 3, 2, 4}; <span class="comment">/// for the above sample data, this is the expected output</span></div>
+<div class="line"><span class="lineno">  150</span>    assert(graph::depth_first_search::dfs(g2, start_pos - 1) == expected2);</div>
+<div class="line"><span class="lineno">  151</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  152</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  153</span><span class="comment">    /// Test 3</span></div>
+<div class="line"><span class="lineno">  154</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Case 3: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  155</span>    start_pos = 2;</div>
+<div class="line"><span class="lineno">  156</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;size_t&gt;</a> &gt; g3(4, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a>());</div>
+<div class="line"><span class="lineno">  157</span> </div>
+<div class="line"><span class="lineno">  158</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g3, 1, 2);</div>
+<div class="line"><span class="lineno">  159</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g3, 1, 3);</div>
+<div class="line"><span class="lineno">  160</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g3, 2, 4);</div>
+<div class="line"><span class="lineno">  161</span>    <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a>(&amp;g3, 4, 1);</div>
+<div class="line"><span class="lineno">  162</span> </div>
+<div class="line"><span class="lineno">  163</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a> expected3 {2, 4, 1, 3}; <span class="comment">/// for the above sample data, this is the expected output</span></div>
+<div class="line"><span class="lineno">  164</span>    assert(graph::depth_first_search::dfs(g3, start_pos - 1) == expected3);</div>
+<div class="line"><span class="lineno">  165</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  166</span> </div>
+<div class="line"><span class="lineno">  167</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -505,7 +505,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_12552d7fa429bf94a2e32e5cf39f7e69.html">graph</a></li><li class="navelem"><a class="el" href="../../da/d4b/depth__first__search__with__stack_8cpp.html">depth_first_search_with_stack.cpp</a></li>
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+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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diff --git a/da/d4b/depth__first__search__with__stack_8cpp_a483bb8ccf42aaf7375a83e91490eda1e_cgraph.map b/da/d4b/depth__first__search__with__stack_8cpp_a483bb8ccf42aaf7375a83e91490eda1e_cgraph.map
index f52c24baf..e33e321ec 100644
--- a/da/d4b/depth__first__search__with__stack_8cpp_a483bb8ccf42aaf7375a83e91490eda1e_cgraph.map
+++ b/da/d4b/depth__first__search__with__stack_8cpp_a483bb8ccf42aaf7375a83e91490eda1e_cgraph.map
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diff --git a/da/d4b/depth__first__search__with__stack_8cpp_a483bb8ccf42aaf7375a83e91490eda1e_cgraph.md5 b/da/d4b/depth__first__search__with__stack_8cpp_a483bb8ccf42aaf7375a83e91490eda1e_cgraph.md5
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+<div class="line"><span class="lineno">   68</span>    assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::</div>
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+<div class="line"><span class="lineno">   80</span>    assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::</div>
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-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span><span class="comment">      /// remove all characters of second string</span></div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span><span class="comment"></span>      <span class="keywordflow">else</span> <span class="keywordflow">if</span> (j == 0) {</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>        <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i][j] = i; <span class="comment">/// Minimum operations = i</span></div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>      }</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span><span class="comment"></span> </div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span><span class="comment">      /// If last characters are same, ignore last char</span></div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span><span class="comment">      /// and recur for remaining string</span></div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span><span class="comment"></span>      <span class="keywordflow">else</span> <span class="keywordflow">if</span> (str1[i - 1] == str2[j - 1]) {</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i][j] = <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i - 1][j - 1];</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>      }</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span><span class="comment"></span> </div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span><span class="comment">      /// If the last character is different, consider all</span></div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span><span class="comment">      /// possibilities and find the minimum</span></div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span><span class="comment"></span>      <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>        <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i][j] = 1 + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a>(<a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i][j - 1],      <span class="comment">// Insert</span></div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>                           <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i - 1][j],      <span class="comment">// Remove</span></div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>                           <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i - 1][j - 1]); <span class="comment">// Replace</span></div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>      }</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    }</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>  }</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span> </div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>  <span class="keywordflow">return</span> <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[m][n]; <span class="comment">/// returning the minimum cost of operations needed to convert str1 to str2</span></div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   88</span>                                                                            {<span class="comment"></span></div>
+<div class="line"><span class="lineno">   89</span><span class="comment">  /// Create a table to store results of subproblems</span></div>
+<div class="line"><span class="lineno">   90</span><span class="comment"></span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint64_t&gt;</a>&gt;<a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>(m+1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(n+1)); <span class="comment">/// creasting 2D vector dp to store the results of subproblems</span></div>
+<div class="line"><span class="lineno">   91</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   92</span><span class="comment">  /// Fill d[][] in bottom up manner</span></div>
+<div class="line"><span class="lineno">   93</span><span class="comment"></span>  <span class="keywordflow">for</span> (uint64_t i = 0; i &lt;= m; i++) {</div>
+<div class="line"><span class="lineno">   94</span>    <span class="keywordflow">for</span> (uint64_t j = 0; j &lt;= n; j++) {<span class="comment"></span></div>
+<div class="line"><span class="lineno">   95</span><span class="comment">      /// If first string is empty, only option is to</span></div>
+<div class="line"><span class="lineno">   96</span><span class="comment">      /// insert all characters of second string</span></div>
+<div class="line"><span class="lineno">   97</span><span class="comment"></span>      <span class="keywordflow">if</span> (i == 0) {</div>
+<div class="line"><span class="lineno">   98</span>        <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i][j] = j; <span class="comment">/// Minimum operations = j</span></div>
+<div class="line"><span class="lineno">   99</span>      }</div>
+<div class="line"><span class="lineno">  100</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  101</span><span class="comment">      /// If second string is empty, only option is to</span></div>
+<div class="line"><span class="lineno">  102</span><span class="comment">      /// remove all characters of second string</span></div>
+<div class="line"><span class="lineno">  103</span><span class="comment"></span>      <span class="keywordflow">else</span> <span class="keywordflow">if</span> (j == 0) {</div>
+<div class="line"><span class="lineno">  104</span>        <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i][j] = i; <span class="comment">/// Minimum operations = i</span></div>
+<div class="line"><span class="lineno">  105</span>      }</div>
+<div class="line"><span class="lineno">  106</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  107</span><span class="comment">      /// If last characters are same, ignore last char</span></div>
+<div class="line"><span class="lineno">  108</span><span class="comment">      /// and recur for remaining string</span></div>
+<div class="line"><span class="lineno">  109</span><span class="comment"></span>      <span class="keywordflow">else</span> <span class="keywordflow">if</span> (str1[i - 1] == str2[j - 1]) {</div>
+<div class="line"><span class="lineno">  110</span>        <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i][j] = <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i - 1][j - 1];</div>
+<div class="line"><span class="lineno">  111</span>      }</div>
+<div class="line"><span class="lineno">  112</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  113</span><span class="comment">      /// If the last character is different, consider all</span></div>
+<div class="line"><span class="lineno">  114</span><span class="comment">      /// possibilities and find the minimum</span></div>
+<div class="line"><span class="lineno">  115</span><span class="comment"></span>      <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  116</span>        <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i][j] = 1 + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a>(<a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i][j - 1],      <span class="comment">// Insert</span></div>
+<div class="line"><span class="lineno">  117</span>                           <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i - 1][j],      <span class="comment">// Remove</span></div>
+<div class="line"><span class="lineno">  118</span>                           <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i - 1][j - 1]); <span class="comment">// Replace</span></div>
+<div class="line"><span class="lineno">  119</span>      }</div>
+<div class="line"><span class="lineno">  120</span>    }</div>
+<div class="line"><span class="lineno">  121</span>  }</div>
+<div class="line"><span class="lineno">  122</span> </div>
+<div class="line"><span class="lineno">  123</span>  <span class="keywordflow">return</span> <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[m][n]; <span class="comment">/// returning the minimum cost of operations needed to convert str1 to str2</span></div>
+<div class="line"><span class="lineno">  124</span>}</div>
 <div class="ttc" id="amin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a></div><div class="ttdeci">T min(T... args)</div></div>
 <div class="ttc" id="anamespacedp_html"><div class="ttname"><a href="../../df/d88/namespacedp.html">dp</a></div><div class="ttdoc">for std::vector</div><div class="ttdef"><b>Definition:</b> partition_problem.cpp:39</div></div>
 <div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
@@ -282,10 +282,10 @@ Algorithm</h3>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>                                 {</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>  <a class="code hl_function" href="../../da/d52/minimum__edit__distance_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>  <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  160</span>                                 {</div>
+<div class="line"><span class="lineno">  161</span>  <a class="code hl_function" href="../../da/d52/minimum__edit__distance_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
+<div class="line"><span class="lineno">  162</span>  <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  163</span>}</div>
 <div class="ttc" id="aminimum__edit__distance_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../da/d52/minimum__edit__distance_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition:</b> minimum_edit_distance.cpp:132</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -345,17 +345,17 @@ z if <code>z</code> is the minimum value </dd></dl>
 <p >returns x, if x is the minimum value</p>
 <p >returns y, if y is the minimum value</p>
 <p >returns z if z is the minimum value</p>
-<div class="fragment"><div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>                                                 {</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>  <span class="keywordflow">if</span> (x &lt;= y &amp;&amp; x &lt;= z) {</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <span class="keywordflow">return</span> x; <span class="comment">/// returns x, if x is the minimum value</span></div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>  }</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>  <span class="keywordflow">if</span> (y &lt;= x &amp;&amp; y &lt;= z) {</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <span class="keywordflow">return</span> y; <span class="comment">/// returns y, if y is the minimum value</span></div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>  }</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>  <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    <span class="keywordflow">return</span> z; <span class="comment">/// returns z if z is the minimum value</span></div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>  }</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   63</span>                                                 {</div>
+<div class="line"><span class="lineno">   64</span>  <span class="keywordflow">if</span> (x &lt;= y &amp;&amp; x &lt;= z) {</div>
+<div class="line"><span class="lineno">   65</span>    <span class="keywordflow">return</span> x; <span class="comment">/// returns x, if x is the minimum value</span></div>
+<div class="line"><span class="lineno">   66</span>  }</div>
+<div class="line"><span class="lineno">   67</span>  <span class="keywordflow">if</span> (y &lt;= x &amp;&amp; y &lt;= z) {</div>
+<div class="line"><span class="lineno">   68</span>    <span class="keywordflow">return</span> y; <span class="comment">/// returns y, if y is the minimum value</span></div>
+<div class="line"><span class="lineno">   69</span>  }</div>
+<div class="line"><span class="lineno">   70</span>  <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   71</span>    <span class="keywordflow">return</span> z; <span class="comment">/// returns z if z is the minimum value</span></div>
+<div class="line"><span class="lineno">   72</span>  }</div>
+<div class="line"><span class="lineno">   73</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -384,27 +384,27 @@ z if <code>z</code> is the minimum value </dd></dl>
 
 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>                   {</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>  <span class="comment">// 1st test</span></div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> str1 = <span class="stringliteral">&quot;INTENTION&quot;</span>; <span class="comment">// Sample input of 1st string</span></div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> str2 = <span class="stringliteral">&quot;EXECUTION&quot;</span>; <span class="comment">// Sample input of 2nd string</span></div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>  uint64_t expected_output1 = 5; <span class="comment">// Expected minimum cost</span></div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>  uint64_t output1 = <a class="code hl_function" href="../../da/d52/minimum__edit__distance_8cpp.html#ade2fcfe0359f3c7691bfaa04b14943e2">dynamic_programming::minimum_edit_distance::editDistDP</a>(</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>      str1, str2, str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>(), str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>()); <span class="comment">// calling the editDistDP function and storing the result on output1</span></div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>  assert(output1 == expected_output1); <span class="comment">// comparing the output with the expected output</span></div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Minimum Number of Operations Required: &quot;</span> &lt;&lt; output1</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>            &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span> </div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>  <span class="comment">// 2nd test</span></div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> str3 = <span class="stringliteral">&quot;SATURDAY&quot;</span>;</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> str4 = <span class="stringliteral">&quot;SUNDAY&quot;</span>;</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>  uint64_t expected_output2 = 3;</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>  uint64_t output2 = <a class="code hl_function" href="../../da/d52/minimum__edit__distance_8cpp.html#ade2fcfe0359f3c7691bfaa04b14943e2">dynamic_programming::minimum_edit_distance::editDistDP</a>(</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>      str3, str4, str3.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>(), str4.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>());</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>  assert(output2 == expected_output2);</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Minimum Number of Operations Required: &quot;</span> &lt;&lt; output2</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>            &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  132</span>                   {</div>
+<div class="line"><span class="lineno">  133</span>  <span class="comment">// 1st test</span></div>
+<div class="line"><span class="lineno">  134</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> str1 = <span class="stringliteral">&quot;INTENTION&quot;</span>; <span class="comment">// Sample input of 1st string</span></div>
+<div class="line"><span class="lineno">  135</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> str2 = <span class="stringliteral">&quot;EXECUTION&quot;</span>; <span class="comment">// Sample input of 2nd string</span></div>
+<div class="line"><span class="lineno">  136</span>  uint64_t expected_output1 = 5; <span class="comment">// Expected minimum cost</span></div>
+<div class="line"><span class="lineno">  137</span>  uint64_t output1 = <a class="code hl_function" href="../../da/d52/minimum__edit__distance_8cpp.html#ade2fcfe0359f3c7691bfaa04b14943e2">dynamic_programming::minimum_edit_distance::editDistDP</a>(</div>
+<div class="line"><span class="lineno">  138</span>      str1, str2, str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>(), str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>()); <span class="comment">// calling the editDistDP function and storing the result on output1</span></div>
+<div class="line"><span class="lineno">  139</span>  assert(output1 == expected_output1); <span class="comment">// comparing the output with the expected output</span></div>
+<div class="line"><span class="lineno">  140</span>  <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Minimum Number of Operations Required: &quot;</span> &lt;&lt; output1</div>
+<div class="line"><span class="lineno">  141</span>            &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  142</span> </div>
+<div class="line"><span class="lineno">  143</span>  <span class="comment">// 2nd test</span></div>
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 <p>Member function to give the modulus of our complex number. Member function to which gives the absolute value (modulus) of our complex number. </p>
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-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>                       this-&gt;re * other.im + this-&gt;im * other.re);</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  117</span>                                            {</div>
+<div class="line"><span class="lineno">  118</span>        <a class="code hl_class" href="../../da/d5a/class_complex.html">Complex</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(this-&gt;re * other.re - this-&gt;im * other.im,</div>
+<div class="line"><span class="lineno">  119</span>                       this-&gt;re * other.im + this-&gt;im * other.re);</div>
+<div class="line"><span class="lineno">  120</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  121</span>    }</div>
 <div class="ttc" id="aclass_complex_html"><div class="ttname"><a href="../../da/d5a/class_complex.html">Complex</a></div><div class="ttdoc">Class Complex to represent complex numbers as a field.</div><div class="ttdef"><b>Definition:</b> complex_numbers.cpp:20</div></div>
 <div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
 </div><!-- fragment -->
@@ -436,10 +436,10 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>result current number plus other number </dd></dl>
-<div class="fragment"><div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>                                            {</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>        <a class="code hl_class" href="../../da/d5a/class_complex.html">Complex</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(this-&gt;re + other.re, this-&gt;im + other.im);</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   95</span>                                            {</div>
+<div class="line"><span class="lineno">   96</span>        <a class="code hl_class" href="../../da/d5a/class_complex.html">Complex</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(this-&gt;re + other.re, this-&gt;im + other.im);</div>
+<div class="line"><span class="lineno">   97</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">   98</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -475,10 +475,10 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>result current number subtract other number </dd></dl>
-<div class="fragment"><div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>                                            {</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>        <a class="code hl_class" href="../../da/d5a/class_complex.html">Complex</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(this-&gt;re - other.re, this-&gt;im - other.im);</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  106</span>                                            {</div>
+<div class="line"><span class="lineno">  107</span>        <a class="code hl_class" href="../../da/d5a/class_complex.html">Complex</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(this-&gt;re - other.re, this-&gt;im - other.im);</div>
+<div class="line"><span class="lineno">  108</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  109</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -514,18 +514,18 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>result Current number divided by other number. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>                                            {</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>        <a class="code hl_class" href="../../da/d5a/class_complex.html">Complex</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = *<span class="keyword">this</span> * ~other;</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>        <span class="keywordtype">double</span> denominator =</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>            other.<a class="code hl_function" href="../../da/d5a/class_complex.html#a312e4b19146128408fb06e0150b0faf6">real</a>() * other.<a class="code hl_function" href="../../da/d5a/class_complex.html#a312e4b19146128408fb06e0150b0faf6">real</a>() + other.<a class="code hl_function" href="../../da/d5a/class_complex.html#af8aacf982e2e6c142921bc850f6dc974">imag</a>() * other.<a class="code hl_function" href="../../da/d5a/class_complex.html#af8aacf982e2e6c142921bc850f6dc974">imag</a>();</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>        <span class="keywordflow">if</span> (denominator != 0) {</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>            <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../da/d5a/class_complex.html#a3cfc522c782726f49ee20af17b77f867">Complex</a>(<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.real() / denominator,</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>                             <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.imag() / denominator);</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>            <span class="keywordflow">throw</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a>(<span class="stringliteral">&quot;Undefined Value&quot;</span>);</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>        }</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  142</span>                                            {</div>
+<div class="line"><span class="lineno">  143</span>        <a class="code hl_class" href="../../da/d5a/class_complex.html">Complex</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = *<span class="keyword">this</span> * ~other;</div>
+<div class="line"><span class="lineno">  144</span>        <span class="keywordtype">double</span> denominator =</div>
+<div class="line"><span class="lineno">  145</span>            other.<a class="code hl_function" href="../../da/d5a/class_complex.html#a312e4b19146128408fb06e0150b0faf6">real</a>() * other.<a class="code hl_function" href="../../da/d5a/class_complex.html#a312e4b19146128408fb06e0150b0faf6">real</a>() + other.<a class="code hl_function" href="../../da/d5a/class_complex.html#af8aacf982e2e6c142921bc850f6dc974">imag</a>() * other.<a class="code hl_function" href="../../da/d5a/class_complex.html#af8aacf982e2e6c142921bc850f6dc974">imag</a>();</div>
+<div class="line"><span class="lineno">  146</span>        <span class="keywordflow">if</span> (denominator != 0) {</div>
+<div class="line"><span class="lineno">  147</span>            <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../da/d5a/class_complex.html#a3cfc522c782726f49ee20af17b77f867">Complex</a>(<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.real() / denominator,</div>
+<div class="line"><span class="lineno">  148</span>                             <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.imag() / denominator);</div>
+<div class="line"><span class="lineno">  149</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  150</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  151</span>            <span class="keywordflow">throw</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a>(<span class="stringliteral">&quot;Undefined Value&quot;</span>);</div>
+<div class="line"><span class="lineno">  152</span>        }</div>
+<div class="line"><span class="lineno">  153</span>    }</div>
 <div class="ttc" id="aclass_complex_html_a3cfc522c782726f49ee20af17b77f867"><div class="ttname"><a href="../../da/d5a/class_complex.html#a3cfc522c782726f49ee20af17b77f867">Complex::Complex</a></div><div class="ttdeci">Complex(double x=0.f, double y=0.f, bool is_polar=false)</div><div class="ttdoc">Complex Constructor which initialises our complex number.</div><div class="ttdef"><b>Definition:</b> complex_numbers.cpp:43</div></div>
 <div class="ttc" id="ainvalid_argument_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a></div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -562,11 +562,11 @@ Here is the call graph for this function:</div>
 </div><div class="memdoc">
 
 <p>Operator overload of '=' on <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> class. Operator overload to be able to copy RHS instance of <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> to LHS instance of <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a>. </p>
-<div class="fragment"><div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>                                                   {</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>        this-&gt;re = other.<a class="code hl_function" href="../../da/d5a/class_complex.html#a312e4b19146128408fb06e0150b0faf6">real</a>();</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>        this-&gt;im = other.<a class="code hl_function" href="../../da/d5a/class_complex.html#af8aacf982e2e6c142921bc850f6dc974">imag</a>();</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  160</span>                                                   {</div>
+<div class="line"><span class="lineno">  161</span>        this-&gt;re = other.<a class="code hl_function" href="../../da/d5a/class_complex.html#a312e4b19146128408fb06e0150b0faf6">real</a>();</div>
+<div class="line"><span class="lineno">  162</span>        this-&gt;im = other.<a class="code hl_function" href="../../da/d5a/class_complex.html#af8aacf982e2e6c142921bc850f6dc974">imag</a>();</div>
+<div class="line"><span class="lineno">  163</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  164</span>    }</div>
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 Here is the call graph for this function:</div>
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@@ -601,10 +601,10 @@ Here is the call graph for this function:</div>
 
 <p>Operator overload of '~' on <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> class. Operator overload of the BITWISE NOT which gives us the conjugate of our complex number. NOTE: This is overloading the BITWISE operator but its not a BITWISE operation in this definition. </p>
 <dl class="section return"><dt>Returns</dt><dd>result The conjugate of our complex number. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>                              {</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>        <a class="code hl_class" href="../../da/d5a/class_complex.html">Complex</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(this-&gt;re, -(this-&gt;im));</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  130</span>                              {</div>
+<div class="line"><span class="lineno">  131</span>        <a class="code hl_class" href="../../da/d5a/class_complex.html">Complex</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(this-&gt;re, -(this-&gt;im));</div>
+<div class="line"><span class="lineno">  132</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  133</span>    }</div>
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 <p>Member function to get real value of our complex number. Member function (getter) to access the class' re value. </p>
-<div class="fragment"><div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>{ <span class="keywordflow">return</span> this-&gt;re; }</div>
+<div class="fragment"><div class="line"><span class="lineno">   64</span>{ <span class="keywordflow">return</span> this-&gt;re; }</div>
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+<div class="line"><span class="lineno">   53</span>    <span class="keywordtype">size_t</span> s_index = 0;               <span class="comment">///&lt; Index for the second array</span></div>
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+<div class="line"><span class="lineno">   55</span>    <span class="keywordtype">size_t</span> s_length = second.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();  <span class="comment">///&lt; Length of second array</span></div>
+<div class="line"><span class="lineno">   56</span> </div>
+<div class="line"><span class="lineno">   57</span>    <span class="keywordflow">while</span> (f_index &lt; f_length &amp;&amp; s_index &lt; s_length) {</div>
+<div class="line"><span class="lineno">   58</span>        <span class="keywordflow">if</span> (first[f_index] &lt; second[s_index]) {</div>
+<div class="line"><span class="lineno">   59</span>            f_index++;  <span class="comment">///&lt; Increment index of second array</span></div>
+<div class="line"><span class="lineno">   60</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (first[f_index] &gt; second[s_index]) {</div>
+<div class="line"><span class="lineno">   61</span>            s_index++;  <span class="comment">///&lt; Increment index of second array</span></div>
+<div class="line"><span class="lineno">   62</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   63</span>            <span class="keywordflow">if</span> ((res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() == 0) || (first[f_index] != res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/back.html">back</a>())) {</div>
+<div class="line"><span class="lineno">   64</span>                res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(</div>
+<div class="line"><span class="lineno">   65</span>                    first[f_index]);  <span class="comment">///&lt; Add the element if it is unique</span></div>
+<div class="line"><span class="lineno">   66</span>            }</div>
+<div class="line"><span class="lineno">   67</span>            f_index++;  <span class="comment">///&lt; Increment index of first array</span></div>
+<div class="line"><span class="lineno">   68</span>            s_index++;  <span class="comment">///&lt; Increment index of second array too</span></div>
+<div class="line"><span class="lineno">   69</span>        }</div>
+<div class="line"><span class="lineno">   70</span>    }</div>
+<div class="line"><span class="lineno">   71</span>    <span class="keywordflow">return</span> res;</div>
+<div class="line"><span class="lineno">   72</span>}</div>
 <div class="ttc" id="aback_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/back.html">std::vector::back</a></div><div class="ttdeci">T back(T... args)</div></div>
 <div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
 <div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
@@ -266,46 +266,46 @@ Here is the call graph for this function:</div>
 <p >&lt; Add the element if it is unique</p>
 <p >&lt; Add remaining elements</p>
 <p >&lt; Add the element if it is unique</p>
-<div class="fragment"><div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>                                                                 {</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> res;         <span class="comment">///&lt; Vector to hold the union</span></div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    <span class="keywordtype">size_t</span> f_index = 0;               <span class="comment">///&lt; Index for the first array</span></div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    <span class="keywordtype">size_t</span> s_index = 0;               <span class="comment">///&lt; Index for the second array</span></div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>    <span class="keywordtype">size_t</span> f_length = first.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();   <span class="comment">///&lt; Length of first array</span></div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <span class="keywordtype">size_t</span> s_length = second.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();  <span class="comment">///&lt; Length of second array</span></div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    int32_t next = 0;  <span class="comment">///&lt; Integer to store value of the next element</span></div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span> </div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <span class="keywordflow">while</span> (f_index &lt; f_length &amp;&amp; s_index &lt; s_length) {</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>        <span class="keywordflow">if</span> (first[f_index] &lt; second[s_index]) {</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>            next = first[f_index];  <span class="comment">///&lt; Append from first array</span></div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>            f_index++;              <span class="comment">///&lt; Increment index of second array</span></div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (first[f_index] &gt; second[s_index]) {</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>            next = second[s_index];  <span class="comment">///&lt; Append from second array</span></div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>            s_index++;               <span class="comment">///&lt; Increment index of second array</span></div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> = first[f_index];  <span class="comment">///&lt; Element is the same in both</span></div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>            f_index++;              <span class="comment">///&lt; Increment index of first array</span></div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>            s_index++;              <span class="comment">///&lt; Increment index of second array too</span></div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        }</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        <span class="keywordflow">if</span> ((res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() == 0) || (next != res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/back.html">back</a>())) {</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>            res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(next);  <span class="comment">///&lt; Add the element if it is unique</span></div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>        }</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    }</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    <span class="keywordflow">while</span> (f_index &lt; f_length) {</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> = first[f_index];  <span class="comment">///&lt; Add remaining elements</span></div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        <span class="keywordflow">if</span> ((res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() == 0) || (next != res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/back.html">back</a>())) {</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>            res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(next);  <span class="comment">///&lt; Add the element if it is unique</span></div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        }</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>        f_index++;</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    }</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    <span class="keywordflow">while</span> (s_index &lt; s_length) {</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> = second[s_index];  <span class="comment">///&lt; Add remaining elements</span></div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>        <span class="keywordflow">if</span> ((res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() == 0) || (next != res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/back.html">back</a>())) {</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>            res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(next);  <span class="comment">///&lt; Add the element if it is unique</span></div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>        }</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>        s_index++;</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    }</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    <span class="keywordflow">return</span> res;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   50</span>                                                                 {</div>
+<div class="line"><span class="lineno">   51</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> res;         <span class="comment">///&lt; Vector to hold the union</span></div>
+<div class="line"><span class="lineno">   52</span>    <span class="keywordtype">size_t</span> f_index = 0;               <span class="comment">///&lt; Index for the first array</span></div>
+<div class="line"><span class="lineno">   53</span>    <span class="keywordtype">size_t</span> s_index = 0;               <span class="comment">///&lt; Index for the second array</span></div>
+<div class="line"><span class="lineno">   54</span>    <span class="keywordtype">size_t</span> f_length = first.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();   <span class="comment">///&lt; Length of first array</span></div>
+<div class="line"><span class="lineno">   55</span>    <span class="keywordtype">size_t</span> s_length = second.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();  <span class="comment">///&lt; Length of second array</span></div>
+<div class="line"><span class="lineno">   56</span>    int32_t next = 0;  <span class="comment">///&lt; Integer to store value of the next element</span></div>
+<div class="line"><span class="lineno">   57</span> </div>
+<div class="line"><span class="lineno">   58</span>    <span class="keywordflow">while</span> (f_index &lt; f_length &amp;&amp; s_index &lt; s_length) {</div>
+<div class="line"><span class="lineno">   59</span>        <span class="keywordflow">if</span> (first[f_index] &lt; second[s_index]) {</div>
+<div class="line"><span class="lineno">   60</span>            next = first[f_index];  <span class="comment">///&lt; Append from first array</span></div>
+<div class="line"><span class="lineno">   61</span>            f_index++;              <span class="comment">///&lt; Increment index of second array</span></div>
+<div class="line"><span class="lineno">   62</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (first[f_index] &gt; second[s_index]) {</div>
+<div class="line"><span class="lineno">   63</span>            next = second[s_index];  <span class="comment">///&lt; Append from second array</span></div>
+<div class="line"><span class="lineno">   64</span>            s_index++;               <span class="comment">///&lt; Increment index of second array</span></div>
+<div class="line"><span class="lineno">   65</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   66</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> = first[f_index];  <span class="comment">///&lt; Element is the same in both</span></div>
+<div class="line"><span class="lineno">   67</span>            f_index++;              <span class="comment">///&lt; Increment index of first array</span></div>
+<div class="line"><span class="lineno">   68</span>            s_index++;              <span class="comment">///&lt; Increment index of second array too</span></div>
+<div class="line"><span class="lineno">   69</span>        }</div>
+<div class="line"><span class="lineno">   70</span>        <span class="keywordflow">if</span> ((res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() == 0) || (next != res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/back.html">back</a>())) {</div>
+<div class="line"><span class="lineno">   71</span>            res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(next);  <span class="comment">///&lt; Add the element if it is unique</span></div>
+<div class="line"><span class="lineno">   72</span>        }</div>
+<div class="line"><span class="lineno">   73</span>    }</div>
+<div class="line"><span class="lineno">   74</span>    <span class="keywordflow">while</span> (f_index &lt; f_length) {</div>
+<div class="line"><span class="lineno">   75</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> = first[f_index];  <span class="comment">///&lt; Add remaining elements</span></div>
+<div class="line"><span class="lineno">   76</span>        <span class="keywordflow">if</span> ((res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() == 0) || (next != res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/back.html">back</a>())) {</div>
+<div class="line"><span class="lineno">   77</span>            res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(next);  <span class="comment">///&lt; Add the element if it is unique</span></div>
+<div class="line"><span class="lineno">   78</span>        }</div>
+<div class="line"><span class="lineno">   79</span>        f_index++;</div>
+<div class="line"><span class="lineno">   80</span>    }</div>
+<div class="line"><span class="lineno">   81</span>    <span class="keywordflow">while</span> (s_index &lt; s_length) {</div>
+<div class="line"><span class="lineno">   82</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> = second[s_index];  <span class="comment">///&lt; Add remaining elements</span></div>
+<div class="line"><span class="lineno">   83</span>        <span class="keywordflow">if</span> ((res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() == 0) || (next != res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/back.html">back</a>())) {</div>
+<div class="line"><span class="lineno">   84</span>            res.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(next);  <span class="comment">///&lt; Add the element if it is unique</span></div>
+<div class="line"><span class="lineno">   85</span>        }</div>
+<div class="line"><span class="lineno">   86</span>        s_index++;</div>
+<div class="line"><span class="lineno">   87</span>    }</div>
+<div class="line"><span class="lineno">   88</span>    <span class="keywordflow">return</span> res;</div>
+<div class="line"><span class="lineno">   89</span>}</div>
 <div class="ttc" id="anext_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/next.html">std::next</a></div><div class="ttdeci">T next(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -354,12 +354,12 @@ Here is the call graph for this function:</div>
 <p >Print newline</p>
 <p >Print each value in the array</p>
 <p >Print newline</p>
-<div class="fragment"><div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>                                            {</div>
-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>    <span class="keywordflow">for</span> (int32_t i : array) {</div>
-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;  <span class="comment">/// Print each value in the array</span></div>
-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>    }</div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;  <span class="comment">/// Print newline</span></div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   29</span>                                            {</div>
+<div class="line"><span class="lineno">   30</span>    <span class="keywordflow">for</span> (int32_t i : array) {</div>
+<div class="line"><span class="lineno">   31</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;  <span class="comment">/// Print each value in the array</span></div>
+<div class="line"><span class="lineno">   32</span>    }</div>
+<div class="line"><span class="lineno">   33</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;  <span class="comment">/// Print newline</span></div>
+<div class="line"><span class="lineno">   34</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 </div><!-- fragment -->
 </div>
@@ -403,20 +403,20 @@ Here is the call graph for this function:</div>
 <p >&lt; Result array</p>
 <p >&lt; Add values after the shift index</p>
 <p >&lt; Add the values from the start</p>
-<div class="fragment"><div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>                                              {</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <span class="keywordflow">if</span> (array.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;= shift) {</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        <span class="keywordflow">return</span> {};  <span class="comment">///&lt; We got an invalid shift, return empty array</span></div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    }</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> res(array.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());  <span class="comment">///&lt; Result array</span></div>
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diff --git a/da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html b/da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html
index 56a468142..163ab4283 100644
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@@ -30,8 +30,8 @@ MathJax.Hub.Config({
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-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
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@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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+<!-- Generated by Doxygen 1.9.3 -->
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@@ -100,6 +100,12 @@ $(document).ready(function(){initNavTree('da/d70/structmachine__learning_1_1ayst
 
 <p>Struct that handles all the information related to the current state.  
  <a href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#details">More...</a></p>
+<div class="dynheader">
+Collaboration diagram for machine_learning::aystar_search::AyStarSearch&lt; Puzzle &gt;::Info:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/d9e/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info__coll__graph.svg" width="184" height="156"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+<center><span class="legend">[<a target="top" href="../../graph_legend.html">legend</a>]</span></center></div>
 <table class="memberdecls">
 <tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
 Public Member Functions</h2></td></tr>
@@ -210,7 +216,7 @@ template&lt;typename Puzzle &gt; </div>
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-<div class="fragment"><div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>: state(std::make_shared&lt;Puzzle&gt;(A)) {}</div>
+<div class="fragment"><div class="line"><span class="lineno">  307</span>: state(std::make_shared&lt;Puzzle&gt;(A)) {}</div>
 </div><!-- fragment -->
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@@ -265,9 +271,9 @@ template&lt;typename Puzzle &gt; </div>
   </table>
   </dd>
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-<div class="fragment"><div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>            : state(std::make_shared&lt;Puzzle&gt;(A)),</div>
-<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span>              <a class="code hl_variable" href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#a331d1070d008a4f9d55775a51013baa3">heuristic_value</a>(h_value),</div>
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+<div class="fragment"><div class="line"><span class="lineno">  316</span>            : state(std::make_shared&lt;Puzzle&gt;(A)),</div>
+<div class="line"><span class="lineno">  317</span>              <a class="code hl_variable" href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#a331d1070d008a4f9d55775a51013baa3">heuristic_value</a>(h_value),</div>
+<div class="line"><span class="lineno">  318</span>              <a class="code hl_variable" href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#a003a30bb165be50ce503c17df90c128d">depth</a>(d) {}</div>
 <div class="ttc" id="astructmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info_html_a003a30bb165be50ce503c17df90c128d"><div class="ttname"><a href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#a003a30bb165be50ce503c17df90c128d">machine_learning::aystar_search::AyStarSearch::Info::depth</a></div><div class="ttdeci">size_t depth</div><div class="ttdoc">stores h score</div><div class="ttdef"><b>Definition:</b> a_star_search.cpp:296</div></div>
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@@ -306,9 +312,9 @@ template&lt;typename Puzzle &gt; </div>
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+<div class="fragment"><div class="line"><span class="lineno">  325</span>            : state(std::make_shared&lt;Puzzle&gt;(A.state)),</div>
+<div class="line"><span class="lineno">  326</span>              <a class="code hl_variable" href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#a331d1070d008a4f9d55775a51013baa3">heuristic_value</a>(A.heuristic_value),</div>
+<div class="line"><span class="lineno">  327</span>              <a class="code hl_variable" href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#a003a30bb165be50ce503c17df90c128d">depth</a>(A.depth) {}</div>
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+<div class="fragment"><div class="line"><span class="lineno">  334</span>            : state(std::make_shared&lt;Puzzle&gt;(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(A.state))),</div>
+<div class="line"><span class="lineno">  335</span>              <a class="code hl_variable" href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#a331d1070d008a4f9d55775a51013baa3">heuristic_value</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(A.heuristic_value)),</div>
+<div class="line"><span class="lineno">  336</span>              <a class="code hl_variable" href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#a003a30bb165be50ce503c17df90c128d">depth</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(A.depth)) {}</div>
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 </div><!-- fragment -->
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@@ -386,12 +392,12 @@ template&lt;typename Puzzle &gt; </div>
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-<div class="line"><a id="l00344" name="l00344"></a><span class="lineno">  344</span>            <a class="code hl_variable" href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#a331d1070d008a4f9d55775a51013baa3">heuristic_value</a> = A.heuristic_value;</div>
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-<div class="line"><a id="l00346" name="l00346"></a><span class="lineno">  346</span>            <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00347" name="l00347"></a><span class="lineno">  347</span>        }</div>
+<div class="fragment"><div class="line"><span class="lineno">  342</span>                                       {</div>
+<div class="line"><span class="lineno">  343</span>            state = A.state;</div>
+<div class="line"><span class="lineno">  344</span>            <a class="code hl_variable" href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#a331d1070d008a4f9d55775a51013baa3">heuristic_value</a> = A.heuristic_value;</div>
+<div class="line"><span class="lineno">  345</span>            <a class="code hl_variable" href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#a003a30bb165be50ce503c17df90c128d">depth</a> = A.depth;</div>
+<div class="line"><span class="lineno">  346</span>            <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  347</span>        }</div>
 </div><!-- fragment -->
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@@ -428,12 +434,12 @@ template&lt;typename Puzzle &gt; </div>
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-<div class="line"><a id="l00355" name="l00355"></a><span class="lineno">  355</span>            <a class="code hl_variable" href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#a331d1070d008a4f9d55775a51013baa3">heuristic_value</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(A.heuristic_value);</div>
-<div class="line"><a id="l00356" name="l00356"></a><span class="lineno">  356</span>            <a class="code hl_variable" href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#a003a30bb165be50ce503c17df90c128d">depth</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(A.depth);</div>
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-<div class="line"><a id="l00358" name="l00358"></a><span class="lineno">  358</span>        }</div>
+<div class="fragment"><div class="line"><span class="lineno">  353</span>                                           {</div>
+<div class="line"><span class="lineno">  354</span>            state = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(A.state);</div>
+<div class="line"><span class="lineno">  355</span>            <a class="code hl_variable" href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#a331d1070d008a4f9d55775a51013baa3">heuristic_value</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(A.heuristic_value);</div>
+<div class="line"><span class="lineno">  356</span>            <a class="code hl_variable" href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#a003a30bb165be50ce503c17df90c128d">depth</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(A.depth);</div>
+<div class="line"><span class="lineno">  357</span>            <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  358</span>        }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -452,7 +458,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../d8/d77/namespacemachine__learning.html">machine_learning</a></li><li class="navelem"><b>aystar_search</b></li><li class="navelem"><a class="el" href="../../da/d02/classmachine__learning_1_1aystar__search_1_1_ay_star_search.html">AyStarSearch</a></li><li class="navelem"><a class="el" href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html">Info</a></li>
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+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
 <div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Primality_test" target="_blank">Primality test</a> implementation. </p>
 <p >A simple and efficient implementation of a function to test if a number is prime, based on the fact that </p><blockquote class="doxtable">
-<p >Every Prime number, except 2 and 3, are of the form \(6k\pm1\) for integer values of k. </p>
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 <dl class="section return"><dt>Returns</dt><dd>true if prime else false </dd></dl>
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-<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>}</div>
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@@ -251,11 +251,11 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>max_flow</b> = 0</td><
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-<div class="fragment"><div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span>                        {</div>
-<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span>        this-&gt;vertexNum = V;</div>
-<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>        this-&gt;edgeNum = E;</div>
-<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>        this-&gt;edges = (<a class="code hl_struct" href="../../d7/d77/class_edge.html">Edge</a> *)<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/c/malloc.html">malloc</a>(E * <span class="keyword">sizeof</span>(<a class="code hl_struct" href="../../d7/d77/class_edge.html">Edge</a>));</div>
-<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   19</span>                        {</div>
+<div class="line"><span class="lineno">   20</span>        this-&gt;vertexNum = V;</div>
+<div class="line"><span class="lineno">   21</span>        this-&gt;edgeNum = E;</div>
+<div class="line"><span class="lineno">   22</span>        this-&gt;edges = (<a class="code hl_struct" href="../../d7/d77/class_edge.html">Edge</a> *)<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/c/malloc.html">malloc</a>(E * <span class="keyword">sizeof</span>(<a class="code hl_struct" href="../../d7/d77/class_edge.html">Edge</a>));</div>
+<div class="line"><span class="lineno">   23</span>    }</div>
 <div class="ttc" id="aclass_edge_html"><div class="ttname"><a href="../../d7/d77/class_edge.html">Edge</a></div><div class="ttdef"><b>Definition:</b> bellman_ford.cpp:7</div></div>
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@@ -284,15 +284,15 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>max_flow</b> = 0</td><
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-<div class="fragment"><div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span>                 {</div>
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-<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span>        this-&gt;edges = <span class="keyword">new</span> <span class="keywordtype">int</span> *[V];</div>
-<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; V; i++) {</div>
-<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span>            this-&gt;edges[i] = <span class="keyword">new</span> <span class="keywordtype">int</span>[V];</div>
-<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; V; j++) this-&gt;edges[i][j] = INT_MAX;</div>
-<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>            this-&gt;edges[i][i] = 0;</div>
-<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>        }</div>
-<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   16</span>                 {</div>
+<div class="line"><span class="lineno">   17</span>        this-&gt;vertexNum = V;</div>
+<div class="line"><span class="lineno">   18</span>        this-&gt;edges = <span class="keyword">new</span> <span class="keywordtype">int</span> *[V];</div>
+<div class="line"><span class="lineno">   19</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; V; i++) {</div>
+<div class="line"><span class="lineno">   20</span>            this-&gt;edges[i] = <span class="keyword">new</span> <span class="keywordtype">int</span>[V];</div>
+<div class="line"><span class="lineno">   21</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; V; j++) this-&gt;edges[i][j] = INT_MAX;</div>
+<div class="line"><span class="lineno">   22</span>            this-&gt;edges[i][i] = 0;</div>
+<div class="line"><span class="lineno">   23</span>        }</div>
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-<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>        <span class="keyword">delete</span>[] edges;</div>
-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   26</span>             {</div>
+<div class="line"><span class="lineno">   27</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; vertexNum; i++) <span class="keyword">delete</span>[] edges[i];</div>
+<div class="line"><span class="lineno">   28</span>        <span class="keyword">delete</span>[] edges;</div>
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-<div class="fragment"><div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>: m_adjList({}) {}</div>
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+<div class="fragment"><div class="line"><span class="lineno">   69</span>        : m_vertices(vertices), m_adjList(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(adjList)) {}</div>
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+<div class="fragment"><div class="line"><span class="lineno">   77</span>        : m_vertices(vertices), m_adjList(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(adjList)) {}</div>
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-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>                    <span class="stringliteral">&quot;Either src or dest of edge out of range&quot;</span>);</div>
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-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   89</span>        : m_vertices(vertices) {</div>
+<div class="line"><span class="lineno">   90</span>        <span class="keywordflow">for</span> (<span class="keyword">auto</span> <span class="keyword">const</span>&amp; edge : edges) {</div>
+<div class="line"><span class="lineno">   91</span>            <span class="keywordflow">if</span> (edge.src &gt;= vertices || edge.dest &gt;= vertices) {</div>
+<div class="line"><span class="lineno">   92</span>                <span class="keywordflow">throw</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/range_error.html">std::range_error</a>(</div>
+<div class="line"><span class="lineno">   93</span>                    <span class="stringliteral">&quot;Either src or dest of edge out of range&quot;</span>);</div>
+<div class="line"><span class="lineno">   94</span>            }</div>
+<div class="line"><span class="lineno">   95</span>            m_adjList[edge.src].emplace_back(edge.dest);</div>
+<div class="line"><span class="lineno">   96</span>        }</div>
+<div class="line"><span class="lineno">   97</span>    }</div>
 <div class="ttc" id="arange_error_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/error/range_error.html">std::range_error</a></div></div>
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-<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span>        this-&gt;edges = <span class="keyword">new</span> <span class="keywordtype">int</span> *[V];</div>
-<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; V; i++) {</div>
-<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span>            edges[i] = <span class="keyword">new</span> <span class="keywordtype">int</span>[V];</div>
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-<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span> </div>
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-<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; V; i++) {</div>
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+<div class="fragment"><div class="line"><span class="lineno">   13</span>                       {</div>
+<div class="line"><span class="lineno">   14</span>        <span class="comment">// initializes the array edges.</span></div>
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+<div class="line"><span class="lineno">   16</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; V; i++) {</div>
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+<div class="line"><span class="lineno">   19</span> </div>
+<div class="line"><span class="lineno">   20</span>        <span class="comment">// fills the array with zeros.</span></div>
+<div class="line"><span class="lineno">   21</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; V; i++) {</div>
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+<div class="line"><span class="lineno">   26</span> </div>
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+<div class="line"><span class="lineno">  127</span>        }</div>
+<div class="line"><span class="lineno">  128</span>        m_adjList[edge.src].emplace_back(edge.dest);</div>
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+<div class="line"><span class="lineno">   33</span>        this-&gt;edges[src][dst] = weight;</div>
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-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>        this-&gt;edges[src][dst] = weight;</div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   31</span>                                               {</div>
+<div class="line"><span class="lineno">   32</span>        this-&gt;edges[src][dst] = weight;</div>
+<div class="line"><span class="lineno">   33</span>    }</div>
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 </div>
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@@ -762,13 +762,13 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>max_flow</b> = 0</td><
   </table>
   </dd>
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-<div class="fragment"><div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>                                                                {</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        <span class="keywordflow">if</span> (source &gt;= m_vertices || destination &gt;= m_vertices) {</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>            <span class="keywordflow">throw</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/range_error.html">std::range_error</a>(</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>                <span class="stringliteral">&quot;Either source or destination of edge out of range&quot;</span>);</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>        }</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>        m_adjList[source].emplace_back(destination);</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  136</span>                                                                {</div>
+<div class="line"><span class="lineno">  137</span>        <span class="keywordflow">if</span> (source &gt;= m_vertices || destination &gt;= m_vertices) {</div>
+<div class="line"><span class="lineno">  138</span>            <span class="keywordflow">throw</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/range_error.html">std::range_error</a>(</div>
+<div class="line"><span class="lineno">  139</span>                <span class="stringliteral">&quot;Either source or destination of edge out of range&quot;</span>);</div>
+<div class="line"><span class="lineno">  140</span>        }</div>
+<div class="line"><span class="lineno">  141</span>        m_adjList[source].emplace_back(destination);</div>
+<div class="line"><span class="lineno">  142</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -802,7 +802,7 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>max_flow</b> = 0</td><
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>{ m_vertices += num; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  118</span>{ m_vertices += num; }</div>
 </div><!-- fragment -->
 </div>
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@@ -839,29 +839,31 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>max_flow</b> = 0</td><
   </tr>
 </table>
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-<div class="fragment"><div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>                                   {  <span class="comment">//  to find the augmented - path</span></div>
-<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>        visited.reset();</div>
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-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>        q.push(source);</div>
-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>        <span class="keywordtype">bool</span> is_path_found = <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>        <span class="keywordflow">while</span> (q.empty() == <span class="keyword">false</span> &amp;&amp; is_path_found == <span class="keyword">false</span>) {</div>
-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>            <span class="keywordtype">int</span> current_node = q.front();</div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>            visited.set(current_node);</div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>            q.pop();</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; total_nodes; ++i) {</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>                <span class="keywordflow">if</span> (residual_capacity[current_node][i] &gt; 0 &amp;&amp; !visited[i]) {</div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>                    visited.set(i);</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>                    parent[i] = current_node;</div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>                    <span class="keywordflow">if</span> (i == sink) {</div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>                        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>                    }</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>                    q.push(i);</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>                }</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>            }</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>        }</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   26</span>                                   {  <span class="comment">//  to find the augmented - path</span></div>
+<div class="line"><span class="lineno">   27</span>        visited.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/bitset/reset.html">reset</a>();</div>
+<div class="line"><span class="lineno">   28</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue&lt;int&gt;</a> q;</div>
+<div class="line"><span class="lineno">   29</span>        q.push(source);</div>
+<div class="line"><span class="lineno">   30</span>        <span class="keywordtype">bool</span> is_path_found = <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   31</span>        <span class="keywordflow">while</span> (q.empty() == <span class="keyword">false</span> &amp;&amp; is_path_found == <span class="keyword">false</span>) {</div>
+<div class="line"><span class="lineno">   32</span>            <span class="keywordtype">int</span> current_node = q.front();</div>
+<div class="line"><span class="lineno">   33</span>            visited.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/bitset/set.html">set</a>(current_node);</div>
+<div class="line"><span class="lineno">   34</span>            q.pop();</div>
+<div class="line"><span class="lineno">   35</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; total_nodes; ++i) {</div>
+<div class="line"><span class="lineno">   36</span>                <span class="keywordflow">if</span> (residual_capacity[current_node][i] &gt; 0 &amp;&amp; !visited[i]) {</div>
+<div class="line"><span class="lineno">   37</span>                    visited.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/bitset/set.html">set</a>(i);</div>
+<div class="line"><span class="lineno">   38</span>                    parent[i] = current_node;</div>
+<div class="line"><span class="lineno">   39</span>                    <span class="keywordflow">if</span> (i == sink) {</div>
+<div class="line"><span class="lineno">   40</span>                        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   41</span>                    }</div>
+<div class="line"><span class="lineno">   42</span>                    q.push(i);</div>
+<div class="line"><span class="lineno">   43</span>                }</div>
+<div class="line"><span class="lineno">   44</span>            }</div>
+<div class="line"><span class="lineno">   45</span>        }</div>
+<div class="line"><span class="lineno">   46</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   47</span>    }</div>
 <div class="ttc" id="aqueue_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue</a></div></div>
+<div class="ttc" id="areset_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/bitset/reset.html">std::bitset::reset</a></div><div class="ttdeci">T reset(T... args)</div></div>
+<div class="ttc" id="aset_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/bitset/set.html">std::bitset::set</a></div><div class="ttdeci">T set(T... args)</div></div>
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 </div>
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@@ -887,25 +889,25 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>max_flow</b> = 0</td><
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 </table>
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-<div class="fragment"><div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>                          {</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        <span class="keywordflow">while</span> (bfs(source, sink)) {</div>
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-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>            <span class="keywordflow">while</span> (current_node != source) {</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>                <span class="keywordtype">int</span> parent_ = parent[current_node];</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>                flow = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(flow, residual_capacity[parent_][current_node]);</div>
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-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>            <span class="keywordflow">while</span> (current_node != source) {</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>                <span class="keywordtype">int</span> parent_ = parent[current_node];</div>
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-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>                residual_capacity[current_node][parent_] += flow;</div>
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-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>            }</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>        }</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   62</span>                          {</div>
+<div class="line"><span class="lineno">   63</span>        <span class="keywordflow">while</span> (bfs(source, sink)) {</div>
+<div class="line"><span class="lineno">   64</span>            <span class="keywordtype">int</span> current_node = sink;</div>
+<div class="line"><span class="lineno">   65</span>            <span class="keywordtype">int</span> flow = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/numeric_limits/max.html">std::numeric_limits&lt;int&gt;::max</a>();</div>
+<div class="line"><span class="lineno">   66</span>            <span class="keywordflow">while</span> (current_node != source) {</div>
+<div class="line"><span class="lineno">   67</span>                <span class="keywordtype">int</span> parent_ = parent[current_node];</div>
+<div class="line"><span class="lineno">   68</span>                flow = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(flow, residual_capacity[parent_][current_node]);</div>
+<div class="line"><span class="lineno">   69</span>                current_node = parent_;</div>
+<div class="line"><span class="lineno">   70</span>            }</div>
+<div class="line"><span class="lineno">   71</span>            current_node = sink;</div>
+<div class="line"><span class="lineno">   72</span>            max_flow += flow;</div>
+<div class="line"><span class="lineno">   73</span>            <span class="keywordflow">while</span> (current_node != source) {</div>
+<div class="line"><span class="lineno">   74</span>                <span class="keywordtype">int</span> parent_ = parent[current_node];</div>
+<div class="line"><span class="lineno">   75</span>                residual_capacity[parent_][current_node] -= flow;</div>
+<div class="line"><span class="lineno">   76</span>                residual_capacity[current_node][parent_] += flow;</div>
+<div class="line"><span class="lineno">   77</span>                current_node = parent_;</div>
+<div class="line"><span class="lineno">   78</span>            }</div>
+<div class="line"><span class="lineno">   79</span>        }</div>
+<div class="line"><span class="lineno">   80</span>    }</div>
 <div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/numeric_limits/max.html">std::numeric_limits::max</a></div><div class="ttdeci">T max(T... args)</div></div>
 <div class="ttc" id="amin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a></div><div class="ttdeci">T min(T... args)</div></div>
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@@ -935,9 +937,9 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>max_flow</b> = 0</td><
 </div><div class="memdoc">
 <p >Return a const reference of the adjacency list.</p>
 <dl class="section return"><dt>Returns</dt><dd>const reference to the adjacency list </dd></dl>
-<div class="fragment"><div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>                                                               {</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>        <span class="keywordflow">return</span> m_adjList;</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  103</span>                                                               {</div>
+<div class="line"><span class="lineno">  104</span>        <span class="keywordflow">return</span> m_adjList;</div>
+<div class="line"><span class="lineno">  105</span>    }</div>
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@@ -964,7 +966,7 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>max_flow</b> = 0</td><
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 <dl class="section return"><dt>Returns</dt><dd>number of vertices in the graph. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>{ <span class="keywordflow">return</span> m_vertices; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  110</span>{ <span class="keywordflow">return</span> m_vertices; }</div>
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@@ -990,29 +992,31 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>max_flow</b> = 0</td><
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-<div class="fragment"><div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>                           {</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; total_nodes; ++i) {</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; total_nodes; ++j) {</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>                <span class="keywordflow">if</span> (capacity[i][j] &amp;&amp;</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>                    residual_capacity[i][j] &lt; capacity[i][j]) {</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>                    edge_participated.emplace_back(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/tuple/make_tuple.html">std::make_tuple</a>(</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>                        i, j, capacity[i][j] - residual_capacity[i][j]));</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>                }</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>            }</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>        }</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nNodes : &quot;</span> &lt;&lt; total_nodes &lt;&lt; <span class="stringliteral">&quot;\nMax flow: &quot;</span> &lt;&lt; max_flow</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>                  &lt;&lt; <span class="stringliteral">&quot;\nEdge present in flow: &quot;</span> &lt;&lt; edge_participated.size()</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>                  &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nSource\tDestination\tCapacity\total_nodes&quot;</span>;</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>        <span class="keywordflow">for</span> (<span class="keyword">auto</span>&amp; edge_data : edge_participated) {</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>            <span class="keywordtype">int</span> source = 0, destination = 0, capacity_ = 0;</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/tuple/tie.html">std::tie</a>(source, destination, capacity_) = edge_data;</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; source &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span> &lt;&lt; destination &lt;&lt; <span class="stringliteral">&quot;\t\t&quot;</span> &lt;&lt; capacity_</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>                      &lt;&lt; <span class="charliteral">&#39;\t&#39;</span>;</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>        }</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   81</span>                           {</div>
+<div class="line"><span class="lineno">   82</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; total_nodes; ++i) {</div>
+<div class="line"><span class="lineno">   83</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; total_nodes; ++j) {</div>
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 <p >check in the row</p>
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+<div class="line"><span class="lineno">   67</span><span class="comment">    /// check the first diagonal</span></div>
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+<div class="line"><span class="lineno">  113</span>    <span class="keywordflow">if</span> (n % 2 == 0) {</div>
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+<div class="line"><span class="lineno">  124</span>                board[i][0] = 1;</div>
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+<div class="line"><span class="lineno">   96</span>            board[i][col] = 1;</div>
+<div class="line"><span class="lineno">   97</span>            NQueenSol&lt;n&gt;(board, col + 1);</div>
+<div class="line"><span class="lineno">   98</span>            board[i][col] = 0;</div>
+<div class="line"><span class="lineno">   99</span>        }</div>
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-<p>Implementation to <a href="https://www.geeksforgeeks.org/count-set-bits-in-an-integer/" target="_blank">count number of set bits of a number</a> in an integer.  
+<p>Implementation to [count number of set bits of a number] (<a href="https://www.geeksforgeeks.org/count-set-bits-in-an-integer/">https://www.geeksforgeeks.org/count-set-bits-in-an-integer/</a>) in an integer.  
 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;cassert&gt;</code><br />
 <code>#include &lt;iostream&gt;</code><br />
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 </table>
 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
-<div class="textblock"><p >Implementation to <a href="https://www.geeksforgeeks.org/count-set-bits-in-an-integer/" target="_blank">count number of set bits of a number</a> in an integer. </p>
+<div class="textblock"><p >Implementation to [count number of set bits of a number] (<a href="https://www.geeksforgeeks.org/count-set-bits-in-an-integer/">https://www.geeksforgeeks.org/count-set-bits-in-an-integer/</a>) in an integer. </p>
 <p >We are given an integer number. We need to calculate the number of set bits in it.</p>
 <p >A binary number consists of two digits. They are 0 &amp; 1. Digit 1 is known as set bit in computer terms. Worst Case Time Complexity: O(log n) Space complexity: O(1) </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Swastyy" target="_blank">Swastika Gupta</a> </dd>
 <dd>
@@ -159,21 +159,21 @@ Functions</h2></td></tr>
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 <dl class="section return"><dt>Returns</dt><dd>total number of set-bits in the binary representation of number <code>n</code> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>                   {  <span class="comment">// int64_t is preferred over int so that</span></div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>                        <span class="comment">// no Overflow can be there.</span></div>
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-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    <span class="keywordtype">int</span> count = 0;  <span class="comment">// &quot;count&quot; variable is used to count number of set-bits(&#39;1&#39;)</span></div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>                    <span class="comment">// in binary representation of number &#39;n&#39;</span></div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>    <span class="keywordflow">while</span> (n != 0) {</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>        ++count;</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>        n = (n &amp; (n - 1));</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>    }</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>    <span class="keywordflow">return</span> count;</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <span class="comment">// Why this algorithm is better than the standard one?</span></div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    <span class="comment">// Because this algorithm runs the same number of times as the number of</span></div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    <span class="comment">// set-bits in it. Means if my number is having &quot;3&quot; set bits, then this</span></div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    <span class="comment">// while loop will run only &quot;3&quot; times!!</span></div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   38</span>                   {  <span class="comment">// int64_t is preferred over int so that</span></div>
+<div class="line"><span class="lineno">   39</span>                        <span class="comment">// no Overflow can be there.</span></div>
+<div class="line"><span class="lineno">   40</span> </div>
+<div class="line"><span class="lineno">   41</span>    <span class="keywordtype">int</span> count = 0;  <span class="comment">// &quot;count&quot; variable is used to count number of set-bits(&#39;1&#39;)</span></div>
+<div class="line"><span class="lineno">   42</span>                    <span class="comment">// in binary representation of number &#39;n&#39;</span></div>
+<div class="line"><span class="lineno">   43</span>    <span class="keywordflow">while</span> (n != 0) {</div>
+<div class="line"><span class="lineno">   44</span>        ++count;</div>
+<div class="line"><span class="lineno">   45</span>        n = (n &amp; (n - 1));</div>
+<div class="line"><span class="lineno">   46</span>    }</div>
+<div class="line"><span class="lineno">   47</span>    <span class="keywordflow">return</span> count;</div>
+<div class="line"><span class="lineno">   48</span>    <span class="comment">// Why this algorithm is better than the standard one?</span></div>
+<div class="line"><span class="lineno">   49</span>    <span class="comment">// Because this algorithm runs the same number of times as the number of</span></div>
+<div class="line"><span class="lineno">   50</span>    <span class="comment">// set-bits in it. Means if my number is having &quot;3&quot; set bits, then this</span></div>
+<div class="line"><span class="lineno">   51</span>    <span class="comment">// while loop will run only &quot;3&quot; times!!</span></div>
+<div class="line"><span class="lineno">   52</span>}</div>
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 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>           {</div>
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-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   79</span>           {</div>
+<div class="line"><span class="lineno">   80</span>    test();  <span class="comment">// run self-test implementations</span></div>
+<div class="line"><span class="lineno">   81</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">   82</span>}</div>
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-<div class="fragment"><div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>                   {</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    <span class="comment">// n = 4 return 1</span></div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    assert(bit_manipulation::count_of_set_bits::countSetBits(4) == 1);</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <span class="comment">// n = 6 return 2</span></div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    assert(bit_manipulation::count_of_set_bits::countSetBits(6) == 2);</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    <span class="comment">// n = 13 return 3</span></div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>    assert(bit_manipulation::count_of_set_bits::countSetBits(13) == 3);</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    <span class="comment">// n = 9 return 2</span></div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    assert(bit_manipulation::count_of_set_bits::countSetBits(9) == 2);</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <span class="comment">// n = 15 return 4</span></div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    assert(bit_manipulation::count_of_set_bits::countSetBits(15) == 4);</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <span class="comment">// n = 25 return 3</span></div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    assert(bit_manipulation::count_of_set_bits::countSetBits(25) == 3);</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    <span class="comment">// n = 97 return 3</span></div>
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-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    <span class="comment">// n = 31 return 5</span></div>
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-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   56</span>                   {</div>
+<div class="line"><span class="lineno">   57</span>    <span class="comment">// n = 4 return 1</span></div>
+<div class="line"><span class="lineno">   58</span>    assert(bit_manipulation::count_of_set_bits::countSetBits(4) == 1);</div>
+<div class="line"><span class="lineno">   59</span>    <span class="comment">// n = 6 return 2</span></div>
+<div class="line"><span class="lineno">   60</span>    assert(bit_manipulation::count_of_set_bits::countSetBits(6) == 2);</div>
+<div class="line"><span class="lineno">   61</span>    <span class="comment">// n = 13 return 3</span></div>
+<div class="line"><span class="lineno">   62</span>    assert(bit_manipulation::count_of_set_bits::countSetBits(13) == 3);</div>
+<div class="line"><span class="lineno">   63</span>    <span class="comment">// n = 9 return 2</span></div>
+<div class="line"><span class="lineno">   64</span>    assert(bit_manipulation::count_of_set_bits::countSetBits(9) == 2);</div>
+<div class="line"><span class="lineno">   65</span>    <span class="comment">// n = 15 return 4</span></div>
+<div class="line"><span class="lineno">   66</span>    assert(bit_manipulation::count_of_set_bits::countSetBits(15) == 4);</div>
+<div class="line"><span class="lineno">   67</span>    <span class="comment">// n = 25 return 3</span></div>
+<div class="line"><span class="lineno">   68</span>    assert(bit_manipulation::count_of_set_bits::countSetBits(25) == 3);</div>
+<div class="line"><span class="lineno">   69</span>    <span class="comment">// n = 97 return 3</span></div>
+<div class="line"><span class="lineno">   70</span>    assert(bit_manipulation::count_of_set_bits::countSetBits(97) == 3);</div>
+<div class="line"><span class="lineno">   71</span>    <span class="comment">// n = 31 return 5</span></div>
+<div class="line"><span class="lineno">   72</span>    assert(bit_manipulation::count_of_set_bits::countSetBits(31) == 5);</div>
+<div class="line"><span class="lineno">   73</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All test cases successfully passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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@@ -138,7 +138,8 @@ Functions</h2></td></tr>
 <p >The linked list is a data structure used for holding a sequence of values, which can be added, removed and displayed. </p>
 <h3><a class="anchor" id="autotoc_md39"></a>
 Algorithm</h3>
-<p >Values can be added by iterating to the end of a list(by following the pointers) starting from the first link. Whichever link points to null is considered the last link and is pointed to the new value.</p>
+<p >Values can be added by iterating to the end of a <a class="el" href="../../d8/d10/structlist.html">list(by following
+the pointers)</a> starting from the first link. Whichever link points to null is considered the last link and is pointed to the new value.</p>
 <p >Values can be removed by also iterating through the list. When the node containing the value is found, the node pointing to the current node is made to point to the node that the current node is pointing to, and then returning the current node to heap store. </p>
 </div><h2 class="groupheader">Function Documentation</h2>
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 <dl class="section return"><dt>Returns</dt><dd>true if there are only digits present in the string </dd>
 <dd>
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-<div class="fragment"><div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>                                 {</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    <span class="comment">// function statements here</span></div>
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-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>}</div>
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+<div class="line"><span class="lineno">   41</span>    <span class="comment">// function statements here</span></div>
+<div class="line"><span class="lineno">   42</span>    <span class="keywordflow">for</span> (<span class="keywordtype">char</span> i : s) {</div>
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+<div class="line"><span class="lineno">   44</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   45</span>        }</div>
+<div class="line"><span class="lineno">   46</span>    }</div>
+<div class="line"><span class="lineno">   47</span>    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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 Here is the call graph for this function:</div>
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 <p >Main function: Allows the user add and delete values from the list. Also allows user to search for and display values in the list. </p><dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
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    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
    </div>
    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
 </table>
 </div>
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+<!-- Generated by Doxygen 1.9.3 -->
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@@ -157,69 +157,69 @@ Functions</h2></td></tr>
   </table>
   </dd>
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-<div class="fragment"><div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span>{</div>
-<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(2,0);</div>
-<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint64_t&gt;</a>&gt; transition(2,<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(2,0));</div>
-<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint64_t&gt;</a>&gt; Identity(2,<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(2,0));</div>
-<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>    n--;</div>
-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[0]=1, <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[1]=1;</div>
-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>    Identity[0][0]=1; Identity[0][1]=0;</div>
-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>    Identity[1][0]=0; Identity[1][1]=1;</div>
-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>     </div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>    transition[0][0]=0;</div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>    transition[1][0]=transition[1][1]=transition[0][1]=1;</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    </div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>    <span class="keywordflow">while</span>(n)</div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    {</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>        <span class="keywordflow">if</span>(n%2)</div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>        {</div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint64_t&gt;</a>&gt; res(2, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(2,0));</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>                    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0;i&lt;2;i++)</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>            {</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>                <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=0;j&lt;2;j++)</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>                {</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>                    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> k=0;<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>&lt;2;<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++)</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>                        {</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>                            res[i][j]=(res[i][j]%mod+((Identity[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>]%mod*transition[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j]%mod))%mod)%mod;</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>                        }</div>
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-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>                <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0;i&lt;2;i++)</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>            {</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>                <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=0;j&lt;2;j++)</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>                {</div>
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-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>            <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0;i&lt;2;i++)</div>
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-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>                {</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>                    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> k=0;<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>&lt;2;<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++)</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>                    {</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>                        res1[i][j]=(res1[i][j]%mod+((transition[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>]%mod*transition[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j]%mod))%mod)%mod;</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>                    }</div>
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-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>            <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0;i&lt;2;i++)</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>            {</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>                <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=0;j&lt;2;j++)</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>                {</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>                    transition[i][j]=res1[i][j];</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>                }</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>            } </div>
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-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    }</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <span class="keywordflow">return</span> ((result[0]%mod*Identity[0][0]%mod)%mod+(<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[1]%mod*Identity[1][0]%mod)%mod)%mod;</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   24</span>{</div>
+<div class="line"><span class="lineno">   25</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(2,0);</div>
+<div class="line"><span class="lineno">   26</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint64_t&gt;</a>&gt; transition(2,<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(2,0));</div>
+<div class="line"><span class="lineno">   27</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint64_t&gt;</a>&gt; Identity(2,<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(2,0));</div>
+<div class="line"><span class="lineno">   28</span>    n--;</div>
+<div class="line"><span class="lineno">   29</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[0]=1, <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[1]=1;</div>
+<div class="line"><span class="lineno">   30</span>    Identity[0][0]=1; Identity[0][1]=0;</div>
+<div class="line"><span class="lineno">   31</span>    Identity[1][0]=0; Identity[1][1]=1;</div>
+<div class="line"><span class="lineno">   32</span>     </div>
+<div class="line"><span class="lineno">   33</span>    transition[0][0]=0;</div>
+<div class="line"><span class="lineno">   34</span>    transition[1][0]=transition[1][1]=transition[0][1]=1;</div>
+<div class="line"><span class="lineno">   35</span>    </div>
+<div class="line"><span class="lineno">   36</span>    <span class="keywordflow">while</span>(n)</div>
+<div class="line"><span class="lineno">   37</span>    {</div>
+<div class="line"><span class="lineno">   38</span>        <span class="keywordflow">if</span>(n%2)</div>
+<div class="line"><span class="lineno">   39</span>        {</div>
+<div class="line"><span class="lineno">   40</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint64_t&gt;</a>&gt; res(2, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(2,0));</div>
+<div class="line"><span class="lineno">   41</span>                    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0;i&lt;2;i++)</div>
+<div class="line"><span class="lineno">   42</span>            {</div>
+<div class="line"><span class="lineno">   43</span>                <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=0;j&lt;2;j++)</div>
+<div class="line"><span class="lineno">   44</span>                {</div>
+<div class="line"><span class="lineno">   45</span>                    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> k=0;<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>&lt;2;<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++)</div>
+<div class="line"><span class="lineno">   46</span>                        {</div>
+<div class="line"><span class="lineno">   47</span>                            res[i][j]=(res[i][j]%mod+((Identity[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>]%mod*transition[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j]%mod))%mod)%mod;</div>
+<div class="line"><span class="lineno">   48</span>                        }</div>
+<div class="line"><span class="lineno">   49</span>                }</div>
+<div class="line"><span class="lineno">   50</span>            }</div>
+<div class="line"><span class="lineno">   51</span>                <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0;i&lt;2;i++)</div>
+<div class="line"><span class="lineno">   52</span>            {</div>
+<div class="line"><span class="lineno">   53</span>                <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=0;j&lt;2;j++)</div>
+<div class="line"><span class="lineno">   54</span>                {</div>
+<div class="line"><span class="lineno">   55</span>                Identity[i][j]=res[i][j];</div>
+<div class="line"><span class="lineno">   56</span>                }</div>
+<div class="line"><span class="lineno">   57</span>                }</div>
+<div class="line"><span class="lineno">   58</span>            n--;</div>
+<div class="line"><span class="lineno">   59</span>        }</div>
+<div class="line"><span class="lineno">   60</span>        <span class="keywordflow">else</span>{</div>
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+<div class="line"><span class="lineno">   62</span>            <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0;i&lt;2;i++)</div>
+<div class="line"><span class="lineno">   63</span>            {</div>
+<div class="line"><span class="lineno">   64</span>                <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=0;j&lt;2;j++)</div>
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+<div class="line"><span class="lineno">   66</span>                    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> k=0;<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>&lt;2;<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++)</div>
+<div class="line"><span class="lineno">   67</span>                    {</div>
+<div class="line"><span class="lineno">   68</span>                        res1[i][j]=(res1[i][j]%mod+((transition[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>]%mod*transition[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j]%mod))%mod)%mod;</div>
+<div class="line"><span class="lineno">   69</span>                    }</div>
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+<div class="line"><span class="lineno">   72</span>            <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0;i&lt;2;i++)</div>
+<div class="line"><span class="lineno">   73</span>            {</div>
+<div class="line"><span class="lineno">   74</span>                <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=0;j&lt;2;j++)</div>
+<div class="line"><span class="lineno">   75</span>                {</div>
+<div class="line"><span class="lineno">   76</span>                    transition[i][j]=res1[i][j];</div>
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+<div class="line"><span class="lineno">   78</span>            } </div>
+<div class="line"><span class="lineno">   79</span>            n=n/2;</div>
+<div class="line"><span class="lineno">   80</span>            }</div>
+<div class="line"><span class="lineno">   81</span>    }</div>
+<div class="line"><span class="lineno">   82</span>    <span class="keywordflow">return</span> ((result[0]%mod*Identity[0][0]%mod)%mod+(<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[1]%mod*Identity[1][0]%mod)%mod)%mod;</div>
+<div class="line"><span class="lineno">   83</span>}</div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
 <div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; uint64_t &gt;</a></div></div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -239,13 +239,13 @@ Functions</h2></td></tr>
       </table>
 </div><div class="memdoc">
 <p >Main function </p>
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    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
    </div>
    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
 </table>
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@@ -173,46 +173,46 @@ Functions</h2></td></tr>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>the concatenated string </dd></dl>
-<div class="fragment"><div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>                                                        {</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;  <span class="comment">// To store the resulting sum bits</span></div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span> </div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    int64_t len1 = first.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    int64_t len2 = second.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>    int64_t length = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(len1, len2);</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    <span class="keywordflow">if</span> (len1 &lt; len2)  <span class="comment">// make the string lengths equal</span></div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>    {</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>        <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len2 - len1; i++) {</div>
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-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len1 &gt; len2) {</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>        zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>        <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len1 - len2; i++) {</div>
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-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    int64_t carry = 0;</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <span class="keywordflow">for</span> (int64_t i = length - 1; i &gt;= 0; i--) {</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>        int64_t firstBit = first.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/at.html">at</a>(i) - <span class="charliteral">&#39;0&#39;</span>;</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        int64_t secondBit = second.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/at.html">at</a>(i) - <span class="charliteral">&#39;0&#39;</span>;</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span> </div>
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-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> temp;</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        temp = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/to_string.html">std::to_string</a>(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>);</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        temp += <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = temp;</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span> </div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        carry = (firstBit &amp; secondBit) | (secondBit &amp; carry) |</div>
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-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    }</div>
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-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   37</span>                                                        {</div>
+<div class="line"><span class="lineno">   38</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;  <span class="comment">// To store the resulting sum bits</span></div>
+<div class="line"><span class="lineno">   39</span> </div>
+<div class="line"><span class="lineno">   40</span>    int64_t len1 = first.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   41</span>    int64_t len2 = second.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   42</span>    int64_t length = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(len1, len2);</div>
+<div class="line"><span class="lineno">   43</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
+<div class="line"><span class="lineno">   44</span>    <span class="keywordflow">if</span> (len1 &lt; len2)  <span class="comment">// make the string lengths equal</span></div>
+<div class="line"><span class="lineno">   45</span>    {</div>
+<div class="line"><span class="lineno">   46</span>        <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len2 - len1; i++) {</div>
+<div class="line"><span class="lineno">   47</span>            zero += first;</div>
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+<div class="line"><span class="lineno">   49</span>        }</div>
+<div class="line"><span class="lineno">   50</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len1 &gt; len2) {</div>
+<div class="line"><span class="lineno">   51</span>        zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
+<div class="line"><span class="lineno">   52</span>        <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len1 - len2; i++) {</div>
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+<div class="line"><span class="lineno">   54</span>            second = zero;</div>
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+<div class="line"><span class="lineno">   56</span>    }</div>
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+<div class="line"><span class="lineno">   60</span>        int64_t secondBit = second.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/at.html">at</a>(i) - <span class="charliteral">&#39;0&#39;</span>;</div>
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+<div class="line"><span class="lineno">   64</span>        temp = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/to_string.html">std::to_string</a>(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>);</div>
+<div class="line"><span class="lineno">   65</span>        temp += <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">   66</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = temp;</div>
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+<div class="line"><span class="lineno">   68</span>        carry = (firstBit &amp; secondBit) | (secondBit &amp; carry) |</div>
+<div class="line"><span class="lineno">   69</span>                (firstBit &amp; carry);  <span class="comment">// sum of 3 bits</span></div>
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+<div class="line"><span class="lineno">   73</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="charliteral">&#39;1&#39;</span> + <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;  <span class="comment">// adding 1 incase of overflow</span></div>
+<div class="line"><span class="lineno">   74</span>    }</div>
+<div class="line"><span class="lineno">   75</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">   76</span>}</div>
 <div class="ttc" id="aat_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/at.html">std::string::at</a></div><div class="ttdeci">T at(T... args)</div></div>
 <div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
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@@ -264,49 +264,49 @@ Here is the call graph for this function:</div>
   </dd>
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 <dl class="section return"><dt>Returns</dt><dd>the multiplicative number value </dd></dl>
-<div class="fragment"><div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>                                                            {</div>
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-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    int64_t n = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(len1, len2);</div>
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-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span> </div>
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-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span> </div>
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-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span> </div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    <span class="comment">// Calculating the three products of inputs of size n/2 recursively</span></div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    int64_t product1 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xl, Yl);</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    int64_t product2 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xr, Yr);</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    int64_t product3 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        divide_and_conquer::karatsuba_algorithm::addStrings(Xl, Xr),</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>        divide_and_conquer::karatsuba_algorithm::addStrings(Yl, Yr));</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span> </div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <span class="keywordflow">return</span> product1 * (1 &lt;&lt; (2 * sh)) +</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>           (product3 - product1 - product2) * (1 &lt;&lt; sh) +</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>           product2;  <span class="comment">// combining the three products to get the final result.</span></div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   84</span>                                                            {</div>
+<div class="line"><span class="lineno">   85</span>    int64_t len1 = str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   86</span>    int64_t len2 = str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   87</span>    int64_t n = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(len1, len2);</div>
+<div class="line"><span class="lineno">   88</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
+<div class="line"><span class="lineno">   89</span>    <span class="keywordflow">if</span> (len1 &lt; len2) {</div>
+<div class="line"><span class="lineno">   90</span>        <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len2 - len1; i++) {</div>
+<div class="line"><span class="lineno">   91</span>            zero += str1;</div>
+<div class="line"><span class="lineno">   92</span>            str1 = zero;</div>
+<div class="line"><span class="lineno">   93</span>        }</div>
+<div class="line"><span class="lineno">   94</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len1 &gt; len2) {</div>
+<div class="line"><span class="lineno">   95</span>        zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
+<div class="line"><span class="lineno">   96</span>        <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len1 - len2; i++) {</div>
+<div class="line"><span class="lineno">   97</span>            zero += str2;</div>
+<div class="line"><span class="lineno">   98</span>            str2 = zero;</div>
+<div class="line"><span class="lineno">   99</span>        }</div>
+<div class="line"><span class="lineno">  100</span>    }</div>
+<div class="line"><span class="lineno">  101</span>    <span class="keywordflow">if</span> (n == 0) {</div>
+<div class="line"><span class="lineno">  102</span>        <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  103</span>    }</div>
+<div class="line"><span class="lineno">  104</span>    <span class="keywordflow">if</span> (n == 1) {</div>
+<div class="line"><span class="lineno">  105</span>        <span class="keywordflow">return</span> (str1[0] - <span class="charliteral">&#39;0&#39;</span>) * (str2[0] - <span class="charliteral">&#39;0&#39;</span>);</div>
+<div class="line"><span class="lineno">  106</span>    }</div>
+<div class="line"><span class="lineno">  107</span>    int64_t fh = n / 2;     <span class="comment">// first half of string</span></div>
+<div class="line"><span class="lineno">  108</span>    int64_t sh = (n - fh);  <span class="comment">// second half of string</span></div>
+<div class="line"><span class="lineno">  109</span> </div>
+<div class="line"><span class="lineno">  110</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Xl = str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(0, fh);   <span class="comment">// first half of first string</span></div>
+<div class="line"><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Xr = str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(fh, sh);  <span class="comment">// second half of first string</span></div>
+<div class="line"><span class="lineno">  112</span> </div>
+<div class="line"><span class="lineno">  113</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Yl = str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(0, fh);   <span class="comment">// first half of second string</span></div>
+<div class="line"><span class="lineno">  114</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Yr = str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(fh, sh);  <span class="comment">// second half of second string</span></div>
+<div class="line"><span class="lineno">  115</span> </div>
+<div class="line"><span class="lineno">  116</span>    <span class="comment">// Calculating the three products of inputs of size n/2 recursively</span></div>
+<div class="line"><span class="lineno">  117</span>    int64_t product1 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xl, Yl);</div>
+<div class="line"><span class="lineno">  118</span>    int64_t product2 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xr, Yr);</div>
+<div class="line"><span class="lineno">  119</span>    int64_t product3 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(</div>
+<div class="line"><span class="lineno">  120</span>        divide_and_conquer::karatsuba_algorithm::addStrings(Xl, Xr),</div>
+<div class="line"><span class="lineno">  121</span>        divide_and_conquer::karatsuba_algorithm::addStrings(Yl, Yr));</div>
+<div class="line"><span class="lineno">  122</span> </div>
+<div class="line"><span class="lineno">  123</span>    <span class="keywordflow">return</span> product1 * (1 &lt;&lt; (2 * sh)) +</div>
+<div class="line"><span class="lineno">  124</span>           (product3 - product1 - product2) * (1 &lt;&lt; sh) +</div>
+<div class="line"><span class="lineno">  125</span>           product2;  <span class="comment">// combining the three products to get the final result.</span></div>
+<div class="line"><span class="lineno">  126</span>}</div>
 <div class="ttc" id="anamespacekaratsuba__algorithm_html"><div class="ttname"><a href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a></div><div class="ttdoc">Functions for the Karatsuba algorithm for fast multiplication</div></div>
 <div class="ttc" id="asubstr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">std::string::substr</a></div><div class="ttdeci">T substr(T... args)</div></div>
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 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>           {</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>    <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  164</span>           {</div>
+<div class="line"><span class="lineno">  165</span>    <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
+<div class="line"><span class="lineno">  166</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  167</span>}</div>
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 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -375,31 +375,31 @@ Here is the call graph for this function:</div>
 
 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>                   {</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    <span class="comment">// 1st test</span></div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s11 = <span class="stringliteral">&quot;1&quot;</span>;</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s12 = <span class="stringliteral">&quot;1010&quot;</span>;</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test... &quot;</span>;</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>    assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>               s11, s12) == 10);  <span class="comment">// here the multiplication is 10</span></div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span> </div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    <span class="comment">// 2nd test</span></div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s21 = <span class="stringliteral">&quot;11&quot;</span>;</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s22 = <span class="stringliteral">&quot;1010&quot;</span>;</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test... &quot;</span>;</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>               s21, s22) == 30);  <span class="comment">// here the multiplication is 30</span></div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span> </div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    <span class="comment">// 3rd test</span></div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s31 = <span class="stringliteral">&quot;110&quot;</span>;</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s32 = <span class="stringliteral">&quot;1010&quot;</span>;</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3rd test... &quot;</span>;</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>    assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>               s31, s32) == 60);  <span class="comment">// here the multiplication is 60</span></div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  134</span>                   {</div>
+<div class="line"><span class="lineno">  135</span>    <span class="comment">// 1st test</span></div>
+<div class="line"><span class="lineno">  136</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s11 = <span class="stringliteral">&quot;1&quot;</span>;</div>
+<div class="line"><span class="lineno">  137</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s12 = <span class="stringliteral">&quot;1010&quot;</span>;</div>
+<div class="line"><span class="lineno">  138</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test... &quot;</span>;</div>
+<div class="line"><span class="lineno">  139</span>    assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
+<div class="line"><span class="lineno">  140</span>               s11, s12) == 10);  <span class="comment">// here the multiplication is 10</span></div>
+<div class="line"><span class="lineno">  141</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  142</span> </div>
+<div class="line"><span class="lineno">  143</span>    <span class="comment">// 2nd test</span></div>
+<div class="line"><span class="lineno">  144</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s21 = <span class="stringliteral">&quot;11&quot;</span>;</div>
+<div class="line"><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s22 = <span class="stringliteral">&quot;1010&quot;</span>;</div>
+<div class="line"><span class="lineno">  146</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test... &quot;</span>;</div>
+<div class="line"><span class="lineno">  147</span>    assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
+<div class="line"><span class="lineno">  148</span>               s21, s22) == 30);  <span class="comment">// here the multiplication is 30</span></div>
+<div class="line"><span class="lineno">  149</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  150</span> </div>
+<div class="line"><span class="lineno">  151</span>    <span class="comment">// 3rd test</span></div>
+<div class="line"><span class="lineno">  152</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s31 = <span class="stringliteral">&quot;110&quot;</span>;</div>
+<div class="line"><span class="lineno">  153</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s32 = <span class="stringliteral">&quot;1010&quot;</span>;</div>
+<div class="line"><span class="lineno">  154</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3rd test... &quot;</span>;</div>
+<div class="line"><span class="lineno">  155</span>    assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
+<div class="line"><span class="lineno">  156</span>               s31, s32) == 60);  <span class="comment">// here the multiplication is 60</span></div>
+<div class="line"><span class="lineno">  157</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  158</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -417,7 +417,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_93bc990c5cceb745f78af6949e9ef947.html">divide_and_conquer</a></li><li class="navelem"><a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html">karatsuba_algorithm_for_fast_multiplication.cpp</a></li>
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@@ -175,23 +175,23 @@ template&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/
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+<div class="fragment"><div class="line"><span class="lineno">   71</span>                                      {</div>
+<div class="line"><span class="lineno">   72</span>    <span class="keywordtype">double</span> dt = rot * 2.f * M_PI / N;</div>
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+<div class="line"><span class="lineno">   77</span><span class="preprocessor">#ifdef _OPENMP</span></div>
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+<div class="line"><span class="lineno">   79</span><span class="preprocessor">#endif</span></div>
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+<div class="line"><span class="lineno">   81</span>        <span class="keywordtype">double</span> t = dt * step;</div>
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+<div class="line"><span class="lineno">   83</span>        <span class="keywordtype">double</span> second = R * (k1 * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a>(t) - l * k * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a>(k1 * t / k));</div>
+<div class="line"><span class="lineno">   84</span>        points[0][step].first = first;</div>
+<div class="line"><span class="lineno">   85</span>        points[0][step].second = second;</div>
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@@ -219,31 +219,31 @@ Here is the call graph for this function:</div>
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 <p>Test function to save resulting points to a CSV file. </p>
-<div class="fragment"><div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>            {</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>    <span class="keyword">const</span> <span class="keywordtype">size_t</span> N = 500;</div>
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-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    fname &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(3) &lt;&lt; <span class="stringliteral">&quot;spirograph_&quot;</span> &lt;&lt; l &lt;&lt; <span class="stringliteral">&quot;_&quot;</span> &lt;&lt; k &lt;&lt; <span class="stringliteral">&quot;_&quot;</span> &lt;&lt; rot</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>          &lt;&lt; <span class="stringliteral">&quot;.csv&quot;</span>;</div>
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-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span> </div>
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-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span> </div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; N; i++) {</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        fp &lt;&lt; points[i].first &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; points[i].first;</div>
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-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>            fp &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;</div>
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-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   93</span>            {</div>
+<div class="line"><span class="lineno">   94</span>    <span class="keyword">const</span> <span class="keywordtype">size_t</span> N = 500;</div>
+<div class="line"><span class="lineno">   95</span>    <span class="keywordtype">double</span> l = 0.3, k = 0.75, rot = 10.;</div>
+<div class="line"><span class="lineno">   96</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_stringstream.html">std::stringstream</a> fname;</div>
+<div class="line"><span class="lineno">   97</span>    fname &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(3) &lt;&lt; <span class="stringliteral">&quot;spirograph_&quot;</span> &lt;&lt; l &lt;&lt; <span class="stringliteral">&quot;_&quot;</span> &lt;&lt; k &lt;&lt; <span class="stringliteral">&quot;_&quot;</span> &lt;&lt; rot</div>
+<div class="line"><span class="lineno">   98</span>          &lt;&lt; <span class="stringliteral">&quot;.csv&quot;</span>;</div>
+<div class="line"><span class="lineno">   99</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp(fname.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_stringstream/str.html">str</a>());</div>
+<div class="line"><span class="lineno">  100</span>    <span class="keywordflow">if</span> (!fp.is_open()) {</div>
+<div class="line"><span class="lineno">  101</span>        perror(fname.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_stringstream/str.html">str</a>().c_str());</div>
+<div class="line"><span class="lineno">  102</span>        exit(EXIT_FAILURE);</div>
+<div class="line"><span class="lineno">  103</span>    }</div>
+<div class="line"><span class="lineno">  104</span> </div>
+<div class="line"><span class="lineno">  105</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::pair&lt;double, double&gt;</a>, N&gt; points;</div>
+<div class="line"><span class="lineno">  106</span> </div>
+<div class="line"><span class="lineno">  107</span>    <a class="code hl_function" href="../../da/dd3/namespacespirograph.html#aeca22dbe4563358960e907a40cd3e1ac">spirograph</a>(&amp;points, l, k, rot);</div>
+<div class="line"><span class="lineno">  108</span> </div>
+<div class="line"><span class="lineno">  109</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; N; i++) {</div>
+<div class="line"><span class="lineno">  110</span>        fp &lt;&lt; points[i].first &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; points[i].first;</div>
+<div class="line"><span class="lineno">  111</span>        <span class="keywordflow">if</span> (i &lt; N - 1) {</div>
+<div class="line"><span class="lineno">  112</span>            fp &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;</div>
+<div class="line"><span class="lineno">  113</span>        }</div>
+<div class="line"><span class="lineno">  114</span>    }</div>
+<div class="line"><span class="lineno">  115</span> </div>
+<div class="line"><span class="lineno">  116</span>    fp.close();</div>
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+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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+<div class="line"><span class="lineno">   94</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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+<div class="line"><span class="lineno">   79</span> </div>
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-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>                          &lt;&lt; std::abs(delta) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>                <span class="comment">// return std::pair&lt;uint32_t, double&gt;(iter, tol_condition);</span></div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>                break_loop = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>            }</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span> </div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>            (*roots)[n] -= delta;</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span> </div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span><span class="preprocessor">#pragma omp critical</span></div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>            tol_condition = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(tol_condition, std::abs(std::abs(delta)));</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>        }</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>        <span class="comment">// tol_condition /= (degree - 1);</span></div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span> </div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>        <span class="keywordflow">if</span> (break_loop)</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>            <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span> </div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>        <span class="keywordflow">if</span> (log_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>            <span class="keywordflow">for</span> (n = 0; n &lt; roots-&gt;size(); n++)</div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>                log_file &lt;&lt; <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>((*roots)[n]) &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>        }</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span> </div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span><span class="preprocessor">#if defined(DEBUG) || !defined(NDEBUG)</span></div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>        <span class="keywordflow">if</span> (iter % 500 == 0) {</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Iter: &quot;</span> &lt;&lt; iter &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>            <span class="keywordflow">for</span> (n = 0; n &lt; roots-&gt;size(); n++)</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span> &lt;&lt; <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>((*roots)[n]);</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\t\tabsolute average change: &quot;</span> &lt;&lt; tol_condition</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>                      &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>        }</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span> </div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>        <span class="keywordflow">if</span> (log_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>())</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>            log_file &lt;&lt; tol_condition;</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>    }</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span> </div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint32_t, long double&gt;</a>(iter, tol_condition);</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  111</span>                                                                    {</div>
+<div class="line"><span class="lineno">  112</span>    <span class="keywordtype">long</span> <span class="keywordtype">double</span> tol_condition = 1;</div>
+<div class="line"><span class="lineno">  113</span>    uint32_t iter = 0;</div>
+<div class="line"><span class="lineno">  114</span>    <span class="keywordtype">int</span> n;</div>
+<div class="line"><span class="lineno">  115</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> log_file;</div>
+<div class="line"><span class="lineno">  116</span> </div>
+<div class="line"><span class="lineno">  117</span>    <span class="keywordflow">if</span> (write_log) {</div>
+<div class="line"><span class="lineno">  118</span>        <span class="comment">/*</span></div>
+<div class="line"><span class="lineno">  119</span><span class="comment">         * store intermediate values to a CSV file</span></div>
+<div class="line"><span class="lineno">  120</span><span class="comment">         */</span></div>
+<div class="line"><span class="lineno">  121</span>        log_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">open</a>(<span class="stringliteral">&quot;durand_kerner.log.csv&quot;</span>);</div>
+<div class="line"><span class="lineno">  122</span>        <span class="keywordflow">if</span> (!log_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
+<div class="line"><span class="lineno">  123</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">perror</a>(<span class="stringliteral">&quot;Unable to create a storage log file!&quot;</span>);</div>
+<div class="line"><span class="lineno">  124</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><span class="lineno">  125</span>        }</div>
+<div class="line"><span class="lineno">  126</span>        log_file &lt;&lt; <span class="stringliteral">&quot;iter#,&quot;</span>;</div>
+<div class="line"><span class="lineno">  127</span> </div>
+<div class="line"><span class="lineno">  128</span>        <span class="keywordflow">for</span> (n = 0; n &lt; roots-&gt;size(); n++) log_file &lt;&lt; <span class="stringliteral">&quot;root_&quot;</span> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><span class="lineno">  129</span> </div>
+<div class="line"><span class="lineno">  130</span>        log_file &lt;&lt; <span class="stringliteral">&quot;avg. correction&quot;</span>;</div>
+<div class="line"><span class="lineno">  131</span>        log_file &lt;&lt; <span class="stringliteral">&quot;\n0,&quot;</span>;</div>
+<div class="line"><span class="lineno">  132</span>        <span class="keywordflow">for</span> (n = 0; n &lt; roots-&gt;size(); n++)</div>
+<div class="line"><span class="lineno">  133</span>            log_file &lt;&lt; <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>((*roots)[n]) &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><span class="lineno">  134</span>    }</div>
+<div class="line"><span class="lineno">  135</span> </div>
+<div class="line"><span class="lineno">  136</span>    <span class="keywordtype">bool</span> break_loop = <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  137</span>    <span class="keywordflow">while</span> (!<a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a024b8bc4755863315456d573a6732377">check_termination</a>(tol_condition) &amp;&amp; iter &lt; INT16_MAX &amp;&amp;</div>
+<div class="line"><span class="lineno">  138</span>           !break_loop) {</div>
+<div class="line"><span class="lineno">  139</span>        tol_condition = 0;</div>
+<div class="line"><span class="lineno">  140</span>        iter++;</div>
+<div class="line"><span class="lineno">  141</span>        break_loop = <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  142</span> </div>
+<div class="line"><span class="lineno">  143</span>        <span class="keywordflow">if</span> (log_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>())</div>
+<div class="line"><span class="lineno">  144</span>            log_file &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span> &lt;&lt; iter &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><span class="lineno">  145</span> </div>
+<div class="line"><span class="lineno">  146</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  147</span><span class="preprocessor">#pragma omp parallel for shared(break_loop, tol_condition)</span></div>
+<div class="line"><span class="lineno">  148</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  149</span>        <span class="keywordflow">for</span> (n = 0; n &lt; roots-&gt;size(); n++) {</div>
+<div class="line"><span class="lineno">  150</span>            <span class="keywordflow">if</span> (break_loop)</div>
+<div class="line"><span class="lineno">  151</span>                <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno">  152</span> </div>
+<div class="line"><span class="lineno">  153</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> numerator, denominator;</div>
+<div class="line"><span class="lineno">  154</span>            numerator = <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#ae2ab49ba1969d7a5988f9bc2c8924569">poly_function</a>(coeffs, (*roots)[n]);</div>
+<div class="line"><span class="lineno">  155</span>            denominator = 1.0;</div>
+<div class="line"><span class="lineno">  156</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; roots-&gt;size(); i++)</div>
+<div class="line"><span class="lineno">  157</span>                <span class="keywordflow">if</span> (i != n)</div>
+<div class="line"><span class="lineno">  158</span>                    denominator *= (*roots)[n] - (*roots)[i];</div>
+<div class="line"><span class="lineno">  159</span> </div>
+<div class="line"><span class="lineno">  160</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a> delta = numerator / denominator;</div>
+<div class="line"><span class="lineno">  161</span> </div>
+<div class="line"><span class="lineno">  162</span>            <span class="keywordflow">if</span> (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/isnan.html">std::isnan</a>(std::abs(delta)) || <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/isinf.html">std::isinf</a>(std::abs(delta))) {</div>
+<div class="line"><span class="lineno">  163</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;\n\nOverflow/underrun error - got value = &quot;</span></div>
+<div class="line"><span class="lineno">  164</span>                          &lt;&lt; std::abs(delta) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  165</span>                <span class="comment">// return std::pair&lt;uint32_t, double&gt;(iter, tol_condition);</span></div>
+<div class="line"><span class="lineno">  166</span>                break_loop = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  167</span>            }</div>
+<div class="line"><span class="lineno">  168</span> </div>
+<div class="line"><span class="lineno">  169</span>            (*roots)[n] -= delta;</div>
+<div class="line"><span class="lineno">  170</span> </div>
+<div class="line"><span class="lineno">  171</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">  172</span><span class="preprocessor">#pragma omp critical</span></div>
+<div class="line"><span class="lineno">  173</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  174</span>            tol_condition = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(tol_condition, std::abs(std::abs(delta)));</div>
+<div class="line"><span class="lineno">  175</span>        }</div>
+<div class="line"><span class="lineno">  176</span>        <span class="comment">// tol_condition /= (degree - 1);</span></div>
+<div class="line"><span class="lineno">  177</span> </div>
+<div class="line"><span class="lineno">  178</span>        <span class="keywordflow">if</span> (break_loop)</div>
+<div class="line"><span class="lineno">  179</span>            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  180</span> </div>
+<div class="line"><span class="lineno">  181</span>        <span class="keywordflow">if</span> (log_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
+<div class="line"><span class="lineno">  182</span>            <span class="keywordflow">for</span> (n = 0; n &lt; roots-&gt;size(); n++)</div>
+<div class="line"><span class="lineno">  183</span>                log_file &lt;&lt; <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>((*roots)[n]) &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><span class="lineno">  184</span>        }</div>
+<div class="line"><span class="lineno">  185</span> </div>
+<div class="line"><span class="lineno">  186</span><span class="preprocessor">#if defined(DEBUG) || !defined(NDEBUG)</span></div>
+<div class="line"><span class="lineno">  187</span>        <span class="keywordflow">if</span> (iter % 500 == 0) {</div>
+<div class="line"><span class="lineno">  188</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Iter: &quot;</span> &lt;&lt; iter &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
+<div class="line"><span class="lineno">  189</span>            <span class="keywordflow">for</span> (n = 0; n &lt; roots-&gt;size(); n++)</div>
+<div class="line"><span class="lineno">  190</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span> &lt;&lt; <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>((*roots)[n]);</div>
+<div class="line"><span class="lineno">  191</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\t\tabsolute average change: &quot;</span> &lt;&lt; tol_condition</div>
+<div class="line"><span class="lineno">  192</span>                      &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  193</span>        }</div>
+<div class="line"><span class="lineno">  194</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  195</span> </div>
+<div class="line"><span class="lineno">  196</span>        <span class="keywordflow">if</span> (log_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>())</div>
+<div class="line"><span class="lineno">  197</span>            log_file &lt;&lt; tol_condition;</div>
+<div class="line"><span class="lineno">  198</span>    }</div>
+<div class="line"><span class="lineno">  199</span> </div>
+<div class="line"><span class="lineno">  200</span>    <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint32_t, long double&gt;</a>(iter, tol_condition);</div>
+<div class="line"><span class="lineno">  201</span>}</div>
 <div class="ttc" id="abasic_ofstream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div></div>
 <div class="ttc" id="acomplex_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a></div></div>
@@ -424,63 +424,63 @@ Here is the call graph for this function:</div>
         </tr>
       </table>
 </div><div class="memdoc">
-<div class="fragment"><div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>                                {</div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>    <span class="comment">/* initialize random seed: */</span></div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span> </div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>    <span class="keywordflow">if</span> (argc &lt; 2) {</div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>        <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();  <span class="comment">// run tests when no input is provided</span></div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>        <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();  <span class="comment">// and skip tests when input polynomial is provided</span></div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Please pass the coefficients of the polynomial as &quot;</span></div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>                     <span class="stringliteral">&quot;commandline &quot;</span></div>
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-<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>    }</div>
-<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span> </div>
-<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>    <span class="keywordtype">int</span> n, degree = argc - 1;              <span class="comment">// detected polynomial degree</span></div>
-<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> coeffs(degree);  <span class="comment">// create coefficiencts array</span></div>
-<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span> </div>
-<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>    <span class="comment">// number of roots = degree - 1</span></div>
-<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::complex&lt;double&gt;</a>&gt; s0(degree - 1);</div>
-<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span> </div>
-<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Computing the roots for:\n\t&quot;</span>;</div>
-<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span>    <span class="keywordflow">for</span> (n = 0; n &lt; degree; n++) {</div>
-<div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span>        coeffs[n] = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/strtof.html">strtod</a>(argv[n + 1], <span class="keyword">nullptr</span>);</div>
-<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span>        <span class="keywordflow">if</span> (n &lt; degree - 1 &amp;&amp; coeffs[n] != 0)</div>
-<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;(&quot;</span> &lt;&lt; coeffs[n] &lt;&lt; <span class="stringliteral">&quot;) x^&quot;</span> &lt;&lt; degree - n - 1 &lt;&lt; <span class="stringliteral">&quot; + &quot;</span>;</div>
-<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>        <span class="keywordflow">else</span> <span class="keywordflow">if</span> (coeffs[n] != 0)</div>
-<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;(&quot;</span> &lt;&lt; coeffs[n] &lt;&lt; <span class="stringliteral">&quot;) x^&quot;</span> &lt;&lt; degree - n - 1</div>
-<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span>                      &lt;&lt; <span class="stringliteral">&quot; = 0\n&quot;</span>;</div>
-<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span> </div>
-<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>        <span class="comment">/* initialize root approximations with random values */</span></div>
-<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>        <span class="keywordflow">if</span> (n &lt; degree - 1) {</div>
-<div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span>            s0[n] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100);</div>
-<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span>            s0[n] -= 50.f;</div>
-<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span>            s0[n] /= 50.f;</div>
-<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>        }</div>
-<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span>    }</div>
-<div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span> </div>
-<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>    <span class="comment">// numerical errors less when the first coefficient is &quot;1&quot;</span></div>
-<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>    <span class="comment">// hence, we normalize the first coefficient</span></div>
-<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>    {</div>
-<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>        <span class="keywordtype">double</span> tmp = coeffs[0];</div>
-<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>        coeffs /= tmp;</div>
-<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>    }</div>
-<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span> </div>
-<div class="line"><a id="l00326" name="l00326"></a><span class="lineno">  326</span>    clock_t end_time, start_time = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>();</div>
-<div class="line"><a id="l00327" name="l00327"></a><span class="lineno">  327</span>    <span class="keyword">auto</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a2c35b320ace8677f9b331faf94f8b2fd">durand_kerner_algo</a>(coeffs, &amp;s0, <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00328" name="l00328"></a><span class="lineno">  328</span>    end_time = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>();</div>
-<div class="line"><a id="l00329" name="l00329"></a><span class="lineno">  329</span> </div>
-<div class="line"><a id="l00330" name="l00330"></a><span class="lineno">  330</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nIterations: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.first &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00331" name="l00331"></a><span class="lineno">  331</span>    <span class="keywordflow">for</span> (n = 0; n &lt; degree - 1; n++)</div>
-<div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span> &lt;&lt; <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>(s0[n]) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;absolute average change: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.second &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time taken: &quot;</span></div>
-<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span>              &lt;&lt; <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(end_time - start_time) / CLOCKS_PER_SEC</div>
-<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span>              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
-<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span> </div>
-<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00339" name="l00339"></a><span class="lineno">  339</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  283</span>                                {</div>
+<div class="line"><span class="lineno">  284</span>    <span class="comment">/* initialize random seed: */</span></div>
+<div class="line"><span class="lineno">  285</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
+<div class="line"><span class="lineno">  286</span> </div>
+<div class="line"><span class="lineno">  287</span>    <span class="keywordflow">if</span> (argc &lt; 2) {</div>
+<div class="line"><span class="lineno">  288</span>        <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();  <span class="comment">// run tests when no input is provided</span></div>
+<div class="line"><span class="lineno">  289</span>        <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();  <span class="comment">// and skip tests when input polynomial is provided</span></div>
+<div class="line"><span class="lineno">  290</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Please pass the coefficients of the polynomial as &quot;</span></div>
+<div class="line"><span class="lineno">  291</span>                     <span class="stringliteral">&quot;commandline &quot;</span></div>
+<div class="line"><span class="lineno">  292</span>                     <span class="stringliteral">&quot;arguments.\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  293</span>        <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  294</span>    }</div>
+<div class="line"><span class="lineno">  295</span> </div>
+<div class="line"><span class="lineno">  296</span>    <span class="keywordtype">int</span> n, degree = argc - 1;              <span class="comment">// detected polynomial degree</span></div>
+<div class="line"><span class="lineno">  297</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> coeffs(degree);  <span class="comment">// create coefficiencts array</span></div>
+<div class="line"><span class="lineno">  298</span> </div>
+<div class="line"><span class="lineno">  299</span>    <span class="comment">// number of roots = degree - 1</span></div>
+<div class="line"><span class="lineno">  300</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::complex&lt;double&gt;</a>&gt; s0(degree - 1);</div>
+<div class="line"><span class="lineno">  301</span> </div>
+<div class="line"><span class="lineno">  302</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Computing the roots for:\n\t&quot;</span>;</div>
+<div class="line"><span class="lineno">  303</span>    <span class="keywordflow">for</span> (n = 0; n &lt; degree; n++) {</div>
+<div class="line"><span class="lineno">  304</span>        coeffs[n] = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/strtof.html">strtod</a>(argv[n + 1], <span class="keyword">nullptr</span>);</div>
+<div class="line"><span class="lineno">  305</span>        <span class="keywordflow">if</span> (n &lt; degree - 1 &amp;&amp; coeffs[n] != 0)</div>
+<div class="line"><span class="lineno">  306</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;(&quot;</span> &lt;&lt; coeffs[n] &lt;&lt; <span class="stringliteral">&quot;) x^&quot;</span> &lt;&lt; degree - n - 1 &lt;&lt; <span class="stringliteral">&quot; + &quot;</span>;</div>
+<div class="line"><span class="lineno">  307</span>        <span class="keywordflow">else</span> <span class="keywordflow">if</span> (coeffs[n] != 0)</div>
+<div class="line"><span class="lineno">  308</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;(&quot;</span> &lt;&lt; coeffs[n] &lt;&lt; <span class="stringliteral">&quot;) x^&quot;</span> &lt;&lt; degree - n - 1</div>
+<div class="line"><span class="lineno">  309</span>                      &lt;&lt; <span class="stringliteral">&quot; = 0\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  310</span> </div>
+<div class="line"><span class="lineno">  311</span>        <span class="comment">/* initialize root approximations with random values */</span></div>
+<div class="line"><span class="lineno">  312</span>        <span class="keywordflow">if</span> (n &lt; degree - 1) {</div>
+<div class="line"><span class="lineno">  313</span>            s0[n] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100);</div>
+<div class="line"><span class="lineno">  314</span>            s0[n] -= 50.f;</div>
+<div class="line"><span class="lineno">  315</span>            s0[n] /= 50.f;</div>
+<div class="line"><span class="lineno">  316</span>        }</div>
+<div class="line"><span class="lineno">  317</span>    }</div>
+<div class="line"><span class="lineno">  318</span> </div>
+<div class="line"><span class="lineno">  319</span>    <span class="comment">// numerical errors less when the first coefficient is &quot;1&quot;</span></div>
+<div class="line"><span class="lineno">  320</span>    <span class="comment">// hence, we normalize the first coefficient</span></div>
+<div class="line"><span class="lineno">  321</span>    {</div>
+<div class="line"><span class="lineno">  322</span>        <span class="keywordtype">double</span> tmp = coeffs[0];</div>
+<div class="line"><span class="lineno">  323</span>        coeffs /= tmp;</div>
+<div class="line"><span class="lineno">  324</span>    }</div>
+<div class="line"><span class="lineno">  325</span> </div>
+<div class="line"><span class="lineno">  326</span>    clock_t end_time, start_time = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>();</div>
+<div class="line"><span class="lineno">  327</span>    <span class="keyword">auto</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a2c35b320ace8677f9b331faf94f8b2fd">durand_kerner_algo</a>(coeffs, &amp;s0, <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  328</span>    end_time = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>();</div>
+<div class="line"><span class="lineno">  329</span> </div>
+<div class="line"><span class="lineno">  330</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nIterations: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.first &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  331</span>    <span class="keywordflow">for</span> (n = 0; n &lt; degree - 1; n++)</div>
+<div class="line"><span class="lineno">  332</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span> &lt;&lt; <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>(s0[n]) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  333</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;absolute average change: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.second &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  334</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time taken: &quot;</span></div>
+<div class="line"><span class="lineno">  335</span>              &lt;&lt; <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(end_time - start_time) / CLOCKS_PER_SEC</div>
+<div class="line"><span class="lineno">  336</span>              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  337</span> </div>
+<div class="line"><span class="lineno">  338</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  339</span>}</div>
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@@ -490,7 +490,7 @@ Here is the call graph for this function:</div>
 <div class="ttc" id="asrand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a></div><div class="ttdeci">T srand(T... args)</div></div>
 <div class="ttc" id="astrtof_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/strtof.html">std::strtod</a></div><div class="ttdeci">T strtod(T... args)</div></div>
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-<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a></div></div>
+<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt; double &gt;</a></div></div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -527,22 +527,22 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>\(f(x)\) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>                                                         {</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <span class="keywordtype">double</span> real = 0.f, imag = 0.f;</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    <span class="keywordtype">int</span> n;</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span> </div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <span class="comment">// #ifdef _OPENMP</span></div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <span class="comment">// #pragma omp target teams distribute reduction(+ : real, imag)</span></div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <span class="comment">// #endif</span></div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    <span class="keywordflow">for</span> (n = 0; n &lt; coeffs.size(); n++) {</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> tmp =</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>            coeffs[n] * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(x, coeffs.size() - n - 1);</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        real += tmp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>();</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        imag += tmp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>();</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    }</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span> </div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(real, imag);</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   54</span>                                                         {</div>
+<div class="line"><span class="lineno">   55</span>    <span class="keywordtype">double</span> real = 0.f, imag = 0.f;</div>
+<div class="line"><span class="lineno">   56</span>    <span class="keywordtype">int</span> n;</div>
+<div class="line"><span class="lineno">   57</span> </div>
+<div class="line"><span class="lineno">   58</span>    <span class="comment">// #ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">   59</span>    <span class="comment">// #pragma omp target teams distribute reduction(+ : real, imag)</span></div>
+<div class="line"><span class="lineno">   60</span>    <span class="comment">// #endif</span></div>
+<div class="line"><span class="lineno">   61</span>    <span class="keywordflow">for</span> (n = 0; n &lt; coeffs.size(); n++) {</div>
+<div class="line"><span class="lineno">   62</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> tmp =</div>
+<div class="line"><span class="lineno">   63</span>            coeffs[n] * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(x, coeffs.size() - n - 1);</div>
+<div class="line"><span class="lineno">   64</span>        real += tmp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>();</div>
+<div class="line"><span class="lineno">   65</span>        imag += tmp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>();</div>
+<div class="line"><span class="lineno">   66</span>    }</div>
+<div class="line"><span class="lineno">   67</span> </div>
+<div class="line"><span class="lineno">   68</span>    <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(real, imag);</div>
+<div class="line"><span class="lineno">   69</span>}</div>
 <div class="ttc" id="apow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a></div><div class="ttdeci">T pow(T... args)</div></div>
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       </table>
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 <p >Self test the algorithm by checking the roots for \(x^2+4=0\) to which the roots are \(0 \pm 2i\) </p>
-<div class="fragment"><div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>             {</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> coeffs = {1, 0, 4};  <span class="comment">// x^2 - 2 = 0</span></div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::complex&lt;double&gt;</a>&gt; roots(2);</div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::complex&lt;double&gt;</a>&gt; expected = {</div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(0., 2.),</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(0., -2.)  <span class="comment">// known expected roots</span></div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>    };</div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span> </div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>    <span class="comment">/* initialize root approximations with random values */</span></div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> n = 0; n &lt; roots.size(); n++) {</div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>        roots[n] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100);</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>        roots[n] -= 50.f;</div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>        roots[n] /= 25.f;</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>    }</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span> </div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>    <span class="keyword">auto</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a2c35b320ace8677f9b331faf94f8b2fd">durand_kerner_algo</a>(coeffs, &amp;roots, <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span> </div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; roots.size(); i++) {</div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>        <span class="comment">// check if approximations are have &lt; 0.1% error with one of the</span></div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>        <span class="comment">// expected roots</span></div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>        <span class="keywordtype">bool</span> err1 = <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; roots.size(); j++)</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>            err1 |= std::abs(std::abs(roots[i] - expected[j])) &lt; 1e-3;</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>        assert(err1);</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>    }</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span> </div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 passed! - &quot;</span> &lt;&lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.first &lt;&lt; <span class="stringliteral">&quot; iterations, &quot;</span></div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>              &lt;&lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.second &lt;&lt; <span class="stringliteral">&quot; accuracy&quot;</span></div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>              &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  207</span>             {</div>
+<div class="line"><span class="lineno">  208</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> coeffs = {1, 0, 4};  <span class="comment">// x^2 - 2 = 0</span></div>
+<div class="line"><span class="lineno">  209</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::complex&lt;double&gt;</a>&gt; roots(2);</div>
+<div class="line"><span class="lineno">  210</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::complex&lt;double&gt;</a>&gt; expected = {</div>
+<div class="line"><span class="lineno">  211</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(0., 2.),</div>
+<div class="line"><span class="lineno">  212</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(0., -2.)  <span class="comment">// known expected roots</span></div>
+<div class="line"><span class="lineno">  213</span>    };</div>
+<div class="line"><span class="lineno">  214</span> </div>
+<div class="line"><span class="lineno">  215</span>    <span class="comment">/* initialize root approximations with random values */</span></div>
+<div class="line"><span class="lineno">  216</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> n = 0; n &lt; roots.size(); n++) {</div>
+<div class="line"><span class="lineno">  217</span>        roots[n] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100);</div>
+<div class="line"><span class="lineno">  218</span>        roots[n] -= 50.f;</div>
+<div class="line"><span class="lineno">  219</span>        roots[n] /= 25.f;</div>
+<div class="line"><span class="lineno">  220</span>    }</div>
+<div class="line"><span class="lineno">  221</span> </div>
+<div class="line"><span class="lineno">  222</span>    <span class="keyword">auto</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a2c35b320ace8677f9b331faf94f8b2fd">durand_kerner_algo</a>(coeffs, &amp;roots, <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  223</span> </div>
+<div class="line"><span class="lineno">  224</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; roots.size(); i++) {</div>
+<div class="line"><span class="lineno">  225</span>        <span class="comment">// check if approximations are have &lt; 0.1% error with one of the</span></div>
+<div class="line"><span class="lineno">  226</span>        <span class="comment">// expected roots</span></div>
+<div class="line"><span class="lineno">  227</span>        <span class="keywordtype">bool</span> err1 = <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  228</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; roots.size(); j++)</div>
+<div class="line"><span class="lineno">  229</span>            err1 |= std::abs(std::abs(roots[i] - expected[j])) &lt; 1e-3;</div>
+<div class="line"><span class="lineno">  230</span>        assert(err1);</div>
+<div class="line"><span class="lineno">  231</span>    }</div>
+<div class="line"><span class="lineno">  232</span> </div>
+<div class="line"><span class="lineno">  233</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 passed! - &quot;</span> &lt;&lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.first &lt;&lt; <span class="stringliteral">&quot; iterations, &quot;</span></div>
+<div class="line"><span class="lineno">  234</span>              &lt;&lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.second &lt;&lt; <span class="stringliteral">&quot; accuracy&quot;</span></div>
+<div class="line"><span class="lineno">  235</span>              &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  236</span>}</div>
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@@ -622,37 +622,37 @@ Here is the call graph for this function:</div>
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 <p >Self test the algorithm by checking the roots for \(0.015625x^3-1=0\) to which the roots are \((4+0i),\,(-2\pm3.464i)\) </p>
-<div class="fragment"><div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>             {</div>
-<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> coeffs = {<span class="comment">// 0.015625 x^3 - 1 = 0</span></div>
-<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>                                          1. / 64., 0., 0., -1.};</div>
-<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::complex&lt;double&gt;</a>&gt; roots(3);</div>
-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::complex&lt;double&gt;</a>&gt; expected = {</div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(4., 0.), <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(-2., 3.46410162),</div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(-2., -3.46410162)  <span class="comment">// known expected roots</span></div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>    };</div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span> </div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>    <span class="comment">/* initialize root approximations with random values */</span></div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> n = 0; n &lt; roots.size(); n++) {</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>        roots[n] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100);</div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>        roots[n] -= 50.f;</div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>        roots[n] /= 25.f;</div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>    }</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span> </div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>    <span class="keyword">auto</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a2c35b320ace8677f9b331faf94f8b2fd">durand_kerner_algo</a>(coeffs, &amp;roots, <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span> </div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; roots.size(); i++) {</div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>        <span class="comment">// check if approximations are have &lt; 0.1% error with one of the</span></div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>        <span class="comment">// expected roots</span></div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>        <span class="keywordtype">bool</span> err1 = <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; roots.size(); j++)</div>
-<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>            err1 |= std::abs(std::abs(roots[i] - expected[j])) &lt; 1e-3;</div>
-<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>        assert(err1);</div>
-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>    }</div>
-<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span> </div>
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+<div class="fragment"><div class="line"><span class="lineno">  242</span>             {</div>
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+<div class="line"><span class="lineno">  244</span>                                          1. / 64., 0., 0., -1.};</div>
+<div class="line"><span class="lineno">  245</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::complex&lt;double&gt;</a>&gt; roots(3);</div>
+<div class="line"><span class="lineno">  246</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::complex&lt;double&gt;</a>&gt; expected = {</div>
+<div class="line"><span class="lineno">  247</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(4., 0.), <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(-2., 3.46410162),</div>
+<div class="line"><span class="lineno">  248</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(-2., -3.46410162)  <span class="comment">// known expected roots</span></div>
+<div class="line"><span class="lineno">  249</span>    };</div>
+<div class="line"><span class="lineno">  250</span> </div>
+<div class="line"><span class="lineno">  251</span>    <span class="comment">/* initialize root approximations with random values */</span></div>
+<div class="line"><span class="lineno">  252</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> n = 0; n &lt; roots.size(); n++) {</div>
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+<div class="line"><span class="lineno">  271</span>              &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
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-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span> </div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>        <span class="keywordflow">if</span> (std::abs(p) &lt; std::abs(0.5 * q * r) &amp;&amp; p &lt; q * (lim_b - x)) {</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>            <span class="comment">// parabolic interpolation step</span></div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>            d = p / q;</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>            u = x + d;</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>            <span class="keywordflow">if</span> (u - lim_a &lt; tolerance2 || lim_b - u &lt; tolerance2)</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>                d = x &lt; mid_point ? tolerance : -tolerance;</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>            <span class="comment">// golden section interpolation step</span></div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>            e = (x &lt; mid_point ? lim_b : lim_a) - x;</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>            d = M_GOLDEN_RATIO * e;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        }</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span> </div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>        <span class="comment">// evaluate not too close to x</span></div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>        <span class="keywordflow">if</span> (std::abs(d) &gt;= tolerance)</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>            u = d;</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>        <span class="keywordflow">else</span> <span class="keywordflow">if</span> (d &gt; 0)</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>            u = tolerance;</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>        <span class="keywordflow">else</span></div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>            u = -tolerance;</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>        u += x;</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>        fu = <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">f</a>(u);</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span> </div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>        <span class="comment">// update variables</span></div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>        <span class="keywordflow">if</span> (fu &lt;= fx) {</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>            <span class="keywordflow">if</span> (u &lt; x)</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>                lim_b = x;</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>            <span class="keywordflow">else</span></div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>                lim_a = x;</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>            v = w;</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>            fv = fw;</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>            w = x;</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>            fw = fx;</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>            x = u;</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>            fx = fu;</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>            <span class="keywordflow">if</span> (u &lt; x)</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>                lim_a = u;</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>            <span class="keywordflow">else</span></div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>                lim_b = u;</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>            <span class="keywordflow">if</span> (fu &lt;= fw || x == w) {</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>                v = w;</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>                fv = fw;</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>                w = u;</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>                fw = fu;</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (fu &lt;= fv || v == x || v == w) {</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>                v = u;</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>                fv = fu;</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>            }</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>        }</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span> </div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>        iters++;</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    } <span class="keywordflow">while</span> (std::abs(x - mid_point) &gt; (tolerance - (lim_b - lim_a) / 2.f));</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span> </div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; (iters: &quot;</span> &lt;&lt; iters &lt;&lt; <span class="stringliteral">&quot;) &quot;</span>;</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span> </div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    <span class="keywordflow">return</span> x;</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   36</span>                                {</div>
+<div class="line"><span class="lineno">   37</span>    uint32_t iters = 0;</div>
+<div class="line"><span class="lineno">   38</span> </div>
+<div class="line"><span class="lineno">   39</span>    <span class="keywordflow">if</span> (lim_a &gt; lim_b) {</div>
+<div class="line"><span class="lineno">   40</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(lim_a, lim_b);</div>
+<div class="line"><span class="lineno">   41</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (std::abs(lim_a - lim_b) &lt;= <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>) {</div>
+<div class="line"><span class="lineno">   42</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Search range must be greater than &quot;</span> &lt;&lt; <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   43</span>        <span class="keywordflow">return</span> lim_a;</div>
+<div class="line"><span class="lineno">   44</span>    }</div>
+<div class="line"><span class="lineno">   45</span> </div>
+<div class="line"><span class="lineno">   46</span>    <span class="comment">// golden ratio value</span></div>
+<div class="line"><span class="lineno">   47</span>    <span class="keyword">const</span> <span class="keywordtype">double</span> M_GOLDEN_RATIO = (3.f - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(5.f)) / 2.f;</div>
+<div class="line"><span class="lineno">   48</span> </div>
+<div class="line"><span class="lineno">   49</span>    <span class="keywordtype">double</span> v = lim_a + M_GOLDEN_RATIO * (lim_b - lim_a);</div>
+<div class="line"><span class="lineno">   50</span>    <span class="keywordtype">double</span> u, w = v, x = v;</div>
+<div class="line"><span class="lineno">   51</span>    <span class="keywordtype">double</span> fu, fv = <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">f</a>(v);</div>
+<div class="line"><span class="lineno">   52</span>    <span class="keywordtype">double</span> fw = fv, fx = fv;</div>
+<div class="line"><span class="lineno">   53</span> </div>
+<div class="line"><span class="lineno">   54</span>    <span class="keywordtype">double</span> mid_point = (lim_a + lim_b) / 2.f;</div>
+<div class="line"><span class="lineno">   55</span>    <span class="keywordtype">double</span> p = 0, q = 0, r = 0;</div>
+<div class="line"><span class="lineno">   56</span> </div>
+<div class="line"><span class="lineno">   57</span>    <span class="keywordtype">double</span> d, e = 0;</div>
+<div class="line"><span class="lineno">   58</span>    <span class="keywordtype">double</span> tolerance, tolerance2;</div>
+<div class="line"><span class="lineno">   59</span> </div>
+<div class="line"><span class="lineno">   60</span>    <span class="keywordflow">do</span> {</div>
+<div class="line"><span class="lineno">   61</span>        mid_point = (lim_a + lim_b) / 2.f;</div>
+<div class="line"><span class="lineno">   62</span>        tolerance = <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a> * std::abs(x);</div>
+<div class="line"><span class="lineno">   63</span>        tolerance2 = 2 * tolerance;</div>
+<div class="line"><span class="lineno">   64</span> </div>
+<div class="line"><span class="lineno">   65</span>        <span class="keywordflow">if</span> (std::abs(e) &gt; tolerance2) {</div>
+<div class="line"><span class="lineno">   66</span>            <span class="comment">// fit parabola</span></div>
+<div class="line"><span class="lineno">   67</span>            r = (x - w) * (fx - fv);</div>
+<div class="line"><span class="lineno">   68</span>            q = (x - v) * (fx - fw);</div>
+<div class="line"><span class="lineno">   69</span>            p = (x - v) * q - (x - w) * r;</div>
+<div class="line"><span class="lineno">   70</span>            q = 2.f * (q - r);</div>
+<div class="line"><span class="lineno">   71</span>            <span class="keywordflow">if</span> (q &gt; 0)</div>
+<div class="line"><span class="lineno">   72</span>                p = -p;</div>
+<div class="line"><span class="lineno">   73</span>            <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">   74</span>                q = -q;</div>
+<div class="line"><span class="lineno">   75</span>            r = e;</div>
+<div class="line"><span class="lineno">   76</span>            e = d;</div>
+<div class="line"><span class="lineno">   77</span>        }</div>
+<div class="line"><span class="lineno">   78</span> </div>
+<div class="line"><span class="lineno">   79</span>        <span class="keywordflow">if</span> (std::abs(p) &lt; std::abs(0.5 * q * r) &amp;&amp; p &lt; q * (lim_b - x)) {</div>
+<div class="line"><span class="lineno">   80</span>            <span class="comment">// parabolic interpolation step</span></div>
+<div class="line"><span class="lineno">   81</span>            d = p / q;</div>
+<div class="line"><span class="lineno">   82</span>            u = x + d;</div>
+<div class="line"><span class="lineno">   83</span>            <span class="keywordflow">if</span> (u - lim_a &lt; tolerance2 || lim_b - u &lt; tolerance2)</div>
+<div class="line"><span class="lineno">   84</span>                d = x &lt; mid_point ? tolerance : -tolerance;</div>
+<div class="line"><span class="lineno">   85</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   86</span>            <span class="comment">// golden section interpolation step</span></div>
+<div class="line"><span class="lineno">   87</span>            e = (x &lt; mid_point ? lim_b : lim_a) - x;</div>
+<div class="line"><span class="lineno">   88</span>            d = M_GOLDEN_RATIO * e;</div>
+<div class="line"><span class="lineno">   89</span>        }</div>
+<div class="line"><span class="lineno">   90</span> </div>
+<div class="line"><span class="lineno">   91</span>        <span class="comment">// evaluate not too close to x</span></div>
+<div class="line"><span class="lineno">   92</span>        <span class="keywordflow">if</span> (std::abs(d) &gt;= tolerance)</div>
+<div class="line"><span class="lineno">   93</span>            u = d;</div>
+<div class="line"><span class="lineno">   94</span>        <span class="keywordflow">else</span> <span class="keywordflow">if</span> (d &gt; 0)</div>
+<div class="line"><span class="lineno">   95</span>            u = tolerance;</div>
+<div class="line"><span class="lineno">   96</span>        <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">   97</span>            u = -tolerance;</div>
+<div class="line"><span class="lineno">   98</span>        u += x;</div>
+<div class="line"><span class="lineno">   99</span>        fu = <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">f</a>(u);</div>
+<div class="line"><span class="lineno">  100</span> </div>
+<div class="line"><span class="lineno">  101</span>        <span class="comment">// update variables</span></div>
+<div class="line"><span class="lineno">  102</span>        <span class="keywordflow">if</span> (fu &lt;= fx) {</div>
+<div class="line"><span class="lineno">  103</span>            <span class="keywordflow">if</span> (u &lt; x)</div>
+<div class="line"><span class="lineno">  104</span>                lim_b = x;</div>
+<div class="line"><span class="lineno">  105</span>            <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  106</span>                lim_a = x;</div>
+<div class="line"><span class="lineno">  107</span>            v = w;</div>
+<div class="line"><span class="lineno">  108</span>            fv = fw;</div>
+<div class="line"><span class="lineno">  109</span>            w = x;</div>
+<div class="line"><span class="lineno">  110</span>            fw = fx;</div>
+<div class="line"><span class="lineno">  111</span>            x = u;</div>
+<div class="line"><span class="lineno">  112</span>            fx = fu;</div>
+<div class="line"><span class="lineno">  113</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  114</span>            <span class="keywordflow">if</span> (u &lt; x)</div>
+<div class="line"><span class="lineno">  115</span>                lim_a = u;</div>
+<div class="line"><span class="lineno">  116</span>            <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  117</span>                lim_b = u;</div>
+<div class="line"><span class="lineno">  118</span>            <span class="keywordflow">if</span> (fu &lt;= fw || x == w) {</div>
+<div class="line"><span class="lineno">  119</span>                v = w;</div>
+<div class="line"><span class="lineno">  120</span>                fv = fw;</div>
+<div class="line"><span class="lineno">  121</span>                w = u;</div>
+<div class="line"><span class="lineno">  122</span>                fw = fu;</div>
+<div class="line"><span class="lineno">  123</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (fu &lt;= fv || v == x || v == w) {</div>
+<div class="line"><span class="lineno">  124</span>                v = u;</div>
+<div class="line"><span class="lineno">  125</span>                fv = fu;</div>
+<div class="line"><span class="lineno">  126</span>            }</div>
+<div class="line"><span class="lineno">  127</span>        }</div>
+<div class="line"><span class="lineno">  128</span> </div>
+<div class="line"><span class="lineno">  129</span>        iters++;</div>
+<div class="line"><span class="lineno">  130</span>    } <span class="keywordflow">while</span> (std::abs(x - mid_point) &gt; (tolerance - (lim_b - lim_a) / 2.f));</div>
+<div class="line"><span class="lineno">  131</span> </div>
+<div class="line"><span class="lineno">  132</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; (iters: &quot;</span> &lt;&lt; iters &lt;&lt; <span class="stringliteral">&quot;) &quot;</span>;</div>
+<div class="line"><span class="lineno">  133</span> </div>
+<div class="line"><span class="lineno">  134</span>    <span class="keywordflow">return</span> x;</div>
+<div class="line"><span class="lineno">  135</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div></div>
 <div class="ttc" id="abrent__method__extrema_8cpp_html_a002b2f4894492820fe708b1b7e7c5e70"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div><div class="ttdeci">#define EPSILON</div><div class="ttdoc">system accuracy limit</div><div class="ttdef"><b>Definition:</b> brent_method_extrema.cpp:23</div></div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a4251b4df4748a0b9c43a48f61bdd2397"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">numerical_methods::simpson_method::f</a></div><div class="ttdeci">double f(double x)</div><div class="ttdoc">A function f(x) that will be used to test the method.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:113</div></div>
@@ -341,18 +341,18 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Main function </p>
-<div class="fragment"><div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>           {</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>.precision(18);</div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span> </div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Computations performed with machine epsilon: &quot;</span> &lt;&lt; <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>              &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span> </div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>    <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>    <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>    <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>();</div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span> </div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  204</span>           {</div>
+<div class="line"><span class="lineno">  205</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>.precision(18);</div>
+<div class="line"><span class="lineno">  206</span> </div>
+<div class="line"><span class="lineno">  207</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Computations performed with machine epsilon: &quot;</span> &lt;&lt; <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div>
+<div class="line"><span class="lineno">  208</span>              &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  209</span> </div>
+<div class="line"><span class="lineno">  210</span>    <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
+<div class="line"><span class="lineno">  211</span>    <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
+<div class="line"><span class="lineno">  212</span>    <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>();</div>
+<div class="line"><span class="lineno">  213</span> </div>
+<div class="line"><span class="lineno">  214</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  215</span>}</div>
 <div class="ttc" id="abrent__method__extrema_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdoc">Test function to find root for the function  in the interval    Expected result: .</div><div class="ttdef"><b>Definition:</b> brent_method_extrema.cpp:165</div></div>
 <div class="ttc" id="abrent__method__extrema_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdoc">Test function to find root for the function  in the interval    Expected result = 2.</div><div class="ttdef"><b>Definition:</b> brent_method_extrema.cpp:143</div></div>
 <div class="ttc" id="abrent__method__extrema_8cpp_html_a6d0455dd5c30adda100e95f0423c786e"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a></div><div class="ttdeci">void test3()</div><div class="ttdoc">Test function to find maxima for the function  in the interval    Expected result: .</div><div class="ttdef"><b>Definition:</b> brent_method_extrema.cpp:188</div></div>
@@ -382,21 +382,21 @@ Here is the call graph for this function:</div>
 
 <p>Test function to find root for the function \(f(x)= (x-2)^2\) in the interval \([1,5]\) <br  />
  Expected result = 2. </p>
-<div class="fragment"><div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>             {</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    <span class="comment">// define the function to minimize as a lambda function</span></div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(<span class="keywordtype">double</span>)&gt; f1 = [](<span class="keywordtype">double</span> x) {</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>        <span class="keywordflow">return</span> (x - 2) * (x - 2);</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    };</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span> </div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1.... &quot;</span>;</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span> </div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(f1, -1, 5);</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span> </div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minima &lt;&lt; <span class="stringliteral">&quot;...&quot;</span>;</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span> </div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>    assert(std::abs(minima - 2) &lt; <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  143</span>             {</div>
+<div class="line"><span class="lineno">  144</span>    <span class="comment">// define the function to minimize as a lambda function</span></div>
+<div class="line"><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(<span class="keywordtype">double</span>)&gt; f1 = [](<span class="keywordtype">double</span> x) {</div>
+<div class="line"><span class="lineno">  146</span>        <span class="keywordflow">return</span> (x - 2) * (x - 2);</div>
+<div class="line"><span class="lineno">  147</span>    };</div>
+<div class="line"><span class="lineno">  148</span> </div>
+<div class="line"><span class="lineno">  149</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1.... &quot;</span>;</div>
+<div class="line"><span class="lineno">  150</span> </div>
+<div class="line"><span class="lineno">  151</span>    <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(f1, -1, 5);</div>
+<div class="line"><span class="lineno">  152</span> </div>
+<div class="line"><span class="lineno">  153</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minima &lt;&lt; <span class="stringliteral">&quot;...&quot;</span>;</div>
+<div class="line"><span class="lineno">  154</span> </div>
+<div class="line"><span class="lineno">  155</span>    assert(std::abs(minima - 2) &lt; <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
+<div class="line"><span class="lineno">  156</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  157</span>}</div>
 <div class="ttc" id="abrent__method__extrema_8cpp_html_a1aa76a6d5fd4d333f9072beff1dc486b"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a></div><div class="ttdeci">double get_minima(const std::function&lt; double(double)&gt; &amp;f, double lim_a, double lim_b)</div><div class="ttdoc">Get the real root of a function in the given interval.</div><div class="ttdef"><b>Definition:</b> brent_method_extrema.cpp:35</div></div>
 <div class="ttc" id="afunction_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a></div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -425,22 +425,22 @@ Here is the call graph for this function:</div>
 
 <p>Test function to find root for the function \(f(x)= x^{\frac{1}{x}}\) in the interval \([-2,10]\) <br  />
  Expected result: \(e\approx 2.71828182845904509\). </p>
-<div class="fragment"><div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>             {</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    <span class="comment">// define the function to maximize as a lambda function</span></div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>    <span class="comment">// since we are maximixing, we negated the function return value</span></div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(<span class="keywordtype">double</span>)&gt; func = [](<span class="keywordtype">double</span> x) {</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>        <span class="keywordflow">return</span> -<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(x, 1.f / x);</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>    };</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span> </div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2.... &quot;</span>;</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span> </div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>    <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(func, -2, 5);</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span> </div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minima &lt;&lt; <span class="stringliteral">&quot; (&quot;</span> &lt;&lt; M_E &lt;&lt; <span class="stringliteral">&quot;)...&quot;</span>;</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span> </div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>    assert(std::abs(minima - M_E) &lt; <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  165</span>             {</div>
+<div class="line"><span class="lineno">  166</span>    <span class="comment">// define the function to maximize as a lambda function</span></div>
+<div class="line"><span class="lineno">  167</span>    <span class="comment">// since we are maximixing, we negated the function return value</span></div>
+<div class="line"><span class="lineno">  168</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(<span class="keywordtype">double</span>)&gt; func = [](<span class="keywordtype">double</span> x) {</div>
+<div class="line"><span class="lineno">  169</span>        <span class="keywordflow">return</span> -<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(x, 1.f / x);</div>
+<div class="line"><span class="lineno">  170</span>    };</div>
+<div class="line"><span class="lineno">  171</span> </div>
+<div class="line"><span class="lineno">  172</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2.... &quot;</span>;</div>
+<div class="line"><span class="lineno">  173</span> </div>
+<div class="line"><span class="lineno">  174</span>    <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(func, -2, 5);</div>
+<div class="line"><span class="lineno">  175</span> </div>
+<div class="line"><span class="lineno">  176</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minima &lt;&lt; <span class="stringliteral">&quot; (&quot;</span> &lt;&lt; M_E &lt;&lt; <span class="stringliteral">&quot;)...&quot;</span>;</div>
+<div class="line"><span class="lineno">  177</span> </div>
+<div class="line"><span class="lineno">  178</span>    assert(std::abs(minima - M_E) &lt; <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
+<div class="line"><span class="lineno">  179</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  180</span>}</div>
 <div class="ttc" id="apow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a></div><div class="ttdeci">T pow(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -468,20 +468,20 @@ Here is the call graph for this function:</div>
 
 <p>Test function to find <em>maxima</em> for the function \(f(x)= \cos x\) in the interval \([0,12]\) <br  />
  Expected result: \(\pi\approx 3.14159265358979312\). </p>
-<div class="fragment"><div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>             {</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>    <span class="comment">// define the function to maximize as a lambda function</span></div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>    <span class="comment">// since we are maximixing, we negated the function return value</span></div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(<span class="keywordtype">double</span>)&gt; func = [](<span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a>(x); };</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span> </div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3.... &quot;</span>;</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span> </div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>    <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(func, -4, 12);</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span> </div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minima &lt;&lt; <span class="stringliteral">&quot; (&quot;</span> &lt;&lt; M_PI &lt;&lt; <span class="stringliteral">&quot;)...&quot;</span>;</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span> </div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>    assert(std::abs(minima - M_PI) &lt; <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  188</span>             {</div>
+<div class="line"><span class="lineno">  189</span>    <span class="comment">// define the function to maximize as a lambda function</span></div>
+<div class="line"><span class="lineno">  190</span>    <span class="comment">// since we are maximixing, we negated the function return value</span></div>
+<div class="line"><span class="lineno">  191</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(<span class="keywordtype">double</span>)&gt; func = [](<span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a>(x); };</div>
+<div class="line"><span class="lineno">  192</span> </div>
+<div class="line"><span class="lineno">  193</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3.... &quot;</span>;</div>
+<div class="line"><span class="lineno">  194</span> </div>
+<div class="line"><span class="lineno">  195</span>    <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(func, -4, 12);</div>
+<div class="line"><span class="lineno">  196</span> </div>
+<div class="line"><span class="lineno">  197</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minima &lt;&lt; <span class="stringliteral">&quot; (&quot;</span> &lt;&lt; M_PI &lt;&lt; <span class="stringliteral">&quot;)...&quot;</span>;</div>
+<div class="line"><span class="lineno">  198</span> </div>
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 <div class="ttc" id="aspiral__print_8cpp_html_acfff36db81326fb990a643ab198ee8a5"><div class="ttname"><a href="../../db/d07/spiral__print_8cpp.html#acfff36db81326fb990a643ab198ee8a5">genArray</a></div><div class="ttdeci">void genArray(int **a, int r, int c)</div><div class="ttdef"><b>Definition:</b> spiral_print.cpp:12</div></div>
@@ -263,44 +263,44 @@ Here is the call graph for this function:</div>
 <p >Print the end col</p>
 <p >Print the end row</p>
 <p >Print the start Col</p>
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-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    <span class="comment">// Prime factors with their powers in the given number in new line</span></div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> it : <a class="code hl_variable" href="../../db/d0d/prime__factorization_8cpp.html#acfb0df439a4beae5a34ef131ce737c1b">factors</a>) {</div>
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-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   62</span>           {</div>
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+<div class="line"><span class="lineno">   64</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\t\tComputes the prime factorization\n\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   65</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Type in a number: &quot;</span>;</div>
+<div class="line"><span class="lineno">   66</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; num;</div>
+<div class="line"><span class="lineno">   67</span> </div>
+<div class="line"><span class="lineno">   68</span>    <a class="code hl_function" href="../../db/d0d/prime__factorization_8cpp.html#affe577b9bce8f604f5e2f861c63c7099">SieveOfEratosthenes</a>(num);</div>
+<div class="line"><span class="lineno">   69</span> </div>
+<div class="line"><span class="lineno">   70</span>    <a class="code hl_function" href="../../db/d0d/prime__factorization_8cpp.html#a0ece0145fb29a5cf48378c23dde2da46">prime_factorization</a>(num);</div>
+<div class="line"><span class="lineno">   71</span> </div>
+<div class="line"><span class="lineno">   72</span>    <span class="comment">// Prime factors with their powers in the given number in new line</span></div>
+<div class="line"><span class="lineno">   73</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> it : <a class="code hl_variable" href="../../db/d0d/prime__factorization_8cpp.html#acfb0df439a4beae5a34ef131ce737c1b">factors</a>) {</div>
+<div class="line"><span class="lineno">   74</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; it.first &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; it.second &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   75</span>    }</div>
+<div class="line"><span class="lineno">   76</span> </div>
+<div class="line"><span class="lineno">   77</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">   78</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
@@ -173,7 +173,7 @@ Variables</h2></td></tr>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
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 </div>
 </div>
 
@@ -195,26 +195,26 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Prime factorization of a number </p>
-<div class="fragment"><div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>                                  {</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    <span class="keywordtype">int</span> number = num;</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span> </div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; <a class="code hl_variable" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i] &lt;= num; i++) {</div>
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-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>        <span class="comment">// termination condition</span></div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>        <span class="keywordflow">if</span> (number == 1) {</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>            <span class="keywordflow">break</span>;</div>
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-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>        <span class="keywordflow">while</span> (number % <a class="code hl_variable" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i] == 0) {</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>            count++;</div>
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-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>        }</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span> </div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>        <span class="keywordflow">if</span> (count)</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>            <a class="code hl_variable" href="../../db/d0d/prime__factorization_8cpp.html#acfb0df439a4beae5a34ef131ce737c1b">factors</a>.push_back(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(<a class="code hl_variable" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i], count));</div>
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-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   40</span>                                  {</div>
+<div class="line"><span class="lineno">   41</span>    <span class="keywordtype">int</span> number = num;</div>
+<div class="line"><span class="lineno">   42</span> </div>
+<div class="line"><span class="lineno">   43</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; <a class="code hl_variable" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i] &lt;= num; i++) {</div>
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+<div class="line"><span class="lineno">   45</span> </div>
+<div class="line"><span class="lineno">   46</span>        <span class="comment">// termination condition</span></div>
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+<div class="line"><span class="lineno">   52</span>            count++;</div>
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+<div class="line"><span class="lineno">   54</span>        }</div>
+<div class="line"><span class="lineno">   55</span> </div>
+<div class="line"><span class="lineno">   56</span>        <span class="keywordflow">if</span> (count)</div>
+<div class="line"><span class="lineno">   57</span>            <a class="code hl_variable" href="../../db/d0d/prime__factorization_8cpp.html#acfb0df439a4beae5a34ef131ce737c1b">factors</a>.push_back(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(<a class="code hl_variable" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i], count));</div>
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 </div><!-- fragment --><div class="dynheader">
@@ -242,25 +242,32 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Calculating prime number upto a given range </p>
-<div class="fragment"><div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>                                {</div>
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-<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 2; i &lt;= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
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-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 2; i &lt;= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>[i])</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>            <a class="code hl_variable" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>.push_back(i);</div>
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+<div class="fragment"><div class="line"><span class="lineno">   23</span>                                {</div>
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+<div class="line"><span class="lineno">   26</span> </div>
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+<div class="line"><span class="lineno">   36</span>    }</div>
+<div class="line"><span class="lineno">   37</span>}</div>
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 <div class="ttc" id="amemset_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/memset.html">std::memset</a></div><div class="ttdeci">T memset(T... args)</div></div>
 <div class="ttc" id="aprime__factorization_8cpp_html_a7fe38b570a51e448430d6a0f072c2f23"><div class="ttname"><a href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a></div><div class="ttdeci">bool isprime[1000006]</div><div class="ttdef"><b>Definition:</b> prime_factorization.cpp:13</div></div>
-</div><!-- fragment -->
+<div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
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+</div>
+</div>
+
 </div>
 </div>
 <h2 class="groupheader">Variable Documentation</h2>
@@ -315,7 +322,7 @@ Here is the call graph for this function:</div>
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   <ul>
     <li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../db/d0d/prime__factorization_8cpp.html">prime_factorization.cpp</a></li>
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@@ -97,7 +97,7 @@ $(document).ready(function(){initNavTree('db/d16/0__1__knapsack_8cpp.html','../.
 </div><!--header-->
 <div class="contents">
 
-<p>Implementation of <a href="https://en.wikipedia.org/wiki/Knapsack_problem" target="_blank">0-1 Knapsack Problem</a>  
+<p>Implementation of [0-1 <a class="el" href="../../d7/daf/namespace_knapsack.html" title="Implementation of 0-1 Knapsack problem.">Knapsack</a> Problem] (<a href="https://en.wikipedia.org/wiki/Knapsack_problem">https://en.wikipedia.org/wiki/Knapsack_problem</a>)  
 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;array&gt;</code><br />
 <code>#include &lt;cassert&gt;</code><br />
@@ -133,7 +133,7 @@ Functions</h2></td></tr>
 <tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
 </table>
 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
-<div class="textblock"><p >Implementation of <a href="https://en.wikipedia.org/wiki/Knapsack_problem" target="_blank">0-1 Knapsack Problem</a> </p>
+<div class="textblock"><p >Implementation of [0-1 <a class="el" href="../../d7/daf/namespace_knapsack.html" title="Implementation of 0-1 Knapsack problem.">Knapsack</a> Problem] (<a href="https://en.wikipedia.org/wiki/Knapsack_problem">https://en.wikipedia.org/wiki/Knapsack_problem</a>) </p>
 <p >Given weights and values of n items, put these items in a knapsack of capacity <code>W</code> to get the maximum total value in the knapsack. In other words, given two integer arrays <code>val[0..n-1]</code> and <code>wt[0..n-1]</code> which represent values and weights associated with n items respectively. Also given an integer W which represents knapsack capacity, find out the maximum value subset of <code>val[]</code> such that sum of the weights of this subset is smaller than or equal to W. You cannot break an item, either pick the complete item or don’t pick it (0-1 property)</p>
 <h3><a class="anchor" id="autotoc_md66"></a>
 Algorithm</h3>
@@ -160,11 +160,11 @@ Algorithm</h3>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>           {</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    <span class="comment">// Testing</span></div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    <a class="code hl_function" href="../../db/d16/0__1__knapsack_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  126</span>           {</div>
+<div class="line"><span class="lineno">  127</span>    <span class="comment">// Testing</span></div>
+<div class="line"><span class="lineno">  128</span>    <a class="code hl_function" href="../../db/d16/0__1__knapsack_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
+<div class="line"><span class="lineno">  129</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  130</span>}</div>
 <div class="ttc" id="a0__1__knapsack_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../db/d16/0__1__knapsack_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Function to test above algorithm.</div><div class="ttdef"><b>Definition:</b> 0_1_knapsack.cpp:96</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -225,43 +225,43 @@ template&lt;size_t n&gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>maximum value obtainable with given capacity. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>                                                    {</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a> &gt; maxValue(n + 1,</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>                                            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>(capacity + 1, 0));</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <span class="comment">// outer loop will select no of items allowed</span></div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    <span class="comment">// inner loop will select capcity of knapsack bag</span></div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    <span class="keywordtype">int</span> items = <span class="keyword">sizeof</span>(weight) / <span class="keyword">sizeof</span>(weight[0]);</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; items + 1; ++i) {</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; capacity + 1; ++j) {</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>            <span class="keywordflow">if</span> (i == 0 || j == 0) {</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>                <span class="comment">// if no of items is zero or capacity is zero, then maxValue</span></div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>                <span class="comment">// will be zero</span></div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>                maxValue[i][j] = 0;</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (weight[i - 1] &lt;= j) {</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>                <span class="comment">// if the ith item&#39;s weight(in actual array it will be at i-1)</span></div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>                <span class="comment">// is less than or equal to the allowed weight i.e. j then we</span></div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>                <span class="comment">// can pick that item for our knapsack. maxValue will be the</span></div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>                <span class="comment">// obtained either by picking the current item or by not picking</span></div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>                <span class="comment">// current item</span></div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span> </div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>                <span class="comment">// picking current item</span></div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>                <span class="keywordtype">int</span> profit1 = value[i - 1] + maxValue[i - 1][j - weight[i - 1]];</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span> </div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>                <span class="comment">// not picking current item</span></div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>                <span class="keywordtype">int</span> profit2 = maxValue[i - 1][j];</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span> </div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>                maxValue[i][j] = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(profit1, profit2);</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>                <span class="comment">// as weight of current item is greater than allowed weight, so</span></div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>                <span class="comment">// maxProfit will be profit obtained by excluding current item.</span></div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>                maxValue[i][j] = maxValue[i - 1][j];</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>            }</div>
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-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span> </div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>    <span class="comment">// returning maximum value</span></div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    <span class="keywordflow">return</span> maxValue[items][capacity];</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   52</span>                                                    {</div>
+<div class="line"><span class="lineno">   53</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a> &gt; maxValue(n + 1,</div>
+<div class="line"><span class="lineno">   54</span>                                            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>(capacity + 1, 0));</div>
+<div class="line"><span class="lineno">   55</span>    <span class="comment">// outer loop will select no of items allowed</span></div>
+<div class="line"><span class="lineno">   56</span>    <span class="comment">// inner loop will select capcity of knapsack bag</span></div>
+<div class="line"><span class="lineno">   57</span>    <span class="keywordtype">int</span> items = <span class="keyword">sizeof</span>(weight) / <span class="keyword">sizeof</span>(weight[0]);</div>
+<div class="line"><span class="lineno">   58</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; items + 1; ++i) {</div>
+<div class="line"><span class="lineno">   59</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; capacity + 1; ++j) {</div>
+<div class="line"><span class="lineno">   60</span>            <span class="keywordflow">if</span> (i == 0 || j == 0) {</div>
+<div class="line"><span class="lineno">   61</span>                <span class="comment">// if no of items is zero or capacity is zero, then maxValue</span></div>
+<div class="line"><span class="lineno">   62</span>                <span class="comment">// will be zero</span></div>
+<div class="line"><span class="lineno">   63</span>                maxValue[i][j] = 0;</div>
+<div class="line"><span class="lineno">   64</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (weight[i - 1] &lt;= j) {</div>
+<div class="line"><span class="lineno">   65</span>                <span class="comment">// if the ith item&#39;s weight(in actual array it will be at i-1)</span></div>
+<div class="line"><span class="lineno">   66</span>                <span class="comment">// is less than or equal to the allowed weight i.e. j then we</span></div>
+<div class="line"><span class="lineno">   67</span>                <span class="comment">// can pick that item for our knapsack. maxValue will be the</span></div>
+<div class="line"><span class="lineno">   68</span>                <span class="comment">// obtained either by picking the current item or by not picking</span></div>
+<div class="line"><span class="lineno">   69</span>                <span class="comment">// current item</span></div>
+<div class="line"><span class="lineno">   70</span> </div>
+<div class="line"><span class="lineno">   71</span>                <span class="comment">// picking current item</span></div>
+<div class="line"><span class="lineno">   72</span>                <span class="keywordtype">int</span> profit1 = value[i - 1] + maxValue[i - 1][j - weight[i - 1]];</div>
+<div class="line"><span class="lineno">   73</span> </div>
+<div class="line"><span class="lineno">   74</span>                <span class="comment">// not picking current item</span></div>
+<div class="line"><span class="lineno">   75</span>                <span class="keywordtype">int</span> profit2 = maxValue[i - 1][j];</div>
+<div class="line"><span class="lineno">   76</span> </div>
+<div class="line"><span class="lineno">   77</span>                maxValue[i][j] = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(profit1, profit2);</div>
+<div class="line"><span class="lineno">   78</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   79</span>                <span class="comment">// as weight of current item is greater than allowed weight, so</span></div>
+<div class="line"><span class="lineno">   80</span>                <span class="comment">// maxProfit will be profit obtained by excluding current item.</span></div>
+<div class="line"><span class="lineno">   81</span>                maxValue[i][j] = maxValue[i - 1][j];</div>
+<div class="line"><span class="lineno">   82</span>            }</div>
+<div class="line"><span class="lineno">   83</span>        }</div>
+<div class="line"><span class="lineno">   84</span>    }</div>
+<div class="line"><span class="lineno">   85</span> </div>
+<div class="line"><span class="lineno">   86</span>    <span class="comment">// returning maximum value</span></div>
+<div class="line"><span class="lineno">   87</span>    <span class="keywordflow">return</span> maxValue[items][capacity];</div>
+<div class="line"><span class="lineno">   88</span>}</div>
 <div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
 <div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -298,31 +298,31 @@ Here is the call graph for this function:</div>
 
 <p>Function to test above algorithm. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    <span class="comment">// Test 1</span></div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> n1 = 3;                             <span class="comment">// number of items</span></div>
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-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n1&gt;</a> value1 = {60, 100, 120};  <span class="comment">// value of each item</span></div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> capacity1 = 50;                     <span class="comment">// capacity of carrying bag</span></div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> max_value1 = <a class="code hl_function" href="../../db/d16/0__1__knapsack_8cpp.html#a15edf30f336885e5b851f6b7199c6cd1">dynamic_programming::knapsack::maxKnapsackValue</a>(</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        capacity1, weight1, value1);</div>
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-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    assert(max_value1 == expected_max_value1);</div>
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@@ -155,10 +155,10 @@ Functions</h2></td></tr>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>           {</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    <a class="code hl_function" href="../../db/d27/n__bonacci_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  120</span>           {</div>
+<div class="line"><span class="lineno">  121</span>    <a class="code hl_function" href="../../db/d27/n__bonacci_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
+<div class="line"><span class="lineno">  122</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  123</span>}</div>
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 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -206,22 +206,22 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd>the n-bonacci sequence as vector array </dd></dl>
 <p >we initialise the (n-1)th term as 1 which is the sum of preceding N zeros</p>
 <p >similarily the sum of preceding N zeros and the (N+1)th 1 is also 1</p>
-<div class="fragment"><div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>                                                                    {</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> a(m, 0);  <span class="comment">// we create an empty array of size m</span></div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span> </div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    a[n - 1] = 1;  <span class="comment">/// we initialise the (n-1)th term as 1 which is the sum of</span><span class="comment"></span></div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span><span class="comment">                   /// preceding N zeros</span></div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="comment"></span>    a[n] = 1;  <span class="comment">/// similarily the sum of preceding N zeros and the (N+1)th 1 is</span><span class="comment"></span></div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span><span class="comment">               /// also 1</span></div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span><span class="comment"></span>    <span class="keywordflow">for</span> (uint64_t i = n + 1; i &lt; m; i++) {</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        <span class="comment">// this is an optimized solution that works in O(M) time and takes O(M)</span></div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>        <span class="comment">// extra space here we use the concept of the sliding window the current</span></div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>        <span class="comment">// term can be computed using the given formula</span></div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>        a[i] = 2 * a[i - 1] - a[i - 1 - n];</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    }</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>    <span class="keywordflow">return</span> a;</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>}</div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="fragment"><div class="line"><span class="lineno">   41</span>                                                                    {</div>
+<div class="line"><span class="lineno">   42</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> a(m, 0);  <span class="comment">// we create an empty array of size m</span></div>
+<div class="line"><span class="lineno">   43</span> </div>
+<div class="line"><span class="lineno">   44</span>    a[n - 1] = 1;  <span class="comment">/// we initialise the (n-1)th term as 1 which is the sum of</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">   45</span><span class="comment">                   /// preceding N zeros</span></div>
+<div class="line"><span class="lineno">   46</span><span class="comment"></span>    a[n] = 1;  <span class="comment">/// similarily the sum of preceding N zeros and the (N+1)th 1 is</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">   47</span><span class="comment">               /// also 1</span></div>
+<div class="line"><span class="lineno">   48</span><span class="comment"></span>    <span class="keywordflow">for</span> (uint64_t i = n + 1; i &lt; m; i++) {</div>
+<div class="line"><span class="lineno">   49</span>        <span class="comment">// this is an optimized solution that works in O(M) time and takes O(M)</span></div>
+<div class="line"><span class="lineno">   50</span>        <span class="comment">// extra space here we use the concept of the sliding window the current</span></div>
+<div class="line"><span class="lineno">   51</span>        <span class="comment">// term can be computed using the given formula</span></div>
+<div class="line"><span class="lineno">   52</span>        a[i] = 2 * a[i - 1] - a[i - 1 - n];</div>
+<div class="line"><span class="lineno">   53</span>    }</div>
+<div class="line"><span class="lineno">   54</span>    <span class="keywordflow">return</span> a;</div>
+<div class="line"><span class="lineno">   55</span>}</div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; uint64_t &gt;</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -256,58 +256,58 @@ Here is the call graph for this function:</div>
 
 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>                   {</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    <span class="comment">// n = 1 m = 1 return [1, 1]</span></div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test&quot;</span>;</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> arr1 = <a class="code hl_function" href="../../db/d27/n__bonacci_8cpp.html#a6849b68f760be628d5975ab3eddec63d">math::n_bonacci::N_bonacci</a>(</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        1, 1);  <span class="comment">// first input is the param n and second one is the param m for</span></div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>                <span class="comment">// N-bonacci func</span></div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> output_array1 = {</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        1, 1};  <span class="comment">// It is the expected output series of length m</span></div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/equal.html">std::equal</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr1), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr1),</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>                      <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(output_array1)));</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span> </div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    <span class="comment">// n = 5 m = 15 return [0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 31, 61, 120, 236,</span></div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>    <span class="comment">// 464]</span></div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test&quot;</span>;</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> arr2 = <a class="code hl_function" href="../../db/d27/n__bonacci_8cpp.html#a6849b68f760be628d5975ab3eddec63d">math::n_bonacci::N_bonacci</a>(</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>        5, 15);  <span class="comment">// first input is the param n and second one is the param m for</span></div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>                 <span class="comment">// N-bonacci func</span></div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> output_array2 = {</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        0, 0,  0,  0,  1,   1,   2,  4,</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>        8, 16, 31, 61, 120, 236, 464};  <span class="comment">// It is the expected output series of</span></div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>                                        <span class="comment">// length m</span></div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/equal.html">std::equal</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr2), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr2),</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>                      <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(output_array2)));</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span> </div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    <span class="comment">// n = 6 m = 17 return [0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 63, 125, 248,</span></div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    <span class="comment">// 492, 976]</span></div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3rd test&quot;</span>;</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> arr3 = <a class="code hl_function" href="../../db/d27/n__bonacci_8cpp.html#a6849b68f760be628d5975ab3eddec63d">math::n_bonacci::N_bonacci</a>(</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>        6, 17);  <span class="comment">// first input is the param n and second one is the param m for</span></div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>                 <span class="comment">// N-bonacci func</span></div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> output_array3 = {</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>        0, 0,  0,  0,  0,   1,   1,   2,  4,</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>        8, 16, 32, 63, 125, 248, 492, 976};  <span class="comment">// It is the expected output series</span></div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>                                             <span class="comment">// of length m</span></div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/equal.html">std::equal</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr3), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr3),</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>                      <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(output_array3)));</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span> </div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <span class="comment">// n = 56 m = 15 return [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]</span></div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4th test&quot;</span>;</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> arr4 = <a class="code hl_function" href="../../db/d27/n__bonacci_8cpp.html#a6849b68f760be628d5975ab3eddec63d">math::n_bonacci::N_bonacci</a>(</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>        56, 15);  <span class="comment">// first input is the param n and second one is the param m</span></div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>                  <span class="comment">// for N-bonacci func</span></div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> output_array4 = {</div>
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+<div class="fragment"><div class="line"><span class="lineno">   63</span>                   {</div>
+<div class="line"><span class="lineno">   64</span>    <span class="comment">// n = 1 m = 1 return [1, 1]</span></div>
+<div class="line"><span class="lineno">   65</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test&quot;</span>;</div>
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+<div class="line"><span class="lineno">   84</span>                                        <span class="comment">// length m</span></div>
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+<div class="line"><span class="lineno">   88</span> </div>
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+<div class="line"><span class="lineno">   94</span>                 <span class="comment">// N-bonacci func</span></div>
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+<div class="line"><span class="lineno">   98</span>                                             <span class="comment">// of length m</span></div>
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+<div class="line"><span class="lineno">  102</span> </div>
+<div class="line"><span class="lineno">  103</span>    <span class="comment">// n = 56 m = 15 return [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]</span></div>
+<div class="line"><span class="lineno">  104</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4th test&quot;</span>;</div>
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+<div class="line"><span class="lineno">   41</span>    To-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[To-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>] = From-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[From-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>];</div>
+<div class="line"><span class="lineno">   42</span>    ++To-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>;</div>
+<div class="line"><span class="lineno">   43</span>}</div>
 <div class="ttc" id="astructtower_html_a3ebb75c13c57d51a8a1ba1ea54a515e9"><div class="ttname"><a href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">tower::values</a></div><div class="ttdeci">int values[10]</div><div class="ttdoc">Values in the tower.</div><div class="ttdef"><b>Definition:</b> tower_of_hanoi.cpp:13</div></div>
 </div><!-- fragment -->
 </div>
@@ -251,20 +251,20 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Display the towers </p>
-<div class="fragment"><div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span>                                       {</div>
-<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n\n\tF : &quot;</span>;</div>
-<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; F-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>; i++) {</div>
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-<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span>    }</div>
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-<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; U-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>; i++) {</div>
-<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; U-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[i] &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
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-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; T-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>; i++) {</div>
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+<div class="fragment"><div class="line"><span class="lineno">   20</span>                                       {</div>
+<div class="line"><span class="lineno">   21</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n\n\tF : &quot;</span>;</div>
+<div class="line"><span class="lineno">   22</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; F-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>; i++) {</div>
+<div class="line"><span class="lineno">   23</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; F-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[i] &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
+<div class="line"><span class="lineno">   24</span>    }</div>
+<div class="line"><span class="lineno">   25</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n\tU : &quot;</span>;</div>
+<div class="line"><span class="lineno">   26</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; U-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>; i++) {</div>
+<div class="line"><span class="lineno">   27</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; U-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[i] &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
+<div class="line"><span class="lineno">   28</span>    }</div>
+<div class="line"><span class="lineno">   29</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n\tT : &quot;</span>;</div>
+<div class="line"><span class="lineno">   30</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; T-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>; i++) {</div>
+<div class="line"><span class="lineno">   31</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; T-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[i] &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
+<div class="line"><span class="lineno">   32</span>    }</div>
+<div class="line"><span class="lineno">   33</span>}</div>
 </div><!-- fragment -->
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@@ -314,17 +314,17 @@ Here is the call graph for this function:</div>
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-<div class="fragment"><div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>                                                     {</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    <span class="keywordflow">if</span> (n == 1) {</div>
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-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>        <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#a746d9a3984bba88fd6dd91978f6931ed">show</a>(From, To, Using);</div>
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-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>        <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a>(From, To);</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>        <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#a746d9a3984bba88fd6dd91978f6931ed">show</a>(From, To, Using);</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">TH</a>(n - 1, Using, From, To);</div>
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-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>}</div>
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+<div class="line"><span class="lineno">   53</span>    <span class="keywordflow">if</span> (n == 1) {</div>
+<div class="line"><span class="lineno">   54</span>        <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a>(From, To);</div>
+<div class="line"><span class="lineno">   55</span>        <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#a746d9a3984bba88fd6dd91978f6931ed">show</a>(From, To, Using);</div>
+<div class="line"><span class="lineno">   56</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   57</span>        <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">TH</a>(n - 1, From, To, Using);</div>
+<div class="line"><span class="lineno">   58</span>        <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a>(From, To);</div>
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+<div class="line"><span class="lineno">   60</span>        <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">TH</a>(n - 1, Using, From, To);</div>
+<div class="line"><span class="lineno">   61</span>    }</div>
+<div class="line"><span class="lineno">   62</span>}</div>
 <div class="ttc" id="atower__of__hanoi_8cpp_html_af4cfc41e546f1f8d25f01e0804e8b61d"><div class="ttname"><a href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a></div><div class="ttdeci">void mov(tower *From, tower *To)</div><div class="ttdef"><b>Definition:</b> tower_of_hanoi.cpp:39</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -341,7 +341,7 @@ Here is the call graph for this function:</div>
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@@ -154,10 +154,10 @@ Functions</h2></td></tr>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>           {</div>
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-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   91</span>           {</div>
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+<div class="line"><span class="lineno">   94</span>}</div>
 <div class="ttc" id="awave__sort_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../db/d3f/wave__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition:</b> wave_sort.cpp:53</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -193,42 +193,42 @@ Here is the call graph for this function:</div>
 
 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>                   {</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>    <span class="comment">// [10, 90, 49, 2, 1, 5, 23] return [2, 1, 10, 5, 49, 23, 90]</span></div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array1 = {10, 90, 49, 2, 1, 5, 23};</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1... &quot;</span>;</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr1 = <a class="code hl_function" href="../../db/d3f/wave__sort_8cpp.html#a7d4f243b9dc13ace4ef77e30dbc56f12">sorting::wave_sort::waveSort</a>(array1, 7);</div>
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-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    assert(arr1 == o1);</div>
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-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    assert(arr2 == o2);</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span> </div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>    <span class="comment">// [3, 3, 3, 3] return [3, 3, 3, 3]</span></div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array3 = {3, 3, 3, 3};</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3... &quot;</span>;</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr3 = <a class="code hl_function" href="../../db/d3f/wave__sort_8cpp.html#a7d4f243b9dc13ace4ef77e30dbc56f12">sorting::wave_sort::waveSort</a>(array3, 4);</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> o3 = {3, 3, 3, 3};</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    assert(arr3 == o3);</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span> </div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    <span class="comment">// [9, 4, 6, 8, 14, 3] return [4, 3, 8, 6, 14, 9]</span></div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array4 = {9, 4, 6, 8, 14, 3};</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 4... &quot;</span>;</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr4 = <a class="code hl_function" href="../../db/d3f/wave__sort_8cpp.html#a7d4f243b9dc13ace4ef77e30dbc56f12">sorting::wave_sort::waveSort</a>(array4, 6);</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> o4 = {4, 3, 8, 6, 14, 9};</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    assert(arr4 == o4);</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   53</span>                   {</div>
+<div class="line"><span class="lineno">   54</span>    <span class="comment">// [10, 90, 49, 2, 1, 5, 23] return [2, 1, 10, 5, 49, 23, 90]</span></div>
+<div class="line"><span class="lineno">   55</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array1 = {10, 90, 49, 2, 1, 5, 23};</div>
+<div class="line"><span class="lineno">   56</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1... &quot;</span>;</div>
+<div class="line"><span class="lineno">   57</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr1 = <a class="code hl_function" href="../../db/d3f/wave__sort_8cpp.html#a7d4f243b9dc13ace4ef77e30dbc56f12">sorting::wave_sort::waveSort</a>(array1, 7);</div>
+<div class="line"><span class="lineno">   58</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> o1 = {2, 1, 10, 5, 49, 23, 90};</div>
+<div class="line"><span class="lineno">   59</span>    assert(arr1 == o1);</div>
+<div class="line"><span class="lineno">   60</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   61</span> </div>
+<div class="line"><span class="lineno">   62</span>    <span class="comment">// [1, 3, 4, 2, 7, 8] return [2, 1, 4, 3, 8, 7]</span></div>
+<div class="line"><span class="lineno">   63</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array2 = {1, 3, 4, 2, 7, 8};</div>
+<div class="line"><span class="lineno">   64</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2... &quot;</span>;</div>
+<div class="line"><span class="lineno">   65</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr2 = <a class="code hl_function" href="../../db/d3f/wave__sort_8cpp.html#a7d4f243b9dc13ace4ef77e30dbc56f12">sorting::wave_sort::waveSort</a>(array2, 6);</div>
+<div class="line"><span class="lineno">   66</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> o2 = {2, 1, 4, 3, 8, 7};</div>
+<div class="line"><span class="lineno">   67</span>    assert(arr2 == o2);</div>
+<div class="line"><span class="lineno">   68</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   69</span> </div>
+<div class="line"><span class="lineno">   70</span>    <span class="comment">// [3, 3, 3, 3] return [3, 3, 3, 3]</span></div>
+<div class="line"><span class="lineno">   71</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array3 = {3, 3, 3, 3};</div>
+<div class="line"><span class="lineno">   72</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3... &quot;</span>;</div>
+<div class="line"><span class="lineno">   73</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr3 = <a class="code hl_function" href="../../db/d3f/wave__sort_8cpp.html#a7d4f243b9dc13ace4ef77e30dbc56f12">sorting::wave_sort::waveSort</a>(array3, 4);</div>
+<div class="line"><span class="lineno">   74</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> o3 = {3, 3, 3, 3};</div>
+<div class="line"><span class="lineno">   75</span>    assert(arr3 == o3);</div>
+<div class="line"><span class="lineno">   76</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   77</span> </div>
+<div class="line"><span class="lineno">   78</span>    <span class="comment">// [9, 4, 6, 8, 14, 3] return [4, 3, 8, 6, 14, 9]</span></div>
+<div class="line"><span class="lineno">   79</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array4 = {9, 4, 6, 8, 14, 3};</div>
+<div class="line"><span class="lineno">   80</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 4... &quot;</span>;</div>
+<div class="line"><span class="lineno">   81</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr4 = <a class="code hl_function" href="../../db/d3f/wave__sort_8cpp.html#a7d4f243b9dc13ace4ef77e30dbc56f12">sorting::wave_sort::waveSort</a>(array4, 6);</div>
+<div class="line"><span class="lineno">   82</span>    <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> o4 = {4, 3, 8, 6, 14, 9};</div>
+<div class="line"><span class="lineno">   83</span>    assert(arr4 == o4);</div>
+<div class="line"><span class="lineno">   84</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int64_t &gt;</a></div></div>
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 Here is the call graph for this function:</div>
@@ -281,18 +281,18 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>arr the wave sorted array </dd></dl>
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+<div class="line"><span class="lineno">   35</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> arr(in_arr);</div>
+<div class="line"><span class="lineno">   36</span> </div>
+<div class="line"><span class="lineno">   37</span>    <span class="keywordflow">for</span> (int64_t i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">   38</span>        arr[i] = in_arr[i];</div>
+<div class="line"><span class="lineno">   39</span>    }</div>
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+<div class="line"><span class="lineno">   41</span>    <span class="keywordflow">for</span> (int64_t i = 0; i &lt; n - 1; i += 2) {  <span class="comment">// swap all the adjacent elements</span></div>
+<div class="line"><span class="lineno">   42</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[i], arr[i + 1]);</div>
+<div class="line"><span class="lineno">   43</span>    }</div>
+<div class="line"><span class="lineno">   44</span>    <span class="keywordflow">return</span> arr;</div>
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 <div class="ttc" id="asort_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/sort.html">std::sort</a></div><div class="ttdeci">T sort(T... args)</div></div>
 <div class="ttc" id="aswap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a></div><div class="ttdeci">T swap(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -310,7 +310,7 @@ Here is the call graph for this function:</div>
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-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> samples =</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>        <a class="code hl_function" href="../../db/d40/integral__approximation2_8cpp.html#a71249ee535f16f8ed2e9cc8f0199a2cf">generate_samples</a>(start_point, pdf, num_samples);</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span> </div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    <span class="keywordflow">for</span> (<span class="keywordtype">double</span> sample : samples) {</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        integral += <span class="keyword">function</span>(sample) / pdf(sample);</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    }</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span> </div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <span class="keywordflow">return</span> integral / <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(samples.size());</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  114</span>                                                                   {</div>
+<div class="line"><span class="lineno">  115</span>    <span class="keywordtype">double</span> integral = 0.0;</div>
+<div class="line"><span class="lineno">  116</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> samples =</div>
+<div class="line"><span class="lineno">  117</span>        <a class="code hl_function" href="../../db/d40/integral__approximation2_8cpp.html#a71249ee535f16f8ed2e9cc8f0199a2cf">generate_samples</a>(start_point, pdf, num_samples);</div>
+<div class="line"><span class="lineno">  118</span> </div>
+<div class="line"><span class="lineno">  119</span>    <span class="keywordflow">for</span> (<span class="keywordtype">double</span> sample : samples) {</div>
+<div class="line"><span class="lineno">  120</span>        integral += function(sample) / pdf(sample);</div>
+<div class="line"><span class="lineno">  121</span>    }</div>
+<div class="line"><span class="lineno">  122</span> </div>
+<div class="line"><span class="lineno">  123</span>    <span class="keywordflow">return</span> integral / <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(samples.size());</div>
+<div class="line"><span class="lineno">  124</span>}</div>
 <div class="ttc" id="aintegral__approximation2_8cpp_html_a71249ee535f16f8ed2e9cc8f0199a2cf"><div class="ttname"><a href="../../db/d40/integral__approximation2_8cpp.html#a71249ee535f16f8ed2e9cc8f0199a2cf">math::monte_carlo::generate_samples</a></div><div class="ttdeci">std::vector&lt; double &gt; generate_samples(const double &amp;start_point, const Function &amp;pdf, const uint32_t &amp;num_samples, const uint32_t &amp;discard=100000)</div><div class="ttdoc">short-hand for std::functions used in this implementation</div><div class="ttdef"><b>Definition:</b> integral_approximation2.cpp:64</div></div>
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@@ -336,10 +336,10 @@ Here is the call graph for this function:</div>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>           {</div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>    <a class="code hl_function" href="../../db/d40/integral__approximation2_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  215</span>           {</div>
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+<div class="line"><span class="lineno">  217</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  218</span>}</div>
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@@ -375,83 +375,83 @@ Here is the call graph for this function:</div>
 
 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>                   {</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Disclaimer: Because this is a randomized algorithm,&quot;</span></div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        &lt;&lt; <span class="stringliteral">&quot;it may happen that singular samples deviate from the true result.&quot;</span></div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>        &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>    ;</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span> </div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">math::monte_carlo::Function</a> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">f</a>;</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">math::monte_carlo::Function</a> pdf;</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    <span class="keywordtype">double</span> integral = 0;</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <span class="keywordtype">double</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/lower_bound.html">lower_bound</a> = 0, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/upper_bound.html">upper_bound</a> = 0;</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span> </div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    <span class="comment">/* \int_{-2}^{2} -x^2 + 4 dx */</span></div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>    <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">f</a> = [&amp;](<span class="keywordtype">double</span>&amp; x) { <span class="keywordflow">return</span> -x * x + 4.0; };</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span> </div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/lower_bound.html">lower_bound</a> = -2.0;</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/upper_bound.html">upper_bound</a> = 2.0;</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>    pdf = [&amp;](<span class="keywordtype">double</span>&amp; x) {</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>        <span class="keywordflow">if</span> (x &gt;= lower_bound &amp;&amp; x &lt;= -1.0) {</div>
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-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>        <span class="keywordflow">if</span> (x &lt;= upper_bound &amp;&amp; x &gt;= 1.0) {</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>            <span class="keywordflow">return</span> 0.1;</div>
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-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>        <span class="keywordflow">if</span> (x &gt; -1.0 &amp;&amp; x &lt; 1.0) {</div>
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-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span> </div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>    integral = <a class="code hl_function" href="../../db/d40/integral__approximation2_8cpp.html#af7da9ba8932f1f48b9bbc2d80471af51">math::monte_carlo::integral_monte_carlo</a>(</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>        (upper_bound - lower_bound) / 2.0, f, pdf);</div>
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-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span> </div>
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-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>        <span class="keywordflow">if</span> (x &gt; 0.2 &amp;&amp; x &lt;= 0.4) {</div>
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-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>    integral = <a class="code hl_function" href="../../db/d40/integral__approximation2_8cpp.html#af7da9ba8932f1f48b9bbc2d80471af51">math::monte_carlo::integral_monte_carlo</a>(</div>
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-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    integral = <a class="code hl_function" href="../../db/d40/integral__approximation2_8cpp.html#af7da9ba8932f1f48b9bbc2d80471af51">math::monte_carlo::integral_monte_carlo</a>(0.0, f, pdf, 10000000);</div>
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+<div class="line"><span class="lineno">  146</span> </div>
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+<div class="line"><span class="lineno">  149</span> </div>
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@@ -200,62 +200,62 @@ bool&#160;</td><td class="memItemRight" valign="bottom"><b>quadratic_probing::re
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 <p >Main function </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
-<div class="fragment"><div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>           {</div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>    <span class="keywordtype">int</span> cmd = 0, <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hash</a> = 0, key = 0;</div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the initial size of Hash Table. = &quot;</span>;</div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; totalSize;</div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>    table = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Entry&gt;</a>(totalSize);</div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>    <span class="keywordtype">bool</span> loop = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>    <span class="keywordflow">while</span> (loop) {</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;PLEASE CHOOSE -&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1. Add key. (Numeric only)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2. Remove key.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3. Find key.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4. Generate Hash. (Numeric only)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;5. Display Hash table.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;6. Exit.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; cmd;</div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>        <span class="keywordflow">switch</span> (cmd) {</div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>            <span class="keywordflow">case</span> 1:</div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to add = &quot;</span>;</div>
-<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
-<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>                <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a312143ed316d48978084c025ff8d9768">quadratic_probing::addInfo</a>(key);</div>
-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>            <span class="keywordflow">case</span> 2:</div>
-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to remove = &quot;</span>;</div>
-<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
-<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>                <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a69fe1f7c36fe004ba83eef2ca82e7e30">quadratic_probing::removalInfo</a>(key);</div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>            <span class="keywordflow">case</span> 3: {</div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to search = &quot;</span>;</div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>                <a class="code hl_struct" href="../../da/dd1/structquadratic__probing_1_1_entry.html">quadratic_probing::Entry</a> entry =</div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>                    quadratic_probing::table[<a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#ab431981b54c0bae1b2956f716aee1dcf">quadratic_probing::quadraticProbe</a>(</div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>                        key, <span class="keyword">true</span>)];</div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>                <span class="keywordflow">if</span> (entry.<a class="code hl_variable" href="../../da/dd1/structquadratic__probing_1_1_entry.html#a75f72858f08a2fc8b94402de98db12d8">key</a> == quadratic_probing::notPresent) {</div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Key not present&quot;</span>;</div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>                }</div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>            }</div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>            <span class="keywordflow">case</span> 4:</div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter element to generate hash = &quot;</span>;</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hash of &quot;</span> &lt;&lt; key</div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>                          &lt;&lt; <span class="stringliteral">&quot; is = &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a2093d91dd3d377cf0a5c939e45dcefc7">quadratic_probing::hashFxn</a>(key);</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>            <span class="keywordflow">case</span> 5:</div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>                <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a40d617ebf4d6ba21bcda8d8d1faa2357">quadratic_probing::display</a>();</div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>            <span class="keywordflow">default</span>:</div>
-<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>                loop = <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>                <span class="comment">// delete[] table;</span></div>
-<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>        }</div>
-<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>    }</div>
-<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  246</span>           {</div>
+<div class="line"><span class="lineno">  247</span>    <span class="keywordtype">int</span> cmd = 0, <a class="code hl_function" href="../../d5/d96/md5_8cpp.html#a88705fab5f92adf3427b4cf76ff33edb">hash</a> = 0, key = 0;</div>
+<div class="line"><span class="lineno">  248</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the initial size of Hash Table. = &quot;</span>;</div>
+<div class="line"><span class="lineno">  249</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; totalSize;</div>
+<div class="line"><span class="lineno">  250</span>    table = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Entry&gt;</a>(totalSize);</div>
+<div class="line"><span class="lineno">  251</span>    <span class="keywordtype">bool</span> loop = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  252</span>    <span class="keywordflow">while</span> (loop) {</div>
+<div class="line"><span class="lineno">  253</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  254</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;PLEASE CHOOSE -&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  255</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1. Add key. (Numeric only)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  256</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2. Remove key.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  257</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3. Find key.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  258</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4. Generate Hash. (Numeric only)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  259</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;5. Display Hash table.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  260</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;6. Exit.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  261</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; cmd;</div>
+<div class="line"><span class="lineno">  262</span>        <span class="keywordflow">switch</span> (cmd) {</div>
+<div class="line"><span class="lineno">  263</span>            <span class="keywordflow">case</span> 1:</div>
+<div class="line"><span class="lineno">  264</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to add = &quot;</span>;</div>
+<div class="line"><span class="lineno">  265</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
+<div class="line"><span class="lineno">  266</span>                <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a312143ed316d48978084c025ff8d9768">quadratic_probing::addInfo</a>(key);</div>
+<div class="line"><span class="lineno">  267</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  268</span>            <span class="keywordflow">case</span> 2:</div>
+<div class="line"><span class="lineno">  269</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to remove = &quot;</span>;</div>
+<div class="line"><span class="lineno">  270</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
+<div class="line"><span class="lineno">  271</span>                <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a69fe1f7c36fe004ba83eef2ca82e7e30">quadratic_probing::removalInfo</a>(key);</div>
+<div class="line"><span class="lineno">  272</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  273</span>            <span class="keywordflow">case</span> 3: {</div>
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+<div class="line"><span class="lineno">  295</span>                <span class="keywordflow">break</span>;</div>
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 <div class="ttc" id="aclasslarge__number_html_ac09a05ec4aafb4d9e0b4440d6f0e2a93"><div class="ttname"><a href="../../db/d82/classlarge__number.html#ac09a05ec4aafb4d9e0b4440d6f0e2a93">large_number::num_digits</a></div><div class="ttdeci">size_t num_digits() const</div><div class="ttdef"><b>Definition:</b> large_number.h:130</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d82/classlarge__number_ae35a55607cf52c0b0d485f2129bd39ac_cgraph.svg" width="394" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d82/classlarge__number_ae35a55607cf52c0b0d485f2129bd39ac_cgraph.svg" width="558" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
 </div>
 </div>
 
@@ -420,37 +439,37 @@ template&lt;class T &gt; </div>
 </table>
 </div><div class="memdoc">
 <p >multiply large number with another integer and store the result in the same large number </p>
-<div class="fragment"><div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>                             {</div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>        <span class="keyword">static_assert</span>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/is_integral.html">std::is_integral&lt;T&gt;::value</a>,</div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>                      <span class="stringliteral">&quot;Can only have integer types.&quot;</span>);</div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>        <span class="comment">// assert(!(std::is_signed&lt;T&gt;::value)); //, &quot;Implemented only for</span></div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>        <span class="comment">// unsigned integer types.&quot;);</span></div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span> </div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>        <span class="keywordtype">size_t</span> i;</div>
-<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>        uint64_t carry = 0, temp;</div>
-<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>        <span class="keywordflow">for</span> (i = 0; i &lt; this-&gt;<a class="code hl_function" href="../../db/d82/classlarge__number.html#ac09a05ec4aafb4d9e0b4440d6f0e2a93">num_digits</a>(); i++) {</div>
-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>            temp = <span class="keyword">static_cast&lt;</span>uint64_t<span class="keyword">&gt;</span>((*this)[i]) * n;</div>
-<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>            temp += carry;</div>
-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>            <span class="keywordflow">if</span> (temp &lt; 10) {</div>
-<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>                carry = 0;</div>
-<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>                carry = temp / 10;</div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>                temp = temp % 10;</div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>            }</div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>            (*this)[i] = temp;</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>        }</div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span> </div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>        <span class="keywordflow">while</span> (carry != 0) {</div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>            this-&gt;<a class="code hl_function" href="../../db/d82/classlarge__number.html#a60c436d1a1c5e3795d6177d3815ad615">add_digit</a>(carry % 10);</div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>            carry /= 10;</div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>        }</div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  258</span>                             {</div>
+<div class="line"><span class="lineno">  259</span>        <span class="keyword">static_assert</span>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/is_integral.html">std::is_integral&lt;T&gt;::value</a>,</div>
+<div class="line"><span class="lineno">  260</span>                      <span class="stringliteral">&quot;Can only have integer types.&quot;</span>);</div>
+<div class="line"><span class="lineno">  261</span>        <span class="comment">// assert(!(std::is_signed&lt;T&gt;::value)); //, &quot;Implemented only for</span></div>
+<div class="line"><span class="lineno">  262</span>        <span class="comment">// unsigned integer types.&quot;);</span></div>
+<div class="line"><span class="lineno">  263</span> </div>
+<div class="line"><span class="lineno">  264</span>        <span class="keywordtype">size_t</span> i;</div>
+<div class="line"><span class="lineno">  265</span>        uint64_t carry = 0, temp;</div>
+<div class="line"><span class="lineno">  266</span>        <span class="keywordflow">for</span> (i = 0; i &lt; this-&gt;<a class="code hl_function" href="../../db/d82/classlarge__number.html#ac09a05ec4aafb4d9e0b4440d6f0e2a93">num_digits</a>(); i++) {</div>
+<div class="line"><span class="lineno">  267</span>            temp = <span class="keyword">static_cast&lt;</span>uint64_t<span class="keyword">&gt;</span>((*this)[i]) * n;</div>
+<div class="line"><span class="lineno">  268</span>            temp += carry;</div>
+<div class="line"><span class="lineno">  269</span>            <span class="keywordflow">if</span> (temp &lt; 10) {</div>
+<div class="line"><span class="lineno">  270</span>                carry = 0;</div>
+<div class="line"><span class="lineno">  271</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  272</span>                carry = temp / 10;</div>
+<div class="line"><span class="lineno">  273</span>                temp = temp % 10;</div>
+<div class="line"><span class="lineno">  274</span>            }</div>
+<div class="line"><span class="lineno">  275</span>            (*this)[i] = temp;</div>
+<div class="line"><span class="lineno">  276</span>        }</div>
+<div class="line"><span class="lineno">  277</span> </div>
+<div class="line"><span class="lineno">  278</span>        <span class="keywordflow">while</span> (carry != 0) {</div>
+<div class="line"><span class="lineno">  279</span>            this-&gt;<a class="code hl_function" href="../../db/d82/classlarge__number.html#a60c436d1a1c5e3795d6177d3815ad615">add_digit</a>(carry % 10);</div>
+<div class="line"><span class="lineno">  280</span>            carry /= 10;</div>
+<div class="line"><span class="lineno">  281</span>        }</div>
+<div class="line"><span class="lineno">  282</span>    }</div>
 <div class="ttc" id="aclasslarge__number_html_a60c436d1a1c5e3795d6177d3815ad615"><div class="ttname"><a href="../../db/d82/classlarge__number.html#a60c436d1a1c5e3795d6177d3815ad615">large_number::add_digit</a></div><div class="ttdeci">void add_digit(unsigned int value)</div><div class="ttdef"><b>Definition:</b> large_number.h:118</div></div>
 <div class="ttc" id="ais_integral_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/is_integral.html">std::is_integral</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d82/classlarge__number_a2f5571e66305cf68bb8283e4aeda58bc_cgraph.svg" width="383" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d82/classlarge__number_a2f5571e66305cf68bb8283e4aeda58bc_cgraph.svg" width="586" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
 </div>
 </div>
 
@@ -479,8 +498,15 @@ Here is the call graph for this function:</div>
 </table>
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 <p >Get number of digits in the number </p>
-<div class="fragment"><div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>.size(); }</div>
-</div><!-- fragment -->
+<div class="fragment"><div class="line"><span class="lineno">  130</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); }</div>
+<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d82/classlarge__number_ac09a05ec4aafb4d9e0b4440d6f0e2a93_cgraph.svg" width="346" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
 </div>
 </div>
 <a id="a771e9b28cfddf1ad94668566e396e350" name="a771e9b28cfddf1ad94668566e396e350"></a>
@@ -509,17 +535,17 @@ template&lt;class T &gt; </div>
 </table>
 </div><div class="memdoc">
 <p >operator overload to increment </p>
-<div class="fragment"><div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>                                        {</div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>        <span class="keyword">static_assert</span>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/is_integral.html">std::is_integral&lt;T&gt;::value</a>,</div>
-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>                      <span class="stringliteral">&quot;Must be integer addition unsigned integer types.&quot;</span>);</div>
-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>        this-&gt;<a class="code hl_function" href="../../db/d82/classlarge__number.html#a2f5571e66305cf68bb8283e4aeda58bc">multiply</a>(n);</div>
-<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  238</span>                                        {</div>
+<div class="line"><span class="lineno">  239</span>        <span class="keyword">static_assert</span>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/is_integral.html">std::is_integral&lt;T&gt;::value</a>,</div>
+<div class="line"><span class="lineno">  240</span>                      <span class="stringliteral">&quot;Must be integer addition unsigned integer types.&quot;</span>);</div>
+<div class="line"><span class="lineno">  241</span>        this-&gt;<a class="code hl_function" href="../../db/d82/classlarge__number.html#a2f5571e66305cf68bb8283e4aeda58bc">multiply</a>(n);</div>
+<div class="line"><span class="lineno">  242</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  243</span>    }</div>
 <div class="ttc" id="aclasslarge__number_html_a2f5571e66305cf68bb8283e4aeda58bc"><div class="ttname"><a href="../../db/d82/classlarge__number.html#a2f5571e66305cf68bb8283e4aeda58bc">large_number::multiply</a></div><div class="ttdeci">void multiply(const T n)</div><div class="ttdef"><b>Definition:</b> large_number.h:258</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d82/classlarge__number_a771e9b28cfddf1ad94668566e396e350_cgraph.svg" width="599" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../db/d82/classlarge__number_a771e9b28cfddf1ad94668566e396e350_cgraph.svg" width="100%" height="366"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
 </div>
 </div>
 
@@ -548,10 +574,10 @@ Here is the call graph for this function:</div>
 </table>
 </div><div class="memdoc">
 <p >operator overload to increment (prefix) </p>
-<div class="fragment"><div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>                               {</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>        (*this) += 1;</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  175</span>                               {</div>
+<div class="line"><span class="lineno">  176</span>        (*this) += 1;</div>
+<div class="line"><span class="lineno">  177</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  178</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -579,11 +605,11 @@ Here is the call graph for this function:</div>
 </table>
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 <p >operator overload to increment (postfix) </p>
-<div class="fragment"><div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>                                  {</div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>        <span class="keyword">static</span> <a class="code hl_class" href="../../db/d82/classlarge__number.html">large_number</a> tmp(<a class="code hl_variable" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>);</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>        ++(*this);</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>        <span class="keywordflow">return</span> tmp;</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  183</span>                                  {</div>
+<div class="line"><span class="lineno">  184</span>        <span class="keyword">static</span> <a class="code hl_class" href="../../db/d82/classlarge__number.html">large_number</a> tmp(<a class="code hl_variable" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>);</div>
+<div class="line"><span class="lineno">  185</span>        ++(*this);</div>
+<div class="line"><span class="lineno">  186</span>        <span class="keywordflow">return</span> tmp;</div>
+<div class="line"><span class="lineno">  187</span>    }</div>
 <div class="ttc" id="aclasslarge__number_html"><div class="ttname"><a href="../../db/d82/classlarge__number.html">large_number</a></div><div class="ttdef"><b>Definition:</b> large_number.h:24</div></div>
 </div><!-- fragment -->
 </div>
@@ -611,7 +637,7 @@ Here is the call graph for this function:</div>
   </tr>
 </table>
 </div><div class="memdoc">
-<div class="fragment"><div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>{ <span class="keywordflow">return</span> (*<span class="keyword">this</span>) += <a class="code hl_function" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(n); }</div>
+<div class="fragment"><div class="line"><span class="lineno">  212</span>{ <span class="keywordflow">return</span> (*<span class="keyword">this</span>) += <a class="code hl_function" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(n); }</div>
 <div class="ttc" id="aclasslarge__number_html_a10119a83839e65962621b73df46a5337"><div class="ttname"><a href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number::large_number</a></div><div class="ttdeci">large_number()</div><div class="ttdef"><b>Definition:</b> large_number.h:27</div></div>
 </div><!-- fragment -->
 </div>
@@ -640,30 +666,30 @@ Here is the call graph for this function:</div>
 </table>
 </div><div class="memdoc">
 <p >operator overload to add </p>
-<div class="fragment"><div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>                                             {</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>        <span class="comment">// if adding with another large_number</span></div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>        <a class="code hl_class" href="../../db/d82/classlarge__number.html">large_number</a> *b = <span class="keyword">reinterpret_cast&lt;</span><a class="code hl_class" href="../../db/d82/classlarge__number.html">large_number</a> *<span class="keyword">&gt;</span>(&amp;n);</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>        <span class="keyword">const</span> <span class="keywordtype">size_t</span> max_L = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(this-&gt;<a class="code hl_function" href="../../db/d82/classlarge__number.html#ac09a05ec4aafb4d9e0b4440d6f0e2a93">num_digits</a>(), b-&gt;<a class="code hl_function" href="../../db/d82/classlarge__number.html#ac09a05ec4aafb4d9e0b4440d6f0e2a93">num_digits</a>());</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>        <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> carry = 0;</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>        <span class="keywordtype">size_t</span> i;</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>        <span class="keywordflow">for</span> (i = 0; i &lt; max_L || carry != 0; i++) {</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>            <span class="keywordflow">if</span> (i &lt; b-&gt;<a class="code hl_function" href="../../db/d82/classlarge__number.html#ac09a05ec4aafb4d9e0b4440d6f0e2a93">num_digits</a>())</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>                carry += (*b)[i];</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>            <span class="keywordflow">if</span> (i &lt; this-&gt;<a class="code hl_function" href="../../db/d82/classlarge__number.html#ac09a05ec4aafb4d9e0b4440d6f0e2a93">num_digits</a>())</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>                carry += (*this)[i];</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>            <span class="keywordflow">if</span> (i &lt; this-&gt;<a class="code hl_function" href="../../db/d82/classlarge__number.html#ac09a05ec4aafb4d9e0b4440d6f0e2a93">num_digits</a>())</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>                (*this)[i] = carry % 10;</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>            <span class="keywordflow">else</span></div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>                this-&gt;<a class="code hl_function" href="../../db/d82/classlarge__number.html#a60c436d1a1c5e3795d6177d3815ad615">add_digit</a>(carry % 10);</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>            carry /= 10;</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>        }</div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  192</span>                                             {</div>
+<div class="line"><span class="lineno">  193</span>        <span class="comment">// if adding with another large_number</span></div>
+<div class="line"><span class="lineno">  194</span>        <a class="code hl_class" href="../../db/d82/classlarge__number.html">large_number</a> *b = <span class="keyword">reinterpret_cast&lt;</span><a class="code hl_class" href="../../db/d82/classlarge__number.html">large_number</a> *<span class="keyword">&gt;</span>(&amp;n);</div>
+<div class="line"><span class="lineno">  195</span>        <span class="keyword">const</span> <span class="keywordtype">size_t</span> max_L = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(this-&gt;<a class="code hl_function" href="../../db/d82/classlarge__number.html#ac09a05ec4aafb4d9e0b4440d6f0e2a93">num_digits</a>(), b-&gt;<a class="code hl_function" href="../../db/d82/classlarge__number.html#ac09a05ec4aafb4d9e0b4440d6f0e2a93">num_digits</a>());</div>
+<div class="line"><span class="lineno">  196</span>        <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> carry = 0;</div>
+<div class="line"><span class="lineno">  197</span>        <span class="keywordtype">size_t</span> i;</div>
+<div class="line"><span class="lineno">  198</span>        <span class="keywordflow">for</span> (i = 0; i &lt; max_L || carry != 0; i++) {</div>
+<div class="line"><span class="lineno">  199</span>            <span class="keywordflow">if</span> (i &lt; b-&gt;<a class="code hl_function" href="../../db/d82/classlarge__number.html#ac09a05ec4aafb4d9e0b4440d6f0e2a93">num_digits</a>())</div>
+<div class="line"><span class="lineno">  200</span>                carry += (*b)[i];</div>
+<div class="line"><span class="lineno">  201</span>            <span class="keywordflow">if</span> (i &lt; this-&gt;<a class="code hl_function" href="../../db/d82/classlarge__number.html#ac09a05ec4aafb4d9e0b4440d6f0e2a93">num_digits</a>())</div>
+<div class="line"><span class="lineno">  202</span>                carry += (*this)[i];</div>
+<div class="line"><span class="lineno">  203</span>            <span class="keywordflow">if</span> (i &lt; this-&gt;<a class="code hl_function" href="../../db/d82/classlarge__number.html#ac09a05ec4aafb4d9e0b4440d6f0e2a93">num_digits</a>())</div>
+<div class="line"><span class="lineno">  204</span>                (*this)[i] = carry % 10;</div>
+<div class="line"><span class="lineno">  205</span>            <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">  206</span>                this-&gt;<a class="code hl_function" href="../../db/d82/classlarge__number.html#a60c436d1a1c5e3795d6177d3815ad615">add_digit</a>(carry % 10);</div>
+<div class="line"><span class="lineno">  207</span>            carry /= 10;</div>
+<div class="line"><span class="lineno">  208</span>        }</div>
+<div class="line"><span class="lineno">  209</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  210</span>    }</div>
 <div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d82/classlarge__number_aab5644405094740e34983cedfecb36cf_cgraph.svg" width="400" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d82/classlarge__number_aab5644405094740e34983cedfecb36cf_cgraph.svg" width="603" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
 </div>
 </div>
 
@@ -693,10 +719,10 @@ Here is the call graph for this function:</div>
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 <p >assignment operator </p>
-<div class="fragment"><div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>                                                   {</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>        this-&gt;<a class="code hl_variable" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a> = b.<a class="code hl_variable" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>;</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  229</span>                                                   {</div>
+<div class="line"><span class="lineno">  230</span>        this-&gt;<a class="code hl_variable" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a> = b.<a class="code hl_variable" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>;</div>
+<div class="line"><span class="lineno">  231</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  232</span>    }</div>
 </div><!-- fragment -->
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 </div>
@@ -724,7 +750,7 @@ Here is the call graph for this function:</div>
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 <p >operator over load to access the i^th digit conveniently and also assign value to it </p>
-<div class="fragment"><div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>{ <span class="keywordflow">return</span> this-&gt;<a class="code hl_variable" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>[n]; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  137</span>{ <span class="keywordflow">return</span> this-&gt;<a class="code hl_variable" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>[n]; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -751,9 +777,9 @@ Here is the call graph for this function:</div>
   </tr>
 </table>
 </div><div class="memdoc">
-<div class="fragment"><div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>                                                           {</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>        <span class="keywordflow">return</span> this-&gt;<a class="code hl_variable" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>[n];</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  139</span>                                                           {</div>
+<div class="line"><span class="lineno">  140</span>        <span class="keywordflow">return</span> this-&gt;<a class="code hl_variable" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>[n];</div>
+<div class="line"><span class="lineno">  141</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -780,60 +806,60 @@ Here is the call graph for this function:</div>
 </table>
 </div><div class="memdoc">
 <p >Function to check implementation </p>
-<div class="fragment"><div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>                       {</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------ Checking `large_number` class implementations\t&quot;</span></div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>                  &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        <a class="code hl_class" href="../../db/d82/classlarge__number.html">large_number</a> a(40);</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        <span class="comment">// 1. test multiplication</span></div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        a *= 10;</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        <span class="keywordflow">if</span> (a != <a class="code hl_function" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(400)) {</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;\tFailed 1/6 (&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;!=400)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>        }</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPassed 1/6...&quot;</span>;</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        <span class="comment">// 2. test compound addition with integer</span></div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>        a += 120;</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        <span class="keywordflow">if</span> (a != <a class="code hl_function" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(520)) {</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;\tFailed 2/6 (&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;!=520)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>        }</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPassed 2/6...&quot;</span>;</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>        <span class="comment">// 3. test compound multiplication again</span></div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>        a *= 10;</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>        <span class="keywordflow">if</span> (a != <a class="code hl_function" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(5200)) {</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;\tFailed 3/6 (&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;!=5200)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        }</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPassed 3/6...&quot;</span>;</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>        <span class="comment">// 4. test increment (prefix)</span></div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>        ++a;</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>        <span class="keywordflow">if</span> (a != <a class="code hl_function" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(5201)) {</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;\tFailed 4/6 (&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;!=5201)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>        }</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPassed 4/6...&quot;</span>;</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>        <span class="comment">// 5. test increment (postfix)</span></div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>        a++;</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>        <span class="keywordflow">if</span> (a != <a class="code hl_function" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(5202)) {</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;\tFailed 5/6 (&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;!=5202)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>        }</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPassed 5/6...&quot;</span>;</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>        <span class="comment">// 6. test addition with another large number</span></div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>        a = a + <a class="code hl_function" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(<span class="stringliteral">&quot;7000000000000000000000000000000&quot;</span>);</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>        <span class="keywordflow">if</span> (a != <a class="code hl_function" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(<span class="stringliteral">&quot;7000000000000000000000000005202&quot;</span>)) {</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;\tFailed 6/6 (&quot;</span> &lt;&lt; a</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>                      &lt;&lt; <span class="stringliteral">&quot;!=7000000000000000000000000005202)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        }</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPassed 6/6...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   65</span>                       {</div>
+<div class="line"><span class="lineno">   66</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------ Checking `large_number` class implementations\t&quot;</span></div>
+<div class="line"><span class="lineno">   67</span>                  &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   68</span>        <a class="code hl_class" href="../../db/d82/classlarge__number.html">large_number</a> a(40);</div>
+<div class="line"><span class="lineno">   69</span>        <span class="comment">// 1. test multiplication</span></div>
+<div class="line"><span class="lineno">   70</span>        a *= 10;</div>
+<div class="line"><span class="lineno">   71</span>        <span class="keywordflow">if</span> (a != <a class="code hl_function" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(400)) {</div>
+<div class="line"><span class="lineno">   72</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;\tFailed 1/6 (&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;!=400)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   73</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   74</span>        }</div>
+<div class="line"><span class="lineno">   75</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPassed 1/6...&quot;</span>;</div>
+<div class="line"><span class="lineno">   76</span>        <span class="comment">// 2. test compound addition with integer</span></div>
+<div class="line"><span class="lineno">   77</span>        a += 120;</div>
+<div class="line"><span class="lineno">   78</span>        <span class="keywordflow">if</span> (a != <a class="code hl_function" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(520)) {</div>
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+<div class="line"><span class="lineno">   47</span>    <span class="comment">// perform self-test</span></div>
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-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   69</span>                                                         {</div>
+<div class="line"><span class="lineno">   70</span>        this-&gt;f = this-&gt;s = 0;</div>
+<div class="line"><span class="lineno">   71</span>        <span class="keywordflow">if</span> (str.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() &gt; 1 &amp;&amp; str[1] == <span class="charliteral">&#39;x&#39;</span>) {  <span class="comment">// if hexadecimal</span></div>
+<div class="line"><span class="lineno">   72</span>            <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 2; i &lt; str.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>(); ++i) {</div>
+<div class="line"><span class="lineno">   73</span>                *<span class="keyword">this</span> *= 16LL;</div>
+<div class="line"><span class="lineno">   74</span>                <span class="keywordflow">if</span> (str[i] &gt;= <span class="charliteral">&#39;0&#39;</span> &amp;&amp; str[i] &lt;= <span class="charliteral">&#39;9&#39;</span>) {</div>
+<div class="line"><span class="lineno">   75</span>                    *<span class="keyword">this</span> += (str[i] - <span class="charliteral">&#39;0&#39;</span>);</div>
+<div class="line"><span class="lineno">   76</span>                } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (str[i] &gt;= <span class="charliteral">&#39;A&#39;</span> &amp;&amp; str[i] &lt;= <span class="charliteral">&#39;F&#39;</span>) {</div>
+<div class="line"><span class="lineno">   77</span>                    *<span class="keyword">this</span> += (str[i] - <span class="charliteral">&#39;A&#39;</span> + 10);</div>
+<div class="line"><span class="lineno">   78</span>                } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (str[i] &gt;= <span class="charliteral">&#39;a&#39;</span> &amp;&amp; str[i] &lt;= <span class="charliteral">&#39;f&#39;</span>) {</div>
+<div class="line"><span class="lineno">   79</span>                    *<span class="keyword">this</span> += (str[i] - <span class="charliteral">&#39;a&#39;</span> + 10);</div>
+<div class="line"><span class="lineno">   80</span>                }</div>
+<div class="line"><span class="lineno">   81</span>            }</div>
+<div class="line"><span class="lineno">   82</span>        } <span class="keywordflow">else</span> {  <span class="comment">// if decimal</span></div>
+<div class="line"><span class="lineno">   83</span>            <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;x : str) {</div>
+<div class="line"><span class="lineno">   84</span>                *<span class="keyword">this</span> *= 10LL;</div>
+<div class="line"><span class="lineno">   85</span>                *<span class="keyword">this</span> += (x - <span class="charliteral">&#39;0&#39;</span>);</div>
+<div class="line"><span class="lineno">   86</span>            }</div>
+<div class="line"><span class="lineno">   87</span>        }</div>
+<div class="line"><span class="lineno">   88</span>    }</div>
 <div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">std::string::size</a></div><div class="ttdeci">T size(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -687,23 +687,23 @@ Here is the call graph for this function:</div>
 
 <p>Leading zeroes in binary. </p>
 <p >Calculates leading zeros in 128-bit integer </p><dl class="section return"><dt>Returns</dt><dd>Integer denoting leading zeroes </dd></dl>
-<div class="fragment"><div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>                           {</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span><span class="preprocessor">#ifndef _MSC_VER</span></div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>        <span class="keywordflow">if</span> (f) {</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>            <span class="keywordflow">return</span> __builtin_clzll(f);</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>        }</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>        <span class="keywordflow">return</span> 64 + __builtin_clzll(s);</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span><span class="preprocessor">#else</span></div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>        <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> r = 0;</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>        _BitScanForward64(&amp;r, f);</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>        <span class="keywordflow">if</span> (r == 64) {</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>            <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> = 0;</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>            _BitScanForward64(&amp;l, s);</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>            <span class="keywordflow">return</span> 64 + <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a>;</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>        }</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>        <span class="keywordflow">return</span> r;</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  139</span>                           {</div>
+<div class="line"><span class="lineno">  140</span><span class="preprocessor">#ifndef _MSC_VER</span></div>
+<div class="line"><span class="lineno">  141</span>        <span class="keywordflow">if</span> (f) {</div>
+<div class="line"><span class="lineno">  142</span>            <span class="keywordflow">return</span> __builtin_clzll(f);</div>
+<div class="line"><span class="lineno">  143</span>        }</div>
+<div class="line"><span class="lineno">  144</span>        <span class="keywordflow">return</span> 64 + __builtin_clzll(s);</div>
+<div class="line"><span class="lineno">  145</span><span class="preprocessor">#else</span></div>
+<div class="line"><span class="lineno">  146</span>        <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> r = 0;</div>
+<div class="line"><span class="lineno">  147</span>        _BitScanForward64(&amp;r, f);</div>
+<div class="line"><span class="lineno">  148</span>        <span class="keywordflow">if</span> (r == 64) {</div>
+<div class="line"><span class="lineno">  149</span>            <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> = 0;</div>
+<div class="line"><span class="lineno">  150</span>            _BitScanForward64(&amp;l, s);</div>
+<div class="line"><span class="lineno">  151</span>            <span class="keywordflow">return</span> 64 + <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a>;</div>
+<div class="line"><span class="lineno">  152</span>        }</div>
+<div class="line"><span class="lineno">  153</span>        <span class="keywordflow">return</span> r;</div>
+<div class="line"><span class="lineno">  154</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  155</span>    }</div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a6d8df83a6f26ce24a75d3b358b7f5b8a"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">numerical_methods::simpson_method::l</a></div><div class="ttdeci">double l(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:119</div></div>
 </div><!-- fragment -->
 </div>
@@ -733,23 +733,23 @@ Here is the call graph for this function:</div>
 
 <p>Trailing zeroes in binary. </p>
 <p >Calculates leading zeros in 128-bit integer </p><dl class="section return"><dt>Returns</dt><dd>Integer denoting Trailing zeroes </dd></dl>
-<div class="fragment"><div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>                           {</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span><span class="preprocessor">#ifndef _MSC_VER</span></div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>        <span class="keywordflow">if</span> (f) {</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>            <span class="keywordflow">return</span> __builtin_ctzll(f);</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>        }</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>        <span class="keywordflow">return</span> 64 + __builtin_ctzll(s);</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span><span class="preprocessor">#else</span></div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>        <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> r = 0;</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>        _BitScanReverse64(&amp;r, s);</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>        <span class="keywordflow">if</span> (r == 64) {</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>            <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> = 0;</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>            _BitScanReverse64(&amp;l, f);</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>            <span class="keywordflow">return</span> 64 + <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a>;</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>        }</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>        <span class="keywordflow">return</span> r;</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  162</span>                           {</div>
+<div class="line"><span class="lineno">  163</span><span class="preprocessor">#ifndef _MSC_VER</span></div>
+<div class="line"><span class="lineno">  164</span>        <span class="keywordflow">if</span> (f) {</div>
+<div class="line"><span class="lineno">  165</span>            <span class="keywordflow">return</span> __builtin_ctzll(f);</div>
+<div class="line"><span class="lineno">  166</span>        }</div>
+<div class="line"><span class="lineno">  167</span>        <span class="keywordflow">return</span> 64 + __builtin_ctzll(s);</div>
+<div class="line"><span class="lineno">  168</span><span class="preprocessor">#else</span></div>
+<div class="line"><span class="lineno">  169</span>        <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> r = 0;</div>
+<div class="line"><span class="lineno">  170</span>        _BitScanReverse64(&amp;r, s);</div>
+<div class="line"><span class="lineno">  171</span>        <span class="keywordflow">if</span> (r == 64) {</div>
+<div class="line"><span class="lineno">  172</span>            <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> = 0;</div>
+<div class="line"><span class="lineno">  173</span>            _BitScanReverse64(&amp;l, f);</div>
+<div class="line"><span class="lineno">  174</span>            <span class="keywordflow">return</span> 64 + <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a>;</div>
+<div class="line"><span class="lineno">  175</span>        }</div>
+<div class="line"><span class="lineno">  176</span>        <span class="keywordflow">return</span> r;</div>
+<div class="line"><span class="lineno">  177</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">  178</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -785,34 +785,34 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>pair denoting quotient and remainder. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00454" name="l00454"></a><span class="lineno">  454</span>                                                             {</div>
-<div class="line"><a id="l00455" name="l00455"></a><span class="lineno">  455</span>        <span class="keywordflow">if</span> (*<span class="keyword">this</span> &lt; p) {  <span class="comment">// if this is less than divisor</span></div>
-<div class="line"><a id="l00456" name="l00456"></a><span class="lineno">  456</span>            <span class="keywordflow">return</span> {<a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0), *<span class="keyword">this</span>};</div>
-<div class="line"><a id="l00457" name="l00457"></a><span class="lineno">  457</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (*<span class="keyword">this</span> == p) {  <span class="comment">// if this is equal to divisor</span></div>
-<div class="line"><a id="l00458" name="l00458"></a><span class="lineno">  458</span>            <span class="keywordflow">return</span> {<a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(1), <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0)};</div>
-<div class="line"><a id="l00459" name="l00459"></a><span class="lineno">  459</span>        }</div>
-<div class="line"><a id="l00460" name="l00460"></a><span class="lineno">  460</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> tmp = p, tmp2 = *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00461" name="l00461"></a><span class="lineno">  461</span>        uint16_t <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> = tmp.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#af139bb6e630f1a61919f180978611cd2">_lez</a>() - <a class="code hl_function" href="../../db/d9a/classuint128__t.html#af139bb6e630f1a61919f180978611cd2">_lez</a>();</div>
-<div class="line"><a id="l00462" name="l00462"></a><span class="lineno">  462</span>        tmp &lt;&lt;= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>;</div>
-<div class="line"><a id="l00463" name="l00463"></a><span class="lineno">  463</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> quotient(0);</div>
-<div class="line"><a id="l00464" name="l00464"></a><span class="lineno">  464</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> zero(0);</div>
-<div class="line"><a id="l00465" name="l00465"></a><span class="lineno">  465</span>        <span class="keywordflow">while</span> (tmp2 &gt;= p) {</div>
-<div class="line"><a id="l00466" name="l00466"></a><span class="lineno">  466</span>            uint16_t shf = tmp2._lez() - tmp.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#af139bb6e630f1a61919f180978611cd2">_lez</a>();</div>
-<div class="line"><a id="l00467" name="l00467"></a><span class="lineno">  467</span>            <span class="keywordflow">if</span> (shf) {</div>
-<div class="line"><a id="l00468" name="l00468"></a><span class="lineno">  468</span>                tmp &gt;&gt;= shf;</div>
-<div class="line"><a id="l00469" name="l00469"></a><span class="lineno">  469</span>                quotient &lt;&lt;= shf;</div>
-<div class="line"><a id="l00470" name="l00470"></a><span class="lineno">  470</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> -= shf;</div>
-<div class="line"><a id="l00471" name="l00471"></a><span class="lineno">  471</span>            }</div>
-<div class="line"><a id="l00472" name="l00472"></a><span class="lineno">  472</span>            <span class="keywordflow">if</span> (tmp2 &lt; tmp) {</div>
-<div class="line"><a id="l00473" name="l00473"></a><span class="lineno">  473</span>                tmp &gt;&gt;= 1;</div>
-<div class="line"><a id="l00474" name="l00474"></a><span class="lineno">  474</span>                quotient &lt;&lt;= 1;</div>
-<div class="line"><a id="l00475" name="l00475"></a><span class="lineno">  475</span>                --<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>;</div>
-<div class="line"><a id="l00476" name="l00476"></a><span class="lineno">  476</span>            }</div>
-<div class="line"><a id="l00477" name="l00477"></a><span class="lineno">  477</span>            tmp2 -= tmp;</div>
-<div class="line"><a id="l00478" name="l00478"></a><span class="lineno">  478</span>            ++quotient;</div>
-<div class="line"><a id="l00479" name="l00479"></a><span class="lineno">  479</span>        }</div>
-<div class="line"><a id="l00480" name="l00480"></a><span class="lineno">  480</span>        <span class="keywordflow">return</span> {quotient &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>, tmp2};</div>
-<div class="line"><a id="l00481" name="l00481"></a><span class="lineno">  481</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  454</span>                                                             {</div>
+<div class="line"><span class="lineno">  455</span>        <span class="keywordflow">if</span> (*<span class="keyword">this</span> &lt; p) {  <span class="comment">// if this is less than divisor</span></div>
+<div class="line"><span class="lineno">  456</span>            <span class="keywordflow">return</span> {<a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0), *<span class="keyword">this</span>};</div>
+<div class="line"><span class="lineno">  457</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (*<span class="keyword">this</span> == p) {  <span class="comment">// if this is equal to divisor</span></div>
+<div class="line"><span class="lineno">  458</span>            <span class="keywordflow">return</span> {<a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(1), <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0)};</div>
+<div class="line"><span class="lineno">  459</span>        }</div>
+<div class="line"><span class="lineno">  460</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> tmp = p, tmp2 = *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  461</span>        uint16_t <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> = tmp.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#af139bb6e630f1a61919f180978611cd2">_lez</a>() - <a class="code hl_function" href="../../db/d9a/classuint128__t.html#af139bb6e630f1a61919f180978611cd2">_lez</a>();</div>
+<div class="line"><span class="lineno">  462</span>        tmp &lt;&lt;= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>;</div>
+<div class="line"><span class="lineno">  463</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> quotient(0);</div>
+<div class="line"><span class="lineno">  464</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> zero(0);</div>
+<div class="line"><span class="lineno">  465</span>        <span class="keywordflow">while</span> (tmp2 &gt;= p) {</div>
+<div class="line"><span class="lineno">  466</span>            uint16_t shf = tmp2._lez() - tmp.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#af139bb6e630f1a61919f180978611cd2">_lez</a>();</div>
+<div class="line"><span class="lineno">  467</span>            <span class="keywordflow">if</span> (shf) {</div>
+<div class="line"><span class="lineno">  468</span>                tmp &gt;&gt;= shf;</div>
+<div class="line"><span class="lineno">  469</span>                quotient &lt;&lt;= shf;</div>
+<div class="line"><span class="lineno">  470</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> -= shf;</div>
+<div class="line"><span class="lineno">  471</span>            }</div>
+<div class="line"><span class="lineno">  472</span>            <span class="keywordflow">if</span> (tmp2 &lt; tmp) {</div>
+<div class="line"><span class="lineno">  473</span>                tmp &gt;&gt;= 1;</div>
+<div class="line"><span class="lineno">  474</span>                quotient &lt;&lt;= 1;</div>
+<div class="line"><span class="lineno">  475</span>                --<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>;</div>
+<div class="line"><span class="lineno">  476</span>            }</div>
+<div class="line"><span class="lineno">  477</span>            tmp2 -= tmp;</div>
+<div class="line"><span class="lineno">  478</span>            ++quotient;</div>
+<div class="line"><span class="lineno">  479</span>        }</div>
+<div class="line"><span class="lineno">  480</span>        <span class="keywordflow">return</span> {quotient &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>, tmp2};</div>
+<div class="line"><span class="lineno">  481</span>    }</div>
 <div class="ttc" id="aclassuint128__t_html"><div class="ttname"><a href="../../db/d9a/classuint128__t.html">uint128_t</a></div><div class="ttdoc">class for 128-bit unsigned integer</div><div class="ttdef"><b>Definition:</b> uint128_t.hpp:59</div></div>
 <div class="ttc" id="aclassuint128__t_html_af139bb6e630f1a61919f180978611cd2"><div class="ttname"><a href="../../db/d9a/classuint128__t.html#af139bb6e630f1a61919f180978611cd2">uint128_t::_lez</a></div><div class="ttdeci">uint32_t _lez()</div><div class="ttdoc">Leading zeroes in binary.</div><div class="ttdef"><b>Definition:</b> uint128_t.hpp:139</div></div>
 <div class="ttc" id="aleft_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::left</a></div><div class="ttdeci">T left(T... args)</div></div>
@@ -850,7 +850,7 @@ Here is the call graph for this function:</div>
 
 <p>returns lower 64-bit integer part </p>
 <dl class="section return"><dt>Returns</dt><dd>returns lower 64-bit integer part </dd></dl>
-<div class="fragment"><div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>{ <span class="keywordflow">return</span> s; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  201</span>{ <span class="keywordflow">return</span> s; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -879,7 +879,7 @@ Here is the call graph for this function:</div>
 
 <p>casting operator to boolean value </p>
 <dl class="section return"><dt>Returns</dt><dd>true if value of this is non-zero, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>{ <span class="keywordflow">return</span> (f || s); }</div>
+<div class="fragment"><div class="line"><span class="lineno">  184</span>{ <span class="keywordflow">return</span> (f || s); }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -916,9 +916,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>integer value casted to mentioned type </dd></dl>
-<div class="fragment"><div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>                                       {</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>        <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(s);</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  193</span>                                       {</div>
+<div class="line"><span class="lineno">  194</span>        <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(s);</div>
+<div class="line"><span class="lineno">  195</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -947,7 +947,7 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
 
 <p>operator ! for <a class="el" href="../../db/d9a/classuint128__t.html" title="class for 128-bit unsigned integer">uint128_t</a> </p>
 <dl class="section return"><dt>Returns</dt><dd>true if this has zero value, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00627" name="l00627"></a><span class="lineno">  627</span>{ <span class="keywordflow">return</span> !f &amp;&amp; !s; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  627</span>{ <span class="keywordflow">return</span> !f &amp;&amp; !s; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -991,9 +991,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is not equal to other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00721" name="l00721"></a><span class="lineno">  721</span>                                          {</div>
-<div class="line"><a id="l00722" name="l00722"></a><span class="lineno">  722</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> != <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(other);</div>
-<div class="line"><a id="l00723" name="l00723"></a><span class="lineno">  723</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  721</span>                                          {</div>
+<div class="line"><span class="lineno">  722</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> != <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(other);</div>
+<div class="line"><span class="lineno">  723</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1029,9 +1029,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is not equal than other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00619" name="l00619"></a><span class="lineno">  619</span>                                                   {</div>
-<div class="line"><a id="l00620" name="l00620"></a><span class="lineno">  620</span>        <span class="keywordflow">return</span> f != other.f || s != other.s;</div>
-<div class="line"><a id="l00621" name="l00621"></a><span class="lineno">  621</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  619</span>                                                   {</div>
+<div class="line"><span class="lineno">  620</span>        <span class="keywordflow">return</span> f != other.f || s != other.s;</div>
+<div class="line"><span class="lineno">  621</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1075,9 +1075,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>unsigned 128-bit remainder. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00542" name="l00542"></a><span class="lineno">  542</span>                                           {</div>
-<div class="line"><a id="l00543" name="l00543"></a><span class="lineno">  543</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> % <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(p);</div>
-<div class="line"><a id="l00544" name="l00544"></a><span class="lineno">  544</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  542</span>                                           {</div>
+<div class="line"><span class="lineno">  543</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> % <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(p);</div>
+<div class="line"><span class="lineno">  544</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1113,7 +1113,7 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>unsigned 128-bit remainder. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00532" name="l00532"></a><span class="lineno">  532</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../db/d9a/classuint128__t.html#a8bf81f7f5f5c98f197822ec88e106c6c">divide</a>(p).second; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  532</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../db/d9a/classuint128__t.html#a8bf81f7f5f5c98f197822ec88e106c6c">divide</a>(p).second; }</div>
 <div class="ttc" id="aclassuint128__t_html_a8bf81f7f5f5c98f197822ec88e106c6c"><div class="ttname"><a href="../../db/d9a/classuint128__t.html#a8bf81f7f5f5c98f197822ec88e106c6c">uint128_t::divide</a></div><div class="ttdeci">std::pair&lt; uint128_t, uint128_t &gt; divide(const uint128_t &amp;p)</div><div class="ttdoc">divide function for uint128_t and other integer types.</div><div class="ttdef"><b>Definition:</b> uint128_t.hpp:454</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -1164,10 +1164,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this set as unsigned 128-bit remainder. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00564" name="l00564"></a><span class="lineno">  564</span>                                             {</div>
-<div class="line"><a id="l00565" name="l00565"></a><span class="lineno">  565</span>        *<span class="keyword">this</span> %= <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(p);</div>
-<div class="line"><a id="l00566" name="l00566"></a><span class="lineno">  566</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00567" name="l00567"></a><span class="lineno">  567</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  564</span>                                             {</div>
+<div class="line"><span class="lineno">  565</span>        *<span class="keyword">this</span> %= <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(p);</div>
+<div class="line"><span class="lineno">  566</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  567</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1203,10 +1203,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this set as unsigned 128-bit remainder. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00551" name="l00551"></a><span class="lineno">  551</span>                                                     {</div>
-<div class="line"><a id="l00552" name="l00552"></a><span class="lineno">  552</span>        *<span class="keyword">this</span> = <a class="code hl_function" href="../../db/d9a/classuint128__t.html#a8bf81f7f5f5c98f197822ec88e106c6c">divide</a>(p).second;</div>
-<div class="line"><a id="l00553" name="l00553"></a><span class="lineno">  553</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00554" name="l00554"></a><span class="lineno">  554</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  551</span>                                                     {</div>
+<div class="line"><span class="lineno">  552</span>        *<span class="keyword">this</span> = <a class="code hl_function" href="../../db/d9a/classuint128__t.html#a8bf81f7f5f5c98f197822ec88e106c6c">divide</a>(p).second;</div>
+<div class="line"><span class="lineno">  553</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  554</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -1256,10 +1256,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>value of this &amp; p (&amp; is bit-wise operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00855" name="l00855"></a><span class="lineno">  855</span>                                   {</div>
-<div class="line"><a id="l00856" name="l00856"></a><span class="lineno">  856</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> tmp = *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00857" name="l00857"></a><span class="lineno">  857</span>        <span class="keywordflow">return</span> tmp &amp; <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(p);</div>
-<div class="line"><a id="l00858" name="l00858"></a><span class="lineno">  858</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  855</span>                                   {</div>
+<div class="line"><span class="lineno">  856</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> tmp = *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  857</span>        <span class="keywordflow">return</span> tmp &amp; <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(p);</div>
+<div class="line"><span class="lineno">  858</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1295,9 +1295,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>value of this &amp; p (&amp; is bit-wise operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00843" name="l00843"></a><span class="lineno">  843</span>                                                   {</div>
-<div class="line"><a id="l00844" name="l00844"></a><span class="lineno">  844</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(this-&gt;f &amp; p.f, this-&gt;s &amp; p.s);</div>
-<div class="line"><a id="l00845" name="l00845"></a><span class="lineno">  845</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  843</span>                                                   {</div>
+<div class="line"><span class="lineno">  844</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(this-&gt;f &amp; p.f, this-&gt;s &amp; p.s);</div>
+<div class="line"><span class="lineno">  845</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1341,9 +1341,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is both values are non-zero, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00733" name="l00733"></a><span class="lineno">  733</span>                                      {</div>
-<div class="line"><a id="l00734" name="l00734"></a><span class="lineno">  734</span>        <span class="keywordflow">return</span> (f || s) &amp;&amp; b;</div>
-<div class="line"><a id="l00735" name="l00735"></a><span class="lineno">  735</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  733</span>                                      {</div>
+<div class="line"><span class="lineno">  734</span>        <span class="keywordflow">return</span> (f || s) &amp;&amp; b;</div>
+<div class="line"><span class="lineno">  735</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1379,9 +1379,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if both of the values are not zero, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00634" name="l00634"></a><span class="lineno">  634</span>                                               {</div>
-<div class="line"><a id="l00635" name="l00635"></a><span class="lineno">  635</span>        <span class="keywordflow">return</span> (s || f) &amp;&amp; (b.s || b.f);</div>
-<div class="line"><a id="l00636" name="l00636"></a><span class="lineno">  636</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  634</span>                                               {</div>
+<div class="line"><span class="lineno">  635</span>        <span class="keywordflow">return</span> (s || f) &amp;&amp; (b.s || b.f);</div>
+<div class="line"><span class="lineno">  636</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1425,10 +1425,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this = this &amp; p (&amp; is bit-wise operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00879" name="l00879"></a><span class="lineno">  879</span>                                     {</div>
-<div class="line"><a id="l00880" name="l00880"></a><span class="lineno">  880</span>        *<span class="keyword">this</span> &amp;= <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(p);</div>
-<div class="line"><a id="l00881" name="l00881"></a><span class="lineno">  881</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00882" name="l00882"></a><span class="lineno">  882</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  879</span>                                     {</div>
+<div class="line"><span class="lineno">  880</span>        *<span class="keyword">this</span> &amp;= <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(p);</div>
+<div class="line"><span class="lineno">  881</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  882</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1464,11 +1464,11 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this = this &amp; p (&amp; is bit-wise operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00865" name="l00865"></a><span class="lineno">  865</span>                                              {</div>
-<div class="line"><a id="l00866" name="l00866"></a><span class="lineno">  866</span>        this-&gt;f &amp;= p.f;</div>
-<div class="line"><a id="l00867" name="l00867"></a><span class="lineno">  867</span>        this-&gt;s &amp;= p.s;</div>
-<div class="line"><a id="l00868" name="l00868"></a><span class="lineno">  868</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00869" name="l00869"></a><span class="lineno">  869</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  865</span>                                              {</div>
+<div class="line"><span class="lineno">  866</span>        this-&gt;f &amp;= p.f;</div>
+<div class="line"><span class="lineno">  867</span>        this-&gt;s &amp;= p.s;</div>
+<div class="line"><span class="lineno">  868</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  869</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1497,7 +1497,7 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
 
 <p>operator () for <a class="el" href="../../db/d9a/classuint128__t.html" title="class for 128-bit unsigned integer">uint128_t</a> </p>
 <dl class="section return"><dt>Returns</dt><dd>true if this value is non-zero, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00651" name="l00651"></a><span class="lineno">  651</span>{ <span class="keywordflow">return</span> s || f; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  651</span>{ <span class="keywordflow">return</span> s || f; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1541,9 +1541,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>multiplication of this and p, returning <a class="el" href="../../db/d9a/classuint128__t.html" title="class for 128-bit unsigned integer">uint128_t</a> integer </dd></dl>
-<div class="fragment"><div class="line"><a id="l00392" name="l00392"></a><span class="lineno">  392</span>                                          {</div>
-<div class="line"><a id="l00393" name="l00393"></a><span class="lineno">  393</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> * <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(p);</div>
-<div class="line"><a id="l00394" name="l00394"></a><span class="lineno">  394</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  392</span>                                          {</div>
+<div class="line"><span class="lineno">  393</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> * <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(p);</div>
+<div class="line"><span class="lineno">  394</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1579,19 +1579,19 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>multiplication of this and p, returning <a class="el" href="../../db/d9a/classuint128__t.html" title="class for 128-bit unsigned integer">uint128_t</a> integer </dd></dl>
-<div class="fragment"><div class="line"><a id="l00401" name="l00401"></a><span class="lineno">  401</span>                                            {</div>
-<div class="line"><a id="l00402" name="l00402"></a><span class="lineno">  402</span>        uint64_t f_first = s &gt;&gt; 32, f_second = s &amp; 0xFFFFFFFF,</div>
-<div class="line"><a id="l00403" name="l00403"></a><span class="lineno">  403</span>                 s_first = p.s &gt;&gt; 32, s_second = p.s &amp; 0xFFFFFFFF;</div>
-<div class="line"><a id="l00404" name="l00404"></a><span class="lineno">  404</span>        uint64_t fi = f_first * s_first, se = f_first * s_second,</div>
-<div class="line"><a id="l00405" name="l00405"></a><span class="lineno">  405</span>                 th = s_first * f_second, fo = s_second * f_second;</div>
-<div class="line"><a id="l00406" name="l00406"></a><span class="lineno">  406</span>        uint64_t tmp = ((se &amp; 0xFFFFFFFF) &lt;&lt; 32), tmp2 = (th &amp; 0xFFFFFFFF)</div>
-<div class="line"><a id="l00407" name="l00407"></a><span class="lineno">  407</span>                                                         &lt;&lt; 32;</div>
-<div class="line"><a id="l00408" name="l00408"></a><span class="lineno">  408</span>        <span class="keywordtype">int</span> cc = (tmp + tmp2 &lt; tmp);</div>
-<div class="line"><a id="l00409" name="l00409"></a><span class="lineno">  409</span>        tmp += tmp2;</div>
-<div class="line"><a id="l00410" name="l00410"></a><span class="lineno">  410</span>        cc += (tmp + fo &lt; tmp);</div>
-<div class="line"><a id="l00411" name="l00411"></a><span class="lineno">  411</span>        uint64_t carry = fi + (se &gt;&gt; 32) + (th &gt;&gt; 32);</div>
-<div class="line"><a id="l00412" name="l00412"></a><span class="lineno">  412</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(this-&gt;f * p.s + this-&gt;s * p.f + carry + cc, tmp + fo);</div>
-<div class="line"><a id="l00413" name="l00413"></a><span class="lineno">  413</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  401</span>                                            {</div>
+<div class="line"><span class="lineno">  402</span>        uint64_t f_first = s &gt;&gt; 32, f_second = s &amp; 0xFFFFFFFF,</div>
+<div class="line"><span class="lineno">  403</span>                 s_first = p.s &gt;&gt; 32, s_second = p.s &amp; 0xFFFFFFFF;</div>
+<div class="line"><span class="lineno">  404</span>        uint64_t fi = f_first * s_first, se = f_first * s_second,</div>
+<div class="line"><span class="lineno">  405</span>                 th = s_first * f_second, fo = s_second * f_second;</div>
+<div class="line"><span class="lineno">  406</span>        uint64_t tmp = ((se &amp; 0xFFFFFFFF) &lt;&lt; 32), tmp2 = (th &amp; 0xFFFFFFFF)</div>
+<div class="line"><span class="lineno">  407</span>                                                         &lt;&lt; 32;</div>
+<div class="line"><span class="lineno">  408</span>        <span class="keywordtype">int</span> cc = (tmp + tmp2 &lt; tmp);</div>
+<div class="line"><span class="lineno">  409</span>        tmp += tmp2;</div>
+<div class="line"><span class="lineno">  410</span>        cc += (tmp + fo &lt; tmp);</div>
+<div class="line"><span class="lineno">  411</span>        uint64_t carry = fi + (se &gt;&gt; 32) + (th &gt;&gt; 32);</div>
+<div class="line"><span class="lineno">  412</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(this-&gt;f * p.s + this-&gt;s * p.f + carry + cc, tmp + fo);</div>
+<div class="line"><span class="lineno">  413</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1635,10 +1635,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>multiplication of this and p, returning this </dd></dl>
-<div class="fragment"><div class="line"><a id="l00423" name="l00423"></a><span class="lineno">  423</span>                                            {</div>
-<div class="line"><a id="l00424" name="l00424"></a><span class="lineno">  424</span>        *<span class="keyword">this</span> *= <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(p);</div>
-<div class="line"><a id="l00425" name="l00425"></a><span class="lineno">  425</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00426" name="l00426"></a><span class="lineno">  426</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  423</span>                                            {</div>
+<div class="line"><span class="lineno">  424</span>        *<span class="keyword">this</span> *= <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(p);</div>
+<div class="line"><span class="lineno">  425</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  426</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1674,20 +1674,20 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>multiplication of this and p, returning this </dd></dl>
-<div class="fragment"><div class="line"><a id="l00433" name="l00433"></a><span class="lineno">  433</span>                                              {</div>
-<div class="line"><a id="l00434" name="l00434"></a><span class="lineno">  434</span>        uint64_t f_first = s &gt;&gt; 32, f_second = s &amp; 0xFFFFFFFF,</div>
-<div class="line"><a id="l00435" name="l00435"></a><span class="lineno">  435</span>                 s_first = p.s &gt;&gt; 32, s_second = p.s &amp; 0xFFFFFFFF;</div>
-<div class="line"><a id="l00436" name="l00436"></a><span class="lineno">  436</span>        uint64_t fi = f_first * s_first, se = f_first * s_second,</div>
-<div class="line"><a id="l00437" name="l00437"></a><span class="lineno">  437</span>                 th = s_first * f_second, fo = s_second * f_second;</div>
-<div class="line"><a id="l00438" name="l00438"></a><span class="lineno">  438</span>        uint64_t tmp = (se &lt;&lt; 32), tmp2 = (th &lt;&lt; 32);</div>
-<div class="line"><a id="l00439" name="l00439"></a><span class="lineno">  439</span>        <span class="keywordtype">int</span> cc = (tmp + tmp2 &lt; tmp);</div>
-<div class="line"><a id="l00440" name="l00440"></a><span class="lineno">  440</span>        tmp += tmp2;</div>
-<div class="line"><a id="l00441" name="l00441"></a><span class="lineno">  441</span>        cc += (tmp + fo &lt; tmp);</div>
-<div class="line"><a id="l00442" name="l00442"></a><span class="lineno">  442</span>        uint64_t carry = fi + (se &gt;&gt; 32) + (th &gt;&gt; 32);</div>
-<div class="line"><a id="l00443" name="l00443"></a><span class="lineno">  443</span>        f = this-&gt;f * p.s + this-&gt;s * p.f + carry + cc;</div>
-<div class="line"><a id="l00444" name="l00444"></a><span class="lineno">  444</span>        s = tmp + fo;</div>
-<div class="line"><a id="l00445" name="l00445"></a><span class="lineno">  445</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00446" name="l00446"></a><span class="lineno">  446</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  433</span>                                              {</div>
+<div class="line"><span class="lineno">  434</span>        uint64_t f_first = s &gt;&gt; 32, f_second = s &amp; 0xFFFFFFFF,</div>
+<div class="line"><span class="lineno">  435</span>                 s_first = p.s &gt;&gt; 32, s_second = p.s &amp; 0xFFFFFFFF;</div>
+<div class="line"><span class="lineno">  436</span>        uint64_t fi = f_first * s_first, se = f_first * s_second,</div>
+<div class="line"><span class="lineno">  437</span>                 th = s_first * f_second, fo = s_second * f_second;</div>
+<div class="line"><span class="lineno">  438</span>        uint64_t tmp = (se &lt;&lt; 32), tmp2 = (th &lt;&lt; 32);</div>
+<div class="line"><span class="lineno">  439</span>        <span class="keywordtype">int</span> cc = (tmp + tmp2 &lt; tmp);</div>
+<div class="line"><span class="lineno">  440</span>        tmp += tmp2;</div>
+<div class="line"><span class="lineno">  441</span>        cc += (tmp + fo &lt; tmp);</div>
+<div class="line"><span class="lineno">  442</span>        uint64_t carry = fi + (se &gt;&gt; 32) + (th &gt;&gt; 32);</div>
+<div class="line"><span class="lineno">  443</span>        f = this-&gt;f * p.s + this-&gt;s * p.f + carry + cc;</div>
+<div class="line"><span class="lineno">  444</span>        s = tmp + fo;</div>
+<div class="line"><span class="lineno">  445</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  446</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1731,9 +1731,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>addition of this and p, returning <a class="el" href="../../db/d9a/classuint128__t.html" title="class for 128-bit unsigned integer">uint128_t</a> integer </dd></dl>
-<div class="fragment"><div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>                                          {</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(f + (p + s &lt; s), p + s);</div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  252</span>                                          {</div>
+<div class="line"><span class="lineno">  253</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(f + (p + s &lt; s), p + s);</div>
+<div class="line"><span class="lineno">  254</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1769,9 +1769,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>addition of this and p, returning <a class="el" href="../../db/d9a/classuint128__t.html" title="class for 128-bit unsigned integer">uint128_t</a> integer </dd></dl>
-<div class="fragment"><div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>                                                   {</div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(f + (p.s + s &lt; s) + p.f, p.s + s);</div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  261</span>                                                   {</div>
+<div class="line"><span class="lineno">  262</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(f + (p.s + s &lt; s) + p.f, p.s + s);</div>
+<div class="line"><span class="lineno">  263</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1800,10 +1800,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
 
 <p>pre-increment operator </p>
 <dl class="section return"><dt>Returns</dt><dd>incremented value of this. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>                                   {</div>
-<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>        *<span class="keyword">this</span> += 1;</div>
-<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  296</span>                                   {</div>
+<div class="line"><span class="lineno">  297</span>        *<span class="keyword">this</span> += 1;</div>
+<div class="line"><span class="lineno">  298</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  299</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1833,10 +1833,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
 
 <p>post-increment operator </p>
 <dl class="section return"><dt>Returns</dt><dd>incremented value of this. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span>                                     {</div>
-<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>        ++*<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  305</span>                                     {</div>
+<div class="line"><span class="lineno">  306</span>        ++*<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  307</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  308</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1880,12 +1880,12 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>addition of this and p, returning this </dd></dl>
-<div class="fragment"><div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>                                            {</div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>        <span class="keywordtype">bool</span> app = p + s &lt; s;</div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>        this-&gt;f += app;</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>        this-&gt;s += p;</div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  273</span>                                            {</div>
+<div class="line"><span class="lineno">  274</span>        <span class="keywordtype">bool</span> app = p + s &lt; s;</div>
+<div class="line"><span class="lineno">  275</span>        this-&gt;f += app;</div>
+<div class="line"><span class="lineno">  276</span>        this-&gt;s += p;</div>
+<div class="line"><span class="lineno">  277</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  278</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1921,12 +1921,12 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>addition of this and p, returning this </dd></dl>
-<div class="fragment"><div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>                                              {</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>        <span class="keywordtype">bool</span> app = p.s + s &lt; s;</div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>        f = f + app + p.f;</div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>        s = p.s + s;</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  285</span>                                              {</div>
+<div class="line"><span class="lineno">  286</span>        <span class="keywordtype">bool</span> app = p.s + s &lt; s;</div>
+<div class="line"><span class="lineno">  287</span>        f = f + app + p.f;</div>
+<div class="line"><span class="lineno">  288</span>        s = p.s + s;</div>
+<div class="line"><span class="lineno">  289</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  290</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1955,7 +1955,7 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
 
 <p>operator - using twos complement </p>
 <dl class="section return"><dt>Returns</dt><dd>2's complement of this. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span>{ <span class="keywordflow">return</span> ~*<span class="keyword">this</span> + <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(1); }</div>
+<div class="fragment"><div class="line"><span class="lineno">  337</span>{ <span class="keywordflow">return</span> ~*<span class="keyword">this</span> + <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(1); }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1999,10 +1999,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>subtraction of this and p, returning <a class="el" href="../../db/d9a/classuint128__t.html" title="class for 128-bit unsigned integer">uint128_t</a> integer </dd></dl>
-<div class="fragment"><div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span>                                           {</div>
-<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>        <span class="keywordtype">bool</span> app = p &gt; s;</div>
-<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(f - app, s - p);</div>
-<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  318</span>                                           {</div>
+<div class="line"><span class="lineno">  319</span>        <span class="keywordtype">bool</span> app = p &gt; s;</div>
+<div class="line"><span class="lineno">  320</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(f - app, s - p);</div>
+<div class="line"><span class="lineno">  321</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2038,10 +2038,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>subtraction of this and p, returning <a class="el" href="../../db/d9a/classuint128__t.html" title="class for 128-bit unsigned integer">uint128_t</a> integer </dd></dl>
-<div class="fragment"><div class="line"><a id="l00328" name="l00328"></a><span class="lineno">  328</span>                                                   {</div>
-<div class="line"><a id="l00329" name="l00329"></a><span class="lineno">  329</span>        <span class="keywordtype">bool</span> app = p.s &gt; s;</div>
-<div class="line"><a id="l00330" name="l00330"></a><span class="lineno">  330</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(f - p.f - app, s - p.s);</div>
-<div class="line"><a id="l00331" name="l00331"></a><span class="lineno">  331</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  328</span>                                                   {</div>
+<div class="line"><span class="lineno">  329</span>        <span class="keywordtype">bool</span> app = p.s &gt; s;</div>
+<div class="line"><span class="lineno">  330</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(f - p.f - app, s - p.s);</div>
+<div class="line"><span class="lineno">  331</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2070,10 +2070,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
 
 <p>operator &ndash; (pre-decrement) </p>
 <dl class="section return"><dt>Returns</dt><dd>decremented value of this </dd></dl>
-<div class="fragment"><div class="line"><a id="l00343" name="l00343"></a><span class="lineno">  343</span>                                   {</div>
-<div class="line"><a id="l00344" name="l00344"></a><span class="lineno">  344</span>        *<span class="keyword">this</span> -= 1;</div>
-<div class="line"><a id="l00345" name="l00345"></a><span class="lineno">  345</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00346" name="l00346"></a><span class="lineno">  346</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  343</span>                                   {</div>
+<div class="line"><span class="lineno">  344</span>        *<span class="keyword">this</span> -= 1;</div>
+<div class="line"><span class="lineno">  345</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  346</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2103,10 +2103,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
 
 <p>operator &ndash; (post-decrement) </p>
 <dl class="section return"><dt>Returns</dt><dd>decremented value of this </dd></dl>
-<div class="fragment"><div class="line"><a id="l00352" name="l00352"></a><span class="lineno">  352</span>                                       {</div>
-<div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span>        --*<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00355" name="l00355"></a><span class="lineno">  355</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  352</span>                                       {</div>
+<div class="line"><span class="lineno">  353</span>        --*<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  354</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  355</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2150,12 +2150,12 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>subtraction of this and p, returning this </dd></dl>
-<div class="fragment"><div class="line"><a id="l00365" name="l00365"></a><span class="lineno">  365</span>                                      {</div>
-<div class="line"><a id="l00366" name="l00366"></a><span class="lineno">  366</span>        <span class="keywordtype">bool</span> app = p &gt; s;</div>
-<div class="line"><a id="l00367" name="l00367"></a><span class="lineno">  367</span>        f -= app;</div>
-<div class="line"><a id="l00368" name="l00368"></a><span class="lineno">  368</span>        s -= p;</div>
-<div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  365</span>                                      {</div>
+<div class="line"><span class="lineno">  366</span>        <span class="keywordtype">bool</span> app = p &gt; s;</div>
+<div class="line"><span class="lineno">  367</span>        f -= app;</div>
+<div class="line"><span class="lineno">  368</span>        s -= p;</div>
+<div class="line"><span class="lineno">  369</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  370</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2191,12 +2191,12 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>subtraction of this and p, returning this </dd></dl>
-<div class="fragment"><div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span>                                              {</div>
-<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span>        <span class="keywordtype">bool</span> app = p.s &gt; s;</div>
-<div class="line"><a id="l00379" name="l00379"></a><span class="lineno">  379</span>        f = f - p.f - app;</div>
-<div class="line"><a id="l00380" name="l00380"></a><span class="lineno">  380</span>        s = s - p.s;</div>
-<div class="line"><a id="l00381" name="l00381"></a><span class="lineno">  381</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00382" name="l00382"></a><span class="lineno">  382</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  377</span>                                              {</div>
+<div class="line"><span class="lineno">  378</span>        <span class="keywordtype">bool</span> app = p.s &gt; s;</div>
+<div class="line"><span class="lineno">  379</span>        f = f - p.f - app;</div>
+<div class="line"><span class="lineno">  380</span>        s = s - p.s;</div>
+<div class="line"><span class="lineno">  381</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  382</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2240,11 +2240,11 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>unsigned 128-bit quotient. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00498" name="l00498"></a><span class="lineno">  498</span>                                          {</div>
-<div class="line"><a id="l00499" name="l00499"></a><span class="lineno">  499</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> tmp = *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00500" name="l00500"></a><span class="lineno">  500</span>        tmp /= <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0, p);</div>
-<div class="line"><a id="l00501" name="l00501"></a><span class="lineno">  501</span>        <span class="keywordflow">return</span> tmp;</div>
-<div class="line"><a id="l00502" name="l00502"></a><span class="lineno">  502</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  498</span>                                          {</div>
+<div class="line"><span class="lineno">  499</span>        <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> tmp = *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  500</span>        tmp /= <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0, p);</div>
+<div class="line"><span class="lineno">  501</span>        <span class="keywordflow">return</span> tmp;</div>
+<div class="line"><span class="lineno">  502</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2280,7 +2280,7 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>unsigned 128-bit quotient. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00488" name="l00488"></a><span class="lineno">  488</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../db/d9a/classuint128__t.html#a8bf81f7f5f5c98f197822ec88e106c6c">divide</a>(p).first; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  488</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../db/d9a/classuint128__t.html#a8bf81f7f5f5c98f197822ec88e106c6c">divide</a>(p).first; }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -2330,10 +2330,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this set as unsigned 128-bit quotient. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00522" name="l00522"></a><span class="lineno">  522</span>                                            {</div>
-<div class="line"><a id="l00523" name="l00523"></a><span class="lineno">  523</span>        *<span class="keyword">this</span> /= <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0, p);</div>
-<div class="line"><a id="l00524" name="l00524"></a><span class="lineno">  524</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00525" name="l00525"></a><span class="lineno">  525</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  522</span>                                            {</div>
+<div class="line"><span class="lineno">  523</span>        *<span class="keyword">this</span> /= <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0, p);</div>
+<div class="line"><span class="lineno">  524</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  525</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2369,10 +2369,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this set as unsigned 128-bit quotient. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00509" name="l00509"></a><span class="lineno">  509</span>                                                     {</div>
-<div class="line"><a id="l00510" name="l00510"></a><span class="lineno">  510</span>        *<span class="keyword">this</span> = <a class="code hl_function" href="../../db/d9a/classuint128__t.html#a8bf81f7f5f5c98f197822ec88e106c6c">divide</a>(p).first;</div>
-<div class="line"><a id="l00511" name="l00511"></a><span class="lineno">  511</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00512" name="l00512"></a><span class="lineno">  512</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  509</span>                                                     {</div>
+<div class="line"><span class="lineno">  510</span>        *<span class="keyword">this</span> = <a class="code hl_function" href="../../db/d9a/classuint128__t.html#a8bf81f7f5f5c98f197822ec88e106c6c">divide</a>(p).first;</div>
+<div class="line"><span class="lineno">  511</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  512</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -2422,9 +2422,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is less than other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00661" name="l00661"></a><span class="lineno">  661</span>                                         {</div>
-<div class="line"><a id="l00662" name="l00662"></a><span class="lineno">  662</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> &lt; <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(other);</div>
-<div class="line"><a id="l00663" name="l00663"></a><span class="lineno">  663</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  661</span>                                         {</div>
+<div class="line"><span class="lineno">  662</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> &lt; <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(other);</div>
+<div class="line"><span class="lineno">  663</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2460,9 +2460,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is less than other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00574" name="l00574"></a><span class="lineno">  574</span>                                                  {</div>
-<div class="line"><a id="l00575" name="l00575"></a><span class="lineno">  575</span>        <span class="keywordflow">return</span> f &lt; other.f || (f == other.f &amp;&amp; s &lt; other.s);</div>
-<div class="line"><a id="l00576" name="l00576"></a><span class="lineno">  576</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  574</span>                                                  {</div>
+<div class="line"><span class="lineno">  575</span>        <span class="keywordflow">return</span> f &lt; other.f || (f == other.f &amp;&amp; s &lt; other.s);</div>
+<div class="line"><span class="lineno">  576</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2506,17 +2506,17 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>value of this shifted by p to left </dd></dl>
-<div class="fragment"><div class="line"><a id="l00764" name="l00764"></a><span class="lineno">  764</span>                                    {</div>
-<div class="line"><a id="l00765" name="l00765"></a><span class="lineno">  765</span>        <span class="keywordflow">if</span> (!p) {</div>
-<div class="line"><a id="l00766" name="l00766"></a><span class="lineno">  766</span>            <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(f, s);</div>
-<div class="line"><a id="l00767" name="l00767"></a><span class="lineno">  767</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (p &gt;= 64 &amp;&amp; p &lt;= 128) {</div>
-<div class="line"><a id="l00768" name="l00768"></a><span class="lineno">  768</span>            <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>((this-&gt;s &lt;&lt; (p - 64)), 0);</div>
-<div class="line"><a id="l00769" name="l00769"></a><span class="lineno">  769</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (p &lt; 64 &amp;&amp; p &gt; 0) {</div>
-<div class="line"><a id="l00770" name="l00770"></a><span class="lineno">  770</span>            <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>((this-&gt;f &lt;&lt; p) + ((this-&gt;s &gt;&gt; (64 - p))),</div>
-<div class="line"><a id="l00771" name="l00771"></a><span class="lineno">  771</span>                             this-&gt;s &lt;&lt; p);</div>
-<div class="line"><a id="l00772" name="l00772"></a><span class="lineno">  772</span>        }</div>
-<div class="line"><a id="l00773" name="l00773"></a><span class="lineno">  773</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0);</div>
-<div class="line"><a id="l00774" name="l00774"></a><span class="lineno">  774</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  764</span>                                    {</div>
+<div class="line"><span class="lineno">  765</span>        <span class="keywordflow">if</span> (!p) {</div>
+<div class="line"><span class="lineno">  766</span>            <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(f, s);</div>
+<div class="line"><span class="lineno">  767</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (p &gt;= 64 &amp;&amp; p &lt;= 128) {</div>
+<div class="line"><span class="lineno">  768</span>            <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>((this-&gt;s &lt;&lt; (p - 64)), 0);</div>
+<div class="line"><span class="lineno">  769</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (p &lt; 64 &amp;&amp; p &gt; 0) {</div>
+<div class="line"><span class="lineno">  770</span>            <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>((this-&gt;f &lt;&lt; p) + ((this-&gt;s &gt;&gt; (64 - p))),</div>
+<div class="line"><span class="lineno">  771</span>                             this-&gt;s &lt;&lt; p);</div>
+<div class="line"><span class="lineno">  772</span>        }</div>
+<div class="line"><span class="lineno">  773</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0);</div>
+<div class="line"><span class="lineno">  774</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2560,18 +2560,18 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this shifted by p to left </dd></dl>
-<div class="fragment"><div class="line"><a id="l00784" name="l00784"></a><span class="lineno">  784</span>                                      {</div>
-<div class="line"><a id="l00785" name="l00785"></a><span class="lineno">  785</span>        <span class="keywordflow">if</span> (p) {</div>
-<div class="line"><a id="l00786" name="l00786"></a><span class="lineno">  786</span>            <span class="keywordflow">if</span> (p &gt;= 64 &amp;&amp; p &lt;= 128) {</div>
-<div class="line"><a id="l00787" name="l00787"></a><span class="lineno">  787</span>                this-&gt;f = (this-&gt;s &lt;&lt; (p - 64));</div>
-<div class="line"><a id="l00788" name="l00788"></a><span class="lineno">  788</span>                this-&gt;s = 0;</div>
-<div class="line"><a id="l00789" name="l00789"></a><span class="lineno">  789</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00790" name="l00790"></a><span class="lineno">  790</span>                f = ((this-&gt;f &lt;&lt; p) + (this-&gt;s &gt;&gt; (64 - p)));</div>
-<div class="line"><a id="l00791" name="l00791"></a><span class="lineno">  791</span>                s = (this-&gt;s &lt;&lt; p);</div>
-<div class="line"><a id="l00792" name="l00792"></a><span class="lineno">  792</span>            }</div>
-<div class="line"><a id="l00793" name="l00793"></a><span class="lineno">  793</span>        }</div>
-<div class="line"><a id="l00794" name="l00794"></a><span class="lineno">  794</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00795" name="l00795"></a><span class="lineno">  795</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  784</span>                                      {</div>
+<div class="line"><span class="lineno">  785</span>        <span class="keywordflow">if</span> (p) {</div>
+<div class="line"><span class="lineno">  786</span>            <span class="keywordflow">if</span> (p &gt;= 64 &amp;&amp; p &lt;= 128) {</div>
+<div class="line"><span class="lineno">  787</span>                this-&gt;f = (this-&gt;s &lt;&lt; (p - 64));</div>
+<div class="line"><span class="lineno">  788</span>                this-&gt;s = 0;</div>
+<div class="line"><span class="lineno">  789</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  790</span>                f = ((this-&gt;f &lt;&lt; p) + (this-&gt;s &gt;&gt; (64 - p)));</div>
+<div class="line"><span class="lineno">  791</span>                s = (this-&gt;s &lt;&lt; p);</div>
+<div class="line"><span class="lineno">  792</span>            }</div>
+<div class="line"><span class="lineno">  793</span>        }</div>
+<div class="line"><span class="lineno">  794</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  795</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2615,9 +2615,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is less than or equal to other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00673" name="l00673"></a><span class="lineno">  673</span>                                          {</div>
-<div class="line"><a id="l00674" name="l00674"></a><span class="lineno">  674</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> &lt;= <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(other);</div>
-<div class="line"><a id="l00675" name="l00675"></a><span class="lineno">  675</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  673</span>                                          {</div>
+<div class="line"><span class="lineno">  674</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> &lt;= <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(other);</div>
+<div class="line"><span class="lineno">  675</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2653,9 +2653,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is less than or equal to other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00583" name="l00583"></a><span class="lineno">  583</span>                                                   {</div>
-<div class="line"><a id="l00584" name="l00584"></a><span class="lineno">  584</span>        <span class="keywordflow">return</span> f &lt; other.f || (f == other.f &amp;&amp; s &lt;= other.s);</div>
-<div class="line"><a id="l00585" name="l00585"></a><span class="lineno">  585</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  583</span>                                                   {</div>
+<div class="line"><span class="lineno">  584</span>        <span class="keywordflow">return</span> f &lt; other.f || (f == other.f &amp;&amp; s &lt;= other.s);</div>
+<div class="line"><span class="lineno">  585</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2691,10 +2691,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this pointer with it's value equal to <code>p</code> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>                                                    {</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>        this-&gt;<a class="code hl_function" href="../../db/d9a/classuint128__t.html#a857a3c69c1e775a1bd3935c2bfbb02df">__get_integer_from_string</a>(p);</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  227</span>                                                    {</div>
+<div class="line"><span class="lineno">  228</span>        this-&gt;<a class="code hl_function" href="../../db/d9a/classuint128__t.html#a857a3c69c1e775a1bd3935c2bfbb02df">__get_integer_from_string</a>(p);</div>
+<div class="line"><span class="lineno">  229</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  230</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -2744,10 +2744,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this pointer with it's value equal to <code>p</code> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>                                            {</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>        this-&gt;s = p;</div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  217</span>                                            {</div>
+<div class="line"><span class="lineno">  218</span>        this-&gt;s = p;</div>
+<div class="line"><span class="lineno">  219</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  220</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2826,9 +2826,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is equal to other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00709" name="l00709"></a><span class="lineno">  709</span>                                          {</div>
-<div class="line"><a id="l00710" name="l00710"></a><span class="lineno">  710</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> == <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(other);</div>
-<div class="line"><a id="l00711" name="l00711"></a><span class="lineno">  711</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  709</span>                                          {</div>
+<div class="line"><span class="lineno">  710</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> == <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(other);</div>
+<div class="line"><span class="lineno">  711</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2864,9 +2864,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is equal than other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00610" name="l00610"></a><span class="lineno">  610</span>                                                   {</div>
-<div class="line"><a id="l00611" name="l00611"></a><span class="lineno">  611</span>        <span class="keywordflow">return</span> f == other.f &amp;&amp; s == other.s;</div>
-<div class="line"><a id="l00612" name="l00612"></a><span class="lineno">  612</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  610</span>                                                   {</div>
+<div class="line"><span class="lineno">  611</span>        <span class="keywordflow">return</span> f == other.f &amp;&amp; s == other.s;</div>
+<div class="line"><span class="lineno">  612</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2910,9 +2910,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is greater than other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00685" name="l00685"></a><span class="lineno">  685</span>                                         {</div>
-<div class="line"><a id="l00686" name="l00686"></a><span class="lineno">  686</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> &gt; <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(other);</div>
-<div class="line"><a id="l00687" name="l00687"></a><span class="lineno">  687</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  685</span>                                         {</div>
+<div class="line"><span class="lineno">  686</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> &gt; <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(other);</div>
+<div class="line"><span class="lineno">  687</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2948,9 +2948,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is greater than other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00592" name="l00592"></a><span class="lineno">  592</span>                                                  {</div>
-<div class="line"><a id="l00593" name="l00593"></a><span class="lineno">  593</span>        <span class="keywordflow">return</span> f &gt; other.f || (f == other.f &amp;&amp; s &gt; other.s);</div>
-<div class="line"><a id="l00594" name="l00594"></a><span class="lineno">  594</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  592</span>                                                  {</div>
+<div class="line"><span class="lineno">  593</span>        <span class="keywordflow">return</span> f &gt; other.f || (f == other.f &amp;&amp; s &gt; other.s);</div>
+<div class="line"><span class="lineno">  594</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -2994,9 +2994,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is greater than or equal other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00697" name="l00697"></a><span class="lineno">  697</span>                                          {</div>
-<div class="line"><a id="l00698" name="l00698"></a><span class="lineno">  698</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> &gt;= <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(other);</div>
-<div class="line"><a id="l00699" name="l00699"></a><span class="lineno">  699</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  697</span>                                          {</div>
+<div class="line"><span class="lineno">  698</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span> &gt;= <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(other);</div>
+<div class="line"><span class="lineno">  699</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3032,9 +3032,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>true if this is greater than or equal than other, else false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00601" name="l00601"></a><span class="lineno">  601</span>                                                   {</div>
-<div class="line"><a id="l00602" name="l00602"></a><span class="lineno">  602</span>        <span class="keywordflow">return</span> (f &gt; other.f) || (f == other.f &amp;&amp; s &gt;= other.s);</div>
-<div class="line"><a id="l00603" name="l00603"></a><span class="lineno">  603</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  601</span>                                                   {</div>
+<div class="line"><span class="lineno">  602</span>        <span class="keywordflow">return</span> (f &gt; other.f) || (f == other.f &amp;&amp; s &gt;= other.s);</div>
+<div class="line"><span class="lineno">  603</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3078,17 +3078,17 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>value of this shifted by p to right </dd></dl>
-<div class="fragment"><div class="line"><a id="l00805" name="l00805"></a><span class="lineno">  805</span>                                    {</div>
-<div class="line"><a id="l00806" name="l00806"></a><span class="lineno">  806</span>        <span class="keywordflow">if</span> (!p) {</div>
-<div class="line"><a id="l00807" name="l00807"></a><span class="lineno">  807</span>            <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(this-&gt;f, this-&gt;s);</div>
-<div class="line"><a id="l00808" name="l00808"></a><span class="lineno">  808</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (p &gt;= 64 &amp;&amp; p &lt;= 128) {</div>
-<div class="line"><a id="l00809" name="l00809"></a><span class="lineno">  809</span>            <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0, (this-&gt;f &gt;&gt; (p - 64)));</div>
-<div class="line"><a id="l00810" name="l00810"></a><span class="lineno">  810</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (p &lt; 64 &amp;&amp; p &gt; 0) {</div>
-<div class="line"><a id="l00811" name="l00811"></a><span class="lineno">  811</span>            <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>((this-&gt;f &gt;&gt; p),</div>
-<div class="line"><a id="l00812" name="l00812"></a><span class="lineno">  812</span>                             (this-&gt;s &gt;&gt; p) + (this-&gt;f &lt;&lt; (64 - p)));</div>
-<div class="line"><a id="l00813" name="l00813"></a><span class="lineno">  813</span>        }</div>
-<div class="line"><a id="l00814" name="l00814"></a><span class="lineno">  814</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0);</div>
-<div class="line"><a id="l00815" name="l00815"></a><span class="lineno">  815</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  805</span>                                    {</div>
+<div class="line"><span class="lineno">  806</span>        <span class="keywordflow">if</span> (!p) {</div>
+<div class="line"><span class="lineno">  807</span>            <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(this-&gt;f, this-&gt;s);</div>
+<div class="line"><span class="lineno">  808</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (p &gt;= 64 &amp;&amp; p &lt;= 128) {</div>
+<div class="line"><span class="lineno">  809</span>            <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0, (this-&gt;f &gt;&gt; (p - 64)));</div>
+<div class="line"><span class="lineno">  810</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (p &lt; 64 &amp;&amp; p &gt; 0) {</div>
+<div class="line"><span class="lineno">  811</span>            <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>((this-&gt;f &gt;&gt; p),</div>
+<div class="line"><span class="lineno">  812</span>                             (this-&gt;s &gt;&gt; p) + (this-&gt;f &lt;&lt; (64 - p)));</div>
+<div class="line"><span class="lineno">  813</span>        }</div>
+<div class="line"><span class="lineno">  814</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(0);</div>
+<div class="line"><span class="lineno">  815</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3132,18 +3132,18 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this shifted by p to right </dd></dl>
-<div class="fragment"><div class="line"><a id="l00825" name="l00825"></a><span class="lineno">  825</span>                                      {</div>
-<div class="line"><a id="l00826" name="l00826"></a><span class="lineno">  826</span>        <span class="keywordflow">if</span> (p) {</div>
-<div class="line"><a id="l00827" name="l00827"></a><span class="lineno">  827</span>            <span class="keywordflow">if</span> (p &gt;= 64) {</div>
-<div class="line"><a id="l00828" name="l00828"></a><span class="lineno">  828</span>                f = 0;</div>
-<div class="line"><a id="l00829" name="l00829"></a><span class="lineno">  829</span>                s = (this-&gt;f &gt;&gt; (p - 64));</div>
-<div class="line"><a id="l00830" name="l00830"></a><span class="lineno">  830</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00831" name="l00831"></a><span class="lineno">  831</span>                s = (this-&gt;s &gt;&gt; p) + (this-&gt;f &lt;&lt; (64 - p));</div>
-<div class="line"><a id="l00832" name="l00832"></a><span class="lineno">  832</span>                f = (this-&gt;f &gt;&gt; p);</div>
-<div class="line"><a id="l00833" name="l00833"></a><span class="lineno">  833</span>            }</div>
-<div class="line"><a id="l00834" name="l00834"></a><span class="lineno">  834</span>        }</div>
-<div class="line"><a id="l00835" name="l00835"></a><span class="lineno">  835</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00836" name="l00836"></a><span class="lineno">  836</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  825</span>                                      {</div>
+<div class="line"><span class="lineno">  826</span>        <span class="keywordflow">if</span> (p) {</div>
+<div class="line"><span class="lineno">  827</span>            <span class="keywordflow">if</span> (p &gt;= 64) {</div>
+<div class="line"><span class="lineno">  828</span>                f = 0;</div>
+<div class="line"><span class="lineno">  829</span>                s = (this-&gt;f &gt;&gt; (p - 64));</div>
+<div class="line"><span class="lineno">  830</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  831</span>                s = (this-&gt;s &gt;&gt; p) + (this-&gt;f &lt;&lt; (64 - p));</div>
+<div class="line"><span class="lineno">  832</span>                f = (this-&gt;f &gt;&gt; p);</div>
+<div class="line"><span class="lineno">  833</span>            }</div>
+<div class="line"><span class="lineno">  834</span>        }</div>
+<div class="line"><span class="lineno">  835</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  836</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3187,9 +3187,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>value of this ^ p (^ is bit-wise <a class="el" href="../../d7/d47/namespace_x_o_r.html" title="Functions for XOR cipher algorithm.">XOR</a> operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00937" name="l00937"></a><span class="lineno">  937</span>                                          {</div>
-<div class="line"><a id="l00938" name="l00938"></a><span class="lineno">  938</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(this-&gt;f, this-&gt;s ^ p);</div>
-<div class="line"><a id="l00939" name="l00939"></a><span class="lineno">  939</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  937</span>                                          {</div>
+<div class="line"><span class="lineno">  938</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(this-&gt;f, this-&gt;s ^ p);</div>
+<div class="line"><span class="lineno">  939</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3225,9 +3225,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>value of this ^ p (^ is bit-wise <a class="el" href="../../d7/d47/namespace_x_o_r.html" title="Functions for XOR cipher algorithm.">XOR</a> operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00946" name="l00946"></a><span class="lineno">  946</span>                                                   {</div>
-<div class="line"><a id="l00947" name="l00947"></a><span class="lineno">  947</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(this-&gt;f ^ p.f, this-&gt;s ^ p.s);</div>
-<div class="line"><a id="l00948" name="l00948"></a><span class="lineno">  948</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  946</span>                                                   {</div>
+<div class="line"><span class="lineno">  947</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(this-&gt;f ^ p.f, this-&gt;s ^ p.s);</div>
+<div class="line"><span class="lineno">  948</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3271,10 +3271,10 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this = this ^ p (^ is bit-wise <a class="el" href="../../d7/d47/namespace_x_o_r.html" title="Functions for XOR cipher algorithm.">XOR</a> operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00969" name="l00969"></a><span class="lineno">  969</span>                                             {</div>
-<div class="line"><a id="l00970" name="l00970"></a><span class="lineno">  970</span>        s ^= p;</div>
-<div class="line"><a id="l00971" name="l00971"></a><span class="lineno">  971</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00972" name="l00972"></a><span class="lineno">  972</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  969</span>                                             {</div>
+<div class="line"><span class="lineno">  970</span>        s ^= p;</div>
+<div class="line"><span class="lineno">  971</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  972</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3310,11 +3310,11 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>this = this ^ p (^ is bit-wise <a class="el" href="../../d7/d47/namespace_x_o_r.html" title="Functions for XOR cipher algorithm.">XOR</a> operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00955" name="l00955"></a><span class="lineno">  955</span>                                              {</div>
-<div class="line"><a id="l00956" name="l00956"></a><span class="lineno">  956</span>        f ^= p.f;</div>
-<div class="line"><a id="l00957" name="l00957"></a><span class="lineno">  957</span>        s ^= p.s;</div>
-<div class="line"><a id="l00958" name="l00958"></a><span class="lineno">  958</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00959" name="l00959"></a><span class="lineno">  959</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  955</span>                                              {</div>
+<div class="line"><span class="lineno">  956</span>        f ^= p.f;</div>
+<div class="line"><span class="lineno">  957</span>        s ^= p.s;</div>
+<div class="line"><span class="lineno">  958</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  959</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -3358,9 +3358,9 @@ template&lt;typename T , typename  = typename std::enable_if&lt;
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>value of this | p (| is bit-wise operator) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00892" name="l00892"></a><span class="lineno">  892</span>                                          {</div>
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 <p >Remove the top element of the queue </p>
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@@ -183,15 +183,15 @@ Functions</h2></td></tr>
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-<div class="fragment"><div class="line"><a id="l01298" name="l01298"></a><span class="lineno"> 1298</span>                                 {</div>
-<div class="line"><a id="l01299" name="l01299"></a><span class="lineno"> 1299</span>    <span class="keywordflow">if</span> (argc &lt; 2) {</div>
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-<div class="line"><a id="l01302" name="l01302"></a><span class="lineno"> 1302</span>        <a class="code hl_function" href="../../db/dbc/tree__234_8cpp.html#af1ac73779b0fcfbbdce3976c0ca57342">test2</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/stol.html">std::stoi</a>(argv[1]));  <span class="comment">// execute 2nd test</span></div>
-<div class="line"><a id="l01303" name="l01303"></a><span class="lineno"> 1303</span>    }</div>
-<div class="line"><a id="l01304" name="l01304"></a><span class="lineno"> 1304</span> </div>
-<div class="line"><a id="l01305" name="l01305"></a><span class="lineno"> 1305</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l01306" name="l01306"></a><span class="lineno"> 1306</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno"> 1298</span>                                 {</div>
+<div class="line"><span class="lineno"> 1299</span>    <span class="keywordflow">if</span> (argc &lt; 2) {</div>
+<div class="line"><span class="lineno"> 1300</span>        <a class="code hl_function" href="../../db/dbc/tree__234_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a>();  <span class="comment">// execute 1st test</span></div>
+<div class="line"><span class="lineno"> 1301</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno"> 1302</span>        <a class="code hl_function" href="../../db/dbc/tree__234_8cpp.html#af1ac73779b0fcfbbdce3976c0ca57342">test2</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/stol.html">std::stoi</a>(argv[1]));  <span class="comment">// execute 2nd test</span></div>
+<div class="line"><span class="lineno"> 1303</span>    }</div>
+<div class="line"><span class="lineno"> 1304</span> </div>
+<div class="line"><span class="lineno"> 1305</span>    <span class="keywordflow">return</span> 0;</div>
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 <div class="ttc" id="atree__234_8cpp_html_af1ac73779b0fcfbbdce3976c0ca57342"><div class="ttname"><a href="../../db/dbc/tree__234_8cpp.html#af1ac73779b0fcfbbdce3976c0ca57342">test2</a></div><div class="ttdeci">static void test2(int64_t n)</div><div class="ttdoc">simple test to insert continuous number of range [0, n), and print the tree</div><div class="ttdef"><b>Definition:</b> tree_234.cpp:1281</div></div>
@@ -228,18 +228,18 @@ Here is the call graph for this function:</div>
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 <p>simple test to insert a given array and delete some item, and print the tree </p>
-<div class="fragment"><div class="line"><a id="l01263" name="l01263"></a><span class="lineno"> 1263</span>                    {</div>
-<div class="line"><a id="l01264" name="l01264"></a><span class="lineno"> 1264</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int16_t, 13&gt;</a> arr = {3, 1, 5, 4, 2, 9, 10, 8, 7, 6, 16, 13, 14};</div>
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-<div class="line"><a id="l01267" name="l01267"></a><span class="lineno"> 1267</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i : arr) {</div>
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-<div class="line"><a id="l01274" name="l01274"></a><span class="lineno"> 1274</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno"> 1263</span>                    {</div>
+<div class="line"><span class="lineno"> 1264</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int16_t, 13&gt;</a> arr = {3, 1, 5, 4, 2, 9, 10, 8, 7, 6, 16, 13, 14};</div>
+<div class="line"><span class="lineno"> 1265</span>    <a class="code hl_class" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html">data_structures::tree_234::Tree234</a> tree;</div>
+<div class="line"><span class="lineno"> 1266</span> </div>
+<div class="line"><span class="lineno"> 1267</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i : arr) {</div>
+<div class="line"><span class="lineno"> 1268</span>        tree.<a class="code hl_function" href="../../d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html#a6749ebb40710c9752a2771eda03c6b3e">Insert</a>(i);</div>
+<div class="line"><span class="lineno"> 1269</span>    }</div>
+<div class="line"><span class="lineno"> 1270</span> </div>
+<div class="line"><span class="lineno"> 1271</span>    <span class="comment">// tree.Remove(10);</span></div>
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@@ -178,26 +178,26 @@ template&lt;typename T &gt; </div>
   </dd>
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-<div class="fragment"><div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>                                                                       {</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    <span class="keywordflow">if</span> (n == 0 ||</div>
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-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>        in_arr[0];  <span class="comment">// variable hare is used for shorter jumps in the array</span></div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>    <span class="keywordflow">do</span> {</div>
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-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   37</span>                                                                       {</div>
+<div class="line"><span class="lineno">   38</span>    <span class="keywordflow">if</span> (n == 0 ||</div>
+<div class="line"><span class="lineno">   39</span>        n == 1) {  <span class="comment">// to find duplicate in an array its size should be atleast 2</span></div>
+<div class="line"><span class="lineno">   40</span>        <span class="keywordflow">return</span> -1;</div>
+<div class="line"><span class="lineno">   41</span>    }</div>
+<div class="line"><span class="lineno">   42</span>    uint32_t tortoise = in_arr[0];  <span class="comment">// variable tortoise is used for the longer</span></div>
+<div class="line"><span class="lineno">   43</span>                                    <span class="comment">// jumps in the array</span></div>
+<div class="line"><span class="lineno">   44</span>    uint32_t hare =</div>
+<div class="line"><span class="lineno">   45</span>        in_arr[0];  <span class="comment">// variable hare is used for shorter jumps in the array</span></div>
+<div class="line"><span class="lineno">   46</span>    <span class="keywordflow">do</span> {</div>
+<div class="line"><span class="lineno">   47</span>        tortoise = in_arr[tortoise];</div>
+<div class="line"><span class="lineno">   48</span>        hare = in_arr[in_arr[hare]];</div>
+<div class="line"><span class="lineno">   49</span>    } <span class="keywordflow">while</span> (tortoise != hare);</div>
+<div class="line"><span class="lineno">   50</span>    tortoise = in_arr[0];</div>
+<div class="line"><span class="lineno">   51</span>    <span class="keywordflow">while</span> (tortoise != hare) {</div>
+<div class="line"><span class="lineno">   52</span>        tortoise = in_arr[tortoise];</div>
+<div class="line"><span class="lineno">   53</span>        hare = in_arr[hare];</div>
+<div class="line"><span class="lineno">   54</span>    }</div>
+<div class="line"><span class="lineno">   55</span>    <span class="keywordflow">return</span> tortoise;</div>
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 <p>Main function. </p>
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-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>}</div>
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+<div class="line"><span class="lineno">   97</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">   98</span>}</div>
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 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>                   {</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <span class="comment">// 1st test</span></div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <span class="comment">// [3, 4, 8, 5, 9, 1, 2, 6, 7, 4] return 4</span></div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> array1 = {3, 4, 8, 5, 9, 1, 2, 6, 7, 4};</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1... &quot;</span>;</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    assert(search::cycle_detection::duplicateNumber(array1, array1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) ==</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>           4);  <span class="comment">// here the duplicate number is 4</span></div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span> </div>
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-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2... &quot;</span>;</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    assert(search::cycle_detection::duplicateNumber(array2, array2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) ==</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>           2);  <span class="comment">// here the duplicate number is 2</span></div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <span class="comment">// [] return -1</span></div>
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-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3... &quot;</span>;</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    assert(search::cycle_detection::duplicateNumber(array3, array3.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) ==</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>           -1);  <span class="comment">// since the input array is empty no duplicate number exists in</span></div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>                 <span class="comment">// this case</span></div>
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-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   64</span>                   {</div>
+<div class="line"><span class="lineno">   65</span>    <span class="comment">// 1st test</span></div>
+<div class="line"><span class="lineno">   66</span>    <span class="comment">// [3, 4, 8, 5, 9, 1, 2, 6, 7, 4] return 4</span></div>
+<div class="line"><span class="lineno">   67</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> array1 = {3, 4, 8, 5, 9, 1, 2, 6, 7, 4};</div>
+<div class="line"><span class="lineno">   68</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1... &quot;</span>;</div>
+<div class="line"><span class="lineno">   69</span>    assert(search::cycle_detection::duplicateNumber(array1, array1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) ==</div>
+<div class="line"><span class="lineno">   70</span>           4);  <span class="comment">// here the duplicate number is 4</span></div>
+<div class="line"><span class="lineno">   71</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   72</span> </div>
+<div class="line"><span class="lineno">   73</span>    <span class="comment">// 2nd test</span></div>
+<div class="line"><span class="lineno">   74</span>    <span class="comment">// [1, 2, 3, 4, 2] return 2</span></div>
+<div class="line"><span class="lineno">   75</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> array2 = {1, 2, 3, 4, 2};</div>
+<div class="line"><span class="lineno">   76</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2... &quot;</span>;</div>
+<div class="line"><span class="lineno">   77</span>    assert(search::cycle_detection::duplicateNumber(array2, array2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) ==</div>
+<div class="line"><span class="lineno">   78</span>           2);  <span class="comment">// here the duplicate number is 2</span></div>
+<div class="line"><span class="lineno">   79</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   80</span> </div>
+<div class="line"><span class="lineno">   81</span>    <span class="comment">// 3rd test</span></div>
+<div class="line"><span class="lineno">   82</span>    <span class="comment">// [] return -1</span></div>
+<div class="line"><span class="lineno">   83</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> array3 = {};</div>
+<div class="line"><span class="lineno">   84</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3... &quot;</span>;</div>
+<div class="line"><span class="lineno">   85</span>    assert(search::cycle_detection::duplicateNumber(array3, array3.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) ==</div>
+<div class="line"><span class="lineno">   86</span>           -1);  <span class="comment">// since the input array is empty no duplicate number exists in</span></div>
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+<div class="line"><span class="lineno">   88</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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     <li class="navelem"><a class="el" href="../../dir_19b2bf9199a15c634a08b1ede1dd896a.html">search</a></li><li class="navelem"><a class="el" href="../../db/dc4/floyd__cycle__detection__algo_8cpp.html">floyd_cycle_detection_algo.cpp</a></li>
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 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;array&gt;</code><br />
 <code>#include &lt;climits&gt;</code><br />
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 <p >Kadane algorithm is used to find the maximum sum subarray in an array and maximum sum subarray problem is the task of finding a contiguous subarray with the largest sum</p>
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 Algorithm</h3>
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 <p>Main function. </p>
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 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>                   {</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <span class="comment">// 1st test</span></div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test &quot;</span>;</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> matching1 = <span class="stringliteral">&quot;baaabab&quot;</span>;</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> pattern1 = <span class="stringliteral">&quot;*****ba*****ab&quot;</span>;</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    assert(backtracking::wildcard_matching::wildcard_matching(matching1,</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>                                                              pattern1, 0, 0) ==</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>           1);  <span class="comment">// here the pattern matches with given string</span></div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span> </div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <span class="comment">// 2nd test</span></div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test &quot;</span>;</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> matching2 = <span class="stringliteral">&quot;baaabab&quot;</span>;</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> pattern2 = <span class="stringliteral">&quot;ba*****ab&quot;</span>;</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    assert(backtracking::wildcard_matching::wildcard_matching(matching2,</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>                                                              pattern2, 0, 0) ==</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>           1);  <span class="comment">// here the pattern matches with given string</span></div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span> </div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <span class="comment">// 3rd test</span></div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3rd test &quot;</span>;</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> matching3 = <span class="stringliteral">&quot;baaabab&quot;</span>;</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> pattern3 = <span class="stringliteral">&quot;ba*ab&quot;</span>;</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    assert(backtracking::wildcard_matching::wildcard_matching(matching3,</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>                                                              pattern3, 0, 0) ==</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>           1);  <span class="comment">// here the pattern matches with given string</span></div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span> </div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    <span class="comment">// 4th test</span></div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4th test &quot;</span>;</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> matching4 = <span class="stringliteral">&quot;baaabab&quot;</span>;</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> pattern4 = <span class="stringliteral">&quot;a*ab&quot;</span>;</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    assert(backtracking::wildcard_matching::wildcard_matching(matching4,</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>                                                              pattern4, 0, 0) ==</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>           1);  <span class="comment">// here the pattern matches with given string</span></div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span> </div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    <span class="comment">// 5th test</span></div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;5th test &quot;</span>;</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> matching5 = <span class="stringliteral">&quot;baaabab&quot;</span>;</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> pattern5 = <span class="stringliteral">&quot;aa?ab&quot;</span>;</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    assert(backtracking::wildcard_matching::wildcard_matching(matching5,</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>                                                              pattern5, 0, 0) ==</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>           1);  <span class="comment">// here the pattern matches with given string</span></div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  101</span>                   {</div>
+<div class="line"><span class="lineno">  102</span>    <span class="comment">// 1st test</span></div>
+<div class="line"><span class="lineno">  103</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test &quot;</span>;</div>
+<div class="line"><span class="lineno">  104</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> matching1 = <span class="stringliteral">&quot;baaabab&quot;</span>;</div>
+<div class="line"><span class="lineno">  105</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> pattern1 = <span class="stringliteral">&quot;*****ba*****ab&quot;</span>;</div>
+<div class="line"><span class="lineno">  106</span>    assert(backtracking::wildcard_matching::wildcard_matching(matching1,</div>
+<div class="line"><span class="lineno">  107</span>                                                              pattern1, 0, 0) ==</div>
+<div class="line"><span class="lineno">  108</span>           1);  <span class="comment">// here the pattern matches with given string</span></div>
+<div class="line"><span class="lineno">  109</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  110</span> </div>
+<div class="line"><span class="lineno">  111</span>    <span class="comment">// 2nd test</span></div>
+<div class="line"><span class="lineno">  112</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test &quot;</span>;</div>
+<div class="line"><span class="lineno">  113</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> matching2 = <span class="stringliteral">&quot;baaabab&quot;</span>;</div>
+<div class="line"><span class="lineno">  114</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> pattern2 = <span class="stringliteral">&quot;ba*****ab&quot;</span>;</div>
+<div class="line"><span class="lineno">  115</span>    assert(backtracking::wildcard_matching::wildcard_matching(matching2,</div>
+<div class="line"><span class="lineno">  116</span>                                                              pattern2, 0, 0) ==</div>
+<div class="line"><span class="lineno">  117</span>           1);  <span class="comment">// here the pattern matches with given string</span></div>
+<div class="line"><span class="lineno">  118</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  119</span> </div>
+<div class="line"><span class="lineno">  120</span>    <span class="comment">// 3rd test</span></div>
+<div class="line"><span class="lineno">  121</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3rd test &quot;</span>;</div>
+<div class="line"><span class="lineno">  122</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> matching3 = <span class="stringliteral">&quot;baaabab&quot;</span>;</div>
+<div class="line"><span class="lineno">  123</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> pattern3 = <span class="stringliteral">&quot;ba*ab&quot;</span>;</div>
+<div class="line"><span class="lineno">  124</span>    assert(backtracking::wildcard_matching::wildcard_matching(matching3,</div>
+<div class="line"><span class="lineno">  125</span>                                                              pattern3, 0, 0) ==</div>
+<div class="line"><span class="lineno">  126</span>           1);  <span class="comment">// here the pattern matches with given string</span></div>
+<div class="line"><span class="lineno">  127</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  128</span> </div>
+<div class="line"><span class="lineno">  129</span>    <span class="comment">// 4th test</span></div>
+<div class="line"><span class="lineno">  130</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4th test &quot;</span>;</div>
+<div class="line"><span class="lineno">  131</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> matching4 = <span class="stringliteral">&quot;baaabab&quot;</span>;</div>
+<div class="line"><span class="lineno">  132</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> pattern4 = <span class="stringliteral">&quot;a*ab&quot;</span>;</div>
+<div class="line"><span class="lineno">  133</span>    assert(backtracking::wildcard_matching::wildcard_matching(matching4,</div>
+<div class="line"><span class="lineno">  134</span>                                                              pattern4, 0, 0) ==</div>
+<div class="line"><span class="lineno">  135</span>           1);  <span class="comment">// here the pattern matches with given string</span></div>
+<div class="line"><span class="lineno">  136</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  137</span> </div>
+<div class="line"><span class="lineno">  138</span>    <span class="comment">// 5th test</span></div>
+<div class="line"><span class="lineno">  139</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;5th test &quot;</span>;</div>
+<div class="line"><span class="lineno">  140</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> matching5 = <span class="stringliteral">&quot;baaabab&quot;</span>;</div>
+<div class="line"><span class="lineno">  141</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> pattern5 = <span class="stringliteral">&quot;aa?ab&quot;</span>;</div>
+<div class="line"><span class="lineno">  142</span>    assert(backtracking::wildcard_matching::wildcard_matching(matching5,</div>
+<div class="line"><span class="lineno">  143</span>                                                              pattern5, 0, 0) ==</div>
+<div class="line"><span class="lineno">  144</span>           1);  <span class="comment">// here the pattern matches with given string</span></div>
+<div class="line"><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  146</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
@@ -286,59 +286,59 @@ Here is the call graph for this function:</div>
         </tr>
       </table>
 </div><div class="memdoc">
-<div class="fragment"><div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>                                      {</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    uint32_t n = s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>();</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>    uint32_t m = p.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>();</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>    <span class="comment">// matching is successfull if both strings are done</span></div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    <span class="keywordflow">if</span> (pos1 == n &amp;&amp; pos2 == m) {</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>    }</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span> </div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <span class="comment">// matching is unsuccessfull if pattern is not finished but matching string</span></div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    <span class="comment">// is</span></div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    <span class="keywordflow">if</span> (pos1 != n &amp;&amp; pos2 == m) {</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    }</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span> </div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>    <span class="comment">// all the remaining characters of patterns must be * inorder to match with</span></div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <span class="comment">// finished string</span></div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    <span class="keywordflow">if</span> (pos1 == n &amp;&amp; pos2 != m) {</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>        <span class="keywordflow">while</span> (pos2 &lt; m &amp;&amp; p[pos2] == <span class="charliteral">&#39;*&#39;</span>) {</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>            pos2++;</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>        }</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span> </div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        <span class="keywordflow">return</span> pos2 == m;</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>    }</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span> </div>
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-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dc/d14/wildcard__matching_8cpp.html#a4a5b107f93db24e424b12899fa692c5a">dpTable</a>[pos1][pos2];</div>
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-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>                   <a class="code hl_namespace" href="../../db/d03/namespacewildcard__matching.html">wildcard_matching</a>(s, p, pos1 + 1, pos2 + 1);</div>
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-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>            <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dc/d14/wildcard__matching_8cpp.html#a4a5b107f93db24e424b12899fa692c5a">dpTable</a>[pos1][pos2] =</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>                       <a class="code hl_namespace" href="../../db/d03/namespacewildcard__matching.html">wildcard_matching</a>(s, p, pos1 + 1, pos2 + 1);</div>
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-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>            <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dc/d14/wildcard__matching_8cpp.html#a4a5b107f93db24e424b12899fa692c5a">dpTable</a>[pos1][pos2] =</div>
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+<div class="fragment"><div class="line"><span class="lineno">   40</span>                                      {</div>
+<div class="line"><span class="lineno">   41</span>    uint32_t n = s.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>();</div>
+<div class="line"><span class="lineno">   42</span>    uint32_t m = p.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>();</div>
+<div class="line"><span class="lineno">   43</span>    <span class="comment">// matching is successfull if both strings are done</span></div>
+<div class="line"><span class="lineno">   44</span>    <span class="keywordflow">if</span> (pos1 == n &amp;&amp; pos2 == m) {</div>
+<div class="line"><span class="lineno">   45</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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+<div class="line"><span class="lineno">   47</span> </div>
+<div class="line"><span class="lineno">   48</span>    <span class="comment">// matching is unsuccessfull if pattern is not finished but matching string</span></div>
+<div class="line"><span class="lineno">   49</span>    <span class="comment">// is</span></div>
+<div class="line"><span class="lineno">   50</span>    <span class="keywordflow">if</span> (pos1 != n &amp;&amp; pos2 == m) {</div>
+<div class="line"><span class="lineno">   51</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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+<div class="line"><span class="lineno">   53</span> </div>
+<div class="line"><span class="lineno">   54</span>    <span class="comment">// all the remaining characters of patterns must be * inorder to match with</span></div>
+<div class="line"><span class="lineno">   55</span>    <span class="comment">// finished string</span></div>
+<div class="line"><span class="lineno">   56</span>    <span class="keywordflow">if</span> (pos1 == n &amp;&amp; pos2 != m) {</div>
+<div class="line"><span class="lineno">   57</span>        <span class="keywordflow">while</span> (pos2 &lt; m &amp;&amp; p[pos2] == <span class="charliteral">&#39;*&#39;</span>) {</div>
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+<div class="line"><span class="lineno">   64</span>    <span class="comment">// if already calculted for these positions</span></div>
+<div class="line"><span class="lineno">   65</span>    <span class="keywordflow">if</span> (dpTable[pos1][pos2] != -1) {</div>
+<div class="line"><span class="lineno">   66</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dc/d14/wildcard__matching_8cpp.html#a4a5b107f93db24e424b12899fa692c5a">dpTable</a>[pos1][pos2];</div>
+<div class="line"><span class="lineno">   67</span>    }</div>
+<div class="line"><span class="lineno">   68</span> </div>
+<div class="line"><span class="lineno">   69</span>    <span class="comment">// if the characters are same just go ahead in both the string</span></div>
+<div class="line"><span class="lineno">   70</span>    <span class="keywordflow">if</span> (s[pos1] == p[pos2]) {</div>
+<div class="line"><span class="lineno">   71</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dc/d14/wildcard__matching_8cpp.html#a4a5b107f93db24e424b12899fa692c5a">dpTable</a>[pos1][pos2] =</div>
+<div class="line"><span class="lineno">   72</span>                   <a class="code hl_namespace" href="../../db/d03/namespacewildcard__matching.html">wildcard_matching</a>(s, p, pos1 + 1, pos2 + 1);</div>
+<div class="line"><span class="lineno">   73</span>    }</div>
+<div class="line"><span class="lineno">   74</span> </div>
+<div class="line"><span class="lineno">   75</span>    <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   76</span>        <span class="comment">// can only single character</span></div>
+<div class="line"><span class="lineno">   77</span>        <span class="keywordflow">if</span> (p[pos2] == <span class="charliteral">&#39;?&#39;</span>) {</div>
+<div class="line"><span class="lineno">   78</span>            <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dc/d14/wildcard__matching_8cpp.html#a4a5b107f93db24e424b12899fa692c5a">dpTable</a>[pos1][pos2] =</div>
+<div class="line"><span class="lineno">   79</span>                       <a class="code hl_namespace" href="../../db/d03/namespacewildcard__matching.html">wildcard_matching</a>(s, p, pos1 + 1, pos2 + 1);</div>
+<div class="line"><span class="lineno">   80</span>        }</div>
+<div class="line"><span class="lineno">   81</span>        <span class="comment">// have choice either to match one or more charcters</span></div>
+<div class="line"><span class="lineno">   82</span>        <span class="keywordflow">else</span> <span class="keywordflow">if</span> (p[pos2] == <span class="charliteral">&#39;*&#39;</span>) {</div>
+<div class="line"><span class="lineno">   83</span>            <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dc/d14/wildcard__matching_8cpp.html#a4a5b107f93db24e424b12899fa692c5a">dpTable</a>[pos1][pos2] =</div>
+<div class="line"><span class="lineno">   84</span>                       <a class="code hl_namespace" href="../../db/d03/namespacewildcard__matching.html">wildcard_matching</a>(s, p, pos1, pos2 + 1) ||</div>
+<div class="line"><span class="lineno">   85</span>                       <a class="code hl_namespace" href="../../db/d03/namespacewildcard__matching.html">wildcard_matching</a>(s, p, pos1 + 1, pos2);</div>
+<div class="line"><span class="lineno">   86</span>        }</div>
+<div class="line"><span class="lineno">   87</span>        <span class="comment">// not possible to match</span></div>
+<div class="line"><span class="lineno">   88</span>        <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   89</span>            <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dc/d14/wildcard__matching_8cpp.html#a4a5b107f93db24e424b12899fa692c5a">dpTable</a>[pos1][pos2] = 0;</div>
+<div class="line"><span class="lineno">   90</span>        }</div>
+<div class="line"><span class="lineno">   91</span>    }</div>
+<div class="line"><span class="lineno">   92</span>}</div>
 <div class="ttc" id="anamespacewildcard__matching_html"><div class="ttname"><a href="../../db/d03/namespacewildcard__matching.html">wildcard_matching</a></div><div class="ttdoc">Functions for the Wildcard Matching problem.</div></div>
 <div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">std::string::length</a></div><div class="ttdeci">T length(T... args)</div></div>
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    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
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@@ -136,30 +136,30 @@ Functions</h2></td></tr>
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 <p >main function </p>
-<div class="fragment"><div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>           {</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    <span class="keywordtype">int</span> n = 0;</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span> </div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Set Pascal&#39;s Triangle Height&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span> </div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <span class="comment">// memory allocation (Assign two-dimensional array to store Pascal triangle)</span></div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <span class="keywordtype">int</span> **arr = <span class="keyword">new</span> <span class="keywordtype">int</span> *[n];</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        arr[i] = <span class="keyword">new</span> <span class="keywordtype">int</span>[2 * n - 1];</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/memset.html">memset</a>(arr[i], 0, <span class="keyword">sizeof</span>(<span class="keywordtype">int</span>) * (2 * n - 1));</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    }</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span> </div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <a class="code hl_function" href="../../dc/d1a/pascal__triangle_8cpp.html#a4fc0e5a112f715c3a73989450b2cc5fd">pascal_triangle</a>(arr, n);</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <a class="code hl_function" href="../../dc/d1a/pascal__triangle_8cpp.html#ad7a31d9cb2818d21b1ba12aead7f4c5c">show_pascal</a>(arr, n);</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span> </div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <span class="comment">// deallocation</span></div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        <span class="keyword">delete</span>[] arr[i];</div>
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-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    <span class="keyword">delete</span>[] arr;</div>
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-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   52</span>           {</div>
+<div class="line"><span class="lineno">   53</span>    <span class="keywordtype">int</span> n = 0;</div>
+<div class="line"><span class="lineno">   54</span> </div>
+<div class="line"><span class="lineno">   55</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Set Pascal&#39;s Triangle Height&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   56</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
+<div class="line"><span class="lineno">   57</span> </div>
+<div class="line"><span class="lineno">   58</span>    <span class="comment">// memory allocation (Assign two-dimensional array to store Pascal triangle)</span></div>
+<div class="line"><span class="lineno">   59</span>    <span class="keywordtype">int</span> **arr = <span class="keyword">new</span> <span class="keywordtype">int</span> *[n];</div>
+<div class="line"><span class="lineno">   60</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
+<div class="line"><span class="lineno">   61</span>        arr[i] = <span class="keyword">new</span> <span class="keywordtype">int</span>[2 * n - 1];</div>
+<div class="line"><span class="lineno">   62</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/memset.html">memset</a>(arr[i], 0, <span class="keyword">sizeof</span>(<span class="keywordtype">int</span>) * (2 * n - 1));</div>
+<div class="line"><span class="lineno">   63</span>    }</div>
+<div class="line"><span class="lineno">   64</span> </div>
+<div class="line"><span class="lineno">   65</span>    <a class="code hl_function" href="../../dc/d1a/pascal__triangle_8cpp.html#a4fc0e5a112f715c3a73989450b2cc5fd">pascal_triangle</a>(arr, n);</div>
+<div class="line"><span class="lineno">   66</span>    <a class="code hl_function" href="../../dc/d1a/pascal__triangle_8cpp.html#ad7a31d9cb2818d21b1ba12aead7f4c5c">show_pascal</a>(arr, n);</div>
+<div class="line"><span class="lineno">   67</span> </div>
+<div class="line"><span class="lineno">   68</span>    <span class="comment">// deallocation</span></div>
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@@ -202,25 +202,25 @@ template&lt;typename T &gt; </div>
   </dd>
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 <dl class="section return"><dt>Returns</dt><dd>fitted regression model polynomial coefficients </dd></dl>
-<div class="fragment"><div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>                                                            {</div>
-<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>    <span class="comment">// NxF</span></div>
-<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; X2 = X;</div>
-<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; X2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
-<div class="line"><a id="l00326" name="l00326"></a><span class="lineno">  326</span>        <span class="comment">// add Y-intercept -&gt; Nx(F+1)</span></div>
-<div class="line"><a id="l00327" name="l00327"></a><span class="lineno">  327</span>        X2[i].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(1);</div>
-<div class="line"><a id="l00328" name="l00328"></a><span class="lineno">  328</span>    }</div>
-<div class="line"><a id="l00329" name="l00329"></a><span class="lineno">  329</span>    <span class="comment">// (F+1)xN</span></div>
-<div class="line"><a id="l00330" name="l00330"></a><span class="lineno">  330</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; Xt = <a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a21c80569aaffb7bf1657e54fa4b97deb">get_transpose</a>(X2);</div>
-<div class="line"><a id="l00331" name="l00331"></a><span class="lineno">  331</span>    <span class="comment">// (F+1)x(F+1)</span></div>
-<div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; tmp = <a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#af7243bdc6ae3c7169f01b85bb226e66a">get_inverse</a>(Xt * X2);</div>
-<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>    <span class="comment">// (F+1)xN</span></div>
-<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; out = tmp * Xt;</div>
-<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span>    <span class="comment">// cout &lt;&lt; endl</span></div>
-<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span>    <span class="comment">//      &lt;&lt; &quot;Projection matrix: &quot; &lt;&lt; X2 * out &lt;&lt; endl;</span></div>
-<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span> </div>
-<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span>    <span class="comment">// Fx1,1    -&gt; (F+1)^th element is the independent constant</span></div>
-<div class="line"><a id="l00339" name="l00339"></a><span class="lineno">  339</span>    <span class="keywordflow">return</span> out * Y;</div>
-<div class="line"><a id="l00340" name="l00340"></a><span class="lineno">  340</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  322</span>                                                            {</div>
+<div class="line"><span class="lineno">  323</span>    <span class="comment">// NxF</span></div>
+<div class="line"><span class="lineno">  324</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; X2 = X;</div>
+<div class="line"><span class="lineno">  325</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; X2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
+<div class="line"><span class="lineno">  326</span>        <span class="comment">// add Y-intercept -&gt; Nx(F+1)</span></div>
+<div class="line"><span class="lineno">  327</span>        X2[i].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(1);</div>
+<div class="line"><span class="lineno">  328</span>    }</div>
+<div class="line"><span class="lineno">  329</span>    <span class="comment">// (F+1)xN</span></div>
+<div class="line"><span class="lineno">  330</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; Xt = <a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a21c80569aaffb7bf1657e54fa4b97deb">get_transpose</a>(X2);</div>
+<div class="line"><span class="lineno">  331</span>    <span class="comment">// (F+1)x(F+1)</span></div>
+<div class="line"><span class="lineno">  332</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; tmp = <a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#af7243bdc6ae3c7169f01b85bb226e66a">get_inverse</a>(Xt * X2);</div>
+<div class="line"><span class="lineno">  333</span>    <span class="comment">// (F+1)xN</span></div>
+<div class="line"><span class="lineno">  334</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; out = tmp * Xt;</div>
+<div class="line"><span class="lineno">  335</span>    <span class="comment">// cout &lt;&lt; endl</span></div>
+<div class="line"><span class="lineno">  336</span>    <span class="comment">//      &lt;&lt; &quot;Projection matrix: &quot; &lt;&lt; X2 * out &lt;&lt; endl;</span></div>
+<div class="line"><span class="lineno">  337</span> </div>
+<div class="line"><span class="lineno">  338</span>    <span class="comment">// Fx1,1    -&gt; (F+1)^th element is the independent constant</span></div>
+<div class="line"><span class="lineno">  339</span>    <span class="keywordflow">return</span> out * Y;</div>
+<div class="line"><span class="lineno">  340</span>}</div>
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 <div class="ttc" id="aordinary__least__squares__regressor_8cpp_html_af7243bdc6ae3c7169f01b85bb226e66a"><div class="ttname"><a href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#af7243bdc6ae3c7169f01b85bb226e66a">get_inverse</a></div><div class="ttdeci">std::vector&lt; std::vector&lt; float &gt; &gt; get_inverse(std::vector&lt; std::vector&lt; T &gt; &gt; const &amp;A)</div><div class="ttdef"><b>Definition:</b> ordinary_least_squares_regressor.cpp:226</div></div>
 <div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
@@ -253,73 +253,73 @@ template&lt;typename T &gt; </div>
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 <p >Get matrix inverse using Row-trasnformations. Given matrix must be a square and non-singular. </p><dl class="section return"><dt>Returns</dt><dd>inverse matrix </dd></dl>
-<div class="fragment"><div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>                                      {</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    <span class="comment">// Assuming A is square matrix</span></div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>    <span class="keywordtype">size_t</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span> </div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; inverse(N);</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row++) {</div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>        <span class="comment">// preallocatae a resultant identity matrix</span></div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>        inverse[row] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a>(N);</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; col++) {</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>            inverse[row][col] = (row == col) ? 1.f : 0.f;</div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>        }</div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>    }</div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span> </div>
-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>    <span class="keywordflow">if</span> (!<a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a8fa731952b0ee3bc7ec51c51ed21911e">is_square</a>(A)) {</div>
-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;A must be a square matrix!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>        <span class="keywordflow">return</span> inverse;</div>
-<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>    }</div>
-<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span> </div>
-<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>    <span class="comment">// preallocatae a temporary matrix identical to A</span></div>
-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; temp(N);</div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row++) {</div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> v(N);</div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; col++) {</div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>            v[col] = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(A[row][col]);</div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>        }</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>        temp[row] = v;</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>    }</div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span> </div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>    <span class="comment">// start transformations</span></div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row++) {</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = row; row2 &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> &amp;&amp; temp[row][row] == 0; row2++) {</div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>            <span class="comment">// this to ensure diagonal elements are not 0</span></div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>            temp[row] = temp[row] + temp[row2];</div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>            inverse[row] = inverse[row] + inverse[row2];</div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>        }</div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span> </div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col2 = row; col2 &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> &amp;&amp; temp[row][row] == 0; col2++) {</div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>            <span class="comment">// this to further ensure diagonal elements are not 0</span></div>
-<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = 0; row2 &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row2++) {</div>
-<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>                temp[row2][row] = temp[row2][row] + temp[row2][col2];</div>
-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>                inverse[row2][row] = inverse[row2][row] + inverse[row2][col2];</div>
-<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>            }</div>
-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>        }</div>
-<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span> </div>
-<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>        <span class="keywordflow">if</span> (temp[row][row] == 0) {</div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>            <span class="comment">// Probably a low-rank matrix and hence singular</span></div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Low-rank matrix, no inverse!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>            <span class="keywordflow">return</span> inverse;</div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>        }</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span> </div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>        <span class="comment">// set diagonal to 1</span></div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>        <span class="keyword">auto</span> divisor = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(temp[row][row]);</div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>        temp[row] = temp[row] / divisor;</div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>        inverse[row] = inverse[row] / divisor;</div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>        <span class="comment">// Row transformations</span></div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = 0; row2 &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row2++) {</div>
-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>            <span class="keywordflow">if</span> (row2 == row) {</div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>                <span class="keywordflow">continue</span>;</div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>            }</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>            <span class="keywordtype">float</span> factor = temp[row2][row];</div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>            temp[row2] = temp[row2] - factor * temp[row];</div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>            inverse[row2] = inverse[row2] - factor * inverse[row];</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>        }</div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>    }</div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span> </div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>    <span class="keywordflow">return</span> inverse;</div>
-<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  227</span>                                      {</div>
+<div class="line"><span class="lineno">  228</span>    <span class="comment">// Assuming A is square matrix</span></div>
+<div class="line"><span class="lineno">  229</span>    <span class="keywordtype">size_t</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">  230</span> </div>
+<div class="line"><span class="lineno">  231</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; inverse(N);</div>
+<div class="line"><span class="lineno">  232</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row++) {</div>
+<div class="line"><span class="lineno">  233</span>        <span class="comment">// preallocatae a resultant identity matrix</span></div>
+<div class="line"><span class="lineno">  234</span>        inverse[row] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a>(N);</div>
+<div class="line"><span class="lineno">  235</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; col++) {</div>
+<div class="line"><span class="lineno">  236</span>            inverse[row][col] = (row == col) ? 1.f : 0.f;</div>
+<div class="line"><span class="lineno">  237</span>        }</div>
+<div class="line"><span class="lineno">  238</span>    }</div>
+<div class="line"><span class="lineno">  239</span> </div>
+<div class="line"><span class="lineno">  240</span>    <span class="keywordflow">if</span> (!<a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a8fa731952b0ee3bc7ec51c51ed21911e">is_square</a>(A)) {</div>
+<div class="line"><span class="lineno">  241</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;A must be a square matrix!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  242</span>        <span class="keywordflow">return</span> inverse;</div>
+<div class="line"><span class="lineno">  243</span>    }</div>
+<div class="line"><span class="lineno">  244</span> </div>
+<div class="line"><span class="lineno">  245</span>    <span class="comment">// preallocatae a temporary matrix identical to A</span></div>
+<div class="line"><span class="lineno">  246</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; temp(N);</div>
+<div class="line"><span class="lineno">  247</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row++) {</div>
+<div class="line"><span class="lineno">  248</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> v(N);</div>
+<div class="line"><span class="lineno">  249</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; col++) {</div>
+<div class="line"><span class="lineno">  250</span>            v[col] = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(A[row][col]);</div>
+<div class="line"><span class="lineno">  251</span>        }</div>
+<div class="line"><span class="lineno">  252</span>        temp[row] = v;</div>
+<div class="line"><span class="lineno">  253</span>    }</div>
+<div class="line"><span class="lineno">  254</span> </div>
+<div class="line"><span class="lineno">  255</span>    <span class="comment">// start transformations</span></div>
+<div class="line"><span class="lineno">  256</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row++) {</div>
+<div class="line"><span class="lineno">  257</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = row; row2 &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> &amp;&amp; temp[row][row] == 0; row2++) {</div>
+<div class="line"><span class="lineno">  258</span>            <span class="comment">// this to ensure diagonal elements are not 0</span></div>
+<div class="line"><span class="lineno">  259</span>            temp[row] = temp[row] + temp[row2];</div>
+<div class="line"><span class="lineno">  260</span>            inverse[row] = inverse[row] + inverse[row2];</div>
+<div class="line"><span class="lineno">  261</span>        }</div>
+<div class="line"><span class="lineno">  262</span> </div>
+<div class="line"><span class="lineno">  263</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col2 = row; col2 &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> &amp;&amp; temp[row][row] == 0; col2++) {</div>
+<div class="line"><span class="lineno">  264</span>            <span class="comment">// this to further ensure diagonal elements are not 0</span></div>
+<div class="line"><span class="lineno">  265</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = 0; row2 &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row2++) {</div>
+<div class="line"><span class="lineno">  266</span>                temp[row2][row] = temp[row2][row] + temp[row2][col2];</div>
+<div class="line"><span class="lineno">  267</span>                inverse[row2][row] = inverse[row2][row] + inverse[row2][col2];</div>
+<div class="line"><span class="lineno">  268</span>            }</div>
+<div class="line"><span class="lineno">  269</span>        }</div>
+<div class="line"><span class="lineno">  270</span> </div>
+<div class="line"><span class="lineno">  271</span>        <span class="keywordflow">if</span> (temp[row][row] == 0) {</div>
+<div class="line"><span class="lineno">  272</span>            <span class="comment">// Probably a low-rank matrix and hence singular</span></div>
+<div class="line"><span class="lineno">  273</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Low-rank matrix, no inverse!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  274</span>            <span class="keywordflow">return</span> inverse;</div>
+<div class="line"><span class="lineno">  275</span>        }</div>
+<div class="line"><span class="lineno">  276</span> </div>
+<div class="line"><span class="lineno">  277</span>        <span class="comment">// set diagonal to 1</span></div>
+<div class="line"><span class="lineno">  278</span>        <span class="keyword">auto</span> divisor = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(temp[row][row]);</div>
+<div class="line"><span class="lineno">  279</span>        temp[row] = temp[row] / divisor;</div>
+<div class="line"><span class="lineno">  280</span>        inverse[row] = inverse[row] / divisor;</div>
+<div class="line"><span class="lineno">  281</span>        <span class="comment">// Row transformations</span></div>
+<div class="line"><span class="lineno">  282</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = 0; row2 &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row2++) {</div>
+<div class="line"><span class="lineno">  283</span>            <span class="keywordflow">if</span> (row2 == row) {</div>
+<div class="line"><span class="lineno">  284</span>                <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno">  285</span>            }</div>
+<div class="line"><span class="lineno">  286</span>            <span class="keywordtype">float</span> factor = temp[row2][row];</div>
+<div class="line"><span class="lineno">  287</span>            temp[row2] = temp[row2] - factor * temp[row];</div>
+<div class="line"><span class="lineno">  288</span>            inverse[row2] = inverse[row2] - factor * inverse[row];</div>
+<div class="line"><span class="lineno">  289</span>        }</div>
+<div class="line"><span class="lineno">  290</span>    }</div>
+<div class="line"><span class="lineno">  291</span> </div>
+<div class="line"><span class="lineno">  292</span>    <span class="keywordflow">return</span> inverse;</div>
+<div class="line"><span class="lineno">  293</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div></div>
 <div class="ttc" id="adata__structures_2sparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:47</div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
@@ -351,17 +351,17 @@ template&lt;typename T &gt; </div>
       </table>
 </div><div class="memdoc">
 <p >matrix transpose </p><dl class="section return"><dt>Returns</dt><dd>resultant matrix </dd></dl>
-<div class="fragment"><div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span>                                      {</div>
-<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(A[0].size());</div>
-<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span> </div>
-<div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; A[0].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); row++) {</div>
-<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> v(A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());</div>
-<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); col++) v[col] = A[col][row];</div>
-<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span> </div>
-<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[row] = v;</div>
-<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span>    }</div>
-<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  301</span>                                      {</div>
+<div class="line"><span class="lineno">  302</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(A[0].size());</div>
+<div class="line"><span class="lineno">  303</span> </div>
+<div class="line"><span class="lineno">  304</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; A[0].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); row++) {</div>
+<div class="line"><span class="lineno">  305</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> v(A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());</div>
+<div class="line"><span class="lineno">  306</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); col++) v[col] = A[col][row];</div>
+<div class="line"><span class="lineno">  307</span> </div>
+<div class="line"><span class="lineno">  308</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[row] = v;</div>
+<div class="line"><span class="lineno">  309</span>    }</div>
+<div class="line"><span class="lineno">  310</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  311</span>}</div>
 <div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
 </div><!-- fragment -->
 </div>
@@ -392,16 +392,16 @@ template&lt;typename T &gt; </div>
 </table>
 </div><div class="memdoc">
 <p >function to check if given matrix is a square matrix </p><dl class="section return"><dt>Returns</dt><dd>1 if true, 0 if false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>                                                        {</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <span class="comment">// Assuming A is square matrix</span></div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    <span class="keywordtype">size_t</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        <span class="keywordflow">if</span> (A[i].size() != N) {</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   59</span>                                                        {</div>
+<div class="line"><span class="lineno">   60</span>    <span class="comment">// Assuming A is square matrix</span></div>
+<div class="line"><span class="lineno">   61</span>    <span class="keywordtype">size_t</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   62</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
+<div class="line"><span class="lineno">   63</span>        <span class="keywordflow">if</span> (A[i].size() != N) {</div>
+<div class="line"><span class="lineno">   64</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   65</span>        }</div>
+<div class="line"><span class="lineno">   66</span>    }</div>
+<div class="line"><span class="lineno">   67</span>    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   68</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -421,59 +421,59 @@ template&lt;typename T &gt; </div>
       </table>
 </div><div class="memdoc">
 <p >main function </p>
-<div class="fragment"><div class="line"><a id="l00423" name="l00423"></a><span class="lineno">  423</span>           {</div>
-<div class="line"><a id="l00424" name="l00424"></a><span class="lineno">  424</span>    <a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a4261f3c3c3dfdb86f3004eb8aaffea8d">ols_test</a>();</div>
-<div class="line"><a id="l00425" name="l00425"></a><span class="lineno">  425</span> </div>
-<div class="line"><a id="l00426" name="l00426"></a><span class="lineno">  426</span>    <span class="keywordtype">size_t</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 0, F = 0;</div>
-<div class="line"><a id="l00427" name="l00427"></a><span class="lineno">  427</span> </div>
-<div class="line"><a id="l00428" name="l00428"></a><span class="lineno">  428</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter number of features: &quot;</span>;</div>
-<div class="line"><a id="l00429" name="l00429"></a><span class="lineno">  429</span>    <span class="comment">// number of features = columns</span></div>
-<div class="line"><a id="l00430" name="l00430"></a><span class="lineno">  430</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; F;</div>
-<div class="line"><a id="l00431" name="l00431"></a><span class="lineno">  431</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter number of samples: &quot;</span>;</div>
-<div class="line"><a id="l00432" name="l00432"></a><span class="lineno">  432</span>    <span class="comment">// number of samples = rows</span></div>
-<div class="line"><a id="l00433" name="l00433"></a><span class="lineno">  433</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>;</div>
-<div class="line"><a id="l00434" name="l00434"></a><span class="lineno">  434</span> </div>
-<div class="line"><a id="l00435" name="l00435"></a><span class="lineno">  435</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>(N);</div>
-<div class="line"><a id="l00436" name="l00436"></a><span class="lineno">  436</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> Y(N);</div>
-<div class="line"><a id="l00437" name="l00437"></a><span class="lineno">  437</span> </div>
-<div class="line"><a id="l00438" name="l00438"></a><span class="lineno">  438</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
-<div class="line"><a id="l00439" name="l00439"></a><span class="lineno">  439</span>        &lt;&lt; <span class="stringliteral">&quot;Enter training data. Per sample, provide features and one output.&quot;</span></div>
-<div class="line"><a id="l00440" name="l00440"></a><span class="lineno">  440</span>        &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00441" name="l00441"></a><span class="lineno">  441</span> </div>
-<div class="line"><a id="l00442" name="l00442"></a><span class="lineno">  442</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> rows = 0; rows &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; rows++) {</div>
-<div class="line"><a id="l00443" name="l00443"></a><span class="lineno">  443</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> v(F);</div>
-<div class="line"><a id="l00444" name="l00444"></a><span class="lineno">  444</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Sample# &quot;</span> &lt;&lt; rows + 1 &lt;&lt; <span class="stringliteral">&quot;: &quot;</span>;</div>
-<div class="line"><a id="l00445" name="l00445"></a><span class="lineno">  445</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> cols = 0; cols &lt; F; cols++) {</div>
-<div class="line"><a id="l00446" name="l00446"></a><span class="lineno">  446</span>            <span class="comment">// get the F features</span></div>
-<div class="line"><a id="l00447" name="l00447"></a><span class="lineno">  447</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; v[cols];</div>
-<div class="line"><a id="l00448" name="l00448"></a><span class="lineno">  448</span>        }</div>
-<div class="line"><a id="l00449" name="l00449"></a><span class="lineno">  449</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[rows] = v;</div>
-<div class="line"><a id="l00450" name="l00450"></a><span class="lineno">  450</span>        <span class="comment">// get the corresponding output</span></div>
-<div class="line"><a id="l00451" name="l00451"></a><span class="lineno">  451</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; Y[rows];</div>
-<div class="line"><a id="l00452" name="l00452"></a><span class="lineno">  452</span>    }</div>
-<div class="line"><a id="l00453" name="l00453"></a><span class="lineno">  453</span> </div>
-<div class="line"><a id="l00454" name="l00454"></a><span class="lineno">  454</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> beta = <a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#aaddc683af581b51351e1023d2a01ef3b">fit_OLS_regressor</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, Y);</div>
-<div class="line"><a id="l00455" name="l00455"></a><span class="lineno">  455</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <span class="stringliteral">&quot;beta:&quot;</span> &lt;&lt; beta &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00456" name="l00456"></a><span class="lineno">  456</span> </div>
-<div class="line"><a id="l00457" name="l00457"></a><span class="lineno">  457</span>    <span class="keywordtype">size_t</span> T = 0;</div>
-<div class="line"><a id="l00458" name="l00458"></a><span class="lineno">  458</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter number of test samples: &quot;</span>;</div>
-<div class="line"><a id="l00459" name="l00459"></a><span class="lineno">  459</span>    <span class="comment">// number of test sample inputs</span></div>
-<div class="line"><a id="l00460" name="l00460"></a><span class="lineno">  460</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; T;</div>
-<div class="line"><a id="l00461" name="l00461"></a><span class="lineno">  461</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; data2(T);</div>
-<div class="line"><a id="l00462" name="l00462"></a><span class="lineno">  462</span>    <span class="comment">// vector&lt;float&gt; Y2(T);</span></div>
-<div class="line"><a id="l00463" name="l00463"></a><span class="lineno">  463</span> </div>
-<div class="line"><a id="l00464" name="l00464"></a><span class="lineno">  464</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> rows = 0; rows &lt; T; rows++) {</div>
-<div class="line"><a id="l00465" name="l00465"></a><span class="lineno">  465</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Sample# &quot;</span> &lt;&lt; rows + 1 &lt;&lt; <span class="stringliteral">&quot;: &quot;</span>;</div>
-<div class="line"><a id="l00466" name="l00466"></a><span class="lineno">  466</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> v(F);</div>
-<div class="line"><a id="l00467" name="l00467"></a><span class="lineno">  467</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> cols = 0; cols &lt; F; cols++) std::cin &gt;&gt; v[cols];</div>
-<div class="line"><a id="l00468" name="l00468"></a><span class="lineno">  468</span>        data2[rows] = v;</div>
-<div class="line"><a id="l00469" name="l00469"></a><span class="lineno">  469</span>    }</div>
-<div class="line"><a id="l00470" name="l00470"></a><span class="lineno">  470</span> </div>
-<div class="line"><a id="l00471" name="l00471"></a><span class="lineno">  471</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> out = <a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#ade6e463f37878fe2a219f927c65b5493">predict_OLS_regressor</a>(data2, beta);</div>
-<div class="line"><a id="l00472" name="l00472"></a><span class="lineno">  472</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> rows = 0; rows &lt; T; rows++) <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; out[rows] &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00473" name="l00473"></a><span class="lineno">  473</span> </div>
-<div class="line"><a id="l00474" name="l00474"></a><span class="lineno">  474</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00475" name="l00475"></a><span class="lineno">  475</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  423</span>           {</div>
+<div class="line"><span class="lineno">  424</span>    <a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a4261f3c3c3dfdb86f3004eb8aaffea8d">ols_test</a>();</div>
+<div class="line"><span class="lineno">  425</span> </div>
+<div class="line"><span class="lineno">  426</span>    <span class="keywordtype">size_t</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 0, F = 0;</div>
+<div class="line"><span class="lineno">  427</span> </div>
+<div class="line"><span class="lineno">  428</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter number of features: &quot;</span>;</div>
+<div class="line"><span class="lineno">  429</span>    <span class="comment">// number of features = columns</span></div>
+<div class="line"><span class="lineno">  430</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; F;</div>
+<div class="line"><span class="lineno">  431</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter number of samples: &quot;</span>;</div>
+<div class="line"><span class="lineno">  432</span>    <span class="comment">// number of samples = rows</span></div>
+<div class="line"><span class="lineno">  433</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>;</div>
+<div class="line"><span class="lineno">  434</span> </div>
+<div class="line"><span class="lineno">  435</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>(N);</div>
+<div class="line"><span class="lineno">  436</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> Y(N);</div>
+<div class="line"><span class="lineno">  437</span> </div>
+<div class="line"><span class="lineno">  438</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
+<div class="line"><span class="lineno">  439</span>        &lt;&lt; <span class="stringliteral">&quot;Enter training data. Per sample, provide features and one output.&quot;</span></div>
+<div class="line"><span class="lineno">  440</span>        &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  441</span> </div>
+<div class="line"><span class="lineno">  442</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> rows = 0; rows &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; rows++) {</div>
+<div class="line"><span class="lineno">  443</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> v(F);</div>
+<div class="line"><span class="lineno">  444</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Sample# &quot;</span> &lt;&lt; rows + 1 &lt;&lt; <span class="stringliteral">&quot;: &quot;</span>;</div>
+<div class="line"><span class="lineno">  445</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> cols = 0; cols &lt; F; cols++) {</div>
+<div class="line"><span class="lineno">  446</span>            <span class="comment">// get the F features</span></div>
+<div class="line"><span class="lineno">  447</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; v[cols];</div>
+<div class="line"><span class="lineno">  448</span>        }</div>
+<div class="line"><span class="lineno">  449</span>        <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[rows] = v;</div>
+<div class="line"><span class="lineno">  450</span>        <span class="comment">// get the corresponding output</span></div>
+<div class="line"><span class="lineno">  451</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; Y[rows];</div>
+<div class="line"><span class="lineno">  452</span>    }</div>
+<div class="line"><span class="lineno">  453</span> </div>
+<div class="line"><span class="lineno">  454</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> beta = <a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#aaddc683af581b51351e1023d2a01ef3b">fit_OLS_regressor</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, Y);</div>
+<div class="line"><span class="lineno">  455</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <span class="stringliteral">&quot;beta:&quot;</span> &lt;&lt; beta &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  456</span> </div>
+<div class="line"><span class="lineno">  457</span>    <span class="keywordtype">size_t</span> T = 0;</div>
+<div class="line"><span class="lineno">  458</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter number of test samples: &quot;</span>;</div>
+<div class="line"><span class="lineno">  459</span>    <span class="comment">// number of test sample inputs</span></div>
+<div class="line"><span class="lineno">  460</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; T;</div>
+<div class="line"><span class="lineno">  461</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; data2(T);</div>
+<div class="line"><span class="lineno">  462</span>    <span class="comment">// vector&lt;float&gt; Y2(T);</span></div>
+<div class="line"><span class="lineno">  463</span> </div>
+<div class="line"><span class="lineno">  464</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> rows = 0; rows &lt; T; rows++) {</div>
+<div class="line"><span class="lineno">  465</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Sample# &quot;</span> &lt;&lt; rows + 1 &lt;&lt; <span class="stringliteral">&quot;: &quot;</span>;</div>
+<div class="line"><span class="lineno">  466</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> v(F);</div>
+<div class="line"><span class="lineno">  467</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> cols = 0; cols &lt; F; cols++) std::cin &gt;&gt; v[cols];</div>
+<div class="line"><span class="lineno">  468</span>        data2[rows] = v;</div>
+<div class="line"><span class="lineno">  469</span>    }</div>
+<div class="line"><span class="lineno">  470</span> </div>
+<div class="line"><span class="lineno">  471</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> out = <a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#ade6e463f37878fe2a219f927c65b5493">predict_OLS_regressor</a>(data2, beta);</div>
+<div class="line"><span class="lineno">  472</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> rows = 0; rows &lt; T; rows++) <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; out[rows] &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  473</span> </div>
+<div class="line"><span class="lineno">  474</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  475</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="ahash__search_8cpp_html_a6e1a77282bc65ad359d753d25df23243"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a></div><div class="ttdeci">int data[MAX]</div><div class="ttdoc">test data</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:24</div></div>
 <div class="ttc" id="aordinary__least__squares__regressor_8cpp_html_a4261f3c3c3dfdb86f3004eb8aaffea8d"><div class="ttname"><a href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a4261f3c3c3dfdb86f3004eb8aaffea8d">ols_test</a></div><div class="ttdeci">void ols_test()</div><div class="ttdef"><b>Definition:</b> ordinary_least_squares_regressor.cpp:369</div></div>
@@ -503,56 +503,56 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Self test checks </p>
-<div class="fragment"><div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span>                {</div>
-<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span>    <span class="keywordtype">int</span> F = 3, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 5;</div>
-<div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span> </div>
-<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span>    <span class="comment">/* test function = x^2 -5 */</span></div>
-<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 (quadratic function)....&quot;</span>;</div>
-<div class="line"><a id="l00374" name="l00374"></a><span class="lineno">  374</span>    <span class="comment">// create training data set with features = x, x^2, x^3</span></div>
-<div class="line"><a id="l00375" name="l00375"></a><span class="lineno">  375</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; data1(</div>
-<div class="line"><a id="l00376" name="l00376"></a><span class="lineno">  376</span>        {{-5, 25, -125}, {-1, 1, -1}, {0, 0, 0}, {1, 1, 1}, {6, 36, 216}});</div>
-<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span>    <span class="comment">// create corresponding outputs</span></div>
-<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> Y1({20, -4, -5, -4, 31});</div>
-<div class="line"><a id="l00379" name="l00379"></a><span class="lineno">  379</span>    <span class="comment">// perform regression modelling</span></div>
-<div class="line"><a id="l00380" name="l00380"></a><span class="lineno">  380</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> beta1 = <a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#aaddc683af581b51351e1023d2a01ef3b">fit_OLS_regressor</a>(data1, Y1);</div>
-<div class="line"><a id="l00381" name="l00381"></a><span class="lineno">  381</span>    <span class="comment">// create test data set with same features = x, x^2, x^3</span></div>
-<div class="line"><a id="l00382" name="l00382"></a><span class="lineno">  382</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; test_data1(</div>
-<div class="line"><a id="l00383" name="l00383"></a><span class="lineno">  383</span>        {{-2, 4, -8}, {2, 4, 8}, {-10, 100, -1000}, {10, 100, 1000}});</div>
-<div class="line"><a id="l00384" name="l00384"></a><span class="lineno">  384</span>    <span class="comment">// expected regression outputs</span></div>
-<div class="line"><a id="l00385" name="l00385"></a><span class="lineno">  385</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> expected1({-1, -1, 95, 95});</div>
-<div class="line"><a id="l00386" name="l00386"></a><span class="lineno">  386</span>    <span class="comment">// predicted regression outputs</span></div>
-<div class="line"><a id="l00387" name="l00387"></a><span class="lineno">  387</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> out1 = <a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#ade6e463f37878fe2a219f927c65b5493">predict_OLS_regressor</a>(test_data1, beta1);</div>
-<div class="line"><a id="l00388" name="l00388"></a><span class="lineno">  388</span>    <span class="comment">// compare predicted results are within +-0.01 limit of expected</span></div>
-<div class="line"><a id="l00389" name="l00389"></a><span class="lineno">  389</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> rows = 0; rows &lt; out1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); rows++) {</div>
-<div class="line"><a id="l00390" name="l00390"></a><span class="lineno">  390</span>        assert(std::abs(out1[rows] - expected1[rows]) &lt; 0.01);</div>
-<div class="line"><a id="l00391" name="l00391"></a><span class="lineno">  391</span>    }</div>
-<div class="line"><a id="l00392" name="l00392"></a><span class="lineno">  392</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
-<div class="line"><a id="l00393" name="l00393"></a><span class="lineno">  393</span> </div>
-<div class="line"><a id="l00394" name="l00394"></a><span class="lineno">  394</span>    <span class="comment">/* test function = x^3 + x^2 - 100 */</span></div>
-<div class="line"><a id="l00395" name="l00395"></a><span class="lineno">  395</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 (cubic function)....&quot;</span>;</div>
-<div class="line"><a id="l00396" name="l00396"></a><span class="lineno">  396</span>    <span class="comment">// create training data set with features = x, x^2, x^3</span></div>
-<div class="line"><a id="l00397" name="l00397"></a><span class="lineno">  397</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; data2(</div>
-<div class="line"><a id="l00398" name="l00398"></a><span class="lineno">  398</span>        {{-5, 25, -125}, {-1, 1, -1}, {0, 0, 0}, {1, 1, 1}, {6, 36, 216}});</div>
-<div class="line"><a id="l00399" name="l00399"></a><span class="lineno">  399</span>    <span class="comment">// create corresponding outputs</span></div>
-<div class="line"><a id="l00400" name="l00400"></a><span class="lineno">  400</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> Y2({-200, -100, -100, 98, 152});</div>
-<div class="line"><a id="l00401" name="l00401"></a><span class="lineno">  401</span>    <span class="comment">// perform regression modelling</span></div>
-<div class="line"><a id="l00402" name="l00402"></a><span class="lineno">  402</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> beta2 = <a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#aaddc683af581b51351e1023d2a01ef3b">fit_OLS_regressor</a>(data2, Y2);</div>
-<div class="line"><a id="l00403" name="l00403"></a><span class="lineno">  403</span>    <span class="comment">// create test data set with same features = x, x^2, x^3</span></div>
-<div class="line"><a id="l00404" name="l00404"></a><span class="lineno">  404</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; test_data2(</div>
-<div class="line"><a id="l00405" name="l00405"></a><span class="lineno">  405</span>        {{-2, 4, -8}, {2, 4, 8}, {-10, 100, -1000}, {10, 100, 1000}});</div>
-<div class="line"><a id="l00406" name="l00406"></a><span class="lineno">  406</span>    <span class="comment">// expected regression outputs</span></div>
-<div class="line"><a id="l00407" name="l00407"></a><span class="lineno">  407</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> expected2({-104, -88, -1000, 1000});</div>
-<div class="line"><a id="l00408" name="l00408"></a><span class="lineno">  408</span>    <span class="comment">// predicted regression outputs</span></div>
-<div class="line"><a id="l00409" name="l00409"></a><span class="lineno">  409</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> out2 = <a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#ade6e463f37878fe2a219f927c65b5493">predict_OLS_regressor</a>(test_data2, beta2);</div>
-<div class="line"><a id="l00410" name="l00410"></a><span class="lineno">  410</span>    <span class="comment">// compare predicted results are within +-0.01 limit of expected</span></div>
-<div class="line"><a id="l00411" name="l00411"></a><span class="lineno">  411</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> rows = 0; rows &lt; out2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); rows++) {</div>
-<div class="line"><a id="l00412" name="l00412"></a><span class="lineno">  412</span>        assert(std::abs(out2[rows] - expected2[rows]) &lt; 0.01);</div>
-<div class="line"><a id="l00413" name="l00413"></a><span class="lineno">  413</span>    }</div>
-<div class="line"><a id="l00414" name="l00414"></a><span class="lineno">  414</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
-<div class="line"><a id="l00415" name="l00415"></a><span class="lineno">  415</span> </div>
-<div class="line"><a id="l00416" name="l00416"></a><span class="lineno">  416</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;  <span class="comment">// ensure test results are displayed on screen</span></div>
-<div class="line"><a id="l00417" name="l00417"></a><span class="lineno">  417</span>                             <span class="comment">// (flush stdout)</span></div>
-<div class="line"><a id="l00418" name="l00418"></a><span class="lineno">  418</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  369</span>                {</div>
+<div class="line"><span class="lineno">  370</span>    <span class="keywordtype">int</span> F = 3, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 5;</div>
+<div class="line"><span class="lineno">  371</span> </div>
+<div class="line"><span class="lineno">  372</span>    <span class="comment">/* test function = x^2 -5 */</span></div>
+<div class="line"><span class="lineno">  373</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 (quadratic function)....&quot;</span>;</div>
+<div class="line"><span class="lineno">  374</span>    <span class="comment">// create training data set with features = x, x^2, x^3</span></div>
+<div class="line"><span class="lineno">  375</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; data1(</div>
+<div class="line"><span class="lineno">  376</span>        {{-5, 25, -125}, {-1, 1, -1}, {0, 0, 0}, {1, 1, 1}, {6, 36, 216}});</div>
+<div class="line"><span class="lineno">  377</span>    <span class="comment">// create corresponding outputs</span></div>
+<div class="line"><span class="lineno">  378</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> Y1({20, -4, -5, -4, 31});</div>
+<div class="line"><span class="lineno">  379</span>    <span class="comment">// perform regression modelling</span></div>
+<div class="line"><span class="lineno">  380</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> beta1 = <a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#aaddc683af581b51351e1023d2a01ef3b">fit_OLS_regressor</a>(data1, Y1);</div>
+<div class="line"><span class="lineno">  381</span>    <span class="comment">// create test data set with same features = x, x^2, x^3</span></div>
+<div class="line"><span class="lineno">  382</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; test_data1(</div>
+<div class="line"><span class="lineno">  383</span>        {{-2, 4, -8}, {2, 4, 8}, {-10, 100, -1000}, {10, 100, 1000}});</div>
+<div class="line"><span class="lineno">  384</span>    <span class="comment">// expected regression outputs</span></div>
+<div class="line"><span class="lineno">  385</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> expected1({-1, -1, 95, 95});</div>
+<div class="line"><span class="lineno">  386</span>    <span class="comment">// predicted regression outputs</span></div>
+<div class="line"><span class="lineno">  387</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> out1 = <a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#ade6e463f37878fe2a219f927c65b5493">predict_OLS_regressor</a>(test_data1, beta1);</div>
+<div class="line"><span class="lineno">  388</span>    <span class="comment">// compare predicted results are within +-0.01 limit of expected</span></div>
+<div class="line"><span class="lineno">  389</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> rows = 0; rows &lt; out1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); rows++) {</div>
+<div class="line"><span class="lineno">  390</span>        assert(std::abs(out1[rows] - expected1[rows]) &lt; 0.01);</div>
+<div class="line"><span class="lineno">  391</span>    }</div>
+<div class="line"><span class="lineno">  392</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  393</span> </div>
+<div class="line"><span class="lineno">  394</span>    <span class="comment">/* test function = x^3 + x^2 - 100 */</span></div>
+<div class="line"><span class="lineno">  395</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 (cubic function)....&quot;</span>;</div>
+<div class="line"><span class="lineno">  396</span>    <span class="comment">// create training data set with features = x, x^2, x^3</span></div>
+<div class="line"><span class="lineno">  397</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; data2(</div>
+<div class="line"><span class="lineno">  398</span>        {{-5, 25, -125}, {-1, 1, -1}, {0, 0, 0}, {1, 1, 1}, {6, 36, 216}});</div>
+<div class="line"><span class="lineno">  399</span>    <span class="comment">// create corresponding outputs</span></div>
+<div class="line"><span class="lineno">  400</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> Y2({-200, -100, -100, 98, 152});</div>
+<div class="line"><span class="lineno">  401</span>    <span class="comment">// perform regression modelling</span></div>
+<div class="line"><span class="lineno">  402</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> beta2 = <a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#aaddc683af581b51351e1023d2a01ef3b">fit_OLS_regressor</a>(data2, Y2);</div>
+<div class="line"><span class="lineno">  403</span>    <span class="comment">// create test data set with same features = x, x^2, x^3</span></div>
+<div class="line"><span class="lineno">  404</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; test_data2(</div>
+<div class="line"><span class="lineno">  405</span>        {{-2, 4, -8}, {2, 4, 8}, {-10, 100, -1000}, {10, 100, 1000}});</div>
+<div class="line"><span class="lineno">  406</span>    <span class="comment">// expected regression outputs</span></div>
+<div class="line"><span class="lineno">  407</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> expected2({-104, -88, -1000, 1000});</div>
+<div class="line"><span class="lineno">  408</span>    <span class="comment">// predicted regression outputs</span></div>
+<div class="line"><span class="lineno">  409</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> out2 = <a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#ade6e463f37878fe2a219f927c65b5493">predict_OLS_regressor</a>(test_data2, beta2);</div>
+<div class="line"><span class="lineno">  410</span>    <span class="comment">// compare predicted results are within +-0.01 limit of expected</span></div>
+<div class="line"><span class="lineno">  411</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> rows = 0; rows &lt; out2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); rows++) {</div>
+<div class="line"><span class="lineno">  412</span>        assert(std::abs(out2[rows] - expected2[rows]) &lt; 0.01);</div>
+<div class="line"><span class="lineno">  413</span>    }</div>
+<div class="line"><span class="lineno">  414</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  415</span> </div>
+<div class="line"><span class="lineno">  416</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;  <span class="comment">// ensure test results are displayed on screen</span></div>
+<div class="line"><span class="lineno">  417</span>                             <span class="comment">// (flush stdout)</span></div>
+<div class="line"><span class="lineno">  418</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
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@@ -590,18 +590,18 @@ template&lt;typename T &gt; </div>
       </table>
 </div><div class="memdoc">
 <p >pre-multiplication of a vector by a scalar </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>                                                                      {</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>    <span class="comment">// Number of rows in A</span></div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>    <span class="keywordtype">size_t</span> N_A = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span> </div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(N_A);</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span> </div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N_A; row++) {</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[row] += A[row] * <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(scalar);</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    }</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span> </div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  138</span>                                                                      {</div>
+<div class="line"><span class="lineno">  139</span>    <span class="comment">// Number of rows in A</span></div>
+<div class="line"><span class="lineno">  140</span>    <span class="keywordtype">size_t</span> N_A = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">  141</span> </div>
+<div class="line"><span class="lineno">  142</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(N_A);</div>
+<div class="line"><span class="lineno">  143</span> </div>
+<div class="line"><span class="lineno">  144</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N_A; row++) {</div>
+<div class="line"><span class="lineno">  145</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[row] += A[row] * <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(scalar);</div>
+<div class="line"><span class="lineno">  146</span>    }</div>
+<div class="line"><span class="lineno">  147</span> </div>
+<div class="line"><span class="lineno">  148</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  149</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -640,33 +640,33 @@ template&lt;typename T &gt; </div>
 </div><div class="memdoc">
 <p >Matrix multiplication such that if A is size (mxn) and B is of size (pxq) then the multiplication is defined only when n = p and the resultant matrix is of size (mxq)</p>
 <dl class="section return"><dt>Returns</dt><dd>resultant matrix </dd></dl>
-<div class="fragment"><div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>                                                                        {</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    <span class="comment">// Number of rows in A</span></div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    <span class="keywordtype">size_t</span> N_A = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <span class="comment">// Number of columns in B</span></div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    <span class="keywordtype">size_t</span> N_B = B[0].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span> </div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(N_A);</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span> </div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    <span class="keywordflow">if</span> (A[0].size() != B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) {</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Number of columns in A != Number of rows in B (&quot;</span></div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>                  &lt;&lt; A[0].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    }</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span> </div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N_A; row++) {</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> v(N_B);</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; N_B; col++) {</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>            v[col] = <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(0);</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) {</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>                v[col] += A[row][j] * B[j][col];</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>            }</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>        }</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[row] = v;</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    }</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span> </div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   79</span>                                                                        {</div>
+<div class="line"><span class="lineno">   80</span>    <span class="comment">// Number of rows in A</span></div>
+<div class="line"><span class="lineno">   81</span>    <span class="keywordtype">size_t</span> N_A = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   82</span>    <span class="comment">// Number of columns in B</span></div>
+<div class="line"><span class="lineno">   83</span>    <span class="keywordtype">size_t</span> N_B = B[0].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   84</span> </div>
+<div class="line"><span class="lineno">   85</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(N_A);</div>
+<div class="line"><span class="lineno">   86</span> </div>
+<div class="line"><span class="lineno">   87</span>    <span class="keywordflow">if</span> (A[0].size() != B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) {</div>
+<div class="line"><span class="lineno">   88</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Number of columns in A != Number of rows in B (&quot;</span></div>
+<div class="line"><span class="lineno">   89</span>                  &lt;&lt; A[0].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   90</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">   91</span>    }</div>
+<div class="line"><span class="lineno">   92</span> </div>
+<div class="line"><span class="lineno">   93</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N_A; row++) {</div>
+<div class="line"><span class="lineno">   94</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> v(N_B);</div>
+<div class="line"><span class="lineno">   95</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; N_B; col++) {</div>
+<div class="line"><span class="lineno">   96</span>            v[col] = <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(0);</div>
+<div class="line"><span class="lineno">   97</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) {</div>
+<div class="line"><span class="lineno">   98</span>                v[col] += A[row][j] * B[j][col];</div>
+<div class="line"><span class="lineno">   99</span>            }</div>
+<div class="line"><span class="lineno">  100</span>        }</div>
+<div class="line"><span class="lineno">  101</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[row] = v;</div>
+<div class="line"><span class="lineno">  102</span>    }</div>
+<div class="line"><span class="lineno">  103</span> </div>
+<div class="line"><span class="lineno">  104</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  105</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -698,25 +698,25 @@ template&lt;typename T &gt; </div>
       </table>
 </div><div class="memdoc">
 <p >multiplication of a matrix with a column vector </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>                                                {</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    <span class="comment">// Number of rows in A</span></div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    <span class="keywordtype">size_t</span> N_A = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span> </div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(N_A);</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span> </div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    <span class="keywordflow">if</span> (A[0].size() != B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) {</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Number of columns in A != Number of rows in B (&quot;</span></div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>                  &lt;&lt; A[0].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    }</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span> </div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N_A; row++) {</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[row] = <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(0);</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) result[row] += A[row][j] * B[j];</div>
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-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span> </div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  113</span>                                                {</div>
+<div class="line"><span class="lineno">  114</span>    <span class="comment">// Number of rows in A</span></div>
+<div class="line"><span class="lineno">  115</span>    <span class="keywordtype">size_t</span> N_A = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">  116</span> </div>
+<div class="line"><span class="lineno">  117</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(N_A);</div>
+<div class="line"><span class="lineno">  118</span> </div>
+<div class="line"><span class="lineno">  119</span>    <span class="keywordflow">if</span> (A[0].size() != B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) {</div>
+<div class="line"><span class="lineno">  120</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Number of columns in A != Number of rows in B (&quot;</span></div>
+<div class="line"><span class="lineno">  121</span>                  &lt;&lt; A[0].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  122</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  123</span>    }</div>
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+<div class="line"><span class="lineno">  125</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N_A; row++) {</div>
+<div class="line"><span class="lineno">  126</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[row] = <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(0);</div>
+<div class="line"><span class="lineno">  127</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) result[row] += A[row][j] * B[j];</div>
+<div class="line"><span class="lineno">  128</span>    }</div>
+<div class="line"><span class="lineno">  129</span> </div>
+<div class="line"><span class="lineno">  130</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  131</span>}</div>
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 </div>
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@@ -748,18 +748,18 @@ template&lt;typename T &gt; </div>
       </table>
 </div><div class="memdoc">
 <p >post-multiplication of a vector by a scalar </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>                                                                      {</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>    <span class="comment">// Number of rows in A</span></div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    <span class="keywordtype">size_t</span> N_A = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span> </div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(N_A);</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span> </div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N_A; row++) {</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[row] = A[row] * <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(scalar);</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>    }</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span> </div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  156</span>                                                                      {</div>
+<div class="line"><span class="lineno">  157</span>    <span class="comment">// Number of rows in A</span></div>
+<div class="line"><span class="lineno">  158</span>    <span class="keywordtype">size_t</span> N_A = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">  159</span> </div>
+<div class="line"><span class="lineno">  160</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(N_A);</div>
+<div class="line"><span class="lineno">  161</span> </div>
+<div class="line"><span class="lineno">  162</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N_A; row++) {</div>
+<div class="line"><span class="lineno">  163</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[row] = A[row] * <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(scalar);</div>
+<div class="line"><span class="lineno">  164</span>    }</div>
+<div class="line"><span class="lineno">  165</span> </div>
+<div class="line"><span class="lineno">  166</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  167</span>}</div>
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@@ -797,21 +797,21 @@ template&lt;typename T &gt; </div>
       </table>
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 <p >addition of two vectors of identical lengths </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>                                                                     {</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    <span class="comment">// Number of rows in A</span></div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    <span class="keywordtype">size_t</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span> </div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(N);</div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span> </div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>    <span class="keywordflow">if</span> (B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() != N) {</div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Vector dimensions shouldbe identical!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>        <span class="keywordflow">return</span> A;</div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>    }</div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span> </div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row++) result[row] = A[row] + B[row];</div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span> </div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  204</span>                                                                     {</div>
+<div class="line"><span class="lineno">  205</span>    <span class="comment">// Number of rows in A</span></div>
+<div class="line"><span class="lineno">  206</span>    <span class="keywordtype">size_t</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">  207</span> </div>
+<div class="line"><span class="lineno">  208</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(N);</div>
+<div class="line"><span class="lineno">  209</span> </div>
+<div class="line"><span class="lineno">  210</span>    <span class="keywordflow">if</span> (B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() != N) {</div>
+<div class="line"><span class="lineno">  211</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Vector dimensions shouldbe identical!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  212</span>        <span class="keywordflow">return</span> A;</div>
+<div class="line"><span class="lineno">  213</span>    }</div>
+<div class="line"><span class="lineno">  214</span> </div>
+<div class="line"><span class="lineno">  215</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row++) result[row] = A[row] + B[row];</div>
+<div class="line"><span class="lineno">  216</span> </div>
+<div class="line"><span class="lineno">  217</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  218</span>}</div>
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@@ -849,21 +849,21 @@ template&lt;typename T &gt; </div>
       </table>
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 <p >subtraction of two vectors of identical lengths </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>                                                                     {</div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>    <span class="comment">// Number of rows in A</span></div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>    <span class="keywordtype">size_t</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span> </div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(N);</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span> </div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>    <span class="keywordflow">if</span> (B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() != N) {</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Vector dimensions shouldbe identical!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>        <span class="keywordflow">return</span> A;</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>    }</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span> </div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row++) result[row] = A[row] - B[row];</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span> </div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  183</span>                                                                     {</div>
+<div class="line"><span class="lineno">  184</span>    <span class="comment">// Number of rows in A</span></div>
+<div class="line"><span class="lineno">  185</span>    <span class="keywordtype">size_t</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">  186</span> </div>
+<div class="line"><span class="lineno">  187</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(N);</div>
+<div class="line"><span class="lineno">  188</span> </div>
+<div class="line"><span class="lineno">  189</span>    <span class="keywordflow">if</span> (B.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() != N) {</div>
+<div class="line"><span class="lineno">  190</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Vector dimensions shouldbe identical!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  191</span>        <span class="keywordflow">return</span> A;</div>
+<div class="line"><span class="lineno">  192</span>    }</div>
+<div class="line"><span class="lineno">  193</span> </div>
+<div class="line"><span class="lineno">  194</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; row++) result[row] = A[row] - B[row];</div>
+<div class="line"><span class="lineno">  195</span> </div>
+<div class="line"><span class="lineno">  196</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  197</span>}</div>
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@@ -901,9 +901,9 @@ template&lt;typename T &gt; </div>
       </table>
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 <p >division of a vector by a scalar </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
-<div class="fragment"><div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>                                                                      {</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>    <span class="keywordflow">return</span> (1.f / scalar) * A;</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  174</span>                                                                      {</div>
+<div class="line"><span class="lineno">  175</span>    <span class="keywordflow">return</span> (1.f / scalar) * A;</div>
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@@ -935,20 +935,20 @@ template&lt;typename T &gt; </div>
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 <p >operator to print a matrix </p>
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-<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> width = 10;</div>
-<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>    <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">&#39; &#39;</span>;</div>
-<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span> </div>
-<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; v.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); row++) {</div>
-<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; v[row].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); col++) {</div>
-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>            out &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::left</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(width) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a>(separator)</div>
-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>                &lt;&lt; v[row][col];</div>
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-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>        out &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span> </div>
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+<div class="fragment"><div class="line"><span class="lineno">   23</span>                                                           {</div>
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@@ -160,10 +160,10 @@ solve-a-rat-in-a-maze-c-java-pytho/". </p>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
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@@ -233,36 +233,36 @@ template&lt;size_t size&gt; </div>
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if there exists a solution to move one step ahead in a column or in a row </dd>
 <dd>
 <code>false</code> for the backtracking part </dd></dl>
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+<div class="line"><span class="lineno">   94</span>    <span class="comment">// Backtracking: setup matrix solution to zero</span></div>
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+Collaboration diagram for graph::Graph&lt; T &gt;:</div>
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+</div>
+<center><span class="legend">[<a target="top" href="../../graph_legend.html">legend</a>]</span></center></div>
 <table class="memberdecls">
 <tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
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+          <td class="memname"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html">graph::Graph</a>&lt; T &gt;<a class="el" href="../../da/d9a/class_graph.html">::Graph</a> </td>
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-<div class="fragment"><div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>                                                                           {</div>
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+<div class="line"><span class="lineno">   64</span>        <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;edge : undirected_edges) {</div>
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+<div class="line"><span class="lineno">   66</span>            <a class="code hl_variable" href="../../dc/d61/classgraph_1_1_graph.html#a59940c462861f2fcf4951d1b6c084e6a">neighbors</a>[edge.second].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(edge.first);</div>
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-</div><!-- fragment -->
+<div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
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+</div><!-- fragment --><div class="dynheader">
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 <h2 class="groupheader">Member Function Documentation</h2>
@@ -232,22 +246,22 @@ template&lt;typename T &gt; </div>
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 <p >add_edge(u,v,bidir) is used to add an edge between node u and node v by default , bidir is made true , i.e graph is bidirectional . It means if edge(u,v) is added then u--&gt;v and v--&gt;u both edges exist.</p>
 <p >to make the graph unidirectional pass the third parameter of add_edge as false which will</p>
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+<div class="line"><span class="lineno">   75</span><span class="comment">        /**</span></div>
+<div class="line"><span class="lineno">   76</span><span class="comment">         *  add_edge(u,v,bidir) is used to add an edge between node u and</span></div>
+<div class="line"><span class="lineno">   77</span><span class="comment">         * node v by default , bidir is made true , i.e graph is</span></div>
+<div class="line"><span class="lineno">   78</span><span class="comment">         * bidirectional . It means if edge(u,v) is added then u--&gt;v  and</span></div>
+<div class="line"><span class="lineno">   79</span><span class="comment">         * v--&gt;u both edges exist.</span></div>
+<div class="line"><span class="lineno">   80</span><span class="comment">         *</span></div>
+<div class="line"><span class="lineno">   81</span><span class="comment">         *  to make the graph unidirectional pass the third parameter of</span></div>
+<div class="line"><span class="lineno">   82</span><span class="comment">         * add_edge as false which will</span></div>
+<div class="line"><span class="lineno">   83</span><span class="comment">         */</span></div>
+<div class="line"><span class="lineno">   84</span>        <a class="code hl_variable" href="../../dc/d61/classgraph_1_1_graph.html#acebf0505d625b043bb9c8c27c7a8def0">adjacency_list</a>[u].push_back(v);  <span class="comment">// u--&gt;v edge added</span></div>
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@@ -288,44 +302,44 @@ template&lt;typename T &gt; </div>
 <p >check every vertex connected to the node which are still unvisited</p>
 <p >if the neighbour is unvisited , push it into the queue</p>
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+<div class="fragment"><div class="line"><span class="lineno">   96</span>                                                {<span class="comment"></span></div>
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-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    <span class="keywordtype">double</span> double_expected = NAN;  <span class="comment">// double expected output</span></div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    <span class="keywordtype">double</span> double_area = NAN;      <span class="comment">// double output</span></div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span> </div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    <span class="comment">// 1st test</span></div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>    int_length = 5;</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>    int_expected = 25;</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    int_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a971ce57e368f2f631cf1f4ff3f864049">math::square_area</a>(int_length);</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span> </div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;AREA OF A SQUARE (int)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Length: &quot;</span> &lt;&lt; int_length &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; int_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; int_area &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    assert(int_area == int_expected);</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span> </div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    <span class="comment">// 2nd test</span></div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    float_length = 2.5;</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>    float_expected = 6.25;</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>    float_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a971ce57e368f2f631cf1f4ff3f864049">math::square_area</a>(float_length);</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span> </div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;AREA OF A SQUARE (float)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Length: &quot;</span> &lt;&lt; float_length &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; float_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; float_area &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>    assert(float_area == float_expected);</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span> </div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>    <span class="comment">// 3rd test</span></div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>    int_length = 4;</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>    int_width = 7;</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>    int_expected = 28;</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    int_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#ab31d141f7c5b551746b1eee0eb4dedca">math::rect_area</a>(int_length, int_width);</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span> </div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;AREA OF A RECTANGLE (int)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Length: &quot;</span> &lt;&lt; int_length &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Width: &quot;</span> &lt;&lt; int_width &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; int_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; int_area &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>    assert(int_area == int_expected);</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span> </div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>    <span class="comment">// 4th test</span></div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>    double_length = 2.5;</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>    double_width = 5.7;</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>    double_expected = 14.25;</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>    double_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#ab31d141f7c5b551746b1eee0eb4dedca">math::rect_area</a>(double_length, double_width);</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span> </div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;AREA OF A RECTANGLE (double)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Length: &quot;</span> &lt;&lt; double_length &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Width: &quot;</span> &lt;&lt; double_width &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; double_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; double_area &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>    assert(double_area == double_expected);</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span> </div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>    <span class="comment">// 5th test</span></div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>    int_base = 10;</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>    int_height = 3;</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>    int_expected = 15;</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>    int_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#ab3b920cc56442abd92279ba23b50f4dc">math::triangle_area</a>(int_base, int_height);</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span> </div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;AREA OF A TRIANGLE&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Base: &quot;</span> &lt;&lt; int_base &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Height: &quot;</span> &lt;&lt; int_height &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; int_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; int_area &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>    assert(int_area == int_expected);</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span> </div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>    <span class="comment">// 6th test</span></div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    double_radius = 6;</div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    double_expected =</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>        113.09733552923255;  <span class="comment">// rounded down because the double datatype</span></div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>                             <span class="comment">// truncates after 14 decimal places</span></div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>    double_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a40e36c67da78d2131408c57ee091ad75">math::circle_area</a>(double_radius);</div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span> </div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;AREA OF A CIRCLE&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Radius: &quot;</span> &lt;&lt; double_radius &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; double_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; double_area &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>    assert(double_area == double_expected);</div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span> </div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>    <span class="comment">// 7th test</span></div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>    int_base = 6;</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>    int_height = 7;</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>    int_expected = 42;</div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>    int_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a5de184925e68658f15415dd53954df4f">math::parallelogram_area</a>(int_base, int_height);</div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span> </div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;AREA OF A PARALLELOGRAM&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Base: &quot;</span> &lt;&lt; int_base &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Height: &quot;</span> &lt;&lt; int_height &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; int_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; int_area &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>    assert(int_area == int_expected);</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span> </div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>    <span class="comment">// 8th test</span></div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>    double_length = 5.5;</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>    double_expected = 181.5;</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>    double_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#abc46c784a297fc1d2eb8b33a327fba4c">math::cube_surface_area</a>(double_length);</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span> </div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;SURFACE AREA OF A CUBE&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Length: &quot;</span> &lt;&lt; double_length &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; double_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; double_area &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>    assert(double_area == double_expected);</div>
-<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span> </div>
-<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>    <span class="comment">// 9th test</span></div>
-<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>    double_radius = 10.0;</div>
-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>    double_expected = 1256.6370614359172;  <span class="comment">// rounded down because the whole</span></div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>                                           <span class="comment">// value gets truncated</span></div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>    double_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#ab7f29862d30df351c317eedd60a0c656">math::sphere_surface_area</a>(double_radius);</div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span> </div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;SURFACE AREA OF A SPHERE&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Radius: &quot;</span> &lt;&lt; double_radius &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; double_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; double_area &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>    assert(double_area == double_expected);</div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span> </div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>    <span class="comment">// 10th test</span></div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>    double_radius = 4.0;</div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>    double_height = 7.0;</div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>    double_expected = 276.46015351590177;</div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>    double_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#ac5803413618fcfb922cb32c6db0fc864">math::cylinder_surface_area</a>(double_radius, double_height);</div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span> </div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;SURFACE AREA OF A CYLINDER&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Radius: &quot;</span> &lt;&lt; double_radius &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Height: &quot;</span> &lt;&lt; double_height &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; double_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; double_area &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>    assert(double_area == double_expected);</div>
-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  118</span>                   {</div>
+<div class="line"><span class="lineno">  119</span>    <span class="comment">// I/O variables for testing</span></div>
+<div class="line"><span class="lineno">  120</span>    uint16_t int_length = 0;    <span class="comment">// 16 bit integer length input</span></div>
+<div class="line"><span class="lineno">  121</span>    uint16_t int_width = 0;     <span class="comment">// 16 bit integer width input</span></div>
+<div class="line"><span class="lineno">  122</span>    uint16_t int_base = 0;      <span class="comment">// 16 bit integer base input</span></div>
+<div class="line"><span class="lineno">  123</span>    uint16_t int_height = 0;    <span class="comment">// 16 bit integer height input</span></div>
+<div class="line"><span class="lineno">  124</span>    uint16_t int_expected = 0;  <span class="comment">// 16 bit integer expected output</span></div>
+<div class="line"><span class="lineno">  125</span>    uint16_t int_area = 0;      <span class="comment">// 16 bit integer output</span></div>
+<div class="line"><span class="lineno">  126</span> </div>
+<div class="line"><span class="lineno">  127</span>    <span class="keywordtype">float</span> float_length = NAN;    <span class="comment">// float length input</span></div>
+<div class="line"><span class="lineno">  128</span>    <span class="keywordtype">float</span> float_expected = NAN;  <span class="comment">// float expected output</span></div>
+<div class="line"><span class="lineno">  129</span>    <span class="keywordtype">float</span> float_area = NAN;      <span class="comment">// float output</span></div>
+<div class="line"><span class="lineno">  130</span> </div>
+<div class="line"><span class="lineno">  131</span>    <span class="keywordtype">double</span> double_length = NAN;    <span class="comment">// double length input</span></div>
+<div class="line"><span class="lineno">  132</span>    <span class="keywordtype">double</span> double_width = NAN;     <span class="comment">// double width input</span></div>
+<div class="line"><span class="lineno">  133</span>    <span class="keywordtype">double</span> double_radius = NAN;    <span class="comment">// double radius input</span></div>
+<div class="line"><span class="lineno">  134</span>    <span class="keywordtype">double</span> double_height = NAN;    <span class="comment">// double height input</span></div>
+<div class="line"><span class="lineno">  135</span>    <span class="keywordtype">double</span> double_expected = NAN;  <span class="comment">// double expected output</span></div>
+<div class="line"><span class="lineno">  136</span>    <span class="keywordtype">double</span> double_area = NAN;      <span class="comment">// double output</span></div>
+<div class="line"><span class="lineno">  137</span> </div>
+<div class="line"><span class="lineno">  138</span>    <span class="comment">// 1st test</span></div>
+<div class="line"><span class="lineno">  139</span>    int_length = 5;</div>
+<div class="line"><span class="lineno">  140</span>    int_expected = 25;</div>
+<div class="line"><span class="lineno">  141</span>    int_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a971ce57e368f2f631cf1f4ff3f864049">math::square_area</a>(int_length);</div>
+<div class="line"><span class="lineno">  142</span> </div>
+<div class="line"><span class="lineno">  143</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;AREA OF A SQUARE (int)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  144</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Length: &quot;</span> &lt;&lt; int_length &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; int_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  146</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; int_area &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  147</span>    assert(int_area == int_expected);</div>
+<div class="line"><span class="lineno">  148</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  149</span> </div>
+<div class="line"><span class="lineno">  150</span>    <span class="comment">// 2nd test</span></div>
+<div class="line"><span class="lineno">  151</span>    float_length = 2.5;</div>
+<div class="line"><span class="lineno">  152</span>    float_expected = 6.25;</div>
+<div class="line"><span class="lineno">  153</span>    float_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a971ce57e368f2f631cf1f4ff3f864049">math::square_area</a>(float_length);</div>
+<div class="line"><span class="lineno">  154</span> </div>
+<div class="line"><span class="lineno">  155</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;AREA OF A SQUARE (float)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  156</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Length: &quot;</span> &lt;&lt; float_length &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  157</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; float_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  158</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; float_area &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  159</span>    assert(float_area == float_expected);</div>
+<div class="line"><span class="lineno">  160</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  161</span> </div>
+<div class="line"><span class="lineno">  162</span>    <span class="comment">// 3rd test</span></div>
+<div class="line"><span class="lineno">  163</span>    int_length = 4;</div>
+<div class="line"><span class="lineno">  164</span>    int_width = 7;</div>
+<div class="line"><span class="lineno">  165</span>    int_expected = 28;</div>
+<div class="line"><span class="lineno">  166</span>    int_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#ab31d141f7c5b551746b1eee0eb4dedca">math::rect_area</a>(int_length, int_width);</div>
+<div class="line"><span class="lineno">  167</span> </div>
+<div class="line"><span class="lineno">  168</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;AREA OF A RECTANGLE (int)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  169</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Length: &quot;</span> &lt;&lt; int_length &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  170</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Width: &quot;</span> &lt;&lt; int_width &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  171</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; int_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  172</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; int_area &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  173</span>    assert(int_area == int_expected);</div>
+<div class="line"><span class="lineno">  174</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  175</span> </div>
+<div class="line"><span class="lineno">  176</span>    <span class="comment">// 4th test</span></div>
+<div class="line"><span class="lineno">  177</span>    double_length = 2.5;</div>
+<div class="line"><span class="lineno">  178</span>    double_width = 5.7;</div>
+<div class="line"><span class="lineno">  179</span>    double_expected = 14.25;</div>
+<div class="line"><span class="lineno">  180</span>    double_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#ab31d141f7c5b551746b1eee0eb4dedca">math::rect_area</a>(double_length, double_width);</div>
+<div class="line"><span class="lineno">  181</span> </div>
+<div class="line"><span class="lineno">  182</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;AREA OF A RECTANGLE (double)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  183</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Length: &quot;</span> &lt;&lt; double_length &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  184</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Width: &quot;</span> &lt;&lt; double_width &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  185</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; double_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  186</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; double_area &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  187</span>    assert(double_area == double_expected);</div>
+<div class="line"><span class="lineno">  188</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  189</span> </div>
+<div class="line"><span class="lineno">  190</span>    <span class="comment">// 5th test</span></div>
+<div class="line"><span class="lineno">  191</span>    int_base = 10;</div>
+<div class="line"><span class="lineno">  192</span>    int_height = 3;</div>
+<div class="line"><span class="lineno">  193</span>    int_expected = 15;</div>
+<div class="line"><span class="lineno">  194</span>    int_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#ab3b920cc56442abd92279ba23b50f4dc">math::triangle_area</a>(int_base, int_height);</div>
+<div class="line"><span class="lineno">  195</span> </div>
+<div class="line"><span class="lineno">  196</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;AREA OF A TRIANGLE&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  197</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Base: &quot;</span> &lt;&lt; int_base &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  198</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Height: &quot;</span> &lt;&lt; int_height &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  199</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; int_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  200</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; int_area &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  201</span>    assert(int_area == int_expected);</div>
+<div class="line"><span class="lineno">  202</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  203</span> </div>
+<div class="line"><span class="lineno">  204</span>    <span class="comment">// 6th test</span></div>
+<div class="line"><span class="lineno">  205</span>    double_radius = 6;</div>
+<div class="line"><span class="lineno">  206</span>    double_expected =</div>
+<div class="line"><span class="lineno">  207</span>        113.09733552923255;  <span class="comment">// rounded down because the double datatype</span></div>
+<div class="line"><span class="lineno">  208</span>                             <span class="comment">// truncates after 14 decimal places</span></div>
+<div class="line"><span class="lineno">  209</span>    double_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a40e36c67da78d2131408c57ee091ad75">math::circle_area</a>(double_radius);</div>
+<div class="line"><span class="lineno">  210</span> </div>
+<div class="line"><span class="lineno">  211</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;AREA OF A CIRCLE&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  212</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Radius: &quot;</span> &lt;&lt; double_radius &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  213</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; double_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  214</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; double_area &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  215</span>    assert(double_area == double_expected);</div>
+<div class="line"><span class="lineno">  216</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  217</span> </div>
+<div class="line"><span class="lineno">  218</span>    <span class="comment">// 7th test</span></div>
+<div class="line"><span class="lineno">  219</span>    int_base = 6;</div>
+<div class="line"><span class="lineno">  220</span>    int_height = 7;</div>
+<div class="line"><span class="lineno">  221</span>    int_expected = 42;</div>
+<div class="line"><span class="lineno">  222</span>    int_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a5de184925e68658f15415dd53954df4f">math::parallelogram_area</a>(int_base, int_height);</div>
+<div class="line"><span class="lineno">  223</span> </div>
+<div class="line"><span class="lineno">  224</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;AREA OF A PARALLELOGRAM&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  225</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Base: &quot;</span> &lt;&lt; int_base &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  226</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Height: &quot;</span> &lt;&lt; int_height &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  227</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; int_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  228</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; int_area &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  229</span>    assert(int_area == int_expected);</div>
+<div class="line"><span class="lineno">  230</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  231</span> </div>
+<div class="line"><span class="lineno">  232</span>    <span class="comment">// 8th test</span></div>
+<div class="line"><span class="lineno">  233</span>    double_length = 5.5;</div>
+<div class="line"><span class="lineno">  234</span>    double_expected = 181.5;</div>
+<div class="line"><span class="lineno">  235</span>    double_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#abc46c784a297fc1d2eb8b33a327fba4c">math::cube_surface_area</a>(double_length);</div>
+<div class="line"><span class="lineno">  236</span> </div>
+<div class="line"><span class="lineno">  237</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;SURFACE AREA OF A CUBE&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  238</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Length: &quot;</span> &lt;&lt; double_length &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  239</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Expected Output: &quot;</span> &lt;&lt; double_expected &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  240</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Output: &quot;</span> &lt;&lt; double_area &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  241</span>    assert(double_area == double_expected);</div>
+<div class="line"><span class="lineno">  242</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;TEST PASSED&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  243</span> </div>
+<div class="line"><span class="lineno">  244</span>    <span class="comment">// 9th test</span></div>
+<div class="line"><span class="lineno">  245</span>    double_radius = 10.0;</div>
+<div class="line"><span class="lineno">  246</span>    double_expected = 1256.6370614359172;  <span class="comment">// rounded down because the whole</span></div>
+<div class="line"><span class="lineno">  247</span>                                           <span class="comment">// value gets truncated</span></div>
+<div class="line"><span class="lineno">  248</span>    double_area = <a class="code hl_function" href="../../dd/d47/namespacemath.html#ab7f29862d30df351c317eedd60a0c656">math::sphere_surface_area</a>(double_radius);</div>
+<div class="line"><span class="lineno">  249</span> </div>
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+<div class="line"><span class="lineno">  251</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input Radius: &quot;</span> &lt;&lt; double_radius &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="fragment"><div class="line"><span class="lineno">  143</span>                                          {</div>
+<div class="line"><span class="lineno">  144</span>        <span class="comment">// Choosing activation (and it&#39;s derivative)</span></div>
+<div class="line"><span class="lineno">  145</span>        <span class="keywordflow">if</span> (activation == <span class="stringliteral">&quot;sigmoid&quot;</span>) {</div>
+<div class="line"><span class="lineno">  146</span>            activation_function = neural_network::activations::sigmoid;</div>
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+<div class="line"><span class="lineno">  149</span>            activation_function = neural_network::activations::relu;</div>
+<div class="line"><span class="lineno">  150</span>            dactivation_function = neural_network::activations::drelu;</div>
+<div class="line"><span class="lineno">  151</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (activation == <span class="stringliteral">&quot;tanh&quot;</span>) {</div>
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+<div class="line"><span class="lineno">  153</span>            dactivation_function = neural_network::activations::dtanh;</div>
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+<div class="line"><span class="lineno">  155</span>            <span class="comment">// Set identity function in casse of none is supplied</span></div>
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+<div class="line"><span class="lineno">  157</span>                neural_network::util_functions::identity_function;</div>
+<div class="line"><span class="lineno">  158</span>            dactivation_function =</div>
+<div class="line"><span class="lineno">  159</span>                neural_network::util_functions::identity_function;</div>
+<div class="line"><span class="lineno">  160</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  161</span>            <span class="comment">// If supplied activation is invalid</span></div>
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+<div class="line"><span class="lineno">  164</span>                         <span class="stringliteral">&quot;tanh} got &quot;</span>;</div>
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+<div class="line"><span class="lineno">  167</span>        }</div>
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+<div class="line"><span class="lineno">  169</span>        this-&gt;neurons = neurons;        <span class="comment">// Setting number of neurons</span></div>
+<div class="line"><span class="lineno">  170</span>        <span class="comment">// Initialize kernel according to flag</span></div>
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@@ -291,35 +291,35 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
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-<div class="fragment"><div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>                                                             {</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>        <span class="comment">// Choosing activation (and it&#39;s derivative)</span></div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>        <span class="keywordflow">if</span> (activation == <span class="stringliteral">&quot;sigmoid&quot;</span>) {</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>            activation_function = neural_network::activations::sigmoid;</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>            dactivation_function = neural_network::activations::sigmoid;</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (activation == <span class="stringliteral">&quot;relu&quot;</span>) {</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>            activation_function = neural_network::activations::relu;</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>            dactivation_function = neural_network::activations::drelu;</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (activation == <span class="stringliteral">&quot;tanh&quot;</span>) {</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>            activation_function = neural_network::activations::tanh;</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>            dactivation_function = neural_network::activations::dtanh;</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (activation == <span class="stringliteral">&quot;none&quot;</span>) {</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>            <span class="comment">// Set identity function in casse of none is supplied</span></div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>            activation_function =</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>                neural_network::util_functions::identity_function;</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>            dactivation_function =</div>
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-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>            <span class="comment">// If supplied activation is invalid</span></div>
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+<div class="fragment"><div class="line"><span class="lineno">  184</span>                                                             {</div>
+<div class="line"><span class="lineno">  185</span>        <span class="comment">// Choosing activation (and it&#39;s derivative)</span></div>
+<div class="line"><span class="lineno">  186</span>        <span class="keywordflow">if</span> (activation == <span class="stringliteral">&quot;sigmoid&quot;</span>) {</div>
+<div class="line"><span class="lineno">  187</span>            activation_function = neural_network::activations::sigmoid;</div>
+<div class="line"><span class="lineno">  188</span>            dactivation_function = neural_network::activations::sigmoid;</div>
+<div class="line"><span class="lineno">  189</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (activation == <span class="stringliteral">&quot;relu&quot;</span>) {</div>
+<div class="line"><span class="lineno">  190</span>            activation_function = neural_network::activations::relu;</div>
+<div class="line"><span class="lineno">  191</span>            dactivation_function = neural_network::activations::drelu;</div>
+<div class="line"><span class="lineno">  192</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (activation == <span class="stringliteral">&quot;tanh&quot;</span>) {</div>
+<div class="line"><span class="lineno">  193</span>            activation_function = neural_network::activations::tanh;</div>
+<div class="line"><span class="lineno">  194</span>            dactivation_function = neural_network::activations::dtanh;</div>
+<div class="line"><span class="lineno">  195</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (activation == <span class="stringliteral">&quot;none&quot;</span>) {</div>
+<div class="line"><span class="lineno">  196</span>            <span class="comment">// Set identity function in casse of none is supplied</span></div>
+<div class="line"><span class="lineno">  197</span>            activation_function =</div>
+<div class="line"><span class="lineno">  198</span>                neural_network::util_functions::identity_function;</div>
+<div class="line"><span class="lineno">  199</span>            dactivation_function =</div>
+<div class="line"><span class="lineno">  200</span>                neural_network::util_functions::identity_function;</div>
+<div class="line"><span class="lineno">  201</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  202</span>            <span class="comment">// If supplied activation is invalid</span></div>
+<div class="line"><span class="lineno">  203</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;ERROR (&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;) : &quot;</span>;</div>
+<div class="line"><span class="lineno">  204</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Invalid argument. Expected {none, sigmoid, relu, &quot;</span></div>
+<div class="line"><span class="lineno">  205</span>                         <span class="stringliteral">&quot;tanh} got &quot;</span>;</div>
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+<div class="line"><span class="lineno">  208</span>        }</div>
+<div class="line"><span class="lineno">  209</span>        this-&gt;activation = activation;  <span class="comment">// Setting activation name</span></div>
+<div class="line"><span class="lineno">  210</span>        this-&gt;neurons = neurons;        <span class="comment">// Setting number of neurons</span></div>
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 Here is the call graph for this function:</div>
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+<div class="line"><span class="lineno">   14</span>        <span class="keyword">auto</span>* nn = <span class="keyword">new</span> <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
+<div class="line"><span class="lineno">   15</span>        nn-&gt;data = val;</div>
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+<div class="line"><span class="lineno">   18</span>        rear = nn;</div>
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@@ -195,14 +195,14 @@ Private Attributes</h2></td></tr>
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-<div class="fragment"><div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>                   {</div>
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+<div class="line"><span class="lineno">   35</span>        n = front;</div>
+<div class="line"><span class="lineno">   36</span>        <span class="keywordflow">if</span> (n) {</div>
+<div class="line"><span class="lineno">   37</span>            front = front-&gt;next;</div>
+<div class="line"><span class="lineno">   38</span>            <span class="keyword">delete</span> n;</div>
+<div class="line"><span class="lineno">   39</span>        }</div>
+<div class="line"><span class="lineno">   40</span>    }</div>
 <div class="ttc" id="astructnode_html"><div class="ttname"><a href="../../d5/da1/structnode.html">node</a></div><div class="ttdef"><b>Definition:</b> avltree.cpp:13</div></div>
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@@ -230,19 +230,19 @@ Private Attributes</h2></td></tr>
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+<div class="fragment"><div class="line"><span class="lineno">   20</span>                          {</div>
+<div class="line"><span class="lineno">   21</span>        <span class="keywordflow">if</span> (front == <span class="keyword">nullptr</span> || rear == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">   22</span>            createNode(val);</div>
+<div class="line"><span class="lineno">   23</span>        }</div>
+<div class="line"><span class="lineno">   24</span>        <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   25</span>            <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>* nn;</div>
+<div class="line"><span class="lineno">   26</span>            nn = <span class="keyword">new</span> <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
+<div class="line"><span class="lineno">   27</span>            nn-&gt;data = val;</div>
+<div class="line"><span class="lineno">   28</span>            rear-&gt;next = nn;</div>
+<div class="line"><span class="lineno">   29</span>            nn-&gt;next = front;</div>
+<div class="line"><span class="lineno">   30</span>            rear = nn;</div>
+<div class="line"><span class="lineno">   31</span>        }</div>
+<div class="line"><span class="lineno">   32</span>    }</div>
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+<div class="line"><span class="lineno">   45</span>            <span class="keywordflow">do</span> {</div>
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+<div class="line"><span class="lineno">   47</span>                ptr = ptr-&gt;next;</div>
+<div class="line"><span class="lineno">   48</span>            } <span class="keywordflow">while</span> (ptr != rear-&gt;next);</div>
+<div class="line"><span class="lineno">   49</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; front-&gt;data &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<!-- Generated by Doxygen 1.9.3 -->
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@@ -148,16 +148,16 @@ Functions</h2></td></tr>
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-<div class="fragment"><div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span>                                {</div>
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+<div class="line"><span class="lineno">   21</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> lc = <span class="stringliteral">&quot;&quot;</span>;</div>
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+<div class="line"><span class="lineno">   25</span>    }</div>
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-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Ignore case-sensitive? 1 = Yes, 0 = No&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; ch;</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>            <span class="keywordflow">if</span> (ch == 1) {</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> lowerCase = <a class="code hl_function" href="../../dc/db5/text__search_8cpp.html#a3f8975d227cd0e58f298b380c5dac0d9">lower</a>(</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>                    paragraph);  <span class="comment">// convert std::string paragraph to lowercase</span></div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>                                 <span class="comment">// and store it in std::string lowerCase</span></div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> lowerCaseWord =</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>                    <a class="code hl_function" href="../../dc/db5/text__search_8cpp.html#a3f8975d227cd0e58f298b380c5dac0d9">lower</a>(word);  <span class="comment">// convert std::string paragraph to lowercase</span></div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>                                  <span class="comment">// and store it in std::string lowerCase</span></div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span> </div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hello, your word is &quot;</span> &lt;&lt; word &lt;&lt; <span class="stringliteral">&quot;!\n&quot;</span>;</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>                <span class="keywordflow">if</span> (lowerCase.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/find.html">find</a>(lowerCaseWord) == std::string::npos) {</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; word &lt;&lt; <span class="stringliteral">&quot; does not exist in the sentence&quot;</span></div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>                              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>                } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The word &quot;</span> &lt;&lt; word</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>                              &lt;&lt; <span class="stringliteral">&quot; is now found at location &quot;</span></div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>                              &lt;&lt; lowerCase.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/find.html">find</a>(lowerCaseWord) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>                              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>                }</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hello, your word is &quot;</span> &lt;&lt; word &lt;&lt; <span class="stringliteral">&quot;!\n&quot;</span>;</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>                <span class="keywordflow">if</span> (paragraph.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/find.html">find</a>(word) == std::string::npos) {</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; word &lt;&lt; <span class="stringliteral">&quot; does not exist in the sentence&quot;</span></div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>                              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>                } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The word &quot;</span> &lt;&lt; word</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>                              &lt;&lt; <span class="stringliteral">&quot; is now found at location &quot;</span></div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>                              &lt;&lt; paragraph.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/find.html">find</a>(word) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>                              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>                }</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>            }</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPress Ctrl + C to exit the program.\n\n&quot;</span>;</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>.get();</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>        }</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    }</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   44</span>           {</div>
+<div class="line"><span class="lineno">   45</span>    <a class="code hl_function" href="../../dc/db5/text__search_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// run self-test implementations</span></div>
+<div class="line"><span class="lineno">   46</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> paragraph;</div>
+<div class="line"><span class="lineno">   47</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Please enter your paragraph: \n&quot;</span>;</div>
+<div class="line"><span class="lineno">   48</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/getline.html">std::getline</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>, paragraph);</div>
+<div class="line"><span class="lineno">   49</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nHello, your paragraph is:\n &quot;</span> &lt;&lt; paragraph &lt;&lt; <span class="stringliteral">&quot;!\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   50</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nThe size of your paragraph = &quot;</span> &lt;&lt; paragraph.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>()</div>
+<div class="line"><span class="lineno">   51</span>              &lt;&lt; <span class="stringliteral">&quot; characters. \n\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   52</span> </div>
+<div class="line"><span class="lineno">   53</span>    <span class="keywordflow">if</span> (paragraph.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/empty.html">empty</a>()) {</div>
+<div class="line"><span class="lineno">   54</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nThe paragraph is empty&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   55</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   56</span>        <span class="keywordtype">int</span> ch = 0;</div>
+<div class="line"><span class="lineno">   57</span>        <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
+<div class="line"><span class="lineno">   58</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> word;</div>
+<div class="line"><span class="lineno">   59</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Please enter the word you are searching for: &quot;</span>;</div>
+<div class="line"><span class="lineno">   60</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/getline.html">std::getline</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>, word);</div>
+<div class="line"><span class="lineno">   61</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Ignore case-sensitive? 1 = Yes, 0 = No&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   62</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; ch;</div>
+<div class="line"><span class="lineno">   63</span>            <span class="keywordflow">if</span> (ch == 1) {</div>
+<div class="line"><span class="lineno">   64</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> lowerCase = <a class="code hl_function" href="../../dc/db5/text__search_8cpp.html#a3f8975d227cd0e58f298b380c5dac0d9">lower</a>(</div>
+<div class="line"><span class="lineno">   65</span>                    paragraph);  <span class="comment">// convert std::string paragraph to lowercase</span></div>
+<div class="line"><span class="lineno">   66</span>                                 <span class="comment">// and store it in std::string lowerCase</span></div>
+<div class="line"><span class="lineno">   67</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> lowerCaseWord =</div>
+<div class="line"><span class="lineno">   68</span>                    <a class="code hl_function" href="../../dc/db5/text__search_8cpp.html#a3f8975d227cd0e58f298b380c5dac0d9">lower</a>(word);  <span class="comment">// convert std::string paragraph to lowercase</span></div>
+<div class="line"><span class="lineno">   69</span>                                  <span class="comment">// and store it in std::string lowerCase</span></div>
+<div class="line"><span class="lineno">   70</span> </div>
+<div class="line"><span class="lineno">   71</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hello, your word is &quot;</span> &lt;&lt; word &lt;&lt; <span class="stringliteral">&quot;!\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   72</span>                <span class="keywordflow">if</span> (lowerCase.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/find.html">find</a>(lowerCaseWord) == std::string::npos) {</div>
+<div class="line"><span class="lineno">   73</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; word &lt;&lt; <span class="stringliteral">&quot; does not exist in the sentence&quot;</span></div>
+<div class="line"><span class="lineno">   74</span>                              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   75</span>                } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   76</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The word &quot;</span> &lt;&lt; word</div>
+<div class="line"><span class="lineno">   77</span>                              &lt;&lt; <span class="stringliteral">&quot; is now found at location &quot;</span></div>
+<div class="line"><span class="lineno">   78</span>                              &lt;&lt; lowerCase.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/find.html">find</a>(lowerCaseWord) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
+<div class="line"><span class="lineno">   79</span>                              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   80</span>                }</div>
+<div class="line"><span class="lineno">   81</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   82</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hello, your word is &quot;</span> &lt;&lt; word &lt;&lt; <span class="stringliteral">&quot;!\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   83</span>                <span class="keywordflow">if</span> (paragraph.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/find.html">find</a>(word) == std::string::npos) {</div>
+<div class="line"><span class="lineno">   84</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; word &lt;&lt; <span class="stringliteral">&quot; does not exist in the sentence&quot;</span></div>
+<div class="line"><span class="lineno">   85</span>                              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   86</span>                } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   87</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The word &quot;</span> &lt;&lt; word</div>
+<div class="line"><span class="lineno">   88</span>                              &lt;&lt; <span class="stringliteral">&quot; is now found at location &quot;</span></div>
+<div class="line"><span class="lineno">   89</span>                              &lt;&lt; paragraph.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/find.html">find</a>(word) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
+<div class="line"><span class="lineno">   90</span>                              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   91</span>                }</div>
+<div class="line"><span class="lineno">   92</span>            }</div>
+<div class="line"><span class="lineno">   93</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPress Ctrl + C to exit the program.\n\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   94</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>.get();</div>
+<div class="line"><span class="lineno">   95</span>        }</div>
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+<div class="line"><span class="lineno">   97</span>    <span class="keywordflow">return</span> 0;</div>
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 <div class="ttc" id="aempty_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/empty.html">std::string::empty</a></div><div class="ttdeci">T empty(T... args)</div></div>
@@ -285,11 +285,11 @@ Here is the call graph for this function:</div>
 
 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>                   {</div>
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-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    assert(<a class="code hl_function" href="../../dc/db5/text__search_8cpp.html#a3f8975d227cd0e58f298b380c5dac0d9">lower</a>(<span class="stringliteral">&quot;abcd&quot;</span>).<a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a>(<span class="stringliteral">&quot;abc&quot;</span>) == 1);</div>
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-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>            <a class="code hl_function" href="../../dc/dc5/paranthesis__matching_8cpp.html#aae41c72130114bf31204cde6873b6095">push</a>(<a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#ac00616a4e40d3cd5cfb4da87d9ff9af0">exp</a>[i]);</div>
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@@ -154,10 +154,10 @@ Functions</h2></td></tr>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>           {</div>
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-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   84</span>           {</div>
+<div class="line"><span class="lineno">   85</span>    <a class="code hl_function" href="../../dc/dd9/strand__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
+<div class="line"><span class="lineno">   86</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">   87</span>}</div>
 <div class="ttc" id="astrand__sort_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../dc/dd9/strand__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Function for testing.</div><div class="ttdef"><b>Definition:</b> strand_sort.cpp:64</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -200,27 +200,27 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>Sorted list&lt;T&gt; instance </dd></dl>
-<div class="fragment"><div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>                                               {</div>
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-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>                <span class="keywordflow">return</span> lst; <span class="comment">// Returns list</span></div>
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-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>                    <span class="keywordflow">if</span> (sorted.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/back.html">back</a>() &lt;= *it) { <span class="comment">// If the last reference of the &quot;sorted&quot; list is less than or equal to the current iterator reference.</span></div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>                        sorted.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/push_back.html">push_back</a>(*it); <span class="comment">// Adds the iterator retrieved in the loop under the &quot;sorted&quot; list.</span></div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>                        it = lst.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/erase.html">erase</a>(it); <span class="comment">// Deletes the element with the current iterator and assigns the deleted element to the iterator.</span></div>
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+<div class="line"><span class="lineno">   38</span>                <span class="keywordflow">return</span> lst; <span class="comment">// Returns list</span></div>
+<div class="line"><span class="lineno">   39</span>            }</div>
+<div class="line"><span class="lineno">   40</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">std::list&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>; <span class="comment">// Define new &quot;result&quot; named list instance.</span></div>
+<div class="line"><span class="lineno">   41</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">std::list&lt;T&gt;</a> sorted; <span class="comment">// Define new &quot;sorted&quot; named list instance.</span></div>
+<div class="line"><span class="lineno">   42</span>            <span class="keywordflow">while</span>(!lst.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/empty.html">empty</a>()) <span class="comment">/* if lst is not empty */</span> {</div>
+<div class="line"><span class="lineno">   43</span>                sorted.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/push_back.html">push_back</a>(lst.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/front.html">front</a>()); <span class="comment">// Adds the first element of &quot;lst&quot; list to the bottom of the &quot;sorted&quot; list.</span></div>
+<div class="line"><span class="lineno">   44</span>                lst.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/pop_front.html">pop_front</a>(); <span class="comment">// Remove first element of &quot;lst&quot; list.</span></div>
+<div class="line"><span class="lineno">   45</span>                <span class="keywordflow">for</span> (<span class="keyword">auto</span> it = lst.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/begin.html">begin</a>(); it != lst.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/end.html">end</a>(); ) { <span class="comment">// Return the loop as long as the current iterator is not equal to the last literator of the &quot;lst&quot; list.</span></div>
+<div class="line"><span class="lineno">   46</span>                    <span class="keywordflow">if</span> (sorted.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/back.html">back</a>() &lt;= *it) { <span class="comment">// If the last reference of the &quot;sorted&quot; list is less than or equal to the current iterator reference.</span></div>
+<div class="line"><span class="lineno">   47</span>                        sorted.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/push_back.html">push_back</a>(*it); <span class="comment">// Adds the iterator retrieved in the loop under the &quot;sorted&quot; list.</span></div>
+<div class="line"><span class="lineno">   48</span>                        it = lst.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/erase.html">erase</a>(it); <span class="comment">// Deletes the element with the current iterator and assigns the deleted element to the iterator.</span></div>
+<div class="line"><span class="lineno">   49</span>                    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   50</span>                        it++; <span class="comment">// Next iterator.</span></div>
+<div class="line"><span class="lineno">   51</span>                    }</div>
+<div class="line"><span class="lineno">   52</span>                }</div>
+<div class="line"><span class="lineno">   53</span>                <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.merge(sorted); <span class="comment">// Merge &quot;result&quot; list with &quot;sorted&quot; list.</span></div>
+<div class="line"><span class="lineno">   54</span>            }</div>
+<div class="line"><span class="lineno">   55</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>; <span class="comment">// Returns sorted list</span></div>
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 <div class="ttc" id="aback_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list/back.html">std::list::back</a></div><div class="ttdeci">T back(T... args)</div></div>
 <div class="ttc" id="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list/begin.html">std::list::begin</a></div><div class="ttdeci">T begin(T... args)</div></div>
 <div class="ttc" id="aempty_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list/empty.html">std::list::empty</a></div><div class="ttdeci">T empty(T... args)</div></div>
@@ -266,21 +266,21 @@ Here is the call graph for this function:</div>
 
 <p>Function for testing. </p>
 <dl class="section return"><dt>Returns</dt><dd>N/A </dd></dl>
-<div class="fragment"><div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>                   {</div>
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-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    lst = <a class="code hl_function" href="../../dc/dd9/strand__sort_8cpp.html#a2bea2fe5dd38ed63610fdeaddf5785cd">sorting::strand::strand_sort</a>(lst); <span class="comment">// Sort list.</span></div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span> </div>
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-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; item &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
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-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   64</span>                   {</div>
+<div class="line"><span class="lineno">   65</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">std::list&lt;int&gt;</a> lst = { -333, 525, 1, 0, 94, 52, 33 };</div>
+<div class="line"><span class="lineno">   66</span> </div>
+<div class="line"><span class="lineno">   67</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Before: &quot;</span>;</div>
+<div class="line"><span class="lineno">   68</span>    <span class="keywordflow">for</span>(<span class="keyword">auto</span> item: lst) {</div>
+<div class="line"><span class="lineno">   69</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; item &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">   70</span>    }</div>
+<div class="line"><span class="lineno">   71</span> </div>
+<div class="line"><span class="lineno">   72</span>    lst = <a class="code hl_function" href="../../dc/dd9/strand__sort_8cpp.html#a2bea2fe5dd38ed63610fdeaddf5785cd">sorting::strand::strand_sort</a>(lst); <span class="comment">// Sort list.</span></div>
+<div class="line"><span class="lineno">   73</span> </div>
+<div class="line"><span class="lineno">   74</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nAfter: &quot;</span>;</div>
+<div class="line"><span class="lineno">   75</span>    <span class="keywordflow">for</span>(<span class="keyword">auto</span> item: lst) {</div>
+<div class="line"><span class="lineno">   76</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; item &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">   77</span>    }</div>
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 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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@@ -292,7 +292,7 @@ Here is the call graph for this function:</div>
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-<p>Recursive version of Inorder, Preorder, and Postorder <a href="https://en.wikipedia.org/wiki/Tree_traversal" target="_blank">Traversal of the Tree</a>  
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 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;cassert&gt;</code><br />
 <code>#include &lt;iostream&gt;</code><br />
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 Iterative Inorder Traversal of a tree</h3>
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 <p>Main function. </p>
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 <p >&lt; result stores the inorder traversal of the binary tree</p>
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-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span><span class="comment">                                             ///&lt; traversal of the binary tree</span></div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span><span class="comment"></span> </div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>    uint64_t size = actual_result_inorder.size();</div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span> </div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>    <span class="comment">// Calling inorder() function by passing a root node,</span></div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>    <span class="comment">// and storing the inorder traversal in result_inorder.</span></div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>    result_inorder = obj1.inorder(root);</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testcase #1: Inorder Traversal...&quot;</span>;</div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 0; i &lt; size; ++i) {</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>        assert(actual_result_inorder[i] == result_inorder[i]);</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>    }</div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span> </div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    <span class="comment">// Calling preorder() function by passing a root node,</span></div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>    <span class="comment">// and storing the preorder traversal in result_preorder.</span></div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>    result_preorder = obj1.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#abce10afbf9e16ce4a788af6b58abbebb">preorder</a>(root);</div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testcase #1: Preorder Traversal...&quot;</span>;</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 0; i &lt; size; ++i) {</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>        assert(actual_result_preorder[i] == result_preorder[i]);</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>    }</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span> </div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>    <span class="comment">// Calling postorder() function by passing a root node,</span></div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>    <span class="comment">// and storing the postorder traversal in result_postorder.</span></div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>    result_postorder = obj1.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a5224e6c2ba322b17cc2c3287b77742d5">postorder</a>(root);</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testcase #1: Postorder Traversal...&quot;</span>;</div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 0; i &lt; size; ++i) {</div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>        assert(actual_result_postorder[i] == result_postorder[i]);</div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>    }</div>
-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span> </div>
-<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  191</span>             {</div>
+<div class="line"><span class="lineno">  192</span>    <a class="code hl_class" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html">others::recursive_tree_traversals::BT</a> obj1;</div>
+<div class="line"><span class="lineno">  193</span>    <a class="code hl_struct" href="../../d9/df7/structothers_1_1recursive__tree__traversals_1_1_node.html">others::recursive_tree_traversals::Node</a> *root = obj1.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(2);</div>
+<div class="line"><span class="lineno">  194</span>    root-&gt;left = obj1.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(7);</div>
+<div class="line"><span class="lineno">  195</span>    root-&gt;right = obj1.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(5);</div>
+<div class="line"><span class="lineno">  196</span>    root-&gt;left-&gt;left = obj1.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(2);</div>
+<div class="line"><span class="lineno">  197</span>    root-&gt;left-&gt;right = obj1.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(6);</div>
+<div class="line"><span class="lineno">  198</span>    root-&gt;right-&gt;right = obj1.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(9);</div>
+<div class="line"><span class="lineno">  199</span>    root-&gt;left-&gt;right-&gt;left = obj1.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(5);</div>
+<div class="line"><span class="lineno">  200</span>    root-&gt;left-&gt;right-&gt;right = obj1.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(11);</div>
+<div class="line"><span class="lineno">  201</span>    root-&gt;right-&gt;right-&gt;left = obj1.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(4);</div>
+<div class="line"><span class="lineno">  202</span> </div>
+<div class="line"><span class="lineno">  203</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> actual_result_inorder{2, 7, 5, 6, 11, 2, 5, 4, 9};</div>
+<div class="line"><span class="lineno">  204</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> actual_result_preorder{2, 7, 2, 6, 5, 11, 5, 9, 4};</div>
+<div class="line"><span class="lineno">  205</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> actual_result_postorder{2, 5, 11, 6, 7, 4, 9, 5, 2};</div>
+<div class="line"><span class="lineno">  206</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> result_inorder;    <span class="comment">///&lt; result stores the inorder</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  207</span><span class="comment">                                             ///&lt; traversal of the binary tree</span></div>
+<div class="line"><span class="lineno">  208</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> result_preorder;   <span class="comment">///&lt; result stores the preorder</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  209</span><span class="comment">                                             ///&lt; traversal of the binary tree</span></div>
+<div class="line"><span class="lineno">  210</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> result_postorder;  <span class="comment">///&lt; result stores the postorder</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  211</span><span class="comment">                                             ///&lt; traversal of the binary tree</span></div>
+<div class="line"><span class="lineno">  212</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  213</span>    uint64_t size = actual_result_inorder.size();</div>
+<div class="line"><span class="lineno">  214</span> </div>
+<div class="line"><span class="lineno">  215</span>    <span class="comment">// Calling inorder() function by passing a root node,</span></div>
+<div class="line"><span class="lineno">  216</span>    <span class="comment">// and storing the inorder traversal in result_inorder.</span></div>
+<div class="line"><span class="lineno">  217</span>    result_inorder = obj1.inorder(root);</div>
+<div class="line"><span class="lineno">  218</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testcase #1: Inorder Traversal...&quot;</span>;</div>
+<div class="line"><span class="lineno">  219</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 0; i &lt; size; ++i) {</div>
+<div class="line"><span class="lineno">  220</span>        assert(actual_result_inorder[i] == result_inorder[i]);</div>
+<div class="line"><span class="lineno">  221</span>    }</div>
+<div class="line"><span class="lineno">  222</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  223</span> </div>
+<div class="line"><span class="lineno">  224</span>    <span class="comment">// Calling preorder() function by passing a root node,</span></div>
+<div class="line"><span class="lineno">  225</span>    <span class="comment">// and storing the preorder traversal in result_preorder.</span></div>
+<div class="line"><span class="lineno">  226</span>    result_preorder = obj1.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#abce10afbf9e16ce4a788af6b58abbebb">preorder</a>(root);</div>
+<div class="line"><span class="lineno">  227</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testcase #1: Preorder Traversal...&quot;</span>;</div>
+<div class="line"><span class="lineno">  228</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 0; i &lt; size; ++i) {</div>
+<div class="line"><span class="lineno">  229</span>        assert(actual_result_preorder[i] == result_preorder[i]);</div>
+<div class="line"><span class="lineno">  230</span>    }</div>
+<div class="line"><span class="lineno">  231</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  232</span> </div>
+<div class="line"><span class="lineno">  233</span>    <span class="comment">// Calling postorder() function by passing a root node,</span></div>
+<div class="line"><span class="lineno">  234</span>    <span class="comment">// and storing the postorder traversal in result_postorder.</span></div>
+<div class="line"><span class="lineno">  235</span>    result_postorder = obj1.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a5224e6c2ba322b17cc2c3287b77742d5">postorder</a>(root);</div>
+<div class="line"><span class="lineno">  236</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testcase #1: Postorder Traversal...&quot;</span>;</div>
+<div class="line"><span class="lineno">  237</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 0; i &lt; size; ++i) {</div>
+<div class="line"><span class="lineno">  238</span>        assert(actual_result_postorder[i] == result_postorder[i]);</div>
+<div class="line"><span class="lineno">  239</span>    }</div>
+<div class="line"><span class="lineno">  240</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  241</span> </div>
+<div class="line"><span class="lineno">  242</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  243</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aclassothers_1_1recursive__tree__traversals_1_1_b_t_html"><div class="ttname"><a href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html">others::recursive_tree_traversals::BT</a></div><div class="ttdoc">BT used to make the entire structure of the binary tree and the functions associated with the binary ...</div><div class="ttdef"><b>Definition:</b> recursive_tree_traversal.cpp:87</div></div>
 <div class="ttc" id="aclassothers_1_1recursive__tree__traversals_1_1_b_t_html_a08711eb2d741f4b51d980cff03b53154"><div class="ttname"><a href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">others::recursive_tree_traversals::BT::createNewNode</a></div><div class="ttdeci">Node * createNewNode(uint64_t)</div><div class="ttdoc">will allocate the memory for a node and, along the data and return the node.</div><div class="ttdef"><b>Definition:</b> recursive_tree_traversal.cpp:116</div></div>
@@ -277,7 +277,7 @@ Here is the call graph for this function:</div>
 <div class="ttc" id="aclassothers_1_1recursive__tree__traversals_1_1_b_t_html_abce10afbf9e16ce4a788af6b58abbebb"><div class="ttname"><a href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#abce10afbf9e16ce4a788af6b58abbebb">others::recursive_tree_traversals::BT::preorder</a></div><div class="ttdeci">std::vector&lt; uint64_t &gt; preorder(Node *)</div><div class="ttdoc">preorder function that will perform the preorder traversal recursively, and return the resultant vect...</div><div class="ttdef"><b>Definition:</b> recursive_tree_traversal.cpp:150</div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
 <div class="ttc" id="astructothers_1_1recursive__tree__traversals_1_1_node_html"><div class="ttname"><a href="../../d9/df7/structothers_1_1recursive__tree__traversals_1_1_node.html">others::recursive_tree_traversals::Node</a></div><div class="ttdoc">The structure to hold Nodes of the tree.</div><div class="ttdef"><b>Definition:</b> recursive_tree_traversal.cpp:78</div></div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; uint64_t &gt;</a></div></div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -301,58 +301,58 @@ Here is the call graph for this function:</div>
 <p >&lt; result stores the inorder traversal of the binary tree</p>
 <p >&lt; result stores the preorder traversal of the binary tree</p>
 <p >&lt; result stores the postorder traversal of the binary tree</p>
-<div class="fragment"><div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>             {</div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>    <a class="code hl_class" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html">others::recursive_tree_traversals::BT</a> obj2;</div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>    <a class="code hl_struct" href="../../d9/df7/structothers_1_1recursive__tree__traversals_1_1_node.html">others::recursive_tree_traversals::Node</a> *root = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(1);</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>    root-&gt;left = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(2);</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>    root-&gt;right = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(3);</div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>    root-&gt;left-&gt;left = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(4);</div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>    root-&gt;right-&gt;left = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(5);</div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>    root-&gt;right-&gt;right = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(6);</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>    root-&gt;right-&gt;left-&gt;left = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(7);</div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>    root-&gt;right-&gt;left-&gt;right = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(8);</div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span> </div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> actual_result_inorder{4, 2, 1, 7, 5, 8, 3, 6};</div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> actual_result_preorder{1, 2, 4, 3, 5, 7, 8, 6};</div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> actual_result_postorder{4, 2, 7, 8, 5, 6, 3, 1};</div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> result_inorder;    <span class="comment">///&lt; result stores the inorder</span><span class="comment"></span></div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span><span class="comment">                                             ///&lt; traversal of the binary tree</span></div>
-<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> result_preorder;   <span class="comment">///&lt; result stores the preorder</span><span class="comment"></span></div>
-<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span><span class="comment">                                             ///&lt; traversal of the binary tree</span></div>
-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> result_postorder;  <span class="comment">///&lt; result stores the postorder</span><span class="comment"></span></div>
-<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span><span class="comment">                                             ///&lt; traversal of the binary tree</span></div>
-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span><span class="comment"></span> </div>
-<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>    uint64_t size = actual_result_inorder.size();</div>
-<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span> </div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>    <span class="comment">// Calling inorder() function by passing a root node,</span></div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>    <span class="comment">// and storing the inorder traversal in result_inorder.</span></div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>    result_inorder = obj2.inorder(root);</div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testcase #2: Inorder Traversal...&quot;</span>;</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 0; i &lt; size; ++i) {</div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>        assert(actual_result_inorder[i] == result_inorder[i]);</div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>    }</div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span> </div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>    <span class="comment">// Calling preorder() function by passing a root node,</span></div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>    <span class="comment">// and storing the preorder traversal in result_preorder.</span></div>
-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>    result_preorder = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#abce10afbf9e16ce4a788af6b58abbebb">preorder</a>(root);</div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testcase #2: Preorder Traversal...&quot;</span>;</div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 0; i &lt; size; ++i) {</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>        assert(actual_result_preorder[i] == result_preorder[i]);</div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>    }</div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span> </div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>    <span class="comment">// Calling postorder() function by passing a root node,</span></div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>    <span class="comment">// and storing the postorder traversal in result_postorder.</span></div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>    result_postorder = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a5224e6c2ba322b17cc2c3287b77742d5">postorder</a>(root);</div>
-<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testcase #2: Postorder Traversal...&quot;</span>;</div>
-<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 0; i &lt; size; ++i) {</div>
-<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span>        assert(actual_result_postorder[i] == result_postorder[i]);</div>
-<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>    }</div>
-<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span> </div>
-<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  249</span>             {</div>
+<div class="line"><span class="lineno">  250</span>    <a class="code hl_class" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html">others::recursive_tree_traversals::BT</a> obj2;</div>
+<div class="line"><span class="lineno">  251</span>    <a class="code hl_struct" href="../../d9/df7/structothers_1_1recursive__tree__traversals_1_1_node.html">others::recursive_tree_traversals::Node</a> *root = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(1);</div>
+<div class="line"><span class="lineno">  252</span>    root-&gt;left = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(2);</div>
+<div class="line"><span class="lineno">  253</span>    root-&gt;right = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(3);</div>
+<div class="line"><span class="lineno">  254</span>    root-&gt;left-&gt;left = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(4);</div>
+<div class="line"><span class="lineno">  255</span>    root-&gt;right-&gt;left = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(5);</div>
+<div class="line"><span class="lineno">  256</span>    root-&gt;right-&gt;right = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(6);</div>
+<div class="line"><span class="lineno">  257</span>    root-&gt;right-&gt;left-&gt;left = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(7);</div>
+<div class="line"><span class="lineno">  258</span>    root-&gt;right-&gt;left-&gt;right = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(8);</div>
+<div class="line"><span class="lineno">  259</span> </div>
+<div class="line"><span class="lineno">  260</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> actual_result_inorder{4, 2, 1, 7, 5, 8, 3, 6};</div>
+<div class="line"><span class="lineno">  261</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> actual_result_preorder{1, 2, 4, 3, 5, 7, 8, 6};</div>
+<div class="line"><span class="lineno">  262</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> actual_result_postorder{4, 2, 7, 8, 5, 6, 3, 1};</div>
+<div class="line"><span class="lineno">  263</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> result_inorder;    <span class="comment">///&lt; result stores the inorder</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  264</span><span class="comment">                                             ///&lt; traversal of the binary tree</span></div>
+<div class="line"><span class="lineno">  265</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> result_preorder;   <span class="comment">///&lt; result stores the preorder</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  266</span><span class="comment">                                             ///&lt; traversal of the binary tree</span></div>
+<div class="line"><span class="lineno">  267</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> result_postorder;  <span class="comment">///&lt; result stores the postorder</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  268</span><span class="comment">                                             ///&lt; traversal of the binary tree</span></div>
+<div class="line"><span class="lineno">  269</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  270</span>    uint64_t size = actual_result_inorder.size();</div>
+<div class="line"><span class="lineno">  271</span> </div>
+<div class="line"><span class="lineno">  272</span>    <span class="comment">// Calling inorder() function by passing a root node,</span></div>
+<div class="line"><span class="lineno">  273</span>    <span class="comment">// and storing the inorder traversal in result_inorder.</span></div>
+<div class="line"><span class="lineno">  274</span>    result_inorder = obj2.inorder(root);</div>
+<div class="line"><span class="lineno">  275</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testcase #2: Inorder Traversal...&quot;</span>;</div>
+<div class="line"><span class="lineno">  276</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 0; i &lt; size; ++i) {</div>
+<div class="line"><span class="lineno">  277</span>        assert(actual_result_inorder[i] == result_inorder[i]);</div>
+<div class="line"><span class="lineno">  278</span>    }</div>
+<div class="line"><span class="lineno">  279</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  280</span> </div>
+<div class="line"><span class="lineno">  281</span>    <span class="comment">// Calling preorder() function by passing a root node,</span></div>
+<div class="line"><span class="lineno">  282</span>    <span class="comment">// and storing the preorder traversal in result_preorder.</span></div>
+<div class="line"><span class="lineno">  283</span>    result_preorder = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#abce10afbf9e16ce4a788af6b58abbebb">preorder</a>(root);</div>
+<div class="line"><span class="lineno">  284</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testcase #2: Preorder Traversal...&quot;</span>;</div>
+<div class="line"><span class="lineno">  285</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 0; i &lt; size; ++i) {</div>
+<div class="line"><span class="lineno">  286</span>        assert(actual_result_preorder[i] == result_preorder[i]);</div>
+<div class="line"><span class="lineno">  287</span>    }</div>
+<div class="line"><span class="lineno">  288</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  289</span> </div>
+<div class="line"><span class="lineno">  290</span>    <span class="comment">// Calling postorder() function by passing a root node,</span></div>
+<div class="line"><span class="lineno">  291</span>    <span class="comment">// and storing the postorder traversal in result_postorder.</span></div>
+<div class="line"><span class="lineno">  292</span>    result_postorder = obj2.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a5224e6c2ba322b17cc2c3287b77742d5">postorder</a>(root);</div>
+<div class="line"><span class="lineno">  293</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testcase #2: Postorder Traversal...&quot;</span>;</div>
+<div class="line"><span class="lineno">  294</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 0; i &lt; size; ++i) {</div>
+<div class="line"><span class="lineno">  295</span>        assert(actual_result_postorder[i] == result_postorder[i]);</div>
+<div class="line"><span class="lineno">  296</span>    }</div>
+<div class="line"><span class="lineno">  297</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  298</span> </div>
+<div class="line"><span class="lineno">  299</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  300</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -376,56 +376,56 @@ Here is the call graph for this function:</div>
 <p >&lt; result stores the inorder traversal of the binary tree</p>
 <p >&lt; result stores the preorder traversal of the binary tree</p>
 <p >&lt; result stores the postorder traversal of the binary tree</p>
-<div class="fragment"><div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>             {</div>
-<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>    <a class="code hl_class" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html">others::recursive_tree_traversals::BT</a> obj3;</div>
-<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>    <a class="code hl_struct" href="../../d9/df7/structothers_1_1recursive__tree__traversals_1_1_node.html">others::recursive_tree_traversals::Node</a> *root = obj3.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(1);</div>
-<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span>    root-&gt;left = obj3.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(2);</div>
-<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span>    root-&gt;right = obj3.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(3);</div>
-<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>    root-&gt;left-&gt;left = obj3.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(4);</div>
-<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>    root-&gt;left-&gt;right = obj3.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(5);</div>
-<div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span> </div>
-<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> actual_result_inorder{4, 2, 5, 1, 3};</div>
-<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> actual_result_preorder{1, 2, 4, 5, 3};</div>
-<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> actual_result_postorder{4, 5, 2, 3, 1};</div>
-<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> result_inorder;    <span class="comment">///&lt; result stores the inorder</span><span class="comment"></span></div>
-<div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span><span class="comment">                                             ///&lt; traversal of the binary tree</span></div>
-<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> result_preorder;   <span class="comment">///&lt; result stores the preorder</span><span class="comment"></span></div>
-<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span><span class="comment">                                             ///&lt; traversal of the binary tree</span></div>
-<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> result_postorder;  <span class="comment">///&lt; result stores the postorder</span><span class="comment"></span></div>
-<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span><span class="comment">                                             ///&lt; traversal of the binary tree</span></div>
-<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span><span class="comment"></span> </div>
-<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>    uint64_t size = actual_result_inorder.size();</div>
-<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span> </div>
-<div class="line"><a id="l00326" name="l00326"></a><span class="lineno">  326</span>    <span class="comment">// Calling inorder() function by passing a root node,</span></div>
-<div class="line"><a id="l00327" name="l00327"></a><span class="lineno">  327</span>    <span class="comment">// and storing the inorder traversal in result_inorder.</span></div>
-<div class="line"><a id="l00328" name="l00328"></a><span class="lineno">  328</span> </div>
-<div class="line"><a id="l00329" name="l00329"></a><span class="lineno">  329</span>    result_inorder = obj3.inorder(root);</div>
-<div class="line"><a id="l00330" name="l00330"></a><span class="lineno">  330</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testcase #3: Inorder Traversal...&quot;</span>;</div>
-<div class="line"><a id="l00331" name="l00331"></a><span class="lineno">  331</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 0; i &lt; size; ++i) {</div>
-<div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span>        assert(actual_result_inorder[i] == result_inorder[i]);</div>
-<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>    }</div>
-<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span> </div>
-<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span>    <span class="comment">// Calling preorder() function by passing a root node,</span></div>
-<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span>    <span class="comment">// and storing the preorder traversal in result_preorder.</span></div>
-<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span>    result_preorder = obj3.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#abce10afbf9e16ce4a788af6b58abbebb">preorder</a>(root);</div>
-<div class="line"><a id="l00339" name="l00339"></a><span class="lineno">  339</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testcase #3: Preorder Traversal...&quot;</span>;</div>
-<div class="line"><a id="l00340" name="l00340"></a><span class="lineno">  340</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 0; i &lt; size; ++i) {</div>
-<div class="line"><a id="l00341" name="l00341"></a><span class="lineno">  341</span>        assert(actual_result_preorder[i] == result_preorder[i]);</div>
-<div class="line"><a id="l00342" name="l00342"></a><span class="lineno">  342</span>    }</div>
-<div class="line"><a id="l00343" name="l00343"></a><span class="lineno">  343</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00344" name="l00344"></a><span class="lineno">  344</span> </div>
-<div class="line"><a id="l00345" name="l00345"></a><span class="lineno">  345</span>    <span class="comment">// Calling postorder() function by passing a root node,</span></div>
-<div class="line"><a id="l00346" name="l00346"></a><span class="lineno">  346</span>    <span class="comment">// and storing the postorder traversal in result_postorder.</span></div>
-<div class="line"><a id="l00347" name="l00347"></a><span class="lineno">  347</span>    result_postorder = obj3.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a5224e6c2ba322b17cc2c3287b77742d5">postorder</a>(root);</div>
-<div class="line"><a id="l00348" name="l00348"></a><span class="lineno">  348</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testcase #3: Postorder Traversal...&quot;</span>;</div>
-<div class="line"><a id="l00349" name="l00349"></a><span class="lineno">  349</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 0; i &lt; size; ++i) {</div>
-<div class="line"><a id="l00350" name="l00350"></a><span class="lineno">  350</span>        assert(actual_result_postorder[i] == result_postorder[i]);</div>
-<div class="line"><a id="l00351" name="l00351"></a><span class="lineno">  351</span>    }</div>
-<div class="line"><a id="l00352" name="l00352"></a><span class="lineno">  352</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span> </div>
-<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00355" name="l00355"></a><span class="lineno">  355</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  306</span>             {</div>
+<div class="line"><span class="lineno">  307</span>    <a class="code hl_class" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html">others::recursive_tree_traversals::BT</a> obj3;</div>
+<div class="line"><span class="lineno">  308</span>    <a class="code hl_struct" href="../../d9/df7/structothers_1_1recursive__tree__traversals_1_1_node.html">others::recursive_tree_traversals::Node</a> *root = obj3.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(1);</div>
+<div class="line"><span class="lineno">  309</span>    root-&gt;left = obj3.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(2);</div>
+<div class="line"><span class="lineno">  310</span>    root-&gt;right = obj3.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(3);</div>
+<div class="line"><span class="lineno">  311</span>    root-&gt;left-&gt;left = obj3.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(4);</div>
+<div class="line"><span class="lineno">  312</span>    root-&gt;left-&gt;right = obj3.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a08711eb2d741f4b51d980cff03b53154">createNewNode</a>(5);</div>
+<div class="line"><span class="lineno">  313</span> </div>
+<div class="line"><span class="lineno">  314</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> actual_result_inorder{4, 2, 5, 1, 3};</div>
+<div class="line"><span class="lineno">  315</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> actual_result_preorder{1, 2, 4, 5, 3};</div>
+<div class="line"><span class="lineno">  316</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> actual_result_postorder{4, 5, 2, 3, 1};</div>
+<div class="line"><span class="lineno">  317</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> result_inorder;    <span class="comment">///&lt; result stores the inorder</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  318</span><span class="comment">                                             ///&lt; traversal of the binary tree</span></div>
+<div class="line"><span class="lineno">  319</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> result_preorder;   <span class="comment">///&lt; result stores the preorder</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  320</span><span class="comment">                                             ///&lt; traversal of the binary tree</span></div>
+<div class="line"><span class="lineno">  321</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> result_postorder;  <span class="comment">///&lt; result stores the postorder</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  322</span><span class="comment">                                             ///&lt; traversal of the binary tree</span></div>
+<div class="line"><span class="lineno">  323</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  324</span>    uint64_t size = actual_result_inorder.size();</div>
+<div class="line"><span class="lineno">  325</span> </div>
+<div class="line"><span class="lineno">  326</span>    <span class="comment">// Calling inorder() function by passing a root node,</span></div>
+<div class="line"><span class="lineno">  327</span>    <span class="comment">// and storing the inorder traversal in result_inorder.</span></div>
+<div class="line"><span class="lineno">  328</span> </div>
+<div class="line"><span class="lineno">  329</span>    result_inorder = obj3.inorder(root);</div>
+<div class="line"><span class="lineno">  330</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testcase #3: Inorder Traversal...&quot;</span>;</div>
+<div class="line"><span class="lineno">  331</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 0; i &lt; size; ++i) {</div>
+<div class="line"><span class="lineno">  332</span>        assert(actual_result_inorder[i] == result_inorder[i]);</div>
+<div class="line"><span class="lineno">  333</span>    }</div>
+<div class="line"><span class="lineno">  334</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  335</span> </div>
+<div class="line"><span class="lineno">  336</span>    <span class="comment">// Calling preorder() function by passing a root node,</span></div>
+<div class="line"><span class="lineno">  337</span>    <span class="comment">// and storing the preorder traversal in result_preorder.</span></div>
+<div class="line"><span class="lineno">  338</span>    result_preorder = obj3.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#abce10afbf9e16ce4a788af6b58abbebb">preorder</a>(root);</div>
+<div class="line"><span class="lineno">  339</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testcase #3: Preorder Traversal...&quot;</span>;</div>
+<div class="line"><span class="lineno">  340</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 0; i &lt; size; ++i) {</div>
+<div class="line"><span class="lineno">  341</span>        assert(actual_result_preorder[i] == result_preorder[i]);</div>
+<div class="line"><span class="lineno">  342</span>    }</div>
+<div class="line"><span class="lineno">  343</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  344</span> </div>
+<div class="line"><span class="lineno">  345</span>    <span class="comment">// Calling postorder() function by passing a root node,</span></div>
+<div class="line"><span class="lineno">  346</span>    <span class="comment">// and storing the postorder traversal in result_postorder.</span></div>
+<div class="line"><span class="lineno">  347</span>    result_postorder = obj3.<a class="code hl_function" href="../../dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html#a5224e6c2ba322b17cc2c3287b77742d5">postorder</a>(root);</div>
+<div class="line"><span class="lineno">  348</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testcase #3: Postorder Traversal...&quot;</span>;</div>
+<div class="line"><span class="lineno">  349</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> i = 0; i &lt; size; ++i) {</div>
+<div class="line"><span class="lineno">  350</span>        assert(actual_result_postorder[i] == result_postorder[i]);</div>
+<div class="line"><span class="lineno">  351</span>    }</div>
+<div class="line"><span class="lineno">  352</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  353</span> </div>
+<div class="line"><span class="lineno">  354</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  355</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -454,14 +454,14 @@ Here is the call graph for this function:</div>
 
 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00361" name="l00361"></a><span class="lineno">  361</span>                    {</div>
-<div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test-case&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00363" name="l00363"></a><span class="lineno">  363</span>    <a class="code hl_function" href="../../dc/de1/recursive__tree__traversal_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();  <span class="comment">// run 1st test-case</span></div>
-<div class="line"><a id="l00364" name="l00364"></a><span class="lineno">  364</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test-case&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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 </table>
 </div>
 <!-- end header part -->
-<!-- Generated by Doxygen 1.9.2 -->
+<!-- Generated by Doxygen 1.9.3 -->
 <script type="text/javascript">
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@@ -185,7 +185,7 @@ Functions</h2></td></tr>
       </table>
 </div><div class="memdoc">
 <p >get_input function is to receive input from standard IO </p><dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000014">Todo:</a></b></dt><dd>@christianbender Get input from STDIO or write input to memory as done above. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>{}</div>
+<div class="fragment"><div class="line"><span class="lineno">   36</span>{}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -238,37 +238,37 @@ Functions</h2></td></tr>
 <dl class="section return"><dt>Returns</dt><dd>index where the target value was found </dd>
 <dd>
 -1 if target value not found </dd></dl>
-<div class="fragment"><div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>                                                                {</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    <span class="keywordflow">while</span> (1) {</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>        <span class="keywordflow">if</span> (left &lt; right) {</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>            <span class="keywordflow">if</span> (right - left &lt; <a class="code hl_define" href="../../dc/dfe/ternary__search_8cpp.html#ae01eda5098801bb6b5b778828fb4fddc">absolutePrecision</a>) {</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>                <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = left; i &lt;= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>; i++)</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>                    <span class="keywordflow">if</span> (A[i] == target)</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>                        <span class="keywordflow">return</span> i;</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span> </div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>                <span class="keywordflow">return</span> -1;</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>            }</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span> </div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>            <span class="keywordtype">int</span> oneThird = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>) / 3 + 1;</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>            <span class="keywordtype">int</span> twoThird = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>) * 2 / 3 + 1;</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span> </div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>            <span class="keywordflow">if</span> (A[oneThird] == target)</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>                <span class="keywordflow">return</span> oneThird;</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (A[twoThird] == target)</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>                <span class="keywordflow">return</span> twoThird;</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span> </div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (target &gt; A[twoThird])</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> = twoThird + 1;</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (target &lt; A[oneThird])</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> = oneThird - 1;</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span> </div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>            <span class="keywordflow">else</span></div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> = oneThird + 1, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> = twoThird - 1;</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>            <span class="keywordflow">return</span> -1;</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        }</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    }</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   48</span>                                                                {</div>
+<div class="line"><span class="lineno">   49</span>    <span class="keywordflow">while</span> (1) {</div>
+<div class="line"><span class="lineno">   50</span>        <span class="keywordflow">if</span> (left &lt; right) {</div>
+<div class="line"><span class="lineno">   51</span>            <span class="keywordflow">if</span> (right - left &lt; <a class="code hl_define" href="../../dc/dfe/ternary__search_8cpp.html#ae01eda5098801bb6b5b778828fb4fddc">absolutePrecision</a>) {</div>
+<div class="line"><span class="lineno">   52</span>                <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = left; i &lt;= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>; i++)</div>
+<div class="line"><span class="lineno">   53</span>                    <span class="keywordflow">if</span> (A[i] == target)</div>
+<div class="line"><span class="lineno">   54</span>                        <span class="keywordflow">return</span> i;</div>
+<div class="line"><span class="lineno">   55</span> </div>
+<div class="line"><span class="lineno">   56</span>                <span class="keywordflow">return</span> -1;</div>
+<div class="line"><span class="lineno">   57</span>            }</div>
+<div class="line"><span class="lineno">   58</span> </div>
+<div class="line"><span class="lineno">   59</span>            <span class="keywordtype">int</span> oneThird = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>) / 3 + 1;</div>
+<div class="line"><span class="lineno">   60</span>            <span class="keywordtype">int</span> twoThird = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>) * 2 / 3 + 1;</div>
+<div class="line"><span class="lineno">   61</span> </div>
+<div class="line"><span class="lineno">   62</span>            <span class="keywordflow">if</span> (A[oneThird] == target)</div>
+<div class="line"><span class="lineno">   63</span>                <span class="keywordflow">return</span> oneThird;</div>
+<div class="line"><span class="lineno">   64</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (A[twoThird] == target)</div>
+<div class="line"><span class="lineno">   65</span>                <span class="keywordflow">return</span> twoThird;</div>
+<div class="line"><span class="lineno">   66</span> </div>
+<div class="line"><span class="lineno">   67</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (target &gt; A[twoThird])</div>
+<div class="line"><span class="lineno">   68</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> = twoThird + 1;</div>
+<div class="line"><span class="lineno">   69</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (target &lt; A[oneThird])</div>
+<div class="line"><span class="lineno">   70</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> = oneThird - 1;</div>
+<div class="line"><span class="lineno">   71</span> </div>
+<div class="line"><span class="lineno">   72</span>            <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">   73</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> = oneThird + 1, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> = twoThird - 1;</div>
+<div class="line"><span class="lineno">   74</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   75</span>            <span class="keywordflow">return</span> -1;</div>
+<div class="line"><span class="lineno">   76</span>        }</div>
+<div class="line"><span class="lineno">   77</span>    }</div>
+<div class="line"><span class="lineno">   78</span>}</div>
 <div class="ttc" id="aleft_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::right</a></div><div class="ttdeci">T right(T... args)</div></div>
 <div class="ttc" id="aternary__search_8cpp_html_ae01eda5098801bb6b5b778828fb4fddc"><div class="ttname"><a href="../../dc/dfe/ternary__search_8cpp.html#ae01eda5098801bb6b5b778828fb4fddc">absolutePrecision</a></div><div class="ttdeci">#define absolutePrecision</div><div class="ttdef"><b>Definition:</b> ternary_search.cpp:22</div></div>
 </div><!-- fragment -->
@@ -290,13 +290,13 @@ Functions</h2></td></tr>
       </table>
 </div><div class="memdoc">
 <p >Main function </p>
-<div class="fragment"><div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>           {</div>
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-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    <span class="keywordtype">int</span> A[] = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 10};</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    <a class="code hl_function" href="../../dc/dfe/ternary__search_8cpp.html#a7f7d866eccdabe51bb16818a792618b1">get_input</a>();</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    <a class="code hl_function" href="../../dc/dfe/ternary__search_8cpp.html#aef655a27eb82efa299bf9d0becf6e9c8">ternary_search</a>(N, A, <a class="code hl_define" href="../../dc/dfe/ternary__search_8cpp.html#a23ad617bfce1e7cf4591059c85c1a027">_target</a>);</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  134</span>           {</div>
+<div class="line"><span class="lineno">  135</span>    <span class="keywordtype">int</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 21;</div>
+<div class="line"><span class="lineno">  136</span>    <span class="keywordtype">int</span> A[] = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 10};</div>
+<div class="line"><span class="lineno">  137</span>    <a class="code hl_function" href="../../dc/dfe/ternary__search_8cpp.html#a7f7d866eccdabe51bb16818a792618b1">get_input</a>();</div>
+<div class="line"><span class="lineno">  138</span>    <a class="code hl_function" href="../../dc/dfe/ternary__search_8cpp.html#aef655a27eb82efa299bf9d0becf6e9c8">ternary_search</a>(N, A, <a class="code hl_define" href="../../dc/dfe/ternary__search_8cpp.html#a23ad617bfce1e7cf4591059c85c1a027">_target</a>);</div>
+<div class="line"><span class="lineno">  139</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  140</span>}</div>
 <div class="ttc" id="adata__structures_2sparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:47</div></div>
 <div class="ttc" id="aternary__search_8cpp_html_a23ad617bfce1e7cf4591059c85c1a027"><div class="ttname"><a href="../../dc/dfe/ternary__search_8cpp.html#a23ad617bfce1e7cf4591059c85c1a027">_target</a></div><div class="ttdeci">#define _target</div><div class="ttdef"><b>Definition:</b> ternary_search.cpp:27</div></div>
 <div class="ttc" id="aternary__search_8cpp_html_a7f7d866eccdabe51bb16818a792618b1"><div class="ttname"><a href="../../dc/dfe/ternary__search_8cpp.html#a7f7d866eccdabe51bb16818a792618b1">get_input</a></div><div class="ttdeci">void get_input()</div><div class="ttdef"><b>Definition:</b> ternary_search.cpp:36</div></div>
@@ -359,34 +359,34 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd>index where the target value was found </dd>
 <dd>
 -1 if target value not found </dd></dl>
-<div class="fragment"><div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>                                                                 {</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    <span class="keywordflow">if</span> (left &lt; right) {</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>        <span class="keywordflow">if</span> (right - left &lt; <a class="code hl_define" href="../../dc/dfe/ternary__search_8cpp.html#ae01eda5098801bb6b5b778828fb4fddc">absolutePrecision</a>) {</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = left; i &lt;= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>; i++)</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>                <span class="keywordflow">if</span> (A[i] == target)</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>                    <span class="keywordflow">return</span> i;</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span> </div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>            <span class="keywordflow">return</span> -1;</div>
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-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span> </div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>        <span class="keywordtype">int</span> oneThird = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>) / 3 + 1;</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>        <span class="keywordtype">int</span> twoThird = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>) * 2 / 3 + 1;</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span> </div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        <span class="keywordflow">if</span> (A[oneThird] == target)</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>            <span class="keywordflow">return</span> oneThird;</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>        <span class="keywordflow">if</span> (A[twoThird] == target)</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>            <span class="keywordflow">return</span> twoThird;</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span> </div>
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-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="../../dc/dfe/ternary__search_8cpp.html#a93d0099db95022f1eb90ddfd68f73ead">rec_ternary_search</a>(left, oneThird - 1, A, target);</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        <span class="keywordflow">if</span> (target &gt; A[twoThird])</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="../../dc/dfe/ternary__search_8cpp.html#a93d0099db95022f1eb90ddfd68f73ead">rec_ternary_search</a>(twoThird + 1, right, A, target);</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span> </div>
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-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>        <span class="keywordflow">return</span> -1;</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    }</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   90</span>                                                                 {</div>
+<div class="line"><span class="lineno">   91</span>    <span class="keywordflow">if</span> (left &lt; right) {</div>
+<div class="line"><span class="lineno">   92</span>        <span class="keywordflow">if</span> (right - left &lt; <a class="code hl_define" href="../../dc/dfe/ternary__search_8cpp.html#ae01eda5098801bb6b5b778828fb4fddc">absolutePrecision</a>) {</div>
+<div class="line"><span class="lineno">   93</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = left; i &lt;= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>; i++)</div>
+<div class="line"><span class="lineno">   94</span>                <span class="keywordflow">if</span> (A[i] == target)</div>
+<div class="line"><span class="lineno">   95</span>                    <span class="keywordflow">return</span> i;</div>
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-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a> zeros, ones;</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>        <span class="comment">// finding positions with 1s and 0s and separate them</span></div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> pos = 0; pos &lt; n; ++pos) {</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>            <span class="keywordflow">if</span> ((1 &lt;&lt; pos) &amp; i) {</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>                ones.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(pos);</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>                zeros.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(pos);</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>            }</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        }</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span> </div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>        <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;o : ones) {</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>            <span class="keywordflow">if</span> (!<a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i][o]) {</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>                <span class="keywordflow">continue</span>;</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>            }</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span> </div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>            <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;z : zeros) {</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>                <span class="keywordflow">if</span> (!routes[o][z]) {</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>                    <span class="keywordflow">continue</span>;</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>                }</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>                <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i + (1 &lt;&lt; z)][z] = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>            }</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        }</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    }</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span> </div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <span class="keywordtype">bool</span> is_cycle = <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; n; i++) {</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        is_cycle |= <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[<a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a> - 1][i];</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        <span class="keywordflow">if</span> (is_cycle) {  <span class="comment">// if true, all subsequent loop will be true. hence</span></div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>                         <span class="comment">// break</span></div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>            <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        }</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    }</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <span class="keywordflow">return</span> is_cycle;</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   30</span>                                                              {</div>
+<div class="line"><span class="lineno">   31</span>    <span class="keyword">const</span> <span class="keywordtype">size_t</span> n = routes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   32</span>    <span class="comment">// height of dp array which is 2^n</span></div>
+<div class="line"><span class="lineno">   33</span>    <span class="keyword">const</span> <span class="keywordtype">size_t</span> <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a> = 1 &lt;&lt; n;</div>
+<div class="line"><span class="lineno">   34</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;bool&gt;</a>&gt; <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>(<a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>(n, <span class="keyword">false</span>));</div>
+<div class="line"><span class="lineno">   35</span> </div>
+<div class="line"><span class="lineno">   36</span>    <span class="comment">// to fill in the [2^i, i] cells with true</span></div>
+<div class="line"><span class="lineno">   37</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; n; ++i) {</div>
+<div class="line"><span class="lineno">   38</span>        <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[1 &lt;&lt; i][i] = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   39</span>    }</div>
+<div class="line"><span class="lineno">   40</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 1; i &lt; <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>; i++) {</div>
+<div class="line"><span class="lineno">   41</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a> zeros, ones;</div>
+<div class="line"><span class="lineno">   42</span>        <span class="comment">// finding positions with 1s and 0s and separate them</span></div>
+<div class="line"><span class="lineno">   43</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> pos = 0; pos &lt; n; ++pos) {</div>
+<div class="line"><span class="lineno">   44</span>            <span class="keywordflow">if</span> ((1 &lt;&lt; pos) &amp; i) {</div>
+<div class="line"><span class="lineno">   45</span>                ones.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(pos);</div>
+<div class="line"><span class="lineno">   46</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   47</span>                zeros.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(pos);</div>
+<div class="line"><span class="lineno">   48</span>            }</div>
+<div class="line"><span class="lineno">   49</span>        }</div>
+<div class="line"><span class="lineno">   50</span> </div>
+<div class="line"><span class="lineno">   51</span>        <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;o : ones) {</div>
+<div class="line"><span class="lineno">   52</span>            <span class="keywordflow">if</span> (!<a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i][o]) {</div>
+<div class="line"><span class="lineno">   53</span>                <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno">   54</span>            }</div>
+<div class="line"><span class="lineno">   55</span> </div>
+<div class="line"><span class="lineno">   56</span>            <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;z : zeros) {</div>
+<div class="line"><span class="lineno">   57</span>                <span class="keywordflow">if</span> (!routes[o][z]) {</div>
+<div class="line"><span class="lineno">   58</span>                    <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno">   59</span>                }</div>
+<div class="line"><span class="lineno">   60</span>                <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i + (1 &lt;&lt; z)][z] = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   61</span>            }</div>
+<div class="line"><span class="lineno">   62</span>        }</div>
+<div class="line"><span class="lineno">   63</span>    }</div>
+<div class="line"><span class="lineno">   64</span> </div>
+<div class="line"><span class="lineno">   65</span>    <span class="keywordtype">bool</span> is_cycle = <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   66</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">   67</span>        is_cycle |= <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[<a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a> - 1][i];</div>
+<div class="line"><span class="lineno">   68</span>        <span class="keywordflow">if</span> (is_cycle) {  <span class="comment">// if true, all subsequent loop will be true. hence</span></div>
+<div class="line"><span class="lineno">   69</span>                         <span class="comment">// break</span></div>
+<div class="line"><span class="lineno">   70</span>            <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">   71</span>        }</div>
+<div class="line"><span class="lineno">   72</span>    }</div>
+<div class="line"><span class="lineno">   73</span>    <span class="keywordflow">return</span> is_cycle;</div>
+<div class="line"><span class="lineno">   74</span>}</div>
 <div class="ttc" id="aavltree_8cpp_html_ae4a66d8b0c2b0d626aea45977e358c83"><div class="ttname"><a href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a></div><div class="ttdeci">int height(node *root)</div><div class="ttdef"><b>Definition:</b> avltree.cpp:31</div></div>
 <div class="ttc" id="anamespacedp_html"><div class="ttname"><a href="../../df/d88/namespacedp.html">dp</a></div><div class="ttdoc">for std::vector</div><div class="ttdef"><b>Definition:</b> partition_problem.cpp:39</div></div>
 <div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
@@ -246,12 +246,12 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>                                {</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    <a class="code hl_function" href="../../dd/d0c/hamiltons__cycle_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a>();</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    <a class="code hl_function" href="../../dd/d0c/hamiltons__cycle_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a>();</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <a class="code hl_function" href="../../dd/d0c/hamiltons__cycle_8cpp.html#a0cc94918b6831f308d4fe4fa27f08299">test3</a>();</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  142</span>                                {</div>
+<div class="line"><span class="lineno">  143</span>    <a class="code hl_function" href="../../dd/d0c/hamiltons__cycle_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a>();</div>
+<div class="line"><span class="lineno">  144</span>    <a class="code hl_function" href="../../dd/d0c/hamiltons__cycle_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a>();</div>
+<div class="line"><span class="lineno">  145</span>    <a class="code hl_function" href="../../dd/d0c/hamiltons__cycle_8cpp.html#a0cc94918b6831f308d4fe4fa27f08299">test3</a>();</div>
+<div class="line"><span class="lineno">  146</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  147</span>}</div>
 <div class="ttc" id="ahamiltons__cycle_8cpp_html_a0cc94918b6831f308d4fe4fa27f08299"><div class="ttname"><a href="../../dd/d0c/hamiltons__cycle_8cpp.html#a0cc94918b6831f308d4fe4fa27f08299">test3</a></div><div class="ttdeci">static void test3()</div><div class="ttdef"><b>Definition:</b> hamiltons_cycle.cpp:122</div></div>
 <div class="ttc" id="ahamiltons__cycle_8cpp_html_a45d94ead4cf4e1ff9f87c38bc99f59ae"><div class="ttname"><a href="../../dd/d0c/hamiltons__cycle_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a></div><div class="ttdeci">static void test2()</div><div class="ttdef"><b>Definition:</b> hamiltons_cycle.cpp:103</div></div>
 <div class="ttc" id="ahamiltons__cycle_8cpp_html_ae7880ce913f3058a35ff106d5be9e243"><div class="ttname"><a href="../../dd/d0c/hamiltons__cycle_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a></div><div class="ttdeci">static void test1()</div><div class="ttdef"><b>Definition:</b> hamiltons_cycle.cpp:81</div></div>
@@ -287,18 +287,18 @@ Here is the call graph for this function:</div>
 </table>
 </div><div class="memdoc">
 <p >this test is testing if <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp.html#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a> returns <code>true</code> for graph: <code>1 -&gt; 2 -&gt; 3 -&gt; 4</code> </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
-<div class="fragment"><div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>                    {</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;bool&gt;</a>&gt; arr{</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>({<span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>}),</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>({<span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">false</span>}),</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>({<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">true</span>}),</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>({<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>})};</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span> </div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    <span class="keywordtype">bool</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = <a class="code hl_function" href="../../dd/d0c/hamiltons__cycle_8cpp.html#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a>(arr);</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1... &quot;</span>;</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    assert(<a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>);</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   81</span>                    {</div>
+<div class="line"><span class="lineno">   82</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;bool&gt;</a>&gt; arr{</div>
+<div class="line"><span class="lineno">   83</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>({<span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>}),</div>
+<div class="line"><span class="lineno">   84</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>({<span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">false</span>}),</div>
+<div class="line"><span class="lineno">   85</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>({<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">true</span>}),</div>
+<div class="line"><span class="lineno">   86</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>({<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>})};</div>
+<div class="line"><span class="lineno">   87</span> </div>
+<div class="line"><span class="lineno">   88</span>    <span class="keywordtype">bool</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = <a class="code hl_function" href="../../dd/d0c/hamiltons__cycle_8cpp.html#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a>(arr);</div>
+<div class="line"><span class="lineno">   89</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1... &quot;</span>;</div>
+<div class="line"><span class="lineno">   90</span>    assert(<a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>);</div>
+<div class="line"><span class="lineno">   91</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   92</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="ahamiltons__cycle_8cpp_html_abcf824e347eecfeeb69ea0280f34f3e4"><div class="ttname"><a href="../../dd/d0c/hamiltons__cycle_8cpp.html#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a></div><div class="ttdeci">bool hamilton_cycle(const std::vector&lt; std::vector&lt; bool &gt; &gt; &amp;routes)</div><div class="ttdef"><b>Definition:</b> hamiltons_cycle.cpp:30</div></div>
 <div class="ttc" id="amatrix__exponentiation_8cpp_html_ad8389ed58fd0ec66df248014775ad1fa"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a></div><div class="ttdeci">ll ans(ll n)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:91</div></div>
@@ -339,19 +339,19 @@ Here is the call graph for this function:</div>
       |
       V
       4</pre> <dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
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-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>({<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>}),</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>({<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>})};</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span> </div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    <span class="keywordtype">bool</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = <a class="code hl_function" href="../../dd/d0c/hamiltons__cycle_8cpp.html#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a>(arr);</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span> </div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2... &quot;</span>;</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    assert(!<a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>);  <span class="comment">// not a cycle</span></div>
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-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  103</span>                    {</div>
+<div class="line"><span class="lineno">  104</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;bool&gt;</a>&gt; arr{</div>
+<div class="line"><span class="lineno">  105</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>({<span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>}),</div>
+<div class="line"><span class="lineno">  106</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>({<span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">true</span>}),</div>
+<div class="line"><span class="lineno">  107</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>({<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>}),</div>
+<div class="line"><span class="lineno">  108</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>({<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>})};</div>
+<div class="line"><span class="lineno">  109</span> </div>
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 <p >this test is testing if <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp.html#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a> returns <code>true</code> for clique with 4 vertices </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
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+<div class="line"><span class="lineno">  155</span><span class="comment"></span>    <span class="keywordtype">size_t</span> n;</div>
+<div class="line"><span class="lineno">  156</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the length of your array (0 to exit): &quot;</span>;</div>
+<div class="line"><span class="lineno">  157</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
+<div class="line"><span class="lineno">  158</span>    <span class="keywordflow">if</span> (n == 0) {</div>
+<div class="line"><span class="lineno">  159</span>        <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  160</span>    }</div>
+<div class="line"><span class="lineno">  161</span> </div>
+<div class="line"><span class="lineno">  162</span>    <span class="keywordtype">int</span> *arr = <span class="keyword">new</span> <span class="keywordtype">int</span>[n];</div>
+<div class="line"><span class="lineno">  163</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter any &quot;</span> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; Numbers for Unsorted Array : &quot;</span>;</div>
+<div class="line"><span class="lineno">  164</span> </div>
+<div class="line"><span class="lineno">  165</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">  166</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; arr[i];</div>
+<div class="line"><span class="lineno">  167</span>    }</div>
+<div class="line"><span class="lineno">  168</span> </div>
+<div class="line"><span class="lineno">  169</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a>(arr, n);</div>
+<div class="line"><span class="lineno">  170</span> </div>
+<div class="line"><span class="lineno">  171</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nSorted Array : &quot;</span>;</div>
+<div class="line"><span class="lineno">  172</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">  173</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; arr[i] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">  174</span>    }</div>
+<div class="line"><span class="lineno">  175</span> </div>
+<div class="line"><span class="lineno">  176</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  177</span>    <span class="keyword">delete</span>[] arr;</div>
+<div class="line"><span class="lineno">  178</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  179</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
@@ -307,45 +307,45 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Test Cases to test algorithm </p>
-<div class="fragment"><div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>             {</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    <span class="keywordtype">int</span> arr1[10] = {78, 34, 35, 6, 34, 56, 3, 56, 2, 4};</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1... &quot;</span>;</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a>(arr1, 10);</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(arr1, arr1 + 10));</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span> </div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    <span class="keywordtype">int</span> arr2[5] = {5, -3, 7, -2, 1};</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2... &quot;</span>;</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a>(arr2, 5);</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(arr2, arr2 + 5));</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span> </div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    <span class="keywordtype">float</span> arr3[5] = {5.6, -3.1, -3.0, -2.1, 1.8};</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3... &quot;</span>;</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a>(arr3, 5);</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(arr3, arr3 + 5));</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span> </div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> arr4({5.6, -3.1, -3.0, -2.1, 1.8});</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 4... &quot;</span>;</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a>(&amp;arr4);</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr4), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr4)));</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span> </div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    <span class="keywordtype">int</span> arr5[50];</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 5... &quot;</span>;</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    <a class="code hl_function" href="../../dd/d0d/insertion__sort_8cpp.html#a59914553f24088342c139645a02a8a49">create_random_array</a>(arr5, 50);</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a>(arr5, 50);</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(arr5, arr5 + 50));</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span> </div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    <span class="keywordtype">float</span> arr6[50];</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 6... &quot;</span>;</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    <a class="code hl_function" href="../../dd/d0d/insertion__sort_8cpp.html#a59914553f24088342c139645a02a8a49">create_random_array</a>(arr6, 50);</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a>(arr6, 50);</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(arr6, arr6 + 50));</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  109</span>             {</div>
+<div class="line"><span class="lineno">  110</span>    <span class="keywordtype">int</span> arr1[10] = {78, 34, 35, 6, 34, 56, 3, 56, 2, 4};</div>
+<div class="line"><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1... &quot;</span>;</div>
+<div class="line"><span class="lineno">  112</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a>(arr1, 10);</div>
+<div class="line"><span class="lineno">  113</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(arr1, arr1 + 10));</div>
+<div class="line"><span class="lineno">  114</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  115</span> </div>
+<div class="line"><span class="lineno">  116</span>    <span class="keywordtype">int</span> arr2[5] = {5, -3, 7, -2, 1};</div>
+<div class="line"><span class="lineno">  117</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2... &quot;</span>;</div>
+<div class="line"><span class="lineno">  118</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a>(arr2, 5);</div>
+<div class="line"><span class="lineno">  119</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(arr2, arr2 + 5));</div>
+<div class="line"><span class="lineno">  120</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  121</span> </div>
+<div class="line"><span class="lineno">  122</span>    <span class="keywordtype">float</span> arr3[5] = {5.6, -3.1, -3.0, -2.1, 1.8};</div>
+<div class="line"><span class="lineno">  123</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3... &quot;</span>;</div>
+<div class="line"><span class="lineno">  124</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a>(arr3, 5);</div>
+<div class="line"><span class="lineno">  125</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(arr3, arr3 + 5));</div>
+<div class="line"><span class="lineno">  126</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  127</span> </div>
+<div class="line"><span class="lineno">  128</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> arr4({5.6, -3.1, -3.0, -2.1, 1.8});</div>
+<div class="line"><span class="lineno">  129</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 4... &quot;</span>;</div>
+<div class="line"><span class="lineno">  130</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a>(&amp;arr4);</div>
+<div class="line"><span class="lineno">  131</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr4), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr4)));</div>
+<div class="line"><span class="lineno">  132</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  133</span> </div>
+<div class="line"><span class="lineno">  134</span>    <span class="keywordtype">int</span> arr5[50];</div>
+<div class="line"><span class="lineno">  135</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 5... &quot;</span>;</div>
+<div class="line"><span class="lineno">  136</span>    <a class="code hl_function" href="../../dd/d0d/insertion__sort_8cpp.html#a59914553f24088342c139645a02a8a49">create_random_array</a>(arr5, 50);</div>
+<div class="line"><span class="lineno">  137</span>    <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a>(arr5, 50);</div>
+<div class="line"><span class="lineno">  138</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(arr5, arr5 + 50));</div>
+<div class="line"><span class="lineno">  139</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  140</span> </div>
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- <tr style="height: 56px;">
-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
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    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
    </div>
    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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+<!-- Generated by Doxygen 1.9.3 -->
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@@ -182,19 +182,19 @@ This program implements Vigenère cipher for only uppercase English alphabet cha
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>new decrypted text </dd></dl>
-<div class="fragment"><div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>                                                                        {</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>            <span class="comment">// Going through each character of text and key</span></div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>            <span class="comment">// Note that key is visited in circular way hence  j = (j + 1) % |key|</span></div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> decrypted_text = <span class="stringliteral">&quot;&quot;</span>; <span class="comment">// Empty string to store decrypted text</span></div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>            <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i = 0, j = 0; i &lt; text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>(); i++, j = (j + 1) % key.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>()) {</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>                <span class="keywordtype">int</span> place_value_text = get_value(text[i]); <span class="comment">// Getting value of character in text</span></div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>                <span class="keywordtype">int</span> place_value_key = get_value(key[j]); <span class="comment">// Getting value of character in key</span></div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>                place_value_text = (place_value_text - place_value_key + 26) % 26; <span class="comment">// Applying decryption</span></div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>                <span class="keywordtype">char</span> decrypted_char = get_char(place_value_text); <span class="comment">// Getting new character from decrypted value</span></div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>                decrypted_text += decrypted_char; <span class="comment">// Appending decrypted character</span></div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>            }        </div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>            <span class="keywordflow">return</span> decrypted_text; <span class="comment">// Returning decrypted text</span></div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>        }</div>
+<div class="fragment"><div class="line"><span class="lineno">   92</span>                                                                        {</div>
+<div class="line"><span class="lineno">   93</span>            <span class="comment">// Going through each character of text and key</span></div>
+<div class="line"><span class="lineno">   94</span>            <span class="comment">// Note that key is visited in circular way hence  j = (j + 1) % |key|</span></div>
+<div class="line"><span class="lineno">   95</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> decrypted_text = <span class="stringliteral">&quot;&quot;</span>; <span class="comment">// Empty string to store decrypted text</span></div>
+<div class="line"><span class="lineno">   96</span>            <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i = 0, j = 0; i &lt; text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>(); i++, j = (j + 1) % key.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>()) {</div>
+<div class="line"><span class="lineno">   97</span>                <span class="keywordtype">int</span> place_value_text = get_value(text[i]); <span class="comment">// Getting value of character in text</span></div>
+<div class="line"><span class="lineno">   98</span>                <span class="keywordtype">int</span> place_value_key = get_value(key[j]); <span class="comment">// Getting value of character in key</span></div>
+<div class="line"><span class="lineno">   99</span>                place_value_text = (place_value_text - place_value_key + 26) % 26; <span class="comment">// Applying decryption</span></div>
+<div class="line"><span class="lineno">  100</span>                <span class="keywordtype">char</span> decrypted_char = get_char(place_value_text); <span class="comment">// Getting new character from decrypted value</span></div>
+<div class="line"><span class="lineno">  101</span>                decrypted_text += decrypted_char; <span class="comment">// Appending decrypted character</span></div>
+<div class="line"><span class="lineno">  102</span>            }        </div>
+<div class="line"><span class="lineno">  103</span>            <span class="keywordflow">return</span> decrypted_text; <span class="comment">// Returning decrypted text</span></div>
+<div class="line"><span class="lineno">  104</span>        }</div>
 <div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
 <div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">std::string::length</a></div><div class="ttdeci">T length(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -239,19 +239,19 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>new encrypted text </dd></dl>
-<div class="fragment"><div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>                                                                        {</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> encrypted_text = <span class="stringliteral">&quot;&quot;</span>; <span class="comment">// Empty string to store encrypted text</span></div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>            <span class="comment">// Going through each character of text and key</span></div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>            <span class="comment">// Note that key is visited in circular way hence  j = (j + 1) % |key|</span></div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>            <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i = 0, j = 0; i &lt; text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>(); i++, j = (j + 1) % key.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>()) {</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>                <span class="keywordtype">int</span> place_value_text = get_value(text[i]); <span class="comment">// Getting value of character in text</span></div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>                <span class="keywordtype">int</span> place_value_key = get_value(key[j]); <span class="comment">// Getting value of character in key</span></div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>                place_value_text = (place_value_text + place_value_key) % 26; <span class="comment">// Applying encryption</span></div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>                <span class="keywordtype">char</span> encrypted_char = get_char(place_value_text); <span class="comment">// Getting new character from encrypted value</span></div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>                encrypted_text += encrypted_char; <span class="comment">// Appending encrypted character</span></div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>            }</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>            <span class="keywordflow">return</span> encrypted_text; <span class="comment">// Returning encrypted text</span></div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>        }</div>
+<div class="fragment"><div class="line"><span class="lineno">   73</span>                                                                        {</div>
+<div class="line"><span class="lineno">   74</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> encrypted_text = <span class="stringliteral">&quot;&quot;</span>; <span class="comment">// Empty string to store encrypted text</span></div>
+<div class="line"><span class="lineno">   75</span>            <span class="comment">// Going through each character of text and key</span></div>
+<div class="line"><span class="lineno">   76</span>            <span class="comment">// Note that key is visited in circular way hence  j = (j + 1) % |key|</span></div>
+<div class="line"><span class="lineno">   77</span>            <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i = 0, j = 0; i &lt; text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>(); i++, j = (j + 1) % key.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>()) {</div>
+<div class="line"><span class="lineno">   78</span>                <span class="keywordtype">int</span> place_value_text = get_value(text[i]); <span class="comment">// Getting value of character in text</span></div>
+<div class="line"><span class="lineno">   79</span>                <span class="keywordtype">int</span> place_value_key = get_value(key[j]); <span class="comment">// Getting value of character in key</span></div>
+<div class="line"><span class="lineno">   80</span>                place_value_text = (place_value_text + place_value_key) % 26; <span class="comment">// Applying encryption</span></div>
+<div class="line"><span class="lineno">   81</span>                <span class="keywordtype">char</span> encrypted_char = get_char(place_value_text); <span class="comment">// Getting new character from encrypted value</span></div>
+<div class="line"><span class="lineno">   82</span>                encrypted_text += encrypted_char; <span class="comment">// Appending encrypted character</span></div>
+<div class="line"><span class="lineno">   83</span>            }</div>
+<div class="line"><span class="lineno">   84</span>            <span class="keywordflow">return</span> encrypted_text; <span class="comment">// Returning encrypted text</span></div>
+<div class="line"><span class="lineno">   85</span>        }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -277,11 +277,11 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Driver Code </p>
-<div class="fragment"><div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>           {</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    <span class="comment">// Testing</span></div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    <a class="code hl_function" href="../../dd/d12/vigenere__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>();</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  131</span>           {</div>
+<div class="line"><span class="lineno">  132</span>    <span class="comment">// Testing</span></div>
+<div class="line"><span class="lineno">  133</span>    <a class="code hl_function" href="../../dd/d12/vigenere__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>();</div>
+<div class="line"><span class="lineno">  134</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  135</span>}</div>
 <div class="ttc" id="avigenere__cipher_8cpp_html_ae1a3968e7947464bee7714f6d43b7002"><div class="ttname"><a href="../../dd/d12/vigenere__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a></div><div class="ttdeci">void test()</div><div class="ttdef"><b>Definition:</b> vigenere_cipher.cpp:111</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -307,24 +307,24 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Function to test above algorithm </p>
-<div class="fragment"><div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>            {</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    <span class="comment">// Test 1</span></div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> text1 = <span class="stringliteral">&quot;NIKOLATESLA&quot;</span>;</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> encrypted1 = <a class="code hl_function" href="../../dd/d12/vigenere__cipher_8cpp.html#a6bd3880ea6820c232c1eddf47553c257">ciphers::vigenere::encrypt</a>(text1, <span class="stringliteral">&quot;TESLA&quot;</span>);</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> decrypted1 = <a class="code hl_function" href="../../dd/d12/vigenere__cipher_8cpp.html#a3cfc3f9b20a0f230a2fcefd31dc6848e">ciphers::vigenere::decrypt</a>(encrypted1, <span class="stringliteral">&quot;TESLA&quot;</span>);</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    assert(text1 == decrypted1);</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Original text : &quot;</span> &lt;&lt; text1;</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; , Encrypted text (with key = TESLA) : &quot;</span> &lt;&lt; encrypted1;</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; , Decrypted text : &quot;</span>&lt;&lt; decrypted1 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <span class="comment">// Test 2</span></div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> text2 = <span class="stringliteral">&quot;GOOGLEIT&quot;</span>;</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> encrypted2 = <a class="code hl_function" href="../../dd/d12/vigenere__cipher_8cpp.html#a6bd3880ea6820c232c1eddf47553c257">ciphers::vigenere::encrypt</a>(text2, <span class="stringliteral">&quot;REALLY&quot;</span>);</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> decrypted2 = <a class="code hl_function" href="../../dd/d12/vigenere__cipher_8cpp.html#a3cfc3f9b20a0f230a2fcefd31dc6848e">ciphers::vigenere::decrypt</a>(encrypted2, <span class="stringliteral">&quot;REALLY&quot;</span>);</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    assert(text2 == decrypted2);</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Original text : &quot;</span> &lt;&lt; text2;</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; , Encrypted text (with key = REALLY) : &quot;</span> &lt;&lt; encrypted2;</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; , Decrypted text : &quot;</span>&lt;&lt; decrypted2 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  111</span>            {</div>
+<div class="line"><span class="lineno">  112</span>    <span class="comment">// Test 1</span></div>
+<div class="line"><span class="lineno">  113</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> text1 = <span class="stringliteral">&quot;NIKOLATESLA&quot;</span>;</div>
+<div class="line"><span class="lineno">  114</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> encrypted1 = <a class="code hl_function" href="../../dd/d12/vigenere__cipher_8cpp.html#a6bd3880ea6820c232c1eddf47553c257">ciphers::vigenere::encrypt</a>(text1, <span class="stringliteral">&quot;TESLA&quot;</span>);</div>
+<div class="line"><span class="lineno">  115</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> decrypted1 = <a class="code hl_function" href="../../dd/d12/vigenere__cipher_8cpp.html#a3cfc3f9b20a0f230a2fcefd31dc6848e">ciphers::vigenere::decrypt</a>(encrypted1, <span class="stringliteral">&quot;TESLA&quot;</span>);</div>
+<div class="line"><span class="lineno">  116</span>    assert(text1 == decrypted1);</div>
+<div class="line"><span class="lineno">  117</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Original text : &quot;</span> &lt;&lt; text1;</div>
+<div class="line"><span class="lineno">  118</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; , Encrypted text (with key = TESLA) : &quot;</span> &lt;&lt; encrypted1;</div>
+<div class="line"><span class="lineno">  119</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; , Decrypted text : &quot;</span>&lt;&lt; decrypted1 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  120</span>    <span class="comment">// Test 2</span></div>
+<div class="line"><span class="lineno">  121</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> text2 = <span class="stringliteral">&quot;GOOGLEIT&quot;</span>;</div>
+<div class="line"><span class="lineno">  122</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> encrypted2 = <a class="code hl_function" href="../../dd/d12/vigenere__cipher_8cpp.html#a6bd3880ea6820c232c1eddf47553c257">ciphers::vigenere::encrypt</a>(text2, <span class="stringliteral">&quot;REALLY&quot;</span>);</div>
+<div class="line"><span class="lineno">  123</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> decrypted2 = <a class="code hl_function" href="../../dd/d12/vigenere__cipher_8cpp.html#a3cfc3f9b20a0f230a2fcefd31dc6848e">ciphers::vigenere::decrypt</a>(encrypted2, <span class="stringliteral">&quot;REALLY&quot;</span>);</div>
+<div class="line"><span class="lineno">  124</span>    assert(text2 == decrypted2);</div>
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 <div class="ttc" id="aclasshash__chain_html_ae9ddce410015ed8dda6380130d82d6c2"><div class="ttname"><a href="../../dd/d1c/classhash__chain.html#ae9ddce410015ed8dda6380130d82d6c2">hash_chain::_mod</a></div><div class="ttdeci">int _mod</div><div class="ttdoc">modulus of the class</div><div class="ttdef"><b>Definition:</b> chaining.cpp:27</div></div>
-</div><!-- fragment -->
+<div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dd/d1c/classhash__chain_a80c8b902a15b4fd062ed727ecf8f3595_cgraph.svg" width="376" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
 </div>
 </div>
 <h2 class="groupheader">Member Function Documentation</h2>
@@ -227,22 +240,22 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>_mod</b></td></tr>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>                           {</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Node&gt;</a> curr;</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Node&gt;</a> temp(<span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>);</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>        temp-&gt;data = x;</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        temp-&gt;next = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>        <span class="keywordflow">if</span> (!<a class="code hl_variable" href="../../dd/d1c/classhash__chain.html#ae8457d13620497fa2046ac566252c4b0">head</a>[<a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>]) {</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>            <a class="code hl_variable" href="../../dd/d1c/classhash__chain.html#ae8457d13620497fa2046ac566252c4b0">head</a>[<a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>] = temp;</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>            curr = <a class="code hl_variable" href="../../dd/d1c/classhash__chain.html#ae8457d13620497fa2046ac566252c4b0">head</a>[<a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>];</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>            curr = <a class="code hl_variable" href="../../dd/d1c/classhash__chain.html#ae8457d13620497fa2046ac566252c4b0">head</a>[<a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>];</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>            <span class="keywordflow">while</span> (curr-&gt;next) curr = curr-&gt;next;</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>            curr-&gt;next = temp;</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>        }</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   45</span>                           {</div>
+<div class="line"><span class="lineno">   46</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Node&gt;</a> curr;</div>
+<div class="line"><span class="lineno">   47</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Node&gt;</a> temp(<span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>);</div>
+<div class="line"><span class="lineno">   48</span>        temp-&gt;data = x;</div>
+<div class="line"><span class="lineno">   49</span>        temp-&gt;next = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">   50</span>        <span class="keywordflow">if</span> (!<a class="code hl_variable" href="../../dd/d1c/classhash__chain.html#ae8457d13620497fa2046ac566252c4b0">head</a>[<a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>]) {</div>
+<div class="line"><span class="lineno">   51</span>            <a class="code hl_variable" href="../../dd/d1c/classhash__chain.html#ae8457d13620497fa2046ac566252c4b0">head</a>[<a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>] = temp;</div>
+<div class="line"><span class="lineno">   52</span>            curr = <a class="code hl_variable" href="../../dd/d1c/classhash__chain.html#ae8457d13620497fa2046ac566252c4b0">head</a>[<a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>];</div>
+<div class="line"><span class="lineno">   53</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   54</span>            curr = <a class="code hl_variable" href="../../dd/d1c/classhash__chain.html#ae8457d13620497fa2046ac566252c4b0">head</a>[<a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>];</div>
+<div class="line"><span class="lineno">   55</span>            <span class="keywordflow">while</span> (curr-&gt;next) curr = curr-&gt;next;</div>
+<div class="line"><span class="lineno">   56</span>            curr-&gt;next = temp;</div>
+<div class="line"><span class="lineno">   57</span>        }</div>
+<div class="line"><span class="lineno">   58</span>    }</div>
 <div class="ttc" id="ahash__search_8cpp_html_a566eaf0ffafd50bc61e644561fd27001"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a></div><div class="ttdeci">int h(int key)</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:45</div></div>
-<div class="ttc" id="ashared_ptr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr</a></div></div>
+<div class="ttc" id="ashared_ptr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt; Node &gt;</a></div></div>
 <div class="ttc" id="astruct_node_html"><div class="ttname"><a href="../../db/d8b/struct_node.html">Node</a></div><div class="ttdef"><b>Definition:</b> linkedlist_implentation_usingarray.cpp:14</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -277,24 +290,24 @@ Here is the call graph for this function:</div>
 </div><div class="memdoc">
 
 <p>Display the chain. </p>
-<div class="fragment"><div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>                   {</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Node&gt;</a> temp = <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        <span class="keywordtype">int</span> i = 0;</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../dd/d1c/classhash__chain.html#ae9ddce410015ed8dda6380130d82d6c2">_mod</a>; i++) {</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>            <span class="keywordflow">if</span> (!<a class="code hl_variable" href="../../dd/d1c/classhash__chain.html#ae8457d13620497fa2046ac566252c4b0">head</a>[i]) {</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Key &quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; is empty&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Key &quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; has values = &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>                temp = <a class="code hl_variable" href="../../dd/d1c/classhash__chain.html#ae8457d13620497fa2046ac566252c4b0">head</a>[i];</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>                <span class="keywordflow">while</span> (temp-&gt;next) {</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; temp-&gt;data &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>                    temp = temp-&gt;next;</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>                }</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; temp-&gt;data;</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>            }</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>        }</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   63</span>                   {</div>
+<div class="line"><span class="lineno">   64</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Node&gt;</a> temp = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">   65</span>        <span class="keywordtype">int</span> i = 0;</div>
+<div class="line"><span class="lineno">   66</span>        <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../dd/d1c/classhash__chain.html#ae9ddce410015ed8dda6380130d82d6c2">_mod</a>; i++) {</div>
+<div class="line"><span class="lineno">   67</span>            <span class="keywordflow">if</span> (!<a class="code hl_variable" href="../../dd/d1c/classhash__chain.html#ae8457d13620497fa2046ac566252c4b0">head</a>[i]) {</div>
+<div class="line"><span class="lineno">   68</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Key &quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; is empty&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   69</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   70</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Key &quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; has values = &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   71</span>                temp = <a class="code hl_variable" href="../../dd/d1c/classhash__chain.html#ae8457d13620497fa2046ac566252c4b0">head</a>[i];</div>
+<div class="line"><span class="lineno">   72</span>                <span class="keywordflow">while</span> (temp-&gt;next) {</div>
+<div class="line"><span class="lineno">   73</span>                    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; temp-&gt;data &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   74</span>                    temp = temp-&gt;next;</div>
+<div class="line"><span class="lineno">   75</span>                }</div>
+<div class="line"><span class="lineno">   76</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; temp-&gt;data;</div>
+<div class="line"><span class="lineno">   77</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   78</span>            }</div>
+<div class="line"><span class="lineno">   79</span>        }</div>
+<div class="line"><span class="lineno">   80</span>    }</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -351,33 +364,33 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if element found </dd>
 <dd>
 <code>false</code> if element not found </dd></dl>
-<div class="fragment"><div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>                                  {</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr&lt;Node&gt;</a> temp = <a class="code hl_variable" href="../../dd/d1c/classhash__chain.html#ae8457d13620497fa2046ac566252c4b0">head</a>[<a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>];</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        <span class="keywordflow">if</span> (!<a class="code hl_variable" href="../../dd/d1c/classhash__chain.html#ae8457d13620497fa2046ac566252c4b0">head</a>[<a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>]) {</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>            <span class="comment">// index does not exist!</span></div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Element not found&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span> </div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>        <span class="comment">// scan for data value</span></div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        <span class="keywordflow">while</span> (temp-&gt;data != x &amp;&amp; temp-&gt;next) temp = temp-&gt;next;</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span> </div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>        <span class="keywordflow">if</span> (temp-&gt;next) {</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Element found&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>        }</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span> </div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>        <span class="comment">// implicit else condition</span></div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>        <span class="comment">// i.e., temp-&gt;next == nullptr</span></div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        <span class="keywordflow">if</span> (temp-&gt;data == x) {</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Element found&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>        }</div>
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-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>        <span class="comment">// further implicit else condition</span></div>
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+<div class="line"><span class="lineno">  104</span>            <span class="comment">// index does not exist!</span></div>
+<div class="line"><span class="lineno">  105</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Element not found&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  106</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  107</span>        }</div>
+<div class="line"><span class="lineno">  108</span> </div>
+<div class="line"><span class="lineno">  109</span>        <span class="comment">// scan for data value</span></div>
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+<div class="line"><span class="lineno">  111</span> </div>
+<div class="line"><span class="lineno">  112</span>        <span class="keywordflow">if</span> (temp-&gt;next) {</div>
+<div class="line"><span class="lineno">  113</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Element found&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><span class="lineno">  116</span> </div>
+<div class="line"><span class="lineno">  117</span>        <span class="comment">// implicit else condition</span></div>
+<div class="line"><span class="lineno">  118</span>        <span class="comment">// i.e., temp-&gt;next == nullptr</span></div>
+<div class="line"><span class="lineno">  119</span>        <span class="keywordflow">if</span> (temp-&gt;data == x) {</div>
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+<div class="line"><span class="lineno">  123</span> </div>
+<div class="line"><span class="lineno">  124</span>        <span class="comment">// further implicit else condition</span></div>
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-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>            <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1d77aad7fc39fe7140d834cd347e5c63">minElement</a>[i] = i;</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>        }</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>.assign(n, 0);<span class="comment"></span></div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span><span class="comment">        /// initially set size will be equals to one</span></div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span><span class="comment"></span>        <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; n; i++) {</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>            <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>[i] = 1;</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        }</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   45</span>                             {</div>
+<div class="line"><span class="lineno">   46</span>        <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/assign.html">assign</a>(n, 0);<span class="comment"></span></div>
+<div class="line"><span class="lineno">   47</span><span class="comment">        /// initially, all of them are their own parents</span></div>
+<div class="line"><span class="lineno">   48</span><span class="comment"></span>        <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">   49</span>            <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i] = i;</div>
+<div class="line"><span class="lineno">   50</span>        }<span class="comment"></span></div>
+<div class="line"><span class="lineno">   51</span><span class="comment">        /// initially all have depth are equals to zero</span></div>
+<div class="line"><span class="lineno">   52</span><span class="comment"></span>        <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/assign.html">assign</a>(n, 0);</div>
+<div class="line"><span class="lineno">   53</span>        <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4ade6f16c418fc98b54452f7b0252a53">maxElement</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/assign.html">assign</a>(n, 0);</div>
+<div class="line"><span class="lineno">   54</span>        <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1d77aad7fc39fe7140d834cd347e5c63">minElement</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/assign.html">assign</a>(n, 0);</div>
+<div class="line"><span class="lineno">   55</span>        <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">   56</span>            <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[i] = 0;</div>
+<div class="line"><span class="lineno">   57</span>            <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4ade6f16c418fc98b54452f7b0252a53">maxElement</a>[i] = i;</div>
+<div class="line"><span class="lineno">   58</span>            <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1d77aad7fc39fe7140d834cd347e5c63">minElement</a>[i] = i;</div>
+<div class="line"><span class="lineno">   59</span>        }</div>
+<div class="line"><span class="lineno">   60</span>        <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/assign.html">assign</a>(n, 0);<span class="comment"></span></div>
+<div class="line"><span class="lineno">   61</span><span class="comment">        /// initially set size will be equals to one</span></div>
+<div class="line"><span class="lineno">   62</span><span class="comment"></span>        <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">   63</span>            <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>[i] = 1;</div>
+<div class="line"><span class="lineno">   64</span>        }</div>
+<div class="line"><span class="lineno">   65</span>    }</div>
+<div class="ttc" id="aassign_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/assign.html">std::vector::assign</a></div><div class="ttdeci">T assign(T... args)</div></div>
 <div class="ttc" id="aclassdsu_html_a1d77aad7fc39fe7140d834cd347e5c63"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a1d77aad7fc39fe7140d834cd347e5c63">dsu::minElement</a></div><div class="ttdeci">vector&lt; uint64_t &gt; minElement</div><div class="ttdoc">minimum of each set to which i belongs to</div><div class="ttdef"><b>Definition:</b> dsu_path_compression.cpp:39</div></div>
 <div class="ttc" id="aclassdsu_html_a1ef0b0462a0dda63514f641cbb7dd8cb"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">dsu::p</a></div><div class="ttdeci">vector&lt; uint64_t &gt; p</div><div class="ttdoc">keeps track of the parent of ith element</div><div class="ttdef"><b>Definition:</b> dsu_path_compression.cpp:35</div></div>
 <div class="ttc" id="aclassdsu_html_a4ade6f16c418fc98b54452f7b0252a53"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a4ade6f16c418fc98b54452f7b0252a53">dsu::maxElement</a></div><div class="ttdeci">vector&lt; uint64_t &gt; maxElement</div><div class="ttdoc">maximum of each set to which i belongs to</div><div class="ttdef"><b>Definition:</b> dsu_path_compression.cpp:38</div></div>
 <div class="ttc" id="aclassdsu_html_a4bf54d33fba178998dbbe4c57f2e9429"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">dsu::depth</a></div><div class="ttdeci">vector&lt; uint64_t &gt; depth</div><div class="ttdoc">tracks the depth(rank) of i in the tree</div><div class="ttdef"><b>Definition:</b> dsu_path_compression.cpp:36</div></div>
 <div class="ttc" id="aclassdsu_html_ac0dc3e17e49fe19b159b4ea4096d7b55"><div class="ttname"><a href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">dsu::setSize</a></div><div class="ttdeci">vector&lt; uint64_t &gt; setSize</div><div class="ttdoc">size of each chunk(set)</div><div class="ttdef"><b>Definition:</b> dsu_path_compression.cpp:37</div></div>
-</div><!-- fragment -->
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dd/d1f/classdsu_a126e3002a464e53cd54b07ba56482a72_cgraph.svg" width="262" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
 </div>
 </div>
 <a id="a126e3002a464e53cd54b07ba56482a72" name="a126e3002a464e53cd54b07ba56482a72"></a>
@@ -270,18 +283,24 @@ Private Attributes</h2></td></tr>
   </dd>
 </dl>
 <p >initially all of them are their own parents</p>
-<div class="fragment"><div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>                             {</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>        <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>.assign(n, 0);<span class="comment"></span></div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="comment">        /// initially all of them are their own parents</span></div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span><span class="comment"></span>        <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>.assign(n, 0);</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>        <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>.assign(n, 0);</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; n; i++) {</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>            <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i] = i;</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>            <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[i] = 0;</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>            <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>[i] = 1;</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>        }</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>    }</div>
-</div><!-- fragment -->
+<div class="fragment"><div class="line"><span class="lineno">   44</span>                             {</div>
+<div class="line"><span class="lineno">   45</span>        <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/assign.html">assign</a>(n, 0);<span class="comment"></span></div>
+<div class="line"><span class="lineno">   46</span><span class="comment">        /// initially all of them are their own parents</span></div>
+<div class="line"><span class="lineno">   47</span><span class="comment"></span>        <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/assign.html">assign</a>(n, 0);</div>
+<div class="line"><span class="lineno">   48</span>        <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/assign.html">assign</a>(n, 0);</div>
+<div class="line"><span class="lineno">   49</span>        <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">   50</span>            <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i] = i;</div>
+<div class="line"><span class="lineno">   51</span>            <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[i] = 0;</div>
+<div class="line"><span class="lineno">   52</span>            <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>[i] = 1;</div>
+<div class="line"><span class="lineno">   53</span>        }</div>
+<div class="line"><span class="lineno">   54</span>    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dd/d1f/classdsu_a126e3002a464e53cd54b07ba56482a72_cgraph.svg" width="262" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
 </div>
 </div>
 <h2 class="groupheader">Member Function Documentation</h2>
@@ -318,13 +337,13 @@ Private Attributes</h2></td></tr>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>representative of the set to which i belongs to. </dd></dl>
 <p >using path compression</p>
-<div class="fragment"><div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>                                 {<span class="comment"></span></div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span><span class="comment">        /// using path compression</span></div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span><span class="comment"></span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i] == i) {</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>            <span class="keywordflow">return</span> i;</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>        }</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        <span class="keywordflow">return</span> (<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i] = <a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i]));</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   73</span>                                 {<span class="comment"></span></div>
+<div class="line"><span class="lineno">   74</span><span class="comment">        /// using path compression</span></div>
+<div class="line"><span class="lineno">   75</span><span class="comment"></span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i] == i) {</div>
+<div class="line"><span class="lineno">   76</span>            <span class="keywordflow">return</span> i;</div>
+<div class="line"><span class="lineno">   77</span>        }</div>
+<div class="line"><span class="lineno">   78</span>        <span class="keywordflow">return</span> (<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i] = <a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i]));</div>
+<div class="line"><span class="lineno">   79</span>    }</div>
 <div class="ttc" id="aclassdsu_html_a16851f78fe390fc1430905c83d6a2f1c"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">dsu::findSet</a></div><div class="ttdeci">uint64_t findSet(uint64_t i)</div><div class="ttdoc">Method to find the representative of the set to which i belongs to, T(n) = O(1)</div><div class="ttdef"><b>Definition:</b> dsu_path_compression.cpp:73</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -368,13 +387,13 @@ Here is the call graph for this function:</div>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>representative of the set to which i belongs to </dd></dl>
 <p >using union-rank</p>
-<div class="fragment"><div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>                                 {<span class="comment"></span></div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span><span class="comment">        /// using union-rank</span></div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span><span class="comment"></span>        <span class="keywordflow">while</span> (i != <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i]) {</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>            i = <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i];</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        }</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="keywordflow">return</span> i;</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   61</span>                                 {<span class="comment"></span></div>
+<div class="line"><span class="lineno">   62</span><span class="comment">        /// using union-rank</span></div>
+<div class="line"><span class="lineno">   63</span><span class="comment"></span>        <span class="keywordflow">while</span> (i != <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i]) {</div>
+<div class="line"><span class="lineno">   64</span>            i = <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i];</div>
+<div class="line"><span class="lineno">   65</span>        }</div>
+<div class="line"><span class="lineno">   66</span>        <span class="keywordflow">return</span> i;</div>
+<div class="line"><span class="lineno">   67</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -410,13 +429,13 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>                                     {</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.push_back(<a class="code hl_function" href="../../dd/d1f/classdsu.html#ac713a5b496d0405c82e2808a85e58415">get_min</a>(i));</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>        <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.push_back(<a class="code hl_function" href="../../dd/d1f/classdsu.html#a696141b8b092466767f4bfe1c5e46cde">get_max</a>(i));</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.push_back(<a class="code hl_function" href="../../dd/d1f/classdsu.html#a1c24228b0f2f49220133fb8c3566a55c">size</a>(i));</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  135</span>                                     {</div>
+<div class="line"><span class="lineno">  136</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
+<div class="line"><span class="lineno">  137</span>        <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.push_back(<a class="code hl_function" href="../../dd/d1f/classdsu.html#ac713a5b496d0405c82e2808a85e58415">get_min</a>(i));</div>
+<div class="line"><span class="lineno">  138</span>        <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.push_back(<a class="code hl_function" href="../../dd/d1f/classdsu.html#a696141b8b092466767f4bfe1c5e46cde">get_max</a>(i));</div>
+<div class="line"><span class="lineno">  139</span>        <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.push_back(<a class="code hl_function" href="../../dd/d1f/classdsu.html#a1c24228b0f2f49220133fb8c3566a55c">size</a>(i));</div>
+<div class="line"><span class="lineno">  140</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
+<div class="line"><span class="lineno">  141</span>    }</div>
 <div class="ttc" id="aclassdsu_html_a1c24228b0f2f49220133fb8c3566a55c"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a1c24228b0f2f49220133fb8c3566a55c">dsu::size</a></div><div class="ttdeci">uint64_t size(uint64_t i)</div><div class="ttdoc">A utility function that returns the size of the set to which i belongs to.</div><div class="ttdef"><b>Definition:</b> dsu_path_compression.cpp:148</div></div>
 <div class="ttc" id="aclassdsu_html_a696141b8b092466767f4bfe1c5e46cde"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a696141b8b092466767f4bfe1c5e46cde">dsu::get_max</a></div><div class="ttdeci">uint64_t get_max(uint64_t i)</div><div class="ttdoc">A utility function that returns the max element of the set to which i belongs to.</div><div class="ttdef"><b>Definition:</b> dsu_path_compression.cpp:155</div></div>
 <div class="ttc" id="aclassdsu_html_ac713a5b496d0405c82e2808a85e58415"><div class="ttname"><a href="../../dd/d1f/classdsu.html#ac713a5b496d0405c82e2808a85e58415">dsu::get_min</a></div><div class="ttdeci">uint64_t get_min(uint64_t i)</div><div class="ttdoc">A utility function that returns the min element of the set to which i belongs to.</div><div class="ttdef"><b>Definition:</b> dsu_path_compression.cpp:162</div></div>
@@ -463,7 +482,7 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>maximum of the set to which i belongs to </dd></dl>
-<div class="fragment"><div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4ade6f16c418fc98b54452f7b0252a53">maxElement</a>[<a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(i)]; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  155</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4ade6f16c418fc98b54452f7b0252a53">maxElement</a>[<a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(i)]; }</div>
 </div><!-- fragment --><div class="dynheader">
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@@ -505,7 +524,7 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>minimum of the set to which i belongs to </dd></dl>
-<div class="fragment"><div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1d77aad7fc39fe7140d834cd347e5c63">minElement</a>[<a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(i)]; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  162</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1d77aad7fc39fe7140d834cd347e5c63">minElement</a>[<a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(i)]; }</div>
 </div><!-- fragment --><div class="dynheader">
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 <div class="dyncontent">
@@ -547,15 +566,15 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>                                            {</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>        <span class="keywordflow">while</span> (<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i] != i) {</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>            <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.push_back(i);</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>            i = <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i];</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>        }</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>        <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.push_back(i);</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  119</span>                                            {</div>
+<div class="line"><span class="lineno">  120</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
+<div class="line"><span class="lineno">  121</span>        <span class="keywordflow">while</span> (<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i] != i) {</div>
+<div class="line"><span class="lineno">  122</span>            <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.push_back(i);</div>
+<div class="line"><span class="lineno">  123</span>            i = <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i];</div>
+<div class="line"><span class="lineno">  124</span>        }</div>
+<div class="line"><span class="lineno">  125</span>        <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.push_back(i);</div>
+<div class="line"><span class="lineno">  126</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
+<div class="line"><span class="lineno">  127</span>    }</div>
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@@ -610,12 +629,12 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if element <code>i</code> and <code>j</code> ARE in the same set </dd>
 <dd>
 <code>false</code> if element <code>i</code> and <code>j</code> are NOT in same set </dd></dl>
-<div class="fragment"><div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>                                        {</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(i) == <a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(j)) {</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  123</span>                                        {</div>
+<div class="line"><span class="lineno">  124</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(i) == <a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(j)) {</div>
+<div class="line"><span class="lineno">  125</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  126</span>        }</div>
+<div class="line"><span class="lineno">  127</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  128</span>    }</div>
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@@ -670,12 +689,12 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if element i and j are in same set </dd>
 <dd>
 <code>false</code> if element i and j are not in same set </dd></dl>
-<div class="fragment"><div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>                                        {</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(i) == <a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(j)) {</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        }</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  107</span>                                        {</div>
+<div class="line"><span class="lineno">  108</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(i) == <a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(j)) {</div>
+<div class="line"><span class="lineno">  109</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  110</span>        }</div>
+<div class="line"><span class="lineno">  111</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  112</span>    }</div>
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@@ -717,7 +736,7 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>size of the set to which i belongs to </dd></dl>
-<div class="fragment"><div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>[<a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(i)]; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  148</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>[<a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(i)]; }</div>
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@@ -776,34 +795,34 @@ Here is the call graph for this function:</div>
 <p >if same depth, then increase one's depth</p>
 <p >total size of the resultant set</p>
 <p >changing the maximum elements</p>
-<div class="fragment"><div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>                                          {<span class="comment"></span></div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span><span class="comment">        /// check if both belongs to the same set or not</span></div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span><span class="comment"></span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d1f/classdsu.html#a64d25c5986742f7c234ed449b2ff7303">isSame</a>(i, j)) {</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>            <span class="keywordflow">return</span>;</div>
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-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span> </div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>        <span class="comment">// we find the representative of the i and j</span></div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>        uint64_t x = <a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(i);</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>        uint64_t y = <a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(j);</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span><span class="comment"></span> </div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span><span class="comment">        /// always keeping the min as x</span></div>
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-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span><span class="comment"></span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[x] &gt; <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[y]) {</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(x, y);</div>
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-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span><span class="comment"></span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[x] == <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[y]) {</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>            <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[y]++;</div>
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-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    }</div>
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 <p >making the shallower tree, root parent of the deeper root</p>
 <p >if same depth, then increase one's depth</p>
 <p >total size of the resultant set</p>
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 <tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
@@ -176,9 +176,9 @@ Functions</h2></td></tr>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>value of f(x) for given x. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>                         {</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>    <span class="keywordflow">return</span> (x * x - x);  <span class="comment">// original equation</span></div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   44</span>                         {</div>
+<div class="line"><span class="lineno">   45</span>    <span class="keywordflow">return</span> (x * x - x);  <span class="comment">// original equation</span></div>
+<div class="line"><span class="lineno">   46</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -206,33 +206,33 @@ Here is the call graph for this function:</div>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>           {</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <span class="keywordtype">float</span> a = 0, b = 0, i = 0, root = 0;</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    int16_t count = 0;</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <span class="keywordtype">float</span> range =</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>        100000;       <span class="comment">// Range in which we have to find the root. (-range,range)</span></div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    <span class="keywordtype">float</span> gap = 0.5;  <span class="comment">// interval gap. lesser the gap more the accuracy</span></div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    a = <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">numerical_methods::false_position::eq</a>((-1) * range);</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    i = ((-1) * range + gap);</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    <span class="comment">// while loop for selecting proper interval in provided range and with</span></div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <span class="comment">// provided interval gap.</span></div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    <span class="keywordflow">while</span> (i &lt;= range) {</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        b = <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">numerical_methods::false_position::eq</a>(i);</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>        <span class="keywordflow">if</span> (b == 0) {</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>            count++;</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>            <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a85cb7bfb90abc898e042d624372c5345">numerical_methods::false_position::printRoot</a>(i, count);</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>        }</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>        <span class="keywordflow">if</span> (a * b &lt; 0) {</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>            root = <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a7d69b49dc37da1c02b3ab8c7fe783494">numerical_methods::false_position::regula_falsi</a>(i - gap, i,</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>                                                                   a, b);</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>            count++;</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>            <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a85cb7bfb90abc898e042d624372c5345">numerical_methods::false_position::printRoot</a>(root, count);</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>        }</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>        a = b;</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>        i += gap;</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    }</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  102</span>           {</div>
+<div class="line"><span class="lineno">  103</span>    <span class="keywordtype">float</span> a = 0, b = 0, i = 0, root = 0;</div>
+<div class="line"><span class="lineno">  104</span>    int16_t count = 0;</div>
+<div class="line"><span class="lineno">  105</span>    <span class="keywordtype">float</span> range =</div>
+<div class="line"><span class="lineno">  106</span>        100000;       <span class="comment">// Range in which we have to find the root. (-range,range)</span></div>
+<div class="line"><span class="lineno">  107</span>    <span class="keywordtype">float</span> gap = 0.5;  <span class="comment">// interval gap. lesser the gap more the accuracy</span></div>
+<div class="line"><span class="lineno">  108</span>    a = <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">numerical_methods::false_position::eq</a>((-1) * range);</div>
+<div class="line"><span class="lineno">  109</span>    i = ((-1) * range + gap);</div>
+<div class="line"><span class="lineno">  110</span>    <span class="comment">// while loop for selecting proper interval in provided range and with</span></div>
+<div class="line"><span class="lineno">  111</span>    <span class="comment">// provided interval gap.</span></div>
+<div class="line"><span class="lineno">  112</span>    <span class="keywordflow">while</span> (i &lt;= range) {</div>
+<div class="line"><span class="lineno">  113</span>        b = <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">numerical_methods::false_position::eq</a>(i);</div>
+<div class="line"><span class="lineno">  114</span>        <span class="keywordflow">if</span> (b == 0) {</div>
+<div class="line"><span class="lineno">  115</span>            count++;</div>
+<div class="line"><span class="lineno">  116</span>            <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a85cb7bfb90abc898e042d624372c5345">numerical_methods::false_position::printRoot</a>(i, count);</div>
+<div class="line"><span class="lineno">  117</span>        }</div>
+<div class="line"><span class="lineno">  118</span>        <span class="keywordflow">if</span> (a * b &lt; 0) {</div>
+<div class="line"><span class="lineno">  119</span>            root = <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a7d69b49dc37da1c02b3ab8c7fe783494">numerical_methods::false_position::regula_falsi</a>(i - gap, i,</div>
+<div class="line"><span class="lineno">  120</span>                                                                   a, b);</div>
+<div class="line"><span class="lineno">  121</span>            count++;</div>
+<div class="line"><span class="lineno">  122</span>            <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a85cb7bfb90abc898e042d624372c5345">numerical_methods::false_position::printRoot</a>(root, count);</div>
+<div class="line"><span class="lineno">  123</span>        }</div>
+<div class="line"><span class="lineno">  124</span>        a = b;</div>
+<div class="line"><span class="lineno">  125</span>        i += gap;</div>
+<div class="line"><span class="lineno">  126</span>    }</div>
+<div class="line"><span class="lineno">  127</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  128</span>}</div>
 <div class="ttc" id="afalse__position_8cpp_html_a7d69b49dc37da1c02b3ab8c7fe783494"><div class="ttname"><a href="../../dd/d29/false__position_8cpp.html#a7d69b49dc37da1c02b3ab8c7fe783494">numerical_methods::false_position::regula_falsi</a></div><div class="ttdeci">static float regula_falsi(float x1, float x2, float y1, float y2)</div><div class="ttdoc">This function finds root of the equation in given interval i.e. (x1,x2).</div><div class="ttdef"><b>Definition:</b> false_position.cpp:55</div></div>
 <div class="ttc" id="afalse__position_8cpp_html_a85a6ec58b5064d63d4f0df3854496713"><div class="ttname"><a href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">numerical_methods::false_position::eq</a></div><div class="ttdeci">static float eq(float x)</div><div class="ttdoc">This function gives the value of f(x) for given x.</div><div class="ttdef"><b>Definition:</b> false_position.cpp:44</div></div>
 <div class="ttc" id="afalse__position_8cpp_html_a85cb7bfb90abc898e042d624372c5345"><div class="ttname"><a href="../../dd/d29/false__position_8cpp.html#a85cb7bfb90abc898e042d624372c5345">numerical_methods::false_position::printRoot</a></div><div class="ttdeci">void printRoot(float root, const int16_t &amp;count)</div><div class="ttdoc">This function prints roots of the equation.</div><div class="ttdef"><b>Definition:</b> false_position.cpp:84</div></div>
@@ -273,17 +273,17 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
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-<div class="fragment"><div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>                                                 {</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    <span class="keywordflow">if</span> (count == 1) {</div>
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-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (count == 2) {</div>
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-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (count == 3) {</div>
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-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    }</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   84</span>                                                 {</div>
+<div class="line"><span class="lineno">   85</span>    <span class="keywordflow">if</span> (count == 1) {</div>
+<div class="line"><span class="lineno">   86</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Your 1st root is : &quot;</span> &lt;&lt; root &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   87</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (count == 2) {</div>
+<div class="line"><span class="lineno">   88</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Your 2nd root is : &quot;</span> &lt;&lt; root &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   89</span>    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (count == 3) {</div>
+<div class="line"><span class="lineno">   90</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Your 3rd root is : &quot;</span> &lt;&lt; root &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   91</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   92</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Your &quot;</span> &lt;&lt; count &lt;&lt; <span class="stringliteral">&quot;th root is : &quot;</span> &lt;&lt; root &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   93</span>    }</div>
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 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -350,29 +350,29 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>root of the equation in the given interval. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>                                                                  {</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    <span class="keywordtype">float</span> diff = x1 - x2;</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    <span class="keywordflow">if</span> (diff &lt; 0) {</div>
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-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    }</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <span class="keywordflow">if</span> (diff &lt; 0.00001) {</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        <span class="keywordflow">if</span> (y1 &lt; 0) {</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>            y1 = -y1;</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        }</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        <span class="keywordflow">if</span> (y2 &lt; 0) {</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>            y2 = -y2;</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        }</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        <span class="keywordflow">if</span> (y1 &lt; y2) {</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>            <span class="keywordflow">return</span> x1;</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>            <span class="keywordflow">return</span> x2;</div>
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-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    }</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <span class="keywordtype">float</span> x3 = 0, y3 = 0;</div>
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-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    y3 = <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">eq</a>(x3);</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a7d69b49dc37da1c02b3ab8c7fe783494">regula_falsi</a>(x2, x3, y2, y3);</div>
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+<div class="fragment"><div class="line"><span class="lineno">   55</span>                                                                  {</div>
+<div class="line"><span class="lineno">   56</span>    <span class="keywordtype">float</span> diff = x1 - x2;</div>
+<div class="line"><span class="lineno">   57</span>    <span class="keywordflow">if</span> (diff &lt; 0) {</div>
+<div class="line"><span class="lineno">   58</span>        diff = (-1) * diff;</div>
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+<div class="line"><span class="lineno">   61</span>        <span class="keywordflow">if</span> (y1 &lt; 0) {</div>
+<div class="line"><span class="lineno">   62</span>            y1 = -y1;</div>
+<div class="line"><span class="lineno">   63</span>        }</div>
+<div class="line"><span class="lineno">   64</span>        <span class="keywordflow">if</span> (y2 &lt; 0) {</div>
+<div class="line"><span class="lineno">   65</span>            y2 = -y2;</div>
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+<div class="line"><span class="lineno">   67</span>        <span class="keywordflow">if</span> (y1 &lt; y2) {</div>
+<div class="line"><span class="lineno">   68</span>            <span class="keywordflow">return</span> x1;</div>
+<div class="line"><span class="lineno">   69</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   70</span>            <span class="keywordflow">return</span> x2;</div>
+<div class="line"><span class="lineno">   71</span>        }</div>
+<div class="line"><span class="lineno">   72</span>    }</div>
+<div class="line"><span class="lineno">   73</span>    <span class="keywordtype">float</span> x3 = 0, y3 = 0;</div>
+<div class="line"><span class="lineno">   74</span>    x3 = x1 - (x1 - x2) * (y1) / (y1 - y2);</div>
+<div class="line"><span class="lineno">   75</span>    y3 = <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">eq</a>(x3);</div>
+<div class="line"><span class="lineno">   76</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a7d69b49dc37da1c02b3ab8c7fe783494">regula_falsi</a>(x2, x3, y2, y3);</div>
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   <div class="headertitle"><div class="title">Trie Class Reference</div></div>
 </div><!--header-->
 <div class="contents">
+<div class="dynheader">
+Collaboration diagram for Trie:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/d61/class_trie__coll__graph.svg" width="218" height="142"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
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 <table class="memberdecls">
 <tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="nested-classes" name="nested-classes"></a>
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@@ -168,7 +174,7 @@ static constexpr size_t&#160;</td><td class="memItemRight" valign="bottom"><b>AL
 </div><div class="memdoc">
 
 <p>constructor to initialise the root of the trie. </p>
-<div class="fragment"><div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>: m_root(std::make_shared&lt;TrieNode&gt;()) {}</div>
+<div class="fragment"><div class="line"><span class="lineno">  103</span>: m_root(std::make_shared&lt;TrieNode&gt;()) {}</div>
 </div><!-- fragment -->
 </div>
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@@ -205,14 +211,14 @@ static constexpr size_t&#160;</td><td class="memItemRight" valign="bottom"><b>AL
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if a child is found </dd>
 <dd>
 <code>false</code> if a child is not found </dd></dl>
-<div class="fragment"><div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>                                                                 {</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; ALPHABETS; i++) {</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>            <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;character[i]) {</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   41</span>                                                                 {</div>
+<div class="line"><span class="lineno">   42</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; ALPHABETS; i++) {</div>
+<div class="line"><span class="lineno">   43</span>            <span class="keywordflow">if</span> (<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;character[i]) {</div>
+<div class="line"><span class="lineno">   44</span>                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   45</span>            }</div>
+<div class="line"><span class="lineno">   46</span>        }</div>
+<div class="line"><span class="lineno">   47</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   48</span>    }</div>
 <div class="ttc" id="astructnode_html"><div class="ttname"><a href="../../d5/da1/structnode.html">node</a></div><div class="ttdef"><b>Definition:</b> avltree.cpp:13</div></div>
 </div><!-- fragment -->
 </div>
@@ -246,21 +252,21 @@ static constexpr size_t&#160;</td><td class="memItemRight" valign="bottom"><b>AL
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>                                       {</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        <span class="keyword">auto</span> curr = m_root;</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>        <span class="keywordflow">for</span> (<span class="keywordtype">char</span> ch : word) {</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>            <span class="keywordtype">size_t</span> index = ch - <span class="charliteral">&#39;a&#39;</span>;</div>
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-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>            <span class="comment">// if a node for current word is not already present in trie, create</span></div>
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-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>            <span class="keywordflow">if</span> (!curr-&gt;character[index]) {</div>
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-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>        curr-&gt;isEndOfWord = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  109</span>                                       {</div>
+<div class="line"><span class="lineno">  110</span>        <span class="keyword">auto</span> curr = m_root;</div>
+<div class="line"><span class="lineno">  111</span>        <span class="keywordflow">for</span> (<span class="keywordtype">char</span> ch : word) {</div>
+<div class="line"><span class="lineno">  112</span>            <span class="keywordtype">size_t</span> index = ch - <span class="charliteral">&#39;a&#39;</span>;</div>
+<div class="line"><span class="lineno">  113</span> </div>
+<div class="line"><span class="lineno">  114</span>            <span class="comment">// if a node for current word is not already present in trie, create</span></div>
+<div class="line"><span class="lineno">  115</span>            <span class="comment">// a new node for it.</span></div>
+<div class="line"><span class="lineno">  116</span>            <span class="keywordflow">if</span> (!curr-&gt;character[index]) {</div>
+<div class="line"><span class="lineno">  117</span>                curr-&gt;character[index] = std::make_shared&lt;TrieNode&gt;();</div>
+<div class="line"><span class="lineno">  118</span>            }</div>
+<div class="line"><span class="lineno">  119</span> </div>
+<div class="line"><span class="lineno">  120</span>            curr = curr-&gt;character[index];</div>
+<div class="line"><span class="lineno">  121</span>        }</div>
+<div class="line"><span class="lineno">  122</span>        curr-&gt;isEndOfWord = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  123</span>    }</div>
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-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  148</span>                                           {</div>
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+<div class="line"><span class="lineno">  150</span>    }</div>
 <div class="ttc" id="aclass_trie_html_a26941759ecf94d67a27d4a610bc0f63d"><div class="ttname"><a href="../../dd/d2f/class_trie.html#a26941759ecf94d67a27d4a610bc0f63d">Trie::removeWordHelper</a></div><div class="ttdeci">std::shared_ptr&lt; TrieNode &gt; removeWordHelper(const std::string &amp;word, std::shared_ptr&lt; TrieNode &gt; curr, size_t index)</div><div class="ttdef"><b>Definition:</b> trie_modern.cpp:64</div></div>
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-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        <span class="comment">// This if condition checks if the node has some childern.</span></div>
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+<div class="line"><span class="lineno">   87</span> </div>
+<div class="line"><span class="lineno">   88</span>        <span class="comment">// This if condition checks if the node has some childern.</span></div>
+<div class="line"><span class="lineno">   89</span>        <span class="comment">// The 1st if check, i.e. (curr-&gt;character[idx]) is checked specifically</span></div>
+<div class="line"><span class="lineno">   90</span>        <span class="comment">// because if the older string is a prefix of some other string, then,</span></div>
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+<div class="line"><span class="lineno">   92</span>        <span class="comment">// abbey, str2 = abbex and we want to delete string &quot;abbey&quot;, then in</span></div>
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+<div class="dynheader">
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+<div class="fragment"><div class="line"><span class="lineno">   42</span>        : <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>(1),</div>
+<div class="line"><span class="lineno">   43</span>          <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>({{item, 0, 0}}),</div>
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+<div class="fragment"><div class="line"><span class="lineno">  237</span>                                      {</div>
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+<div class="line"><span class="lineno">  239</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[i] == child) {</div>
+<div class="line"><span class="lineno">  240</span>                <span class="keywordflow">return</span> i;</div>
+<div class="line"><span class="lineno">  241</span>            }</div>
+<div class="line"><span class="lineno">  242</span>        }</div>
+<div class="line"><span class="lineno">  243</span> </div>
+<div class="line"><span class="lineno">  244</span>        <span class="keywordflow">return</span> -1;</div>
+<div class="line"><span class="lineno">  245</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -383,7 +389,7 @@ int8_t&#160;</td><td class="memItemRight" valign="bottom"><b>count</b> = 0</td><
 
 <p>Get the item count that current saved in the node. </p>
 <dl class="section return"><dt>Returns</dt><dd>item count </dd></dl>
-<div class="fragment"><div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>; }</div>
+<div class="fragment"><div class="line"><span class="lineno">   50</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>; }</div>
 </div><!-- fragment -->
 </div>
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@@ -419,7 +425,7 @@ int8_t&#160;</td><td class="memItemRight" valign="bottom"><b>count</b> = 0</td><
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 </dl>
 <dl class="section return"><dt>Returns</dt><dd>the item </dd></dl>
-<div class="fragment"><div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[index]; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  133</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[index]; }</div>
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@@ -455,14 +461,14 @@ int8_t&#160;</td><td class="memItemRight" valign="bottom"><b>count</b> = 0</td><
   </dd>
 </dl>
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-<div class="fragment"><div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>                                      {</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>        <span class="keywordflow">for</span> (int8_t i = 0; i &lt; <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>; i++) {</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[i] == item) {</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>                <span class="keywordflow">return</span> i;</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>            }</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>        }</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        <span class="keywordflow">return</span> -1;</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  107</span>                                      {</div>
+<div class="line"><span class="lineno">  108</span>        <span class="keywordflow">for</span> (int8_t i = 0; i &lt; <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>; i++) {</div>
+<div class="line"><span class="lineno">  109</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[i] == item) {</div>
+<div class="line"><span class="lineno">  110</span>                <span class="keywordflow">return</span> i;</div>
+<div class="line"><span class="lineno">  111</span>            }</div>
+<div class="line"><span class="lineno">  112</span>        }</div>
+<div class="line"><span class="lineno">  113</span>        <span class="keywordflow">return</span> -1;</div>
+<div class="line"><span class="lineno">  114</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -498,13 +504,13 @@ int8_t&#160;</td><td class="memItemRight" valign="bottom"><b>count</b> = 0</td><
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>left child of items[index]'s </dd></dl>
-<div class="fragment"><div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>                                              {</div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>        <span class="keywordflow">if</span> (item_index &lt; 0 || item_index &gt; <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a> - 1) {</div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>            <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>        }</div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span> </div>
-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[item_index];</div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  278</span>                                              {</div>
+<div class="line"><span class="lineno">  279</span>        <span class="keywordflow">if</span> (item_index &lt; 0 || item_index &gt; <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a> - 1) {</div>
+<div class="line"><span class="lineno">  280</span>            <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  281</span>        }</div>
+<div class="line"><span class="lineno">  282</span> </div>
+<div class="line"><span class="lineno">  283</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[item_index];</div>
+<div class="line"><span class="lineno">  284</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -540,13 +546,13 @@ int8_t&#160;</td><td class="memItemRight" valign="bottom"><b>count</b> = 0</td><
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>right child of items[index]'s </dd></dl>
-<div class="fragment"><div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>                                               {</div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>        <span class="keywordflow">if</span> (item_index &lt; 0 || item_index &gt; <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a> - 1) {</div>
-<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>            <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
-<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>        }</div>
-<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span> </div>
-<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[item_index + 1];</div>
-<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  291</span>                                               {</div>
+<div class="line"><span class="lineno">  292</span>        <span class="keywordflow">if</span> (item_index &lt; 0 || item_index &gt; <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a> - 1) {</div>
+<div class="line"><span class="lineno">  293</span>            <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  294</span>        }</div>
+<div class="line"><span class="lineno">  295</span> </div>
+<div class="line"><span class="lineno">  296</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[item_index + 1];</div>
+<div class="line"><span class="lineno">  297</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -575,7 +581,7 @@ int8_t&#160;</td><td class="memItemRight" valign="bottom"><b>count</b> = 0</td><
 
 <p>Get leftmose child of the current node. </p>
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-<div class="fragment"><div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[0]; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  271</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[0]; }</div>
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 </div>
 </div>
@@ -604,7 +610,7 @@ int8_t&#160;</td><td class="memItemRight" valign="bottom"><b>count</b> = 0</td><
 
 <p>Get max item (rightmost) in the current node. </p>
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-<div class="fragment"><div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[<a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a> - 1]; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  120</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[<a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a> - 1]; }</div>
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@@ -633,7 +639,7 @@ int8_t&#160;</td><td class="memItemRight" valign="bottom"><b>count</b> = 0</td><
 
 <p>get min item (leftmost) in the current node </p>
 <dl class="section return"><dt>Returns</dt><dd>min item </dd></dl>
-<div class="fragment"><div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[0]; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  126</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[0]; }</div>
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 </div>
@@ -669,15 +675,15 @@ int8_t&#160;</td><td class="memItemRight" valign="bottom"><b>count</b> = 0</td><
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 </dl>
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-<div class="fragment"><div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span>                                             {</div>
-<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span>        <span class="keywordtype">int</span> i = 0;</div>
-<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>        <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>; i++) {</div>
-<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[i] &gt; item) {</div>
-<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span>            }</div>
-<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span>        }</div>
-<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[i];</div>
-<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  304</span>                                             {</div>
+<div class="line"><span class="lineno">  305</span>        <span class="keywordtype">int</span> i = 0;</div>
+<div class="line"><span class="lineno">  306</span>        <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>; i++) {</div>
+<div class="line"><span class="lineno">  307</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[i] &gt; item) {</div>
+<div class="line"><span class="lineno">  308</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  309</span>            }</div>
+<div class="line"><span class="lineno">  310</span>        }</div>
+<div class="line"><span class="lineno">  311</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[i];</div>
+<div class="line"><span class="lineno">  312</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -706,7 +712,7 @@ int8_t&#160;</td><td class="memItemRight" valign="bottom"><b>count</b> = 0</td><
 
 <p>Get rightmose child of the current node. </p>
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-<div class="fragment"><div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[<a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>]; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  265</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[<a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>]; }</div>
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@@ -743,23 +749,23 @@ int8_t&#160;</td><td class="memItemRight" valign="bottom"><b>count</b> = 0</td><
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 </dl>
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-<div class="fragment"><div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>                             {</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>        assert(!<a class="code hl_function" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a4a37381c0ef93d5ae2118b2e554974dd">IsFull</a>());</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span> </div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a22fd25c6c811c64b6b27b0850d8c532f">Contains</a>(item)) {</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>            <span class="keywordflow">return</span> -1;</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>        }</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span> </div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>        int8_t i = 0;</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>        <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>; i++) {</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[i] &gt; item) {</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>                <span class="keywordflow">break</span>;</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>            }</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>        }</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span> </div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>        <a class="code hl_function" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a306a30931f54c84098b38d6bc8f4a956">InsertItemByIndex</a>(i, item, <span class="keyword">nullptr</span>, <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>        <span class="keywordflow">return</span> i;</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  163</span>                             {</div>
+<div class="line"><span class="lineno">  164</span>        assert(!<a class="code hl_function" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a4a37381c0ef93d5ae2118b2e554974dd">IsFull</a>());</div>
+<div class="line"><span class="lineno">  165</span> </div>
+<div class="line"><span class="lineno">  166</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a22fd25c6c811c64b6b27b0850d8c532f">Contains</a>(item)) {</div>
+<div class="line"><span class="lineno">  167</span>            <span class="keywordflow">return</span> -1;</div>
+<div class="line"><span class="lineno">  168</span>        }</div>
+<div class="line"><span class="lineno">  169</span> </div>
+<div class="line"><span class="lineno">  170</span>        int8_t i = 0;</div>
+<div class="line"><span class="lineno">  171</span>        <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>; i++) {</div>
+<div class="line"><span class="lineno">  172</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[i] &gt; item) {</div>
+<div class="line"><span class="lineno">  173</span>                <span class="keywordflow">break</span>;</div>
+<div class="line"><span class="lineno">  174</span>            }</div>
+<div class="line"><span class="lineno">  175</span>        }</div>
+<div class="line"><span class="lineno">  176</span> </div>
+<div class="line"><span class="lineno">  177</span>        <a class="code hl_function" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a306a30931f54c84098b38d6bc8f4a956">InsertItemByIndex</a>(i, item, <span class="keyword">nullptr</span>, <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  178</span>        <span class="keywordflow">return</span> i;</div>
+<div class="line"><span class="lineno">  179</span>    }</div>
 <div class="ttc" id="aclassdata__structures_1_1tree__234_1_1_node_html_a22fd25c6c811c64b6b27b0850d8c532f"><div class="ttname"><a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a22fd25c6c811c64b6b27b0850d8c532f">data_structures::tree_234::Node::Contains</a></div><div class="ttdeci">bool Contains(int64_t item)</div><div class="ttdoc">Check if item is in the node.</div><div class="ttdef"><b>Definition:</b> tree_234.cpp:92</div></div>
 <div class="ttc" id="aclassdata__structures_1_1tree__234_1_1_node_html_a306a30931f54c84098b38d6bc8f4a956"><div class="ttname"><a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a306a30931f54c84098b38d6bc8f4a956">data_structures::tree_234::Node::InsertItemByIndex</a></div><div class="ttdeci">void InsertItemByIndex(int8_t index, int64_t item, Node *with_child, bool to_left=true)</div><div class="ttdoc">Insert a value to the index position.</div><div class="ttdef"><b>Definition:</b> tree_234.cpp:189</div></div>
 <div class="ttc" id="aclassdata__structures_1_1tree__234_1_1_node_html_a4a37381c0ef93d5ae2118b2e554974dd"><div class="ttname"><a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a4a37381c0ef93d5ae2118b2e554974dd">data_structures::tree_234::Node::IsFull</a></div><div class="ttdeci">bool IsFull()</div><div class="ttdoc">Check if node is a full (4-node)</div><div class="ttdef"><b>Definition:</b> tree_234.cpp:73</div></div>
@@ -828,25 +834,25 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>                                                {</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>        assert(count &lt; 3 &amp;&amp; index &gt;= 0 &amp;&amp; index &lt; 3);</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span> </div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>        <span class="keywordflow">for</span> (int8_t i = <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a> - 1; i &gt;= index; i--) {</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>            <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[i + 1] = <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[i];</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>        }</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span> </div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>        <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[index] = item;</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span> </div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>        int8_t start_index = to_left ? index : index + 1;</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span> </div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>        <span class="keywordflow">for</span> (int8_t i = <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>; i &gt;= start_index; i--) {</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>            <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[i + 1] = <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[i];</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>        }</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span> </div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>        <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[start_index] = with_child;</div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span> </div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>        <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>++;</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  190</span>                                                {</div>
+<div class="line"><span class="lineno">  191</span>        assert(count &lt; 3 &amp;&amp; index &gt;= 0 &amp;&amp; index &lt; 3);</div>
+<div class="line"><span class="lineno">  192</span> </div>
+<div class="line"><span class="lineno">  193</span>        <span class="keywordflow">for</span> (int8_t i = <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a> - 1; i &gt;= index; i--) {</div>
+<div class="line"><span class="lineno">  194</span>            <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[i + 1] = <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[i];</div>
+<div class="line"><span class="lineno">  195</span>        }</div>
+<div class="line"><span class="lineno">  196</span> </div>
+<div class="line"><span class="lineno">  197</span>        <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[index] = item;</div>
+<div class="line"><span class="lineno">  198</span> </div>
+<div class="line"><span class="lineno">  199</span>        int8_t start_index = to_left ? index : index + 1;</div>
+<div class="line"><span class="lineno">  200</span> </div>
+<div class="line"><span class="lineno">  201</span>        <span class="keywordflow">for</span> (int8_t i = <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>; i &gt;= start_index; i--) {</div>
+<div class="line"><span class="lineno">  202</span>            <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[i + 1] = <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[i];</div>
+<div class="line"><span class="lineno">  203</span>        }</div>
+<div class="line"><span class="lineno">  204</span> </div>
+<div class="line"><span class="lineno">  205</span>        <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[start_index] = with_child;</div>
+<div class="line"><span class="lineno">  206</span> </div>
+<div class="line"><span class="lineno">  207</span>        <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>++;</div>
+<div class="line"><span class="lineno">  208</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -875,7 +881,7 @@ Here is the call graph for this function:</div>
 
 <p>Check if node is a 2-node. </p>
 <dl class="section return"><dt>Returns</dt><dd>true if node is 2-node, otherwise false </dd></dl>
-<div class="fragment"><div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a> == 1; }</div>
+<div class="fragment"><div class="line"><span class="lineno">   79</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a> == 1; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -904,7 +910,7 @@ Here is the call graph for this function:</div>
 
 <p>Check if node is a 3-node or 4-node, this is useful when we delete item from 2-3-4 tree. </p>
 <dl class="section return"><dt>Returns</dt><dd>true if node is 3-node or 4-node, false otherwise </dd></dl>
-<div class="fragment"><div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a> == 2 || <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a> == 3; }</div>
+<div class="fragment"><div class="line"><span class="lineno">   85</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a> == 2 || <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a> == 3; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -933,7 +939,7 @@ Here is the call graph for this function:</div>
 
 <p>Check if node is a full (4-node) </p>
 <dl class="section return"><dt>Returns</dt><dd>true if node is full (4-node), false otherwise </dd></dl>
-<div class="fragment"><div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a> == 3; }</div>
+<div class="fragment"><div class="line"><span class="lineno">   73</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a> == 3; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -962,7 +968,7 @@ Here is the call graph for this function:</div>
 
 <p>Check if node is a leaf. </p>
 <dl class="section return"><dt>Returns</dt><dd>true if node is leaf, false otherwise </dd></dl>
-<div class="fragment"><div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[0] == <span class="keyword">nullptr</span>; }</div>
+<div class="fragment"><div class="line"><span class="lineno">   67</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[0] == <span class="keyword">nullptr</span>; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -1009,20 +1015,20 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>the removed child pointer </dd></dl>
-<div class="fragment"><div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>                                                          {</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>        assert(index &gt;= 0 &amp;&amp; index &lt; <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>);</div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *removed_child = keep_left ? <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[index + 1] : <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[index];</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>        <span class="keywordflow">for</span> (int8_t i = index; i &lt; <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a> - 1; i++) {</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>            <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[i] = <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[i + 1];</div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>        }</div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span> </div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>        <span class="keywordflow">for</span> (int8_t i = keep_left ? index + 1 : index; i &lt; <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>; i++) {</div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>            <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[i] = <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[i + 1];</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>        }</div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span> </div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>        <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>--;</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>        <span class="keywordflow">return</span> removed_child;</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  217</span>                                                          {</div>
+<div class="line"><span class="lineno">  218</span>        assert(index &gt;= 0 &amp;&amp; index &lt; <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>);</div>
+<div class="line"><span class="lineno">  219</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *removed_child = keep_left ? <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[index + 1] : <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[index];</div>
+<div class="line"><span class="lineno">  220</span>        <span class="keywordflow">for</span> (int8_t i = index; i &lt; <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a> - 1; i++) {</div>
+<div class="line"><span class="lineno">  221</span>            <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[i] = <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8417d01c88b99ca56289843509fb71f9">items</a>[i + 1];</div>
+<div class="line"><span class="lineno">  222</span>        }</div>
+<div class="line"><span class="lineno">  223</span> </div>
+<div class="line"><span class="lineno">  224</span>        <span class="keywordflow">for</span> (int8_t i = keep_left ? index + 1 : index; i &lt; <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>; i++) {</div>
+<div class="line"><span class="lineno">  225</span>            <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[i] = <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad5d6b6ce5fab21ccc88c6bf3153eee5d">children</a>[i + 1];</div>
+<div class="line"><span class="lineno">  226</span>        }</div>
+<div class="line"><span class="lineno">  227</span> </div>
+<div class="line"><span class="lineno">  228</span>        <a class="code hl_variable" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a934e6d53cfefae2b971e1241a8a4c921">count</a>--;</div>
+<div class="line"><span class="lineno">  229</span>        <span class="keywordflow">return</span> removed_child;</div>
+<div class="line"><span class="lineno">  230</span>    }</div>
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+<div class="fragment"><div class="line"><span class="lineno">  140</span>                                                 {</div>
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@@ -246,10 +246,10 @@ Algorithm</h3>
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-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   26</span>                                      {</div>
+<div class="line"><span class="lineno">   27</span>    <span class="comment">// Calculating 2^n</span></div>
+<div class="line"><span class="lineno">   28</span>    <span class="keywordflow">return</span> (1 &lt;&lt; n);</div>
+<div class="line"><span class="lineno">   29</span>}</div>
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 </div>
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 <dl class="section return"><dt>Returns</dt><dd>area of the circle </dd></dl>
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-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   63</span>                        {</div>
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 </div><!-- fragment -->
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@@ -332,9 +332,9 @@ template&lt;typename T &gt; </div>
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 <dl class="section return"><dt>Returns</dt><dd>The volume of the cone </dd></dl>
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-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   53</span>                                                    {</div>
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+<div class="line"><span class="lineno">   55</span>}</div>
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@@ -375,9 +375,9 @@ template&lt;typename T &gt; </div>
 <dl class="section return"><dt>Returns</dt><dd>surface area of the cube </dd></dl>
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-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   86</span>                              {</div>
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+<div class="line"><span class="lineno">  110</span>    <span class="keywordflow">return</span> 2 * M_PI * radius * <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a> + 2 * M_PI * pow(radius, 2);</div>
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-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   33</span>                                             {</div>
+<div class="line"><span class="lineno">   34</span>    <span class="keywordtype">double</span> result = 0;</div>
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+<div class="line"><span class="lineno">   36</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; numDeltas; i++) {</div>
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+<div class="line"><span class="lineno">   39</span>        result += delta * (func(begin) + func(end)) / 2;</div>
+<div class="line"><span class="lineno">   40</span>    }</div>
+<div class="line"><span class="lineno">   41</span>    <span class="keywordflow">return</span> result;</div>
+<div class="line"><span class="lineno">   42</span>}</div>
 </div><!-- fragment -->
 </div>
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 <dl class="section return"><dt>Returns</dt><dd>largest power </dd></dl>
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+<div class="fragment"><div class="line"><span class="lineno">   27</span>    {  </div>
+<div class="line"><span class="lineno">   28</span>        <span class="comment">// Initialize result  </span></div>
+<div class="line"><span class="lineno">   29</span>        <span class="keywordtype">int</span> x = 0;  </div>
+<div class="line"><span class="lineno">   30</span>  </div>
+<div class="line"><span class="lineno">   31</span>        <span class="comment">// Calculate result </span></div>
+<div class="line"><span class="lineno">   32</span>        <span class="keywordflow">while</span> (n)  </div>
+<div class="line"><span class="lineno">   33</span>        {  </div>
+<div class="line"><span class="lineno">   34</span>            n /= p;  </div>
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+<div class="line"><span class="lineno">   37</span>        <span class="keywordflow">return</span> x;  </div>
+<div class="line"><span class="lineno">   38</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -658,36 +658,36 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>int Sum of LCMs, i.e. ∑LCM(i, num) from i = 1 to num </dd></dl>
-<div class="fragment"><div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>                                     {</div>
-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>    uint64_t i = 0, j = 0;</div>
-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> eulerTotient(num + 1);</div>
-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> sumOfEulerTotient(num + 1);</div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span> </div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>    <span class="comment">// storing initial values in eulerTotient vector</span></div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    <span class="keywordflow">for</span> (i = 1; i &lt;= num; i++) {</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>        eulerTotient[i] = i;</div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    }</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span> </div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>    <span class="comment">// applying totient sieve</span></div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    <span class="keywordflow">for</span> (i = 2; i &lt;= num; i++) {</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>        <span class="keywordflow">if</span> (eulerTotient[i] == i) {</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>            <span class="keywordflow">for</span> (j = i; j &lt;= num; j += i) {</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>                eulerTotient[j] = eulerTotient[j] / i;</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>                eulerTotient[j] = eulerTotient[j] * (i - 1);</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>            }</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>        }</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>    }</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span> </div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    <span class="comment">// computing sum of euler totients</span></div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    <span class="keywordflow">for</span> (i = 1; i &lt;= num; i++) {</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>        <span class="keywordflow">for</span> (j = i; j &lt;= num; j += i) {</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>            sumOfEulerTotient[j] += eulerTotient[i] * i;</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>        }</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>    }</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span> </div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    <span class="keywordflow">return</span> ((sumOfEulerTotient[num] + 1) * num) / 2;</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>}</div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="fragment"><div class="line"><span class="lineno">   29</span>                                     {</div>
+<div class="line"><span class="lineno">   30</span>    uint64_t i = 0, j = 0;</div>
+<div class="line"><span class="lineno">   31</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> eulerTotient(num + 1);</div>
+<div class="line"><span class="lineno">   32</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> sumOfEulerTotient(num + 1);</div>
+<div class="line"><span class="lineno">   33</span> </div>
+<div class="line"><span class="lineno">   34</span>    <span class="comment">// storing initial values in eulerTotient vector</span></div>
+<div class="line"><span class="lineno">   35</span>    <span class="keywordflow">for</span> (i = 1; i &lt;= num; i++) {</div>
+<div class="line"><span class="lineno">   36</span>        eulerTotient[i] = i;</div>
+<div class="line"><span class="lineno">   37</span>    }</div>
+<div class="line"><span class="lineno">   38</span> </div>
+<div class="line"><span class="lineno">   39</span>    <span class="comment">// applying totient sieve</span></div>
+<div class="line"><span class="lineno">   40</span>    <span class="keywordflow">for</span> (i = 2; i &lt;= num; i++) {</div>
+<div class="line"><span class="lineno">   41</span>        <span class="keywordflow">if</span> (eulerTotient[i] == i) {</div>
+<div class="line"><span class="lineno">   42</span>            <span class="keywordflow">for</span> (j = i; j &lt;= num; j += i) {</div>
+<div class="line"><span class="lineno">   43</span>                eulerTotient[j] = eulerTotient[j] / i;</div>
+<div class="line"><span class="lineno">   44</span>                eulerTotient[j] = eulerTotient[j] * (i - 1);</div>
+<div class="line"><span class="lineno">   45</span>            }</div>
+<div class="line"><span class="lineno">   46</span>        }</div>
+<div class="line"><span class="lineno">   47</span>    }</div>
+<div class="line"><span class="lineno">   48</span> </div>
+<div class="line"><span class="lineno">   49</span>    <span class="comment">// computing sum of euler totients</span></div>
+<div class="line"><span class="lineno">   50</span>    <span class="keywordflow">for</span> (i = 1; i &lt;= num; i++) {</div>
+<div class="line"><span class="lineno">   51</span>        <span class="keywordflow">for</span> (j = i; j &lt;= num; j += i) {</div>
+<div class="line"><span class="lineno">   52</span>            sumOfEulerTotient[j] += eulerTotient[i] * i;</div>
+<div class="line"><span class="lineno">   53</span>        }</div>
+<div class="line"><span class="lineno">   54</span>    }</div>
+<div class="line"><span class="lineno">   55</span> </div>
+<div class="line"><span class="lineno">   56</span>    <span class="keywordflow">return</span> ((sumOfEulerTotient[num] + 1) * num) / 2;</div>
+<div class="line"><span class="lineno">   57</span>}</div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; uint64_t &gt;</a></div></div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -713,19 +713,19 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>if number is a magic number, returns true, else false. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>                                     {</div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>    <span class="keywordflow">if</span> (n &lt;= 0) {</div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    }</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>    <span class="comment">// result stores the modulus of @param n with 9</span></div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    uint64_t result = n % 9;</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    <span class="comment">// if result is 1 then the number is a magic number else not</span></div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>    <span class="keywordflow">if</span> (result == 1) {</div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>    }</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   32</span>                                     {</div>
+<div class="line"><span class="lineno">   33</span>    <span class="keywordflow">if</span> (n &lt;= 0) {</div>
+<div class="line"><span class="lineno">   34</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   35</span>    }</div>
+<div class="line"><span class="lineno">   36</span>    <span class="comment">// result stores the modulus of @param n with 9</span></div>
+<div class="line"><span class="lineno">   37</span>    uint64_t result = n % 9;</div>
+<div class="line"><span class="lineno">   38</span>    <span class="comment">// if result is 1 then the number is a magic number else not</span></div>
+<div class="line"><span class="lineno">   39</span>    <span class="keywordflow">if</span> (result == 1) {</div>
+<div class="line"><span class="lineno">   40</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   41</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   42</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   43</span>    }</div>
+<div class="line"><span class="lineno">   44</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -772,17 +772,17 @@ template&lt;class T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>ans \( \binom{n}{r} \) </dd></dl>
-<div class="fragment"><div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>                       {</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>    <span class="keywordflow">if</span> (r &gt; n / 2) {</div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>        r = n - r;  <span class="comment">// Because of the fact that  nCr(n, r) == nCr(n, n - r)</span></div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    }</div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>    T <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = 1;</div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt;= r; i++) {</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>        <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> *= n - r + i;</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>        <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> /= i;</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>    }</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   35</span>                       {</div>
+<div class="line"><span class="lineno">   36</span>    <span class="keywordflow">if</span> (r &gt; n / 2) {</div>
+<div class="line"><span class="lineno">   37</span>        r = n - r;  <span class="comment">// Because of the fact that  nCr(n, r) == nCr(n, n - r)</span></div>
+<div class="line"><span class="lineno">   38</span>    }</div>
+<div class="line"><span class="lineno">   39</span>    T <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = 1;</div>
+<div class="line"><span class="lineno">   40</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt;= r; i++) {</div>
+<div class="line"><span class="lineno">   41</span>        <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> *= n - r + i;</div>
+<div class="line"><span class="lineno">   42</span>        <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> /= i;</div>
+<div class="line"><span class="lineno">   43</span>    }</div>
+<div class="line"><span class="lineno">   44</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
+<div class="line"><span class="lineno">   45</span>}</div>
 <div class="ttc" id="amatrix__exponentiation_8cpp_html_ad8389ed58fd0ec66df248014775ad1fa"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a></div><div class="ttdeci">ll ans(ll n)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:91</div></div>
 </div><!-- fragment --><div class="dynheader">
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@@ -830,9 +830,9 @@ template&lt;typename T &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>area of the parallelogram </dd></dl>
-<div class="fragment"><div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>                                       {</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>    <span class="keywordflow">return</span> base * <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>;</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   75</span>                                       {</div>
+<div class="line"><span class="lineno">   76</span>    <span class="keywordflow">return</span> base * <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>;</div>
+<div class="line"><span class="lineno">   77</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -890,23 +890,23 @@ Here is the call graph for this function:</div>
 <p >If b is odd, multiply a with answer</p>
 <p >b must be even now</p>
 <p >b = b/2</p>
-<div class="fragment"><div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>                                                   {</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>    uint64_t <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = 1;  <span class="comment">/// Initialize the answer to be returned</span></div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    a = a % c;         <span class="comment">/// Update a if it is more than or equal to c</span></div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    <span class="keywordflow">if</span> (a == 0) {</div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>        <span class="keywordflow">return</span> 0;  <span class="comment">/// In case a is divisible by c;</span></div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    }</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    <span class="keywordflow">while</span> (b &gt; 0) {<span class="comment"></span></div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><span class="comment">        /// If b is odd, multiply a with answer</span></div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span><span class="comment"></span>        <span class="keywordflow">if</span> (b &amp; 1) {</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>            <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = ((<a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> % c) * (a % c)) % c;</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>        }<span class="comment"></span></div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="comment">        /// b must be even now</span></div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span><span class="comment"></span>        b = b &gt;&gt; 1;  <span class="comment">/// b = b/2</span></div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>        a = ((a % c) * (a % c)) % c;</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    }</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   35</span>                                                   {</div>
+<div class="line"><span class="lineno">   36</span>    uint64_t <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = 1;  <span class="comment">/// Initialize the answer to be returned</span></div>
+<div class="line"><span class="lineno">   37</span>    a = a % c;         <span class="comment">/// Update a if it is more than or equal to c</span></div>
+<div class="line"><span class="lineno">   38</span>    <span class="keywordflow">if</span> (a == 0) {</div>
+<div class="line"><span class="lineno">   39</span>        <span class="keywordflow">return</span> 0;  <span class="comment">/// In case a is divisible by c;</span></div>
+<div class="line"><span class="lineno">   40</span>    }</div>
+<div class="line"><span class="lineno">   41</span>    <span class="keywordflow">while</span> (b &gt; 0) {<span class="comment"></span></div>
+<div class="line"><span class="lineno">   42</span><span class="comment">        /// If b is odd, multiply a with answer</span></div>
+<div class="line"><span class="lineno">   43</span><span class="comment"></span>        <span class="keywordflow">if</span> (b &amp; 1) {</div>
+<div class="line"><span class="lineno">   44</span>            <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = ((<a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> % c) * (a % c)) % c;</div>
+<div class="line"><span class="lineno">   45</span>        }<span class="comment"></span></div>
+<div class="line"><span class="lineno">   46</span><span class="comment">        /// b must be even now</span></div>
+<div class="line"><span class="lineno">   47</span><span class="comment"></span>        b = b &gt;&gt; 1;  <span class="comment">/// b = b/2</span></div>
+<div class="line"><span class="lineno">   48</span>        a = ((a % c) * (a % c)) % c;</div>
+<div class="line"><span class="lineno">   49</span>    }</div>
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+<div class="line"><span class="lineno">   39</span><span class="comment">     * @param n value for which we want to check</span></div>
+<div class="line"><span class="lineno">   40</span><span class="comment">     * prints the result, as &quot;Yes, the number n is a power of 2&quot; or</span></div>
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+<div class="line"><span class="lineno">   43</span><span class="comment">    /// result stores the</span></div>
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@@ -1011,9 +1011,9 @@ template&lt;typename T &gt; </div>
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+<div class="line"><span class="lineno">   82</span>}</div>
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@@ -1060,9 +1060,9 @@ template&lt;typename T &gt; </div>
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+<div class="line"><span class="lineno">   41</span>    <span class="keywordflow">return</span> length * width;</div>
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+<div class="line"><span class="lineno">   98</span>    <span class="keywordflow">return</span> 4 * M_PI * pow(radius, 2);</div>
+<div class="line"><span class="lineno">   99</span>}</div>
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+<div class="line"><span class="lineno">   52</span>    assert(approx &gt;= expected * (1 - threshold));</div>
+<div class="line"><span class="lineno">   53</span>    assert(approx &lt;= expected * (1 + threshold));</div>
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+<div class="line"><span class="lineno">   53</span>    <span class="keywordflow">return</span> base * <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a> / 2;</div>
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+<div class="fragment"><div class="line"><span class="lineno">   67</span>                                                   {</div>
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+<div class="line"><span class="lineno">   86</span> </div>
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 <p >operator to print a matrix </p>
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+<div class="line"><span class="lineno">   22</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; v.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); row++) {</div>
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 <p >Test LU decomposition </p><dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000006">Todo:</a></b></dt><dd>better ways to self-check a matrix output? </dd></dl>
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-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> U(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>));  <span class="comment">// output</span></div>
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+<div class="line"><span class="lineno">   45</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
+<div class="line"><span class="lineno">   46</span>        <span class="comment">// calloc so that all valeus are &#39;0&#39; by default</span></div>
+<div class="line"><span class="lineno">   47</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; j++)</div>
+<div class="line"><span class="lineno">   48</span>            <span class="comment">/* create random values in the limits [-range2, range-1] */</span></div>
+<div class="line"><span class="lineno">   49</span>            A[i][j] = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range - range2);</div>
+<div class="line"><span class="lineno">   50</span>    }</div>
+<div class="line"><span class="lineno">   51</span> </div>
+<div class="line"><span class="lineno">   52</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start_t = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">   53</span>    <a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition</a>(A, &amp;L, &amp;U);</div>
+<div class="line"><span class="lineno">   54</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> end_t = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">   55</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time taken: &quot;</span></div>
+<div class="line"><span class="lineno">   56</span>              &lt;&lt; <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(end_t - start_t) / CLOCKS_PER_SEC &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   57</span> </div>
+<div class="line"><span class="lineno">   58</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;A = \n&quot;</span> &lt;&lt; A &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   59</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;L = \n&quot;</span> &lt;&lt; L &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   60</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;U = \n&quot;</span> &lt;&lt; U &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   61</span>}</div>
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 <div class="ttc" id="aclock_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a></div></div>
 <div class="ttc" id="alu__decomposition_8h_html_a75b8a228c6419ecda6077255d6d60509"><div class="ttname"><a href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition</a></div><div class="ttdeci">int lu_decomposition(const matrix&lt; T &gt; &amp;A, matrix&lt; double &gt; *L, matrix&lt; double &gt; *U)</div><div class="ttdef"><b>Definition:</b> lu_decomposition.h:29</div></div>
 <div class="ttc" id="amatrix__exponentiation_8cpp_html_a9977ad12548c4a49dee9dc3f0685aa54"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a></div><div class="ttdeci">ll mat_size</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:45</div></div>
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 <p >Test determinant computation using LU decomposition </p>
-<div class="fragment"><div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>             {</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Determinant test 1...&quot;</span>;</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> A1({{1, 2, 3}, {4, 9, 6}, {7, 8, 9}});</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    assert(<a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(A1) == -48);</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span> </div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Determinant test 2...&quot;</span>;</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> A2({{1, 2, 3}, {4, 5, 6}, {7, 8, 9}});</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    assert(<a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(A2) == 0);</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span> </div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Determinant test 3...&quot;</span>;</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;float&gt;</a> A3({{1.2, 2.3, 3.4}, {4.5, 5.6, 6.7}, {7.8, 8.9, 9.0}});</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    assert(<a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(A3) == 3.63);</div>
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-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   66</span>             {</div>
+<div class="line"><span class="lineno">   67</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Determinant test 1...&quot;</span>;</div>
+<div class="line"><span class="lineno">   68</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> A1({{1, 2, 3}, {4, 9, 6}, {7, 8, 9}});</div>
+<div class="line"><span class="lineno">   69</span>    assert(<a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(A1) == -48);</div>
+<div class="line"><span class="lineno">   70</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   71</span> </div>
+<div class="line"><span class="lineno">   72</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Determinant test 2...&quot;</span>;</div>
+<div class="line"><span class="lineno">   73</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> A2({{1, 2, 3}, {4, 5, 6}, {7, 8, 9}});</div>
+<div class="line"><span class="lineno">   74</span>    assert(<a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(A2) == 0);</div>
+<div class="line"><span class="lineno">   75</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   76</span> </div>
+<div class="line"><span class="lineno">   77</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Determinant test 3...&quot;</span>;</div>
+<div class="line"><span class="lineno">   78</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;float&gt;</a> A3({{1.2, 2.3, 3.4}, {4.5, 5.6, 6.7}, {7.8, 8.9, 9.0}});</div>
+<div class="line"><span class="lineno">   79</span>    assert(<a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(A3) == 3.63);</div>
+<div class="line"><span class="lineno">   80</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   81</span>}</div>
 <div class="ttc" id="alu__decomposition_8h_html_a3108d43bd32c6fb3b3c158476c51ba7f"><div class="ttname"><a href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a></div><div class="ttdeci">double determinant_lu(const matrix&lt; T &gt; &amp;A)</div><div class="ttdef"><b>Definition:</b> lu_decomposition.h:90</div></div>
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 Here is the call graph for this function:</div>
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 <p>A class defining <a href="https://en.wikipedia.org/wiki/15_puzzle" target="_blank">EightPuzzle/15-Puzzle game</a>.  
  <a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#details">More...</a></p>
+<div class="dynheader">
+Collaboration diagram for machine_learning::aystar_search::EightPuzzle&lt; N &gt;:</div>
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+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d0/dff/classmachine__learning_1_1aystar__search_1_1_eight_puzzle__coll__graph.svg" width="650" height="118"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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+          <td class="memname"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">machine_learning::aystar_search::EightPuzzle</a>&lt; N &gt;::EightPuzzle </td>
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 <p>Default constructor for <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html" title="A class defining EightPuzzle/15-Puzzle game.">EightPuzzle</a>. </p>
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   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>        : board(init) {}</div>
+<div class="fragment"><div class="line"><span class="lineno">  133</span>        : board(init) {}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -269,7 +275,7 @@ template&lt;size_t N = 3&gt; </div>
   <td class="mlabels-left">
       <table class="memname">
         <tr>
-          <td class="memname"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">machine_learning::aystar_search::EightPuzzle</a>&lt; N &gt;::<a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">EightPuzzle</a> </td>
+          <td class="memname"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">machine_learning::aystar_search::EightPuzzle</a>&lt; N &gt;::EightPuzzle </td>
           <td>(</td>
           <td class="paramtype">const <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">EightPuzzle</a>&lt; N &gt; &amp;&#160;</td>
           <td class="paramname"><em>A</em></td><td>)</td>
@@ -290,7 +296,7 @@ template&lt;size_t N = 3&gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>: board(A.board) {}</div>
+<div class="fragment"><div class="line"><span class="lineno">  139</span>: board(A.board) {}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -306,7 +312,7 @@ template&lt;size_t N = 3&gt; </div>
   <td class="mlabels-left">
       <table class="memname">
         <tr>
-          <td class="memname"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">machine_learning::aystar_search::EightPuzzle</a>&lt; N &gt;::<a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">EightPuzzle</a> </td>
+          <td class="memname"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">machine_learning::aystar_search::EightPuzzle</a>&lt; N &gt;::EightPuzzle </td>
           <td>(</td>
           <td class="paramtype">const <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">EightPuzzle</a>&lt; N &gt; &amp;&amp;&#160;</td>
           <td class="paramname"><em>A</em></td><td>)</td>
@@ -327,7 +333,7 @@ template&lt;size_t N = 3&gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>        : board(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(A.board)) {}</div>
+<div class="fragment"><div class="line"><span class="lineno">  146</span>        : board(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(A.board)) {}</div>
 <div class="ttc" id="amove_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a></div><div class="ttdeci">T move(T... args)</div></div>
 </div><!-- fragment -->
 </div>
@@ -360,16 +366,16 @@ template&lt;size_t N = 3&gt; </div>
 
 <p>A helper array to evaluate the next state from current state;. </p>
 <p >Finds an empty space in puzzle (in this case; a zero) </p><dl class="section return"><dt>Returns</dt><dd>a pair indicating integer distances from top and right respectively, else returns -1, -1 </dd></dl>
-<div class="fragment"><div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>                                            {</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++i) {</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++j) {</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>                <span class="keywordflow">if</span> (!board[i][j]) {</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>                    <span class="keywordflow">return</span> {i, j};</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>                }</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>            }</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        }</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>        <span class="keywordflow">return</span> {-1, -1};</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   75</span>                                            {</div>
+<div class="line"><span class="lineno">   76</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++i) {</div>
+<div class="line"><span class="lineno">   77</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++j) {</div>
+<div class="line"><span class="lineno">   78</span>                <span class="keywordflow">if</span> (!board[i][j]) {</div>
+<div class="line"><span class="lineno">   79</span>                    <span class="keywordflow">return</span> {i, j};</div>
+<div class="line"><span class="lineno">   80</span>                }</div>
+<div class="line"><span class="lineno">   81</span>            }</div>
+<div class="line"><span class="lineno">   82</span>        }</div>
+<div class="line"><span class="lineno">   83</span>        <span class="keywordflow">return</span> {-1, -1};</div>
+<div class="line"><span class="lineno">   84</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -401,25 +407,25 @@ template&lt;size_t N = 3&gt; </div>
 <p>Find all possible states after processing all possible moves, given the current state of the puzzle. </p>
 <dl class="section return"><dt>Returns</dt><dd>list of vector containing all possible next moves </dd></dl>
 <dl class="section note"><dt>Note</dt><dd>the implementation is compulsory to create A* search </dd></dl>
-<div class="fragment"><div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>                                                        {</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>        <span class="keyword">auto</span> zero_pos = <a class="code hl_function" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a94f794bf44f424b1b0ca6ef9f4f6ebd3">find_zero</a>();</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>        <span class="comment">// vector which will contain all possible state from current state</span></div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;EightPuzzle&lt;N&gt;</a>&gt; NewStates;</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>        <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;move : <a class="code hl_variable" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#aa73857052e69b86347859d9148933f71">moves</a>) {</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>            <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a48d054230468b79037964f474d842b6e">in_range</a>(zero_pos.first + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">move</a>.first) &amp;&amp;</div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>                <a class="code hl_function" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a48d054230468b79037964f474d842b6e">in_range</a>(zero_pos.second + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">move</a>.second)) {</div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>                <span class="comment">// swap with the possible moves</span></div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;uint32_t, N&gt;</a>, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>&gt; new_config = board;</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(new_config[zero_pos.first][zero_pos.second],</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>                          new_config[zero_pos.first + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">move</a>.first]</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>                                    [zero_pos.second + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">move</a>.second]);</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>                EightPuzzle&lt;N&gt; new_state(new_config);</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>                <span class="comment">// Store new state and calculate heuristic value, and depth</span></div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>                NewStates.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/emplace_back.html">emplace_back</a>(new_state);</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>            }</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>        }</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>        <span class="keywordflow">return</span> NewStates;</div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  176</span>                                                        {</div>
+<div class="line"><span class="lineno">  177</span>        <span class="keyword">auto</span> zero_pos = <a class="code hl_function" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a94f794bf44f424b1b0ca6ef9f4f6ebd3">find_zero</a>();</div>
+<div class="line"><span class="lineno">  178</span>        <span class="comment">// vector which will contain all possible state from current state</span></div>
+<div class="line"><span class="lineno">  179</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;EightPuzzle&lt;N&gt;</a>&gt; NewStates;</div>
+<div class="line"><span class="lineno">  180</span>        <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;move : <a class="code hl_variable" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#aa73857052e69b86347859d9148933f71">moves</a>) {</div>
+<div class="line"><span class="lineno">  181</span>            <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a48d054230468b79037964f474d842b6e">in_range</a>(zero_pos.first + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">move</a>.first) &amp;&amp;</div>
+<div class="line"><span class="lineno">  182</span>                <a class="code hl_function" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a48d054230468b79037964f474d842b6e">in_range</a>(zero_pos.second + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">move</a>.second)) {</div>
+<div class="line"><span class="lineno">  183</span>                <span class="comment">// swap with the possible moves</span></div>
+<div class="line"><span class="lineno">  184</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;uint32_t, N&gt;</a>, <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>&gt; new_config = board;</div>
+<div class="line"><span class="lineno">  185</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(new_config[zero_pos.first][zero_pos.second],</div>
+<div class="line"><span class="lineno">  186</span>                          new_config[zero_pos.first + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">move</a>.first]</div>
+<div class="line"><span class="lineno">  187</span>                                    [zero_pos.second + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">move</a>.second]);</div>
+<div class="line"><span class="lineno">  188</span>                EightPuzzle&lt;N&gt; new_state(new_config);</div>
+<div class="line"><span class="lineno">  189</span>                <span class="comment">// Store new state and calculate heuristic value, and depth</span></div>
+<div class="line"><span class="lineno">  190</span>                NewStates.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/emplace_back.html">emplace_back</a>(new_state);</div>
+<div class="line"><span class="lineno">  191</span>            }</div>
+<div class="line"><span class="lineno">  192</span>        }</div>
+<div class="line"><span class="lineno">  193</span>        <span class="keywordflow">return</span> NewStates;</div>
+<div class="line"><span class="lineno">  194</span>    }</div>
 <div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
 <div class="ttc" id="aclassmachine__learning_1_1aystar__search_1_1_eight_puzzle_html_a48d054230468b79037964f474d842b6e"><div class="ttname"><a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a48d054230468b79037964f474d842b6e">machine_learning::aystar_search::EightPuzzle::in_range</a></div><div class="ttdeci">bool in_range(const uint32_t value) const</div><div class="ttdoc">check whether the index value is bounded within the puzzle area</div><div class="ttdef"><b>Definition:</b> a_star_search.cpp:90</div></div>
 <div class="ttc" id="aclassmachine__learning_1_1aystar__search_1_1_eight_puzzle_html_a94f794bf44f424b1b0ca6ef9f4f6ebd3"><div class="ttname"><a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a94f794bf44f424b1b0ca6ef9f4f6ebd3">machine_learning::aystar_search::EightPuzzle::find_zero</a></div><div class="ttdeci">std::pair&lt; uint32_t, uint32_t &gt; find_zero()</div><div class="ttdoc">A helper array to evaluate the next state from current state;.</div><div class="ttdef"><b>Definition:</b> a_star_search.cpp:75</div></div>
@@ -483,12 +489,12 @@ template&lt;size_t N = 3&gt; </div>
 <dl class="section return"><dt>Returns</dt><dd>non-negative integer denoting the value at ith row and jth column </dd>
 <dd>
 -1 if invalid i or j position </dd></dl>
-<div class="fragment"><div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>                                           {</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a48d054230468b79037964f474d842b6e">in_range</a>(i) &amp;&amp; <a class="code hl_function" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a48d054230468b79037964f474d842b6e">in_range</a>(j)) {</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>            <span class="keywordflow">return</span> board[i][j];</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>        }</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>        <span class="keywordflow">return</span> -1;</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  102</span>                                           {</div>
+<div class="line"><span class="lineno">  103</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a48d054230468b79037964f474d842b6e">in_range</a>(i) &amp;&amp; <a class="code hl_function" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a48d054230468b79037964f474d842b6e">in_range</a>(j)) {</div>
+<div class="line"><span class="lineno">  104</span>            <span class="keywordflow">return</span> board[i][j];</div>
+<div class="line"><span class="lineno">  105</span>        }</div>
+<div class="line"><span class="lineno">  106</span>        <span class="keywordflow">return</span> -1;</div>
+<div class="line"><span class="lineno">  107</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -525,7 +531,7 @@ template&lt;size_t N = 3&gt; </div>
 
 <p>returns the size of the <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html" title="A class defining EightPuzzle/15-Puzzle game.">EightPuzzle</a> (number of row / column) </p>
 <dl class="section return"><dt>Returns</dt><dd>N, the size of the puzzle. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  117</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -555,7 +561,7 @@ template&lt;size_t N = 3&gt; </div>
 </div><div class="memdoc">
 
 <p>Returns the current state of the board. </p>
-<div class="fragment"><div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>{ <span class="keywordflow">return</span> board; }</div>
+<div class="fragment"><div class="line"><span class="lineno">  111</span>{ <span class="keywordflow">return</span> board; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -593,7 +599,7 @@ template&lt;size_t N = 3&gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if index is within the board, else <code>false</code> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>{ <span class="keywordflow">return</span> value &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; }</div>
+<div class="fragment"><div class="line"><span class="lineno">   90</span>{ <span class="keywordflow">return</span> value &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -625,16 +631,16 @@ template&lt;size_t N = 3&gt; </div>
 
 <p>check whether one board is lexicographically smaller </p>
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if this-&gt;state is lexicographically smaller than <code>check.state</code>, else <code>false</code> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>                                                      {</div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++i) {</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++j) {</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>                <span class="keywordflow">if</span> (board[i][j] != <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">check</a>.board[i][j]) {</div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>                    <span class="keywordflow">return</span> board[i][j] &lt; <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">check</a>.board[i][j];</div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>                }</div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>            }</div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>        }</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  218</span>                                                      {</div>
+<div class="line"><span class="lineno">  219</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++i) {</div>
+<div class="line"><span class="lineno">  220</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++j) {</div>
+<div class="line"><span class="lineno">  221</span>                <span class="keywordflow">if</span> (board[i][j] != <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">check</a>.board[i][j]) {</div>
+<div class="line"><span class="lineno">  222</span>                    <span class="keywordflow">return</span> board[i][j] &lt; <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">check</a>.board[i][j];</div>
+<div class="line"><span class="lineno">  223</span>                }</div>
+<div class="line"><span class="lineno">  224</span>            }</div>
+<div class="line"><span class="lineno">  225</span>        }</div>
+<div class="line"><span class="lineno">  226</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  227</span>    }</div>
 <div class="ttc" id="aword__break_8cpp_html_a272b0f5cdb4e41fd6dee4538b808c06a"><div class="ttname"><a href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">dynamic_programming::word_break::check</a></div><div class="ttdeci">bool check(const std::string &amp;s, const std::unordered_set&lt; std::string &gt; &amp;strSet, int pos, std::vector&lt; int &gt; *dp)</div><div class="ttdoc">Function that checks if the string passed in param can be segmented from position 'pos',...</div><div class="ttdef"><b>Definition:</b> word_break.cpp:80</div></div>
 </div><!-- fragment -->
 </div>
@@ -667,16 +673,16 @@ template&lt;size_t N = 3&gt; </div>
 
 <p>check whether one board is lexicographically smaller or equal </p>
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if this-&gt;state is lexicographically smaller than <code>check.state</code> or same, else <code>false</code> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>                                                       {</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++i) {</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++j) {</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>                <span class="keywordflow">if</span> (board[i][j] != <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">check</a>.board[i][j]) {</div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>                    <span class="keywordflow">return</span> board[i][j] &lt; <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">check</a>.board[i][j];</div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>                }</div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>            }</div>
-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>        }</div>
-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  233</span>                                                       {</div>
+<div class="line"><span class="lineno">  234</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++i) {</div>
+<div class="line"><span class="lineno">  235</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++j) {</div>
+<div class="line"><span class="lineno">  236</span>                <span class="keywordflow">if</span> (board[i][j] != <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">check</a>.board[i][j]) {</div>
+<div class="line"><span class="lineno">  237</span>                    <span class="keywordflow">return</span> board[i][j] &lt; <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">check</a>.board[i][j];</div>
+<div class="line"><span class="lineno">  238</span>                }</div>
+<div class="line"><span class="lineno">  239</span>            }</div>
+<div class="line"><span class="lineno">  240</span>        }</div>
+<div class="line"><span class="lineno">  241</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  242</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -713,10 +719,10 @@ template&lt;size_t N = 3&gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>                                                 {</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>        board = A.board;</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  156</span>                                                 {</div>
+<div class="line"><span class="lineno">  157</span>        board = A.board;</div>
+<div class="line"><span class="lineno">  158</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  159</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -753,10 +759,10 @@ template&lt;size_t N = 3&gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>                                                     {</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>        board = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(A.board);</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  165</span>                                                     {</div>
+<div class="line"><span class="lineno">  166</span>        board = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(A.board);</div>
+<div class="line"><span class="lineno">  167</span>        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><span class="lineno">  168</span>    }</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -794,19 +800,19 @@ template&lt;size_t N = 3&gt; </div>
 
 <p>check whether two boards are equal </p>
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if check.state is equal to <code>this-&gt;state</code>, else <code>false</code> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>                                                       {</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">check</a>.get_size() != N) {</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>        }</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++i) {</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++j) {</div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>                <span class="keywordflow">if</span> (board[i][j] != <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">check</a>.board[i][j]) {</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>                    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>                }</div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>            }</div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>        }</div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  200</span>                                                       {</div>
+<div class="line"><span class="lineno">  201</span>        <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">check</a>.get_size() != N) {</div>
+<div class="line"><span class="lineno">  202</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  203</span>        }</div>
+<div class="line"><span class="lineno">  204</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++i) {</div>
+<div class="line"><span class="lineno">  205</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++j) {</div>
+<div class="line"><span class="lineno">  206</span>                <span class="keywordflow">if</span> (board[i][j] != <a class="code hl_function" href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">check</a>.board[i][j]) {</div>
+<div class="line"><span class="lineno">  207</span>                    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  208</span>                }</div>
+<div class="line"><span class="lineno">  209</span>            }</div>
+<div class="line"><span class="lineno">  210</span>        }</div>
+<div class="line"><span class="lineno">  211</span>        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  212</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -856,15 +862,15 @@ template&lt;size_t N = 3&gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>ostream operator op </dd></dl>
-<div class="fragment"><div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>                                                                     {</div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++i) {</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++j) {</div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>                op &lt;&lt; SomeState.board[i][j] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>            }</div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>            op &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>        }</div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>        <span class="keywordflow">return</span> op;</div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  251</span>                                                                     {</div>
+<div class="line"><span class="lineno">  252</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++i) {</div>
+<div class="line"><span class="lineno">  253</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++j) {</div>
+<div class="line"><span class="lineno">  254</span>                op &lt;&lt; SomeState.board[i][j] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">  255</span>            }</div>
+<div class="line"><span class="lineno">  256</span>            op &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  257</span>        }</div>
+<div class="line"><span class="lineno">  258</span>        <span class="keywordflow">return</span> op;</div>
+<div class="line"><span class="lineno">  259</span>    }</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -910,7 +916,7 @@ template&lt;size_t N = 3&gt; </div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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     <li class="navelem"><a class="el" href="../../d8/d77/namespacemachine__learning.html">machine_learning</a></li><li class="navelem"><b>aystar_search</b></li><li class="navelem"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">EightPuzzle</a></li>
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 <div class="ttc" id="apigeonhole__sort_8cpp_html_a458410412185a5f09199deaff7157a8d"><div class="ttname"><a href="../../dd/da8/pigeonhole__sort_8cpp.html#a458410412185a5f09199deaff7157a8d">test_2</a></div><div class="ttdeci">static void test_2()</div><div class="ttdef"><b>Definition:</b> pigeonhole_sort.cpp:88</div></div>
 <div class="ttc" id="apigeonhole__sort_8cpp_html_af31ec5409537703d9c8a47350386b32a"><div class="ttname"><a href="../../dd/da8/pigeonhole__sort_8cpp.html#af31ec5409537703d9c8a47350386b32a">test_3</a></div><div class="ttdeci">static void test_3()</div><div class="ttdef"><b>Definition:</b> pigeonhole_sort.cpp:109</div></div>
@@ -194,20 +194,20 @@ Here is the call graph for this function:</div>
 </table>
 </div><div class="memdoc">
 <p >Test function 1 with unsorted array {8, 3, 2, 7, 4, 6, 8} </p><dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
-<div class="fragment"><div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>                     {</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> n = 7;</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n&gt;</a> test_array = {8, 3, 2, 7, 4, 6, 8};</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span> </div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    test_array = sorting::pigeonSort&lt;n&gt;(test_array);</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span> </div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(test_array), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(test_array)));</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span> </div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>    <span class="comment">// Printing sorted array</span></div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; test_array.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/at.html">at</a>(i) &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    }</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPassed\n&quot;</span>;</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   68</span>                     {</div>
+<div class="line"><span class="lineno">   69</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> n = 7;</div>
+<div class="line"><span class="lineno">   70</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n&gt;</a> test_array = {8, 3, 2, 7, 4, 6, 8};</div>
+<div class="line"><span class="lineno">   71</span> </div>
+<div class="line"><span class="lineno">   72</span>    test_array = sorting::pigeonSort&lt;n&gt;(test_array);</div>
+<div class="line"><span class="lineno">   73</span> </div>
+<div class="line"><span class="lineno">   74</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(test_array), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(test_array)));</div>
+<div class="line"><span class="lineno">   75</span> </div>
+<div class="line"><span class="lineno">   76</span>    <span class="comment">// Printing sorted array</span></div>
+<div class="line"><span class="lineno">   77</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">   78</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; test_array.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/at.html">at</a>(i) &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">   79</span>    }</div>
+<div class="line"><span class="lineno">   80</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPassed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   81</span>}</div>
 <div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
 <div class="ttc" id="aat_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array/at.html">std::array::at</a></div><div class="ttdeci">T at(T... args)</div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
@@ -246,21 +246,21 @@ Here is the call graph for this function:</div>
 </table>
 </div><div class="memdoc">
 <p >Test function 2 with unsorted array {802, 630, 20, 745, 52, 300, 612, 932, 78, 187} </p><dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
-<div class="fragment"><div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>                     {</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> n = 10;</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n&gt;</a> test_array = {802, 630, 20,  745, 52,</div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>                                     300, 612, 932, 78,  187};</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span> </div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    test_array = sorting::pigeonSort&lt;n&gt;(test_array);</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span> </div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(test_array), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(test_array)));</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span> </div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    <span class="comment">// Printing sorted array</span></div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; test_array.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/at.html">at</a>(i) &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    }</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPassed\n&quot;</span>;</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   88</span>                     {</div>
+<div class="line"><span class="lineno">   89</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> n = 10;</div>
+<div class="line"><span class="lineno">   90</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n&gt;</a> test_array = {802, 630, 20,  745, 52,</div>
+<div class="line"><span class="lineno">   91</span>                                     300, 612, 932, 78,  187};</div>
+<div class="line"><span class="lineno">   92</span> </div>
+<div class="line"><span class="lineno">   93</span>    test_array = sorting::pigeonSort&lt;n&gt;(test_array);</div>
+<div class="line"><span class="lineno">   94</span> </div>
+<div class="line"><span class="lineno">   95</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(test_array), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(test_array)));</div>
+<div class="line"><span class="lineno">   96</span> </div>
+<div class="line"><span class="lineno">   97</span>    <span class="comment">// Printing sorted array</span></div>
+<div class="line"><span class="lineno">   98</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">   99</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; test_array.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/at.html">at</a>(i) &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">  100</span>    }</div>
+<div class="line"><span class="lineno">  101</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPassed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  102</span>}</div>
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 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -293,20 +293,20 @@ Here is the call graph for this function:</div>
 </table>
 </div><div class="memdoc">
 <p >Test function 1 with unsorted array {11,13,12,14} </p><dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
-<div class="fragment"><div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>                     {</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> n = 4;</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n&gt;</a> test_array = {11, 13, 12, 14};</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span> </div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    test_array = sorting::pigeonSort&lt;n&gt;(test_array);</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span> </div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(test_array), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(test_array)));</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span> </div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    <span class="comment">// Printing sorted array</span></div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; test_array.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/at.html">at</a>(i) &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    }</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPassed\n&quot;</span>;</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  109</span>                     {</div>
+<div class="line"><span class="lineno">  110</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> n = 4;</div>
+<div class="line"><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n&gt;</a> test_array = {11, 13, 12, 14};</div>
+<div class="line"><span class="lineno">  112</span> </div>
+<div class="line"><span class="lineno">  113</span>    test_array = sorting::pigeonSort&lt;n&gt;(test_array);</div>
+<div class="line"><span class="lineno">  114</span> </div>
+<div class="line"><span class="lineno">  115</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(test_array), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(test_array)));</div>
+<div class="line"><span class="lineno">  116</span> </div>
+<div class="line"><span class="lineno">  117</span>    <span class="comment">// Printing sorted array</span></div>
+<div class="line"><span class="lineno">  118</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">  119</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; test_array.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/at.html">at</a>(i) &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">  120</span>    }</div>
+<div class="line"><span class="lineno">  121</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPassed\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  122</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
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@@ -100,6 +100,12 @@ $(document).ready(function(){initNavTree('dd/dca/class_f_c_f_s.html','../../');
 
 <p>Class which implements the <a class="el" href="../../dd/dca/class_f_c_f_s.html" title="Class which implements the FCFS scheduling algorithm.">FCFS</a> scheduling algorithm.  
  <a href="../../dd/dca/class_f_c_f_s.html#details">More...</a></p>
+<div class="dynheader">
+Collaboration diagram for FCFS&lt; S, T, E &gt;:</div>
+<div class="dyncontent">
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 <table class="memberdecls">
 <tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
 Public Member Functions</h2></td></tr>
@@ -188,22 +194,26 @@ template&lt;typename S , typename T , typename E &gt; </div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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@@ -236,32 +246,33 @@ template&lt;typename S , typename T , typename E &gt; </div>
 
 <p>Utility function for printing the status of each process after execution. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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@@ -300,38 +311,48 @@ template&lt;typename S , typename T , typename E &gt; </div>
 <p ><a class="el" href="../../dd/dca/class_f_c_f_s.html" title="Class which implements the FCFS scheduling algorithm.">FCFS</a> is a non-preemptive algorithm in which the process which arrives first gets executed first. If two or more processes arrive together then the process with smaller process ID runs first (each process has a unique proces ID).</p>
 <p >I used a min priority queue of tuples to accomplish this task. The processes are ordered by their arrival times. If arrival times of some processes are equal, then they are ordered by their process ID.</p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>                                                                     {</div>
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-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>        <span class="keywordflow">while</span> (!<a class="code hl_variable" href="../../dd/dca/class_f_c_f_s.html#af2594e22a867b308e027623940193d46">schedule</a>.empty()) {</div>
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-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span> </div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>            <span class="comment">// If the current process arrived at time t2, the last process</span></div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>            <span class="comment">// completed its execution at time t1, and t2 &gt; t1.</span></div>
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-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>            <span class="comment">// Add Burst time to time elapsed</span></div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>            timeElapsed += get&lt;2&gt;(cur);</div>
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-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>            <span class="comment">// Completion time of the current process will be same as time</span></div>
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+<div class="fragment"><div class="line"><span class="lineno">  154</span>                                                                     {</div>
+<div class="line"><span class="lineno">  155</span>        <span class="comment">// Variable to keep track of time elapsed so far</span></div>
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+<div class="line"><span class="lineno">  167</span>            <span class="comment">// Add Burst time to time elapsed</span></div>
+<div class="line"><span class="lineno">  168</span>            timeElapsed += get&lt;2&gt;(cur);</div>
+<div class="line"><span class="lineno">  169</span> </div>
+<div class="line"><span class="lineno">  170</span>            <span class="comment">// Completion time of the current process will be same as time</span></div>
+<div class="line"><span class="lineno">  171</span>            <span class="comment">// elapsed so far</span></div>
+<div class="line"><span class="lineno">  172</span>            get&lt;3&gt;(cur) = timeElapsed;</div>
+<div class="line"><span class="lineno">  173</span> </div>
+<div class="line"><span class="lineno">  174</span>            <span class="comment">// Turnaround time = Completion time - Arrival time</span></div>
+<div class="line"><span class="lineno">  175</span>            get&lt;4&gt;(cur) = get&lt;3&gt;(cur) - get&lt;1&gt;(cur);</div>
+<div class="line"><span class="lineno">  176</span> </div>
+<div class="line"><span class="lineno">  177</span>            <span class="comment">// Waiting time = Turnaround time - Burst time</span></div>
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+<div class="line"><span class="lineno">  118</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;data = <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
+<div class="line"><span class="lineno">  119</span>    <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;left = <a class="code hl_class" href="../../d5/da1/structnode.html">node</a>-&gt;right = <span class="keyword">nullptr</span>;</div>
+<div class="line"><span class="lineno">  120</span>    <span class="keywordflow">return</span> <a class="code hl_typedef" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
+<div class="line"><span class="lineno">  121</span>}</div>
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@@ -182,18 +188,19 @@ Public Attributes</h2></td></tr>
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-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    inorder(root-&gt;left);  <span class="comment">// Traverse the left subtree</span></div>
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-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        root-&gt;data);  <span class="comment">// Display the data part of the root (or current node)</span></div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    inorder(root-&gt;right);  <span class="comment">// Traverse the right subtree</span></div>
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+<div class="fragment"><div class="line"><span class="lineno">  130</span>                                          {</div>
+<div class="line"><span class="lineno">  131</span>    <span class="keywordflow">if</span> (root == <span class="keyword">nullptr</span>) {  <span class="comment">// return if the current node is empty</span></div>
+<div class="line"><span class="lineno">  132</span>        <span class="keywordflow">return</span> {};</div>
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+<div class="line"><span class="lineno">  134</span> </div>
+<div class="line"><span class="lineno">  135</span>    inorder(root-&gt;left);  <span class="comment">// Traverse the left subtree</span></div>
+<div class="line"><span class="lineno">  136</span>    BT::inorder_result.push_back(</div>
+<div class="line"><span class="lineno">  137</span>        root-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a>);  <span class="comment">// Display the data part of the root (or current node)</span></div>
+<div class="line"><span class="lineno">  138</span>    inorder(root-&gt;right);  <span class="comment">// Traverse the right subtree</span></div>
+<div class="line"><span class="lineno">  139</span> </div>
+<div class="line"><span class="lineno">  140</span>    <span class="keywordflow">return</span> inorder_result;</div>
+<div class="line"><span class="lineno">  141</span>}</div>
+<div class="ttc" id="adata_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/data.html">std::vector::data</a></div><div class="ttdeci">T data(T... args)</div></div>
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+<div class="line"><span class="lineno">  171</span>    <span class="keywordflow">if</span> (root == <span class="keyword">nullptr</span>) {  <span class="comment">// if the current node is empty</span></div>
+<div class="line"><span class="lineno">  172</span>        <span class="keywordflow">return</span> {};</div>
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+<div class="ttc" id="aresize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/resize.html">std::vector::resize</a></div><div class="ttdeci">T resize(T... args)</div></div>
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@@ -168,53 +168,53 @@ template&lt;typename T &gt; </div>
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 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>                                                   {</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> arr(in_arr);</div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> cycle_start = 0; cycle_start &lt;= arr.size() - 1; cycle_start++) {</div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>        <span class="comment">// initialize item</span></div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>        T item = arr[cycle_start];</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span> </div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>        <span class="comment">// Count the number of elements smaller than item, this  number is the</span></div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>        <span class="comment">// correct index of item.</span></div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>        <span class="keywordtype">int</span> pos = cycle_start;</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = cycle_start + 1; i &lt; arr.size(); i++) {</div>
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-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>        <span class="comment">// item is already in correct position</span></div>
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-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span> </div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>        <span class="comment">// duplicate  elements</span></div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>        <span class="keywordflow">while</span> (item == arr[pos]) pos += 1;</div>
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-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(item, arr[pos]);</div>
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-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        <span class="comment">// Rest of the  elements</span></div>
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-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <span class="keywordflow">return</span> arr;</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>}</div>
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+<div class="line"><span class="lineno">   38</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> arr(in_arr);</div>
+<div class="line"><span class="lineno">   39</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> cycle_start = 0; cycle_start &lt;= arr.size() - 1; cycle_start++) {</div>
+<div class="line"><span class="lineno">   40</span>        <span class="comment">// initialize item</span></div>
+<div class="line"><span class="lineno">   41</span>        T item = arr[cycle_start];</div>
+<div class="line"><span class="lineno">   42</span> </div>
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+<div class="line"><span class="lineno">   46</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = cycle_start + 1; i &lt; arr.size(); i++) {</div>
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+<div class="line"><span class="lineno">   49</span>            }</div>
+<div class="line"><span class="lineno">   50</span>        }</div>
+<div class="line"><span class="lineno">   51</span> </div>
+<div class="line"><span class="lineno">   52</span>        <span class="comment">// item is already in correct position</span></div>
+<div class="line"><span class="lineno">   53</span>        <span class="keywordflow">if</span> (pos == cycle_start) {</div>
+<div class="line"><span class="lineno">   54</span>            <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno">   55</span>        }</div>
+<div class="line"><span class="lineno">   56</span> </div>
+<div class="line"><span class="lineno">   57</span>        <span class="comment">// duplicate  elements</span></div>
+<div class="line"><span class="lineno">   58</span>        <span class="keywordflow">while</span> (item == arr[pos]) pos += 1;</div>
+<div class="line"><span class="lineno">   59</span>        <span class="keywordflow">if</span> (pos == cycle_start) {</div>
+<div class="line"><span class="lineno">   60</span>            <span class="keywordflow">continue</span>;</div>
+<div class="line"><span class="lineno">   61</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   62</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(item, arr[pos]);</div>
+<div class="line"><span class="lineno">   63</span>        }</div>
+<div class="line"><span class="lineno">   64</span>        <span class="comment">// Rest of the  elements</span></div>
+<div class="line"><span class="lineno">   65</span>        <span class="keywordflow">while</span> (pos != cycle_start) {</div>
+<div class="line"><span class="lineno">   66</span>            pos = cycle_start;</div>
+<div class="line"><span class="lineno">   67</span>            <span class="comment">// Find position where we put the element</span></div>
+<div class="line"><span class="lineno">   68</span>            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = cycle_start + 1; i &lt; arr.size(); i++) {</div>
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+<div class="line"><span class="lineno">   72</span>            }</div>
+<div class="line"><span class="lineno">   73</span>            <span class="comment">// duplicate  elements</span></div>
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+<div class="line"><span class="lineno">   75</span>            <span class="keywordflow">if</span> (item == arr[pos]) {</div>
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+<div class="line"><span class="lineno">   77</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   78</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(item, arr[pos]);</div>
+<div class="line"><span class="lineno">   79</span>            }</div>
+<div class="line"><span class="lineno">   80</span>        }</div>
+<div class="line"><span class="lineno">   81</span>    }</div>
+<div class="line"><span class="lineno">   82</span>    <span class="keywordflow">return</span> arr;</div>
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 <p>Main function. </p>
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-<div class="fragment"><div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>           {</div>
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-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  127</span>           {</div>
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+<div class="line"><span class="lineno">  129</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  130</span>}</div>
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 Here is the call graph for this function:</div>
@@ -283,37 +283,37 @@ Here is the call graph for this function:</div>
 
 <p>Test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>                   {</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    <span class="comment">// Test 1</span></div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    <span class="comment">// [4, 3, 2, 1] return [1, 2, 3, 4]</span></div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> array1 = {4, 3, 2, 1};</div>
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-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> arr1 = <a class="code hl_function" href="../../de/d07/cycle__sort_8cpp.html#ae79a9d247691fce0d655fce75f1c04fa">sorting::cycle_sort::cycleSort</a>(array1);</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr1), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr1)));</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> arr2 = <a class="code hl_function" href="../../de/d07/cycle__sort_8cpp.html#ae79a9d247691fce0d655fce75f1c04fa">sorting::cycle_sort::cycleSort</a>(array2);</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr2), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr2)));</div>
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-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span> </div>
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-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> array3 = {3, 3, 3, 3};</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3... &quot;</span>;</div>
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-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr3), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr3)));</div>
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+<div class="line"><span class="lineno">   95</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1... &quot;</span>;</div>
+<div class="line"><span class="lineno">   96</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> arr1 = <a class="code hl_function" href="../../de/d07/cycle__sort_8cpp.html#ae79a9d247691fce0d655fce75f1c04fa">sorting::cycle_sort::cycleSort</a>(array1);</div>
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+<div class="line"><span class="lineno">  106</span> </div>
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+<div class="line"><span class="lineno">  113</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><span class="lineno">   45</span>        <span class="comment">// if value is greater than the value at &quot;index&quot;, eliminate the subarray from offset to index</span></div>
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+<div class="line"><span class="lineno">   47</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> = current;</div>
+<div class="line"><span class="lineno">   48</span>            current = last;</div>
+<div class="line"><span class="lineno">   49</span>            last = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> - current;</div>
+<div class="line"><span class="lineno">   50</span>            offset = index;</div>
+<div class="line"><span class="lineno">   51</span>        <span class="comment">// if value is less than the value at &quot;index&quot;, eliminate the subarray after index+1</span></div>
+<div class="line"><span class="lineno">   52</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span>(arr[index] &gt; value){</div>
+<div class="line"><span class="lineno">   53</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> = last;</div>
+<div class="line"><span class="lineno">   54</span>            current = current - last;</div>
+<div class="line"><span class="lineno">   55</span>            last = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> - current;</div>
+<div class="line"><span class="lineno">   56</span>        <span class="comment">// element is found</span></div>
+<div class="line"><span class="lineno">   57</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   58</span>            <span class="keywordflow">return</span> index;</div>
+<div class="line"><span class="lineno">   59</span>        }</div>
+<div class="line"><span class="lineno">   60</span>    }</div>
+<div class="line"><span class="lineno">   61</span>    <span class="comment">// comparing the last element</span></div>
+<div class="line"><span class="lineno">   62</span>    <span class="keywordflow">if</span>(current &amp;&amp; !arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/empty.html">empty</a>() &amp;&amp; arr[offset+1] == value){</div>
+<div class="line"><span class="lineno">   63</span>        <span class="keywordflow">return</span> offset+1;</div>
+<div class="line"><span class="lineno">   64</span>    }</div>
+<div class="line"><span class="lineno">   65</span>    <span class="comment">// value was not found, return -1</span></div>
+<div class="line"><span class="lineno">   66</span>    <span class="keywordflow">return</span> -1;</div>
+<div class="line"><span class="lineno">   67</span>}</div>
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       </table>
 </div><div class="memdoc">
 <p >Main Function testing the algorithm </p>
-<div class="fragment"><div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>           {</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    assert(<a class="code hl_function" href="../../de/d0d/fibonacci__search_8cpp.html#a5e144326104e57a3808aed7eb098db0d">no_occurence_tests</a>());</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>    assert(<a class="code hl_function" href="../../de/d0d/fibonacci__search_8cpp.html#a2aa09bef74ee063c1331de0883af4f4f">random_tests</a>());</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  123</span>           {</div>
+<div class="line"><span class="lineno">  124</span>    assert(<a class="code hl_function" href="../../de/d0d/fibonacci__search_8cpp.html#a5e144326104e57a3808aed7eb098db0d">no_occurence_tests</a>());</div>
+<div class="line"><span class="lineno">  125</span>    assert(<a class="code hl_function" href="../../de/d0d/fibonacci__search_8cpp.html#a2aa09bef74ee063c1331de0883af4f4f">random_tests</a>());</div>
+<div class="line"><span class="lineno">  126</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  127</span>}</div>
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 </div><!-- fragment --><div class="dynheader">
@@ -269,26 +269,26 @@ Here is the call graph for this function:</div>
 </div><div class="memdoc">
 
 <p>random tests for checking performance when an array doesn't contain an element </p>
-<div class="fragment"><div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>                         {</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <span class="keywordtype">bool</span> passed = <span class="keyword">true</span>;</div>
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-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>    <span class="keywordflow">while</span>(num_tests--){</div>
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-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i &lt; 100; i++){</div>
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-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>            arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(rand_num);</div>
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-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>        <span class="keywordflow">while</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/find.html">std::find</a>(arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>(), rand_value) != arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>()){</div>
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-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   72</span>                         {</div>
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+<div class="line"><span class="lineno">   74</span>    <span class="keywordtype">int</span> rand_num, rand_value, index, num_tests = 1000;</div>
+<div class="line"><span class="lineno">   75</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> arr;</div>
+<div class="line"><span class="lineno">   76</span>    <span class="keywordflow">while</span>(num_tests--){</div>
+<div class="line"><span class="lineno">   77</span>        arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/clear.html">clear</a>();</div>
+<div class="line"><span class="lineno">   78</span>        <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i &lt; 100; i++){</div>
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-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
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 Here is the call graph for this function:</div>
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@@ -324,28 +324,28 @@ Here is the call graph for this function:</div>
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 <p>random tests which cover cases when we have one, multiple or zero occurences of the value we're looking for </p>
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+<div class="line"><span class="lineno">   70</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> fibMinus1 = <span class="stringliteral">&quot;1&quot;</span>;</div>
+<div class="line"><span class="lineno">   71</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> fibMinus2 = <span class="stringliteral">&quot;0&quot;</span>;</div>
+<div class="line"><span class="lineno">   72</span>    <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">   73</span>        tmp = <a class="code hl_function" href="../../de/d47/string__fibonacci_8cpp.html#a28052eee05d43c2ebc5147c52bd50c35">add</a>(fibMinus1, fibMinus2);</div>
+<div class="line"><span class="lineno">   74</span>        fibMinus2 = fibMinus1;</div>
+<div class="line"><span class="lineno">   75</span>        fibMinus1 = tmp;</div>
+<div class="line"><span class="lineno">   76</span>    }</div>
+<div class="line"><span class="lineno">   77</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; fibMinus2;</div>
+<div class="line"><span class="lineno">   78</span>}</div>
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-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   81</span>           {</div>
+<div class="line"><span class="lineno">   82</span>    <span class="keywordtype">int</span> n;</div>
+<div class="line"><span class="lineno">   83</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter whatever number N you want to find the fibonacci of\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   84</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
+<div class="line"><span class="lineno">   85</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; th Fibonacci is \n&quot;</span>;</div>
+<div class="line"><span class="lineno">   86</span>    <a class="code hl_function" href="../../de/d47/string__fibonacci_8cpp.html#ad8055ee368a5d5b24de01bdde6bf8fca">fib_Accurate</a>(n);</div>
+<div class="line"><span class="lineno">   87</span> </div>
+<div class="line"><span class="lineno">   88</span>    <span class="keywordflow">return</span> 0;</div>
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+<div class="line"><span class="lineno">  180</span>    <span class="keywordflow">for</span> (uint32_t i = 0; i &lt; n_tries; ++i) {</div>
+<div class="line"><span class="lineno">  181</span>        var += (tries[i] - mean) * (tries[i] - mean);</div>
+<div class="line"><span class="lineno">  182</span>    }</div>
+<div class="line"><span class="lineno">  183</span> </div>
+<div class="line"><span class="lineno">  184</span>    <span class="comment">// Unbiased estimate of variance</span></div>
+<div class="line"><span class="lineno">  185</span>    var /= <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(n_tries - 1);</div>
+<div class="line"><span class="lineno">  186</span> </div>
+<div class="line"><span class="lineno">  187</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;This value should be near &quot;</span> &lt;&lt; dist.<a class="code hl_function" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a41051365f8ac7700f2ed5880a6760413">expected_value</a>() &lt;&lt; <span class="stringliteral">&quot;: &quot;</span></div>
+<div class="line"><span class="lineno">  188</span>              &lt;&lt; mean &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  189</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;This value should be near &quot;</span> &lt;&lt; dist.<a class="code hl_function" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aea8b0d649f0dc9a6f8baf3341a0b4960">variance</a>() &lt;&lt; <span class="stringliteral">&quot;: &quot;</span> &lt;&lt; var</div>
+<div class="line"><span class="lineno">  190</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  191</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aclassprobability_1_1geometric__dist_1_1geometric__distribution_html_a41051365f8ac7700f2ed5880a6760413"><div class="ttname"><a href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a41051365f8ac7700f2ed5880a6760413">probability::geometric_dist::geometric_distribution::expected_value</a></div><div class="ttdeci">float expected_value() const</div><div class="ttdoc">The expected value of a geometrically distributed random variable X.</div><div class="ttdef"><b>Definition:</b> geometric_dist.cpp:71</div></div>
 <div class="ttc" id="aclassprobability_1_1geometric__dist_1_1geometric__distribution_html_a8aae1cebcf42ed2332f1c7217c401aa3"><div class="ttname"><a href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a8aae1cebcf42ed2332f1c7217c401aa3">probability::geometric_dist::geometric_distribution::draw_sample</a></div><div class="ttdeci">uint32_t draw_sample() const</div><div class="ttdoc">Generates a (discrete) sample according to the geometrical distribution.</div><div class="ttdef"><b>Definition:</b> geometric_dist.cpp:125</div></div>
@@ -306,60 +306,60 @@ Here is the call graph for this function:</div>
 
 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>                   {</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>    <a class="code hl_class" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html">probability::geometric_dist::geometric_distribution</a> dist(0.3);</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span> </div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    <span class="keyword">const</span> <span class="keywordtype">float</span> threshold = 1e-3f;</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span> </div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Starting tests for p = 0.3...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>    assert(std::abs(dist.expected_value() - 3.33333333f) &lt; threshold);</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>    assert(std::abs(dist.variance() - 7.77777777f) &lt; threshold);</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    assert(std::abs(dist.standard_deviation() - 2.788866755) &lt; threshold);</div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    assert(std::abs(dist.probability_density(5) - 0.07203) &lt; threshold);</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>    assert(std::abs(dist.cumulative_distribution(6) - 0.882351) &lt; threshold);</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    assert(std::abs(dist.inverse_cumulative_distribution(</div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>                        dist.cumulative_distribution(8)) -</div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>                    8) &lt; threshold);</div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>    assert(std::abs(dist.range_tries() - 1.0f) &lt; threshold);</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>    assert(std::abs(dist.range_tries(3) - 0.49f) &lt; threshold);</div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>    assert(std::abs(dist.range_tries(5, 11) - 0.2203267f) &lt; threshold);</div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All tests passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>    <a class="code hl_function" href="../../de/d72/geometric__dist_8cpp.html#a70fd1cc5c3a2813f28683dc75dcd65b6">sample_test</a>(dist);</div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span> </div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>    dist = <a class="code hl_class" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html">probability::geometric_dist::geometric_distribution</a>(0.5f);</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span> </div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Starting tests for p = 0.5...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>    assert(std::abs(dist.expected_value() - 2.0f) &lt; threshold);</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>    assert(std::abs(dist.variance() - 2.0f) &lt; threshold);</div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>    assert(std::abs(dist.standard_deviation() - 1.4142135f) &lt; threshold);</div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>    assert(std::abs(dist.probability_density(5) - 0.03125) &lt; threshold);</div>
-<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    assert(std::abs(dist.cumulative_distribution(6) - 0.984375) &lt; threshold);</div>
-<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>    assert(std::abs(dist.inverse_cumulative_distribution(</div>
-<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>                        dist.cumulative_distribution(8)) -</div>
-<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>                    8) &lt; threshold);</div>
-<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    assert(std::abs(dist.range_tries() - 1.0f) &lt; threshold);</div>
-<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>    assert(std::abs(dist.range_tries(3) - 0.25f) &lt; threshold);</div>
-<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>    assert(std::abs(dist.range_tries(5, 11) - 0.062011f) &lt; threshold);</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All tests passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>    <a class="code hl_function" href="../../de/d72/geometric__dist_8cpp.html#a70fd1cc5c3a2813f28683dc75dcd65b6">sample_test</a>(dist);</div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span> </div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>    dist = <a class="code hl_class" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html">probability::geometric_dist::geometric_distribution</a>(0.8f);</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span> </div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Starting tests for p = 0.8...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>    assert(std::abs(dist.expected_value() - 1.25f) &lt; threshold);</div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>    assert(std::abs(dist.variance() - 0.3125f) &lt; threshold);</div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>    assert(std::abs(dist.standard_deviation() - 0.559016f) &lt; threshold);</div>
-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>    assert(std::abs(dist.probability_density(5) - 0.00128) &lt; threshold);</div>
-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>    assert(std::abs(dist.cumulative_distribution(6) - 0.999936) &lt; threshold);</div>
-<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>    assert(std::abs(dist.inverse_cumulative_distribution(</div>
-<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>                        dist.cumulative_distribution(8)) -</div>
-<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>                    8) &lt; threshold);</div>
-<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>    assert(std::abs(dist.range_tries() - 1.0f) &lt; threshold);</div>
-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>    assert(std::abs(dist.range_tries(3) - 0.04f) &lt; threshold);</div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>    assert(std::abs(dist.range_tries(5, 11) - 0.00159997f) &lt; threshold);</div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All tests have successfully passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>    <a class="code hl_function" href="../../de/d72/geometric__dist_8cpp.html#a70fd1cc5c3a2813f28683dc75dcd65b6">sample_test</a>(dist);</div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  197</span>                   {</div>
+<div class="line"><span class="lineno">  198</span>    <a class="code hl_class" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html">probability::geometric_dist::geometric_distribution</a> dist(0.3);</div>
+<div class="line"><span class="lineno">  199</span> </div>
+<div class="line"><span class="lineno">  200</span>    <span class="keyword">const</span> <span class="keywordtype">float</span> threshold = 1e-3f;</div>
+<div class="line"><span class="lineno">  201</span> </div>
+<div class="line"><span class="lineno">  202</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Starting tests for p = 0.3...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  203</span>    assert(std::abs(dist.expected_value() - 3.33333333f) &lt; threshold);</div>
+<div class="line"><span class="lineno">  204</span>    assert(std::abs(dist.variance() - 7.77777777f) &lt; threshold);</div>
+<div class="line"><span class="lineno">  205</span>    assert(std::abs(dist.standard_deviation() - 2.788866755) &lt; threshold);</div>
+<div class="line"><span class="lineno">  206</span>    assert(std::abs(dist.probability_density(5) - 0.07203) &lt; threshold);</div>
+<div class="line"><span class="lineno">  207</span>    assert(std::abs(dist.cumulative_distribution(6) - 0.882351) &lt; threshold);</div>
+<div class="line"><span class="lineno">  208</span>    assert(std::abs(dist.inverse_cumulative_distribution(</div>
+<div class="line"><span class="lineno">  209</span>                        dist.cumulative_distribution(8)) -</div>
+<div class="line"><span class="lineno">  210</span>                    8) &lt; threshold);</div>
+<div class="line"><span class="lineno">  211</span>    assert(std::abs(dist.range_tries() - 1.0f) &lt; threshold);</div>
+<div class="line"><span class="lineno">  212</span>    assert(std::abs(dist.range_tries(3) - 0.49f) &lt; threshold);</div>
+<div class="line"><span class="lineno">  213</span>    assert(std::abs(dist.range_tries(5, 11) - 0.2203267f) &lt; threshold);</div>
+<div class="line"><span class="lineno">  214</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All tests passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  215</span>    <a class="code hl_function" href="../../de/d72/geometric__dist_8cpp.html#a70fd1cc5c3a2813f28683dc75dcd65b6">sample_test</a>(dist);</div>
+<div class="line"><span class="lineno">  216</span> </div>
+<div class="line"><span class="lineno">  217</span>    dist = <a class="code hl_class" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html">probability::geometric_dist::geometric_distribution</a>(0.5f);</div>
+<div class="line"><span class="lineno">  218</span> </div>
+<div class="line"><span class="lineno">  219</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Starting tests for p = 0.5...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  220</span>    assert(std::abs(dist.expected_value() - 2.0f) &lt; threshold);</div>
+<div class="line"><span class="lineno">  221</span>    assert(std::abs(dist.variance() - 2.0f) &lt; threshold);</div>
+<div class="line"><span class="lineno">  222</span>    assert(std::abs(dist.standard_deviation() - 1.4142135f) &lt; threshold);</div>
+<div class="line"><span class="lineno">  223</span>    assert(std::abs(dist.probability_density(5) - 0.03125) &lt; threshold);</div>
+<div class="line"><span class="lineno">  224</span>    assert(std::abs(dist.cumulative_distribution(6) - 0.984375) &lt; threshold);</div>
+<div class="line"><span class="lineno">  225</span>    assert(std::abs(dist.inverse_cumulative_distribution(</div>
+<div class="line"><span class="lineno">  226</span>                        dist.cumulative_distribution(8)) -</div>
+<div class="line"><span class="lineno">  227</span>                    8) &lt; threshold);</div>
+<div class="line"><span class="lineno">  228</span>    assert(std::abs(dist.range_tries() - 1.0f) &lt; threshold);</div>
+<div class="line"><span class="lineno">  229</span>    assert(std::abs(dist.range_tries(3) - 0.25f) &lt; threshold);</div>
+<div class="line"><span class="lineno">  230</span>    assert(std::abs(dist.range_tries(5, 11) - 0.062011f) &lt; threshold);</div>
+<div class="line"><span class="lineno">  231</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All tests passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  232</span>    <a class="code hl_function" href="../../de/d72/geometric__dist_8cpp.html#a70fd1cc5c3a2813f28683dc75dcd65b6">sample_test</a>(dist);</div>
+<div class="line"><span class="lineno">  233</span> </div>
+<div class="line"><span class="lineno">  234</span>    dist = <a class="code hl_class" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html">probability::geometric_dist::geometric_distribution</a>(0.8f);</div>
+<div class="line"><span class="lineno">  235</span> </div>
+<div class="line"><span class="lineno">  236</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Starting tests for p = 0.8...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  237</span>    assert(std::abs(dist.expected_value() - 1.25f) &lt; threshold);</div>
+<div class="line"><span class="lineno">  238</span>    assert(std::abs(dist.variance() - 0.3125f) &lt; threshold);</div>
+<div class="line"><span class="lineno">  239</span>    assert(std::abs(dist.standard_deviation() - 0.559016f) &lt; threshold);</div>
+<div class="line"><span class="lineno">  240</span>    assert(std::abs(dist.probability_density(5) - 0.00128) &lt; threshold);</div>
+<div class="line"><span class="lineno">  241</span>    assert(std::abs(dist.cumulative_distribution(6) - 0.999936) &lt; threshold);</div>
+<div class="line"><span class="lineno">  242</span>    assert(std::abs(dist.inverse_cumulative_distribution(</div>
+<div class="line"><span class="lineno">  243</span>                        dist.cumulative_distribution(8)) -</div>
+<div class="line"><span class="lineno">  244</span>                    8) &lt; threshold);</div>
+<div class="line"><span class="lineno">  245</span>    assert(std::abs(dist.range_tries() - 1.0f) &lt; threshold);</div>
+<div class="line"><span class="lineno">  246</span>    assert(std::abs(dist.range_tries(3) - 0.04f) &lt; threshold);</div>
+<div class="line"><span class="lineno">  247</span>    assert(std::abs(dist.range_tries(5, 11) - 0.00159997f) &lt; threshold);</div>
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-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span> </div>
-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span><span class="preprocessor">#ifdef _OPENMP</span></div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="preprocessor">#pragma omp for</span></div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span><span class="preprocessor">#endif</span></div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>        A[0][i][i] = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % <a class="code hl_define" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>) - lim2;</div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>        <span class="keywordflow">for</span> (j = i + 1; j &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; j++) {</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>            tmp = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % <a class="code hl_define" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>) - lim2;</div>
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+<div class="fragment"><div class="line"><span class="lineno">   28</span>                                                        {</div>
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+<div class="line"><span class="lineno">   30</span>    <span class="keywordtype">int</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = A-&gt;size();</div>
+<div class="line"><span class="lineno">   31</span> </div>
+<div class="line"><span class="lineno">   32</span><span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><span class="lineno">   33</span><span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><span class="lineno">   34</span><span class="preprocessor">#endif</span></div>
+<div class="line"><span class="lineno">   35</span>    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
+<div class="line"><span class="lineno">   36</span>        A[0][i][i] = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % <a class="code hl_define" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>) - lim2;</div>
+<div class="line"><span class="lineno">   37</span>        <span class="keywordflow">for</span> (j = i + 1; j &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; j++) {</div>
+<div class="line"><span class="lineno">   38</span>            tmp = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % <a class="code hl_define" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>) - lim2;</div>
+<div class="line"><span class="lineno">   39</span>            A[0][i][j] = tmp;  <span class="comment">// summetrically distribute random values</span></div>
+<div class="line"><span class="lineno">   40</span>            A[0][j][i] = tmp;</div>
+<div class="line"><span class="lineno">   41</span>        }</div>
+<div class="line"><span class="lineno">   42</span>    }</div>
+<div class="line"><span class="lineno">   43</span>}</div>
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 <div class="ttc" id="aqr__eigen__values_8cpp_html_aee57a411f07599034f5ceb8cc7d65b40"><div class="ttname"><a href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a></div><div class="ttdeci">#define LIMS</div><div class="ttdef"><b>Definition:</b> qr_eigen_values.cpp:20</div></div>
 <div class="ttc" id="arand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a></div><div class="ttdeci">T rand(T... args)</div></div>
@@ -235,48 +235,48 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >main function </p>
-<div class="fragment"><div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>                                {</div>
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-<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>    <span class="keywordflow">if</span> (argc == 2) {</div>
-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>        <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">atoi</a>(argv[1]);</div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>    } <span class="keywordflow">else</span> {  <span class="comment">// if invalid input argument is given run tests</span></div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>        <a class="code hl_function" href="../../de/d75/qr__eigen__values_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>        <a class="code hl_function" href="../../de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Usage: ./qr_eigen_values [mat_size]\n&quot;</span>;</div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>        <span class="keywordflow">return</span> 0;</div>
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-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>    <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> &lt; 2) {</div>
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-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>        <span class="keywordflow">return</span> -1;</div>
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-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span> </div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>    <span class="comment">// initialize random number generator</span></div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
-<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span> </div>
-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>    <span class="keywordtype">int</span> i, rows = <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, columns = <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>;</div>
-<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span> </div>
-<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; A(rows);</div>
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-<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; rows; i++) {</div>
-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>        A[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(columns);</div>
-<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>    }</div>
-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span> </div>
-<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>    <span class="comment">/* create a random matrix */</span></div>
-<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>    <a class="code hl_function" href="../../de/d75/qr__eigen__values_8cpp.html#a9bbf469d5525a816b0d6ca812119093d">create_matrix</a>(&amp;A);</div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span> </div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; A &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span> </div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>    clock_t t1 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>();</div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> eigen_vals = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a28e2fa3e803abaea6c568dc45d69d8cc">qr_algorithm::eigen_values</a>(&amp;A);</div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>    <span class="keywordtype">double</span> dtime = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>() - t1) / CLOCKS_PER_SEC;</div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span> </div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Eigen vals: &quot;</span>;</div>
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+<div class="line"><span class="lineno">  245</span>    <span class="keywordflow">if</span> (argc == 2) {</div>
+<div class="line"><span class="lineno">  246</span>        <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">atoi</a>(argv[1]);</div>
+<div class="line"><span class="lineno">  247</span>    } <span class="keywordflow">else</span> {  <span class="comment">// if invalid input argument is given run tests</span></div>
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+<div class="line"><span class="lineno">  249</span>        <a class="code hl_function" href="../../de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
+<div class="line"><span class="lineno">  250</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Usage: ./qr_eigen_values [mat_size]\n&quot;</span>;</div>
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+<div class="line"><span class="lineno">  255</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/fprintf.html">fprintf</a>(stderr, <span class="stringliteral">&quot;Matrix size should be &gt; 2\n&quot;</span>);</div>
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+<div class="line"><span class="lineno">  259</span>    <span class="comment">// initialize random number generator</span></div>
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+<div class="line"><span class="lineno">  264</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; A(rows);</div>
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+<div class="line"><span class="lineno">  266</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; rows; i++) {</div>
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+<div class="line"><span class="lineno">  275</span>    clock_t t1 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>();</div>
+<div class="line"><span class="lineno">  276</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> eigen_vals = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a28e2fa3e803abaea6c568dc45d69d8cc">qr_algorithm::eigen_values</a>(&amp;A);</div>
+<div class="line"><span class="lineno">  277</span>    <span class="keywordtype">double</span> dtime = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>() - t1) / CLOCKS_PER_SEC;</div>
+<div class="line"><span class="lineno">  278</span> </div>
+<div class="line"><span class="lineno">  279</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Eigen vals: &quot;</span>;</div>
+<div class="line"><span class="lineno">  280</span>    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; eigen_vals[i] &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
+<div class="line"><span class="lineno">  281</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nTime taken to compute: &quot;</span> &lt;&lt; dtime &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  282</span> </div>
+<div class="line"><span class="lineno">  283</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  284</span>}</div>
 <div class="ttc" id="aatoi_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">std::atoi</a></div><div class="ttdeci">T atoi(T... args)</div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aclock_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a></div><div class="ttdeci">T clock(T... args)</div></div>
@@ -342,25 +342,25 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd>pointer to resultant matrix </dd></dl>
 </li>
 </ul>
-<div class="fragment"><div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>                                                    {</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    <span class="keywordtype">int</span> R1 = A.size();</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <span class="keywordtype">int</span> C1 = A[0].size();</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <span class="keywordtype">int</span> R2 = B.size();</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <span class="keywordtype">int</span> C2 = B[0].size();</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    <span class="keywordflow">if</span> (C1 != R2) {</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">perror</a>(<span class="stringliteral">&quot;Matrix dimensions mismatch!&quot;</span>);</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    }</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span> </div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; R1; i++) {</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; C2; j++) {</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>            OUT[0][i][j] = 0.f;</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt; C1; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>                OUT[0][i][j] += A[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] * B[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j];</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>            }</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>        }</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    }</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   56</span>                                                    {</div>
+<div class="line"><span class="lineno">   57</span>    <span class="keywordtype">int</span> R1 = A.size();</div>
+<div class="line"><span class="lineno">   58</span>    <span class="keywordtype">int</span> C1 = A[0].size();</div>
+<div class="line"><span class="lineno">   59</span>    <span class="keywordtype">int</span> R2 = B.size();</div>
+<div class="line"><span class="lineno">   60</span>    <span class="keywordtype">int</span> C2 = B[0].size();</div>
+<div class="line"><span class="lineno">   61</span>    <span class="keywordflow">if</span> (C1 != R2) {</div>
+<div class="line"><span class="lineno">   62</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">perror</a>(<span class="stringliteral">&quot;Matrix dimensions mismatch!&quot;</span>);</div>
+<div class="line"><span class="lineno">   63</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">   64</span>    }</div>
+<div class="line"><span class="lineno">   65</span> </div>
+<div class="line"><span class="lineno">   66</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; R1; i++) {</div>
+<div class="line"><span class="lineno">   67</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; C2; j++) {</div>
+<div class="line"><span class="lineno">   68</span>            OUT[0][i][j] = 0.f;</div>
+<div class="line"><span class="lineno">   69</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt; C1; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
+<div class="line"><span class="lineno">   70</span>                OUT[0][i][j] += A[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] * B[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j];</div>
+<div class="line"><span class="lineno">   71</span>            }</div>
+<div class="line"><span class="lineno">   72</span>        }</div>
+<div class="line"><span class="lineno">   73</span>    }</div>
+<div class="line"><span class="lineno">   74</span>}</div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
 <div class="ttc" id="aperror_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a></div><div class="ttdeci">T perror(T... args)</div></div>
 </div><!-- fragment -->
@@ -384,27 +384,27 @@ Here is the call graph for this function:</div>
 \[\begin{bmatrix} 5 &amp; 7\\ 7 &amp; 11 \end{bmatrix}\]
 </p>
 <p> which are approximately, {15.56158, 0.384227} </p>
-<div class="fragment"><div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>             {</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; X = {{5, 7}, {7, 11}};</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>    <span class="keywordtype">double</span> y[] = {15.56158, 0.384227};  <span class="comment">// corresponding y-values</span></div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span> </div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------- Test 1 -------&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> eig_vals = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a28e2fa3e803abaea6c568dc45d69d8cc">qr_algorithm::eigen_values</a>(&amp;X);</div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span> </div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 2; i++) {</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i + 1 &lt;&lt; <span class="stringliteral">&quot;/2 Checking for &quot;</span> &lt;&lt; y[i] &lt;&lt; <span class="stringliteral">&quot; --&gt; &quot;</span>;</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>        <span class="keywordtype">bool</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; 2 &amp;&amp; !<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>; j++) {</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>            <span class="keywordflow">if</span> (std::abs(y[i] - eig_vals[j]) &lt; 0.1) {</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>                <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;(&quot;</span> &lt;&lt; eig_vals[j] &lt;&lt; <span class="stringliteral">&quot;) &quot;</span>;</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>            }</div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>        }</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>        assert(result);  <span class="comment">// ensure that i^th expected eigen value was computed</span></div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;found\n&quot;</span>;</div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>    }</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 Passed\n\n&quot;</span>;</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  177</span>             {</div>
+<div class="line"><span class="lineno">  178</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; X = {{5, 7}, {7, 11}};</div>
+<div class="line"><span class="lineno">  179</span>    <span class="keywordtype">double</span> y[] = {15.56158, 0.384227};  <span class="comment">// corresponding y-values</span></div>
+<div class="line"><span class="lineno">  180</span> </div>
+<div class="line"><span class="lineno">  181</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------- Test 1 -------&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  182</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> eig_vals = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a28e2fa3e803abaea6c568dc45d69d8cc">qr_algorithm::eigen_values</a>(&amp;X);</div>
+<div class="line"><span class="lineno">  183</span> </div>
+<div class="line"><span class="lineno">  184</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 2; i++) {</div>
+<div class="line"><span class="lineno">  185</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i + 1 &lt;&lt; <span class="stringliteral">&quot;/2 Checking for &quot;</span> &lt;&lt; y[i] &lt;&lt; <span class="stringliteral">&quot; --&gt; &quot;</span>;</div>
+<div class="line"><span class="lineno">  186</span>        <span class="keywordtype">bool</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  187</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; 2 &amp;&amp; !<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>; j++) {</div>
+<div class="line"><span class="lineno">  188</span>            <span class="keywordflow">if</span> (std::abs(y[i] - eig_vals[j]) &lt; 0.1) {</div>
+<div class="line"><span class="lineno">  189</span>                <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  190</span>                <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;(&quot;</span> &lt;&lt; eig_vals[j] &lt;&lt; <span class="stringliteral">&quot;) &quot;</span>;</div>
+<div class="line"><span class="lineno">  191</span>            }</div>
+<div class="line"><span class="lineno">  192</span>        }</div>
+<div class="line"><span class="lineno">  193</span>        assert(result);  <span class="comment">// ensure that i^th expected eigen value was computed</span></div>
+<div class="line"><span class="lineno">  194</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;found\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  195</span>    }</div>
+<div class="line"><span class="lineno">  196</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 Passed\n\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  197</span>}</div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
 <div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -434,35 +434,35 @@ Here is the call graph for this function:</div>
 \[\begin{bmatrix} -4&amp; 4&amp; 2&amp; 0&amp; -3\\ 4&amp; -4&amp; 4&amp; -3&amp; -1\\ 2&amp; 4&amp; 4&amp; 3&amp; -3\\ 0&amp; -3&amp; 3&amp; -1&amp;-1\\ -3&amp; -1&amp; -3&amp; -3&amp; 0 \end{bmatrix}\]
 </p>
 <p> which are approximately, {9.27648, -9.26948, 2.0181, -1.03516, -5.98994} </p>
-<div class="fragment"><div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>             {</div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; X = {{-4, 4, 2, 0, -3},</div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>                                              {4, -4, 4, -3, -1},</div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>                                              {2, 4, 4, 3, -3},</div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>                                              {0, -3, 3, -1, -3},</div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>                                              {-3, -1, -3, -3, 0}};</div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>    <span class="keywordtype">double</span> y[] = {9.27648, -9.26948, 2.0181, -1.03516,</div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>                  -5.98994};  <span class="comment">// corresponding y-values</span></div>
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@@ -208,24 +208,24 @@ template&lt;typename T , size_t N&gt; </div>
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-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span> </div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    <span class="keywordflow">for</span> (i = start; i &lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a>; i++) {</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>        T temp = ptr[i];</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>        j = i;</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>        <span class="keywordflow">while</span> (j &gt; start &amp;&amp; temp &lt; ptr[j - 1]) {</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>            ptr[j] = ptr[j - 1];</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>            j--;</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>        }</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>        <span class="comment">//   for (j = i; j &gt; start &amp;&amp; temp &lt; ptr[j - 1]; --j) {</span></div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        <span class="comment">//       ptr[j] = ptr[j - 1];</span></div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>        <span class="comment">//   }</span></div>
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-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>}</div>
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+<div class="line"><span class="lineno">   38</span>    <span class="keywordtype">size_t</span> i = 0, j = 0;</div>
+<div class="line"><span class="lineno">   39</span>    T *ptr = A-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/data.html">data</a>();</div>
+<div class="line"><span class="lineno">   40</span> </div>
+<div class="line"><span class="lineno">   41</span>    <span class="keywordflow">for</span> (i = start; i &lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a>; i++) {</div>
+<div class="line"><span class="lineno">   42</span>        T temp = ptr[i];</div>
+<div class="line"><span class="lineno">   43</span>        j = i;</div>
+<div class="line"><span class="lineno">   44</span>        <span class="keywordflow">while</span> (j &gt; start &amp;&amp; temp &lt; ptr[j - 1]) {</div>
+<div class="line"><span class="lineno">   45</span>            ptr[j] = ptr[j - 1];</div>
+<div class="line"><span class="lineno">   46</span>            j--;</div>
+<div class="line"><span class="lineno">   47</span>        }</div>
+<div class="line"><span class="lineno">   48</span>        <span class="comment">//   for (j = i; j &gt; start &amp;&amp; temp &lt; ptr[j - 1]; --j) {</span></div>
+<div class="line"><span class="lineno">   49</span>        <span class="comment">//       ptr[j] = ptr[j - 1];</span></div>
+<div class="line"><span class="lineno">   50</span>        <span class="comment">//   }</span></div>
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+<div class="line"><span class="lineno">   52</span>        ptr[j] = temp;</div>
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-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    <span class="comment">//  for (int index = min; index &lt;= max; index++) ptr[index] =</span></div>
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-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   67</span>                                                                             {</div>
+<div class="line"><span class="lineno">   68</span>    <span class="keywordtype">size_t</span> firstIndex = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a>;</div>
+<div class="line"><span class="lineno">   69</span>    <span class="keywordtype">size_t</span> secondIndex = mid + 1;</div>
+<div class="line"><span class="lineno">   70</span> </div>
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+<div class="line"><span class="lineno">   74</span>    <span class="comment">// While there are elements in the left or right runs</span></div>
+<div class="line"><span class="lineno">   75</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> index = min; index &lt;= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">max</a>; index++) {</div>
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+<div class="line"><span class="lineno">  109</span>    <span class="comment">// prerequisite</span></div>
+<div class="line"><span class="lineno">  110</span>    <span class="keywordflow">if</span> ((max - min) &lt;= threshold) {</div>
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+<div class="line"><span class="lineno">  113</span>        <span class="comment">// get the middle point</span></div>
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+<div class="line"><span class="lineno">  115</span> </div>
+<div class="line"><span class="lineno">  116</span>        <span class="comment">// apply merge sort to both parts of this</span></div>
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+<div class="line"><span class="lineno">  119</span> </div>
+<div class="line"><span class="lineno">  120</span>        <span class="comment">// and finally merge all that sorted stuff</span></div>
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@@ -485,28 +485,28 @@ Here is the call graph for this function:</div>
 
 <p>Function to test code using random arrays. </p>
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+<div class="line"><span class="lineno">  135</span>    <span class="comment">// input</span></div>
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+<div class="line"><span class="lineno">  139</span>    }</div>
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+<div class="line"><span class="lineno">  148</span>    }</div>
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-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;i&#39;</span>, 10 - n) + <span class="stringliteral">&quot;x&quot;</span>;</div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>    <span class="keywordflow">if</span> (n &lt; 40)</div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, n / 10) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    <span class="keywordflow">if</span> (n &lt; 60)</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, 5 - n / 10) + <span class="charliteral">&#39;l&#39;</span> + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    <span class="keywordflow">if</span> (n &lt; 90)</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>        <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;l&quot;</span>) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, n / 10 - 5) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>    <span class="keywordflow">if</span> (n &lt; 110)</div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, 10 - n / 10) + <span class="stringliteral">&quot;c&quot;</span> + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    <span class="keywordflow">if</span> (n &lt; 400)</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, n / 100) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>    <span class="keywordflow">if</span> (n &lt; 600)</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, 5 - n / 100) + <span class="charliteral">&#39;d&#39;</span> + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>    <span class="keywordflow">if</span> (n &lt; 900)</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>        <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;d&quot;</span>) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, n / 100 - 5) +</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>               <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <span class="keywordflow">if</span> (n &lt; 1100)</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, 10 - n / 100) + <span class="stringliteral">&quot;m&quot;</span> + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    <span class="keywordflow">if</span> (n &lt; 4000)</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;m&#39;</span>, n / 1000) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 1000);</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    <span class="keywordflow">return</span> <span class="stringliteral">&quot;?&quot;</span>;</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   24</span>                              {</div>
+<div class="line"><span class="lineno">   25</span>    <span class="keywordflow">if</span> (n &lt; 4)</div>
+<div class="line"><span class="lineno">   26</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;i&#39;</span>, n);</div>
+<div class="line"><span class="lineno">   27</span>    <span class="keywordflow">if</span> (n &lt; 6)</div>
+<div class="line"><span class="lineno">   28</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;i&#39;</span>, 5 - n) + <span class="stringliteral">&quot;v&quot;</span>;</div>
+<div class="line"><span class="lineno">   29</span>    <span class="keywordflow">if</span> (n &lt; 9)</div>
+<div class="line"><span class="lineno">   30</span>        <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;v&quot;</span>) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;i&#39;</span>, n - 5);</div>
+<div class="line"><span class="lineno">   31</span>    <span class="keywordflow">if</span> (n &lt; 11)</div>
+<div class="line"><span class="lineno">   32</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;i&#39;</span>, 10 - n) + <span class="stringliteral">&quot;x&quot;</span>;</div>
+<div class="line"><span class="lineno">   33</span>    <span class="keywordflow">if</span> (n &lt; 40)</div>
+<div class="line"><span class="lineno">   34</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, n / 10) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
+<div class="line"><span class="lineno">   35</span>    <span class="keywordflow">if</span> (n &lt; 60)</div>
+<div class="line"><span class="lineno">   36</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, 5 - n / 10) + <span class="charliteral">&#39;l&#39;</span> + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
+<div class="line"><span class="lineno">   37</span>    <span class="keywordflow">if</span> (n &lt; 90)</div>
+<div class="line"><span class="lineno">   38</span>        <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;l&quot;</span>) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, n / 10 - 5) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
+<div class="line"><span class="lineno">   39</span>    <span class="keywordflow">if</span> (n &lt; 110)</div>
+<div class="line"><span class="lineno">   40</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, 10 - n / 10) + <span class="stringliteral">&quot;c&quot;</span> + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
+<div class="line"><span class="lineno">   41</span>    <span class="keywordflow">if</span> (n &lt; 400)</div>
+<div class="line"><span class="lineno">   42</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, n / 100) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
+<div class="line"><span class="lineno">   43</span>    <span class="keywordflow">if</span> (n &lt; 600)</div>
+<div class="line"><span class="lineno">   44</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, 5 - n / 100) + <span class="charliteral">&#39;d&#39;</span> + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
+<div class="line"><span class="lineno">   45</span>    <span class="keywordflow">if</span> (n &lt; 900)</div>
+<div class="line"><span class="lineno">   46</span>        <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;d&quot;</span>) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, n / 100 - 5) +</div>
+<div class="line"><span class="lineno">   47</span>               <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
+<div class="line"><span class="lineno">   48</span>    <span class="keywordflow">if</span> (n &lt; 1100)</div>
+<div class="line"><span class="lineno">   49</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, 10 - n / 100) + <span class="stringliteral">&quot;m&quot;</span> + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
+<div class="line"><span class="lineno">   50</span>    <span class="keywordflow">if</span> (n &lt; 4000)</div>
+<div class="line"><span class="lineno">   51</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;m&#39;</span>, n / 1000) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 1000);</div>
+<div class="line"><span class="lineno">   52</span>    <span class="keywordflow">return</span> <span class="stringliteral">&quot;?&quot;</span>;</div>
+<div class="line"><span class="lineno">   53</span>}</div>
 <div class="ttc" id="adecimal__to__roman__numeral_8cpp_html_a88203bd297e8405160c132faa1187780"><div class="ttname"><a href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a></div><div class="ttdeci">std::string fill(char c, int n)</div><div class="ttdef"><b>Definition:</b> decimal_to_roman_numeral.cpp:15</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -268,36 +268,36 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >to convert to uppercase Roman Numeral the function works recursively </p>
-<div class="fragment"><div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>                              {</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <span class="keywordflow">if</span> (n &lt; 4)</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;I&#39;</span>, n);</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    <span class="keywordflow">if</span> (n &lt; 6)</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;I&#39;</span>, 5 - n) + <span class="stringliteral">&quot;V&quot;</span>;</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    <span class="keywordflow">if</span> (n &lt; 9)</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;V&quot;</span>) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;I&#39;</span>, n - 5);</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <span class="keywordflow">if</span> (n &lt; 11)</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;I&#39;</span>, 10 - n) + <span class="stringliteral">&quot;X&quot;</span>;</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <span class="keywordflow">if</span> (n &lt; 40)</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;X&#39;</span>, n / 10) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 10);</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    <span class="keywordflow">if</span> (n &lt; 60)</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;X&#39;</span>, 5 - n / 10) + <span class="charliteral">&#39;L&#39;</span> + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 10);</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    <span class="keywordflow">if</span> (n &lt; 90)</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>        <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;L&quot;</span>) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;X&#39;</span>, n / 10 - 5) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 10);</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <span class="keywordflow">if</span> (n &lt; 110)</div>
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-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    <span class="keywordflow">if</span> (n &lt; 400)</div>
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+<div class="line"><span class="lineno">   72</span>        <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;L&quot;</span>) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;X&#39;</span>, n / 10 - 5) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 10);</div>
+<div class="line"><span class="lineno">   73</span>    <span class="keywordflow">if</span> (n &lt; 110)</div>
+<div class="line"><span class="lineno">   74</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;X&#39;</span>, 10 - n / 10) + <span class="stringliteral">&quot;C&quot;</span> + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 10);</div>
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 </div><!--header-->
 <div class="contents">
 
-<p><a href="https://en.wikipedia.org/wiki/Travelling_salesman_problem" target="_blank">Travelling Salesman Problem</a> implementation  
+<p>[Travelling Salesman Problem] (<a href="https://en.wikipedia.org/wiki/Travelling_salesman_problem">https://en.wikipedia.org/wiki/Travelling_salesman_problem</a>) implementation  
 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
 <code>#include &lt;cassert&gt;</code><br />
@@ -130,7 +130,7 @@ Functions</h2></td></tr>
 <tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
 </table>
 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
-<div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Travelling_salesman_problem" target="_blank">Travelling Salesman Problem</a> implementation </p>
+<div class="textblock"><p >[Travelling Salesman Problem] (<a href="https://en.wikipedia.org/wiki/Travelling_salesman_problem">https://en.wikipedia.org/wiki/Travelling_salesman_problem</a>) implementation </p>
 <dl class="section author"><dt>Author</dt><dd><a href="http://github.com/Mayank17M" target="_blank">Mayank Mamgain</a></dd></dl>
 <p>Travelling salesman problem asks: Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city? TSP can be modeled as an undirected weighted graph, such that cities are the graph's vertices, paths are the graph's edges, and a path's distance is the edge's weight. It is a minimization problem starting and finishing at a specified vertex after having visited each other vertex exactly once. This is the naive implementation of the problem. </p>
 </div><h2 class="groupheader">Function Documentation</h2>
@@ -152,14 +152,14 @@ Functions</h2></td></tr>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>           {</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <a class="code hl_function" href="../../de/d88/travelling__salesman__problem_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>();  <span class="comment">// run self-test implementations</span></div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint32_t&gt;</a>&gt; cities = {</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>        {0, 5, 10, 15}, {5, 0, 20, 30}, {10, 20, 0, 35}, {15, 30, 35, 0}};</div>
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-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  104</span>           {</div>
+<div class="line"><span class="lineno">  105</span>    <a class="code hl_function" href="../../de/d88/travelling__salesman__problem_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>();  <span class="comment">// run self-test implementations</span></div>
+<div class="line"><span class="lineno">  106</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint32_t&gt;</a>&gt; cities = {</div>
+<div class="line"><span class="lineno">  107</span>        {0, 5, 10, 15}, {5, 0, 20, 30}, {10, 20, 0, 35}, {15, 30, 35, 0}};</div>
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+<div class="line"><span class="lineno">  109</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../df/dce/namespacegraph.html#ab7706341d006e20d1ae58274187a3346">graph::TravellingSalesmanProblem</a>(&amp;cities, 0, V) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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+<div class="line"><span class="lineno">  143</span>    <span class="comment">// test 6Ci for i=0 to 7</span></div>
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+<div class="line"><span class="lineno">  146</span>    }</div>
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-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    assert(ncrObj.<a class="code hl_function" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a6b95277f5f527beacc8d0f3bc91fcd08">ncr</a>(7, 3, 29) == 6);</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  124</span>                                                     {</div>
+<div class="line"><span class="lineno">  125</span>    <span class="comment">// (52323 C 26161) % (1e9 + 7) = 224944353</span></div>
+<div class="line"><span class="lineno">  126</span>    assert(ncrObj.<a class="code hl_function" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a6b95277f5f527beacc8d0f3bc91fcd08">ncr</a>(52323, 26161, 1000000007) == 224944353);</div>
+<div class="line"><span class="lineno">  127</span>    <span class="comment">// 6 C 2 = 30, 30%5 = 0</span></div>
+<div class="line"><span class="lineno">  128</span>    assert(ncrObj.<a class="code hl_function" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a6b95277f5f527beacc8d0f3bc91fcd08">ncr</a>(6, 2, 5) == 0);</div>
+<div class="line"><span class="lineno">  129</span>    <span class="comment">// 7C3 = 35, 35 % 29 = 8</span></div>
+<div class="line"><span class="lineno">  130</span>    assert(ncrObj.<a class="code hl_function" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a6b95277f5f527beacc8d0f3bc91fcd08">ncr</a>(7, 3, 29) == 6);</div>
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diff --git a/de/db6/a1z26__cipher_8cpp.html b/de/db6/a1z26__cipher_8cpp.html
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@@ -186,40 +186,40 @@ Variables</h2></td></tr>
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-<div class="fragment"><div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>                                                                        {</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span> </div>
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-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::string&gt;</a> word_array;</div>
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+<div class="line"><span class="lineno">   80</span> </div>
+<div class="line"><span class="lineno">   81</span>    <span class="comment">// split words seperated by spaces into a vector array</span></div>
+<div class="line"><span class="lineno">   82</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::string&gt;</a> word_array;</div>
+<div class="line"><span class="lineno">   83</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_stringstream.html">std::stringstream</a> sstream(text);</div>
+<div class="line"><span class="lineno">   84</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> word;</div>
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+<div class="line"><span class="lineno">   92</span> </div>
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+<div class="line"><span class="lineno">   94</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> res_text;</div>
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+<div class="line"><span class="lineno">   96</span>            text_array.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(res_text);</div>
+<div class="line"><span class="lineno">   97</span>        }</div>
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+<div class="line"><span class="lineno">   99</span>        <span class="keywordflow">for</span> (<span class="keyword">auto</span>&amp; i : text_array) {</div>
+<div class="line"><span class="lineno">  100</span>            <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> += a1z26_decrypt_map[<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/stol.html">stoi</a>(i)];</div>
+<div class="line"><span class="lineno">  101</span>        }</div>
+<div class="line"><span class="lineno">  102</span> </div>
+<div class="line"><span class="lineno">  103</span>        <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> += <span class="charliteral">&#39; &#39;</span>;</div>
+<div class="line"><span class="lineno">  104</span>    }</div>
+<div class="line"><span class="lineno">  105</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.pop_back();  <span class="comment">// remove any leading whitespace</span></div>
+<div class="line"><span class="lineno">  106</span> </div>
+<div class="line"><span class="lineno">  107</span>    <span class="keywordflow">if</span> (bReturnUppercase) {</div>
+<div class="line"><span class="lineno">  108</span>        <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/transform.html">std::transform</a>(<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.begin(), <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.end(), <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.begin(), ::toupper);</div>
+<div class="line"><span class="lineno">  109</span>    }</div>
+<div class="line"><span class="lineno">  110</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">  111</span>}</div>
 <div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
 <div class="ttc" id="abasic_stringstream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_stringstream.html">std::stringstream</a></div></div>
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@@ -261,25 +261,25 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>encoded string with dashes to seperate letters </dd></dl>
-<div class="fragment"><div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>                                  {</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/transform.html">std::transform</a>(text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/begin.html">begin</a>(), text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/end.html">end</a>(), text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/begin.html">begin</a>(),</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>                   ::tolower);  <span class="comment">// convert string to lowercase</span></div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/replace.html">std::replace</a>(text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/begin.html">begin</a>(), text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/end.html">end</a>(), <span class="charliteral">&#39;:&#39;</span>, <span class="charliteral">&#39; &#39;</span>);</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    <span class="keywordflow">for</span> (<span class="keywordtype">char</span> letter : text) {</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>        <span class="keywordflow">if</span> (letter != <span class="charliteral">&#39; &#39;</span>) {</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>            <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> += <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/to_string.html">std::to_string</a>(</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>                a1z26_encrypt_map[letter]);  <span class="comment">// convert int to string and append</span></div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>                                             <span class="comment">// to result</span></div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>            <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> += <span class="stringliteral">&quot;-&quot;</span>;  <span class="comment">// space out each set of numbers with spaces</span></div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>            <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.pop_back();</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>            <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> += <span class="charliteral">&#39; &#39;</span>;</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        }</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    }</div>
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-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   51</span>                                  {</div>
+<div class="line"><span class="lineno">   52</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">   53</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/transform.html">std::transform</a>(text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/begin.html">begin</a>(), text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/end.html">end</a>(), text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/begin.html">begin</a>(),</div>
+<div class="line"><span class="lineno">   54</span>                   ::tolower);  <span class="comment">// convert string to lowercase</span></div>
+<div class="line"><span class="lineno">   55</span>    <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/replace.html">std::replace</a>(text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/begin.html">begin</a>(), text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/end.html">end</a>(), <span class="charliteral">&#39;:&#39;</span>, <span class="charliteral">&#39; &#39;</span>);</div>
+<div class="line"><span class="lineno">   56</span>    <span class="keywordflow">for</span> (<span class="keywordtype">char</span> letter : text) {</div>
+<div class="line"><span class="lineno">   57</span>        <span class="keywordflow">if</span> (letter != <span class="charliteral">&#39; &#39;</span>) {</div>
+<div class="line"><span class="lineno">   58</span>            <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> += <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/to_string.html">std::to_string</a>(</div>
+<div class="line"><span class="lineno">   59</span>                a1z26_encrypt_map[letter]);  <span class="comment">// convert int to string and append</span></div>
+<div class="line"><span class="lineno">   60</span>                                             <span class="comment">// to result</span></div>
+<div class="line"><span class="lineno">   61</span>            <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> += <span class="stringliteral">&quot;-&quot;</span>;  <span class="comment">// space out each set of numbers with spaces</span></div>
+<div class="line"><span class="lineno">   62</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   63</span>            <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.pop_back();</div>
+<div class="line"><span class="lineno">   64</span>            <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> += <span class="charliteral">&#39; &#39;</span>;</div>
+<div class="line"><span class="lineno">   65</span>        }</div>
+<div class="line"><span class="lineno">   66</span>    }</div>
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+<div class="line"><span class="lineno">   68</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">   69</span>}</div>
 <div class="ttc" id="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/begin.html">std::string::begin</a></div><div class="ttdeci">T begin(T... args)</div></div>
 <div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/end.html">std::string::end</a></div><div class="ttdeci">T end(T... args)</div></div>
 <div class="ttc" id="ato_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/to_string.html">std::to_string</a></div><div class="ttdeci">T to_string(T... args)</div></div>
@@ -310,10 +310,10 @@ Here is the call graph for this function:</div>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>           {</div>
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-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>}</div>
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+<div class="line"><span class="lineno">  161</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  162</span>}</div>
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 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -349,40 +349,40 @@ Here is the call graph for this function:</div>
 
 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>                   {</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    <span class="comment">// 1st test</span></div>
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-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> expected = <span class="stringliteral">&quot;8-5-12-12-15 23-15-18-12-4&quot;</span>;</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> output = <a class="code hl_function" href="../../de/db6/a1z26__cipher_8cpp.html#a77a6b827a0b9c7aca2d705811459d744">ciphers::a1z26::encrypt</a>(input);</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span> </div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input: &quot;</span> &lt;&lt; input &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    assert(output == expected);</div>
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-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    output = <a class="code hl_function" href="../../de/db6/a1z26__cipher_8cpp.html#a0a78954e96c862430904ee3e64623c38">ciphers::a1z26::decrypt</a>(input);</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span> </div>
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+<div class="line"><span class="lineno">   91</span>    <span class="keywordflow">return</span> (<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(m + 2) - <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(n + 1));</div>
+<div class="line"><span class="lineno">   92</span>}</div>
 <div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
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@@ -209,10 +209,10 @@ Here is the call graph for this function:</div>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>           {</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// execute the tests</span></div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  136</span>           {</div>
+<div class="line"><span class="lineno">  137</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// execute the tests</span></div>
+<div class="line"><span class="lineno">  138</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  139</span>}</div>
 <div class="ttc" id="afibonacci__sum_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:101</div></div>
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@@ -256,17 +256,17 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>resultant matrix </dd></dl>
-<div class="fragment"><div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>                                                                       {</div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">math::fibonacci_sum::matrix</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(2, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(2, 0));</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span> </div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>    <span class="comment">// multiplying matrices</span></div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[0][0] = T[0][0] * A[0][0] + T[0][1] * A[1][0];</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[0][1] = T[0][0] * A[0][1] + T[0][1] * A[1][1];</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[1][0] = T[1][0] * A[0][0] + T[1][1] * A[1][0];</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[1][1] = T[1][0] * A[0][1] + T[1][1] * A[1][1];</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span> </div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   39</span>                                                                       {</div>
+<div class="line"><span class="lineno">   40</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">math::fibonacci_sum::matrix</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(2, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(2, 0));</div>
+<div class="line"><span class="lineno">   41</span> </div>
+<div class="line"><span class="lineno">   42</span>    <span class="comment">// multiplying matrices</span></div>
+<div class="line"><span class="lineno">   43</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[0][0] = T[0][0] * A[0][0] + T[0][1] * A[1][0];</div>
+<div class="line"><span class="lineno">   44</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[0][1] = T[0][0] * A[0][1] + T[0][1] * A[1][1];</div>
+<div class="line"><span class="lineno">   45</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[1][0] = T[1][0] * A[0][0] + T[1][1] * A[1][0];</div>
+<div class="line"><span class="lineno">   46</span>    <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[1][1] = T[1][0] * A[0][1] + T[1][1] * A[1][1];</div>
+<div class="line"><span class="lineno">   47</span> </div>
+<div class="line"><span class="lineno">   48</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">   49</span>}</div>
 <div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
 </div><!-- fragment --><div class="dynheader">
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@@ -310,19 +310,19 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>resultant matrix </dd></dl>
-<div class="fragment"><div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>                                                                      {</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">math::fibonacci_sum::matrix</a> A{{1, 1}, {1, 0}};</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <span class="keywordflow">if</span> (ex == 0 || ex == 1) {</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        <span class="keywordflow">return</span> T;</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    }</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span> </div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    T = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">power</a>(T, ex / 2);</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    T = <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#a17f3d667241b88115a95282cdd719cb2">multiply</a>(T, T);</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <span class="keywordflow">if</span> (ex &amp; 1) {</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        T = <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#a17f3d667241b88115a95282cdd719cb2">multiply</a>(T, A);</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    }</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <span class="keywordflow">return</span> T;</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   57</span>                                                                      {</div>
+<div class="line"><span class="lineno">   58</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">math::fibonacci_sum::matrix</a> A{{1, 1}, {1, 0}};</div>
+<div class="line"><span class="lineno">   59</span>    <span class="keywordflow">if</span> (ex == 0 || ex == 1) {</div>
+<div class="line"><span class="lineno">   60</span>        <span class="keywordflow">return</span> T;</div>
+<div class="line"><span class="lineno">   61</span>    }</div>
+<div class="line"><span class="lineno">   62</span> </div>
+<div class="line"><span class="lineno">   63</span>    T = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">power</a>(T, ex / 2);</div>
+<div class="line"><span class="lineno">   64</span>    T = <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#a17f3d667241b88115a95282cdd719cb2">multiply</a>(T, T);</div>
+<div class="line"><span class="lineno">   65</span>    <span class="keywordflow">if</span> (ex &amp; 1) {</div>
+<div class="line"><span class="lineno">   66</span>        T = <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#a17f3d667241b88115a95282cdd719cb2">multiply</a>(T, A);</div>
+<div class="line"><span class="lineno">   67</span>    }</div>
+<div class="line"><span class="lineno">   68</span>    <span class="keywordflow">return</span> T;</div>
+<div class="line"><span class="lineno">   69</span>}</div>
 <div class="ttc" id="afibonacci__sum_8cpp_html_a7cf5feaf168b88e74544da59ed830311"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">math::fibonacci_sum::power</a></div><div class="ttdeci">math::fibonacci_sum::matrix power(math::fibonacci_sum::matrix T, uint64_t ex)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:57</div></div>
 <div class="ttc" id="anamespaceciphers_1_1elliptic__curve__key__exchange_html_a17f3d667241b88115a95282cdd719cb2"><div class="ttname"><a href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#a17f3d667241b88115a95282cdd719cb2">ciphers::elliptic_curve_key_exchange::multiply</a></div><div class="ttdeci">Point multiply(const Point &amp;a, const uint256_t &amp;curve_a_coeff, uint256_t p, const uint256_t &amp;mod)</div><div class="ttdoc">multiply Point and integer</div><div class="ttdef"><b>Definition:</b> elliptic_curve_key_exchange.cpp:165</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -356,13 +356,13 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>uint64_t ans, the sum of sequence </dd></dl>
-<div class="fragment"><div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>                            {</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">math::fibonacci_sum::matrix</a> T{{1, 1}, {1, 0}};</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    T = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">power</a>(T, n);</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    uint64_t <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = T[0][1];</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = (<a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> - 1);</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   76</span>                            {</div>
+<div class="line"><span class="lineno">   77</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">math::fibonacci_sum::matrix</a> T{{1, 1}, {1, 0}};</div>
+<div class="line"><span class="lineno">   78</span>    T = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">power</a>(T, n);</div>
+<div class="line"><span class="lineno">   79</span>    uint64_t <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = T[0][1];</div>
+<div class="line"><span class="lineno">   80</span>    <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = (<a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> - 1);</div>
+<div class="line"><span class="lineno">   81</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
+<div class="line"><span class="lineno">   82</span>}</div>
 <div class="ttc" id="amatrix__exponentiation_8cpp_html_ad8389ed58fd0ec66df248014775ad1fa"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a></div><div class="ttdeci">ll ans(ll n)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:91</div></div>
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@@ -396,36 +396,36 @@ Here is the call graph for this function:</div>
 </table>
 </div><div class="memdoc">
 <p >Function for testing fiboSum function. test cases and assert statement. </p><dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>                   {</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    uint64_t n = 0, m = 3;</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    uint64_t test_1 = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a>(n, m);</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    assert(test_1 == 4);</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 1!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span> </div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    n = 3;</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    m = 5;</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    uint64_t test_2 = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a>(n, m);</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    assert(test_2 == 10);</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 2!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span> </div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    n = 5;</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    m = 7;</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    uint64_t test_3 = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a>(n, m);</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    assert(test_3 == 26);</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 3!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span> </div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    n = 7;</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    m = 10;</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    uint64_t test_4 = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a>(n, m);</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    assert(test_4 == 123);</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 4!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span> </div>
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-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   48</span>                   {</div>
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+<div class="line"><span class="lineno">   50</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int64_t, 5&gt;</a> arr1 = {-1, -2, -4, -6, 7};</div>
+<div class="line"><span class="lineno">   51</span>    assert(<a class="code hl_function" href="../../de/dcd/kadanes3_8cpp.html#a338439a04148ae89f695595acfa5c147">max_subarray_sum</a>(arr, 4) == 10);</div>
+<div class="line"><span class="lineno">   52</span>    assert(<a class="code hl_function" href="../../de/dcd/kadanes3_8cpp.html#a338439a04148ae89f695595acfa5c147">max_subarray_sum</a>(arr1, 5) == 7);</div>
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+<div class="line"><span class="lineno">   54</span>}</div>
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+<!-- Generated by Doxygen 1.9.3 -->
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 <p >Recursive function to calculate exponent in \(O(\log(n))\) using binary exponent. </p>
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+<div class="line"><span class="lineno">   30</span>        <span class="keywordflow">return</span> 1;</div>
+<div class="line"><span class="lineno">   31</span>    }</div>
+<div class="line"><span class="lineno">   32</span>    <span class="keywordtype">int</span> res = <a class="code hl_function" href="../../de/dcf/binary__exponent_8cpp.html#aeb48dce0725e63d19147944f41843c73">binExpo</a>(a, b / 2);</div>
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+<div class="line"><span class="lineno">   36</span>        <span class="keywordflow">return</span> res * res;</div>
+<div class="line"><span class="lineno">   37</span>    }</div>
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 <p >Iterative function to calculate exponent in \(O(\log(n))\) using binary exponent. </p>
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 <p >int resIterate = binExpo_alt(a, b);</p>
 <p >Result of a^b (where '^' denotes exponentiation)</p>
 <p ><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; resIterate &lt;&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</p>
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@@ -36,7 +36,7 @@
 <!-- Node3 -->
 <g id="node3" class="node">
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-<g id="a_node3"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/io/manip/endl.html#" xlink:title=" ">
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@@ -3,7 +3,7 @@
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@@ -30,8 +30,8 @@ MathJax.Hub.Config({
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- <tr style="height: 56px;">
-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
+  <td id="projectalign">
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@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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-<!-- Generated by Doxygen 1.9.2 -->
+<!-- Generated by Doxygen 1.9.3 -->
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@@ -171,7 +171,7 @@ Private Attributes</h2></td></tr>
 </div><div class="memdoc">
 
 <p>Creates a <a class="el" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html" title="A Binary Tree class that implements a Binary Search Tree (BST) by default.">BinaryTree</a> with a root pointing to NULL. </p>
-<div class="fragment"><div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>{ <a class="code hl_variable" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#ab6a17a04aa93aaaef71e038e8cc2edeb">root</a> = <span class="keyword">nullptr</span>; }</div>
+<div class="fragment"><div class="line"><span class="lineno">   98</span>{ <a class="code hl_variable" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#ab6a17a04aa93aaaef71e038e8cc2edeb">root</a> = <span class="keyword">nullptr</span>; }</div>
 <div class="ttc" id="aclassoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree_html_ab6a17a04aa93aaaef71e038e8cc2edeb"><div class="ttname"><a href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#ab6a17a04aa93aaaef71e038e8cc2edeb">operations_on_datastructures::reverse_binary_tree::BinaryTree::root</a></div><div class="ttdeci">Node * root</div><div class="ttdoc">Pointer to root node of Binary Tree.</div><div class="ttdef"><b>Definition:</b> reverse_binary_tree.cpp:54</div></div>
 </div><!-- fragment -->
 </div>
@@ -201,7 +201,7 @@ Private Attributes</h2></td></tr>
 </div><div class="memdoc">
 
 <p>Creates a <a class="el" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html" title="A Binary Tree class that implements a Binary Search Tree (BST) by default.">BinaryTree</a> with a root with an initial value. </p>
-<div class="fragment"><div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>{ <a class="code hl_variable" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#ab6a17a04aa93aaaef71e038e8cc2edeb">root</a> = <span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>); }</div>
+<div class="fragment"><div class="line"><span class="lineno">  102</span>{ <a class="code hl_variable" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#ab6a17a04aa93aaaef71e038e8cc2edeb">root</a> = <span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>); }</div>
 <div class="ttc" id="ahash__search_8cpp_html_a6e1a77282bc65ad359d753d25df23243"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a></div><div class="ttdeci">int data[MAX]</div><div class="ttdoc">test data</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:24</div></div>
 <div class="ttc" id="astruct_node_html"><div class="ttname"><a href="../../db/d8b/struct_node.html">Node</a></div><div class="ttdef"><b>Definition:</b> linkedlist_implentation_usingarray.cpp:14</div></div>
 </div><!-- fragment -->
@@ -233,7 +233,7 @@ Private Attributes</h2></td></tr>
 </div><div class="memdoc">
 
 <p>Adds a new <a class="el" href="../../d8/dfd/structoperations__on__datastructures_1_1reverse__binary__tree_1_1_node.html" title="A Node struct that represents a single node in a Binary Tree.">Node</a> to the Binary Tree. </p>
-<div class="fragment"><div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>{ <a class="code hl_variable" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#ab6a17a04aa93aaaef71e038e8cc2edeb">root</a> = <a class="code hl_function" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#adb2b6be741b0500ee75d89b6d06b5d50">insert</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, <a class="code hl_variable" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#ab6a17a04aa93aaaef71e038e8cc2edeb">root</a>); }</div>
+<div class="fragment"><div class="line"><span class="lineno">  106</span>{ <a class="code hl_variable" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#ab6a17a04aa93aaaef71e038e8cc2edeb">root</a> = <a class="code hl_function" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#adb2b6be741b0500ee75d89b6d06b5d50">insert</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, <a class="code hl_variable" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#ab6a17a04aa93aaaef71e038e8cc2edeb">root</a>); }</div>
 <div class="ttc" id="aclassoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree_html_adb2b6be741b0500ee75d89b6d06b5d50"><div class="ttname"><a href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#adb2b6be741b0500ee75d89b6d06b5d50">operations_on_datastructures::reverse_binary_tree::BinaryTree::insert</a></div><div class="ttdeci">Node * insert(int64_t data, Node *pivot)</div><div class="ttdoc">inserts a node in the Binary Tree, with the behaviouur of a Binary Search Tree.</div><div class="ttdef"><b>Definition:</b> reverse_binary_tree.cpp:65</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -268,7 +268,7 @@ Here is the call graph for this function:</div>
 </div><div class="memdoc">
 
 <p>Level order traversal of a tree consists of visiting its elements, top to bottom, left to right. This function performs level order traversal and returns the node datas as a vector. </p>
-<p >The function uses a queue to append and remove elements as they are visited, and then adds their children, if any. This ensures that the elements are visited layer-by-layer, starting from the root of the Tree. </p><dl class="section return"><dt>Returns</dt><dd>vector&lt;int64_t&gt; of nodes of the tree. </dd></dl>
+<p >The function uses a queue to append and remove elements as they are visited, and then adds their children, if any. This ensures that the elements are visited layer-by-layer, starting from the root of the Tree. </p><dl class="section return"><dt>Returns</dt><dd><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;int64_t&gt;</a> of nodes of the tree. </dd></dl>
 <p >&lt; Result vector of int</p>
 <p >&lt; Return empty vector if root is Invalid</p>
 <p >&lt; <a class="el" href="../../dc/db5/struct_queue.html">Queue</a> of the nodes in the tree</p>
@@ -279,32 +279,32 @@ Here is the call graph for this function:</div>
 <p >&lt; Insert left node</p>
 <p >&lt; Insert right node</p>
 <p >Add nodes while Tree is not empty</p>
-<div class="fragment"><div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>                                         {</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;  <span class="comment">///&lt; Result vector of int</span></div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#ab6a17a04aa93aaaef71e038e8cc2edeb">root</a> == <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>            <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;  <span class="comment">///&lt; Return empty vector if root is Invalid</span></div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>        }</div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue&lt;Node*&gt;</a> nodes;  <span class="comment">///&lt; Queue of the nodes in the tree</span></div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>        nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/push.html">push</a>(<a class="code hl_variable" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#ab6a17a04aa93aaaef71e038e8cc2edeb">root</a>);         <span class="comment">///&lt; Insert root into the queue</span></div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>        <span class="keywordflow">while</span> (!nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/empty.html">empty</a>()) {</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>            <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>* temp = nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/front.html">front</a>();  <span class="comment">///&lt; Copy the first element</span></div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>            <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>.push_back(temp-&gt;data);  <span class="comment">///&lt; Add the element to the data</span></div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>            nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/pop.html">pop</a>();                 <span class="comment">///&lt; Remove element</span></div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>            <span class="keywordflow">if</span> (temp-&gt;left != <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>                nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/push.html">push</a>(temp-&gt;left);  <span class="comment">///&lt; Insert left node</span></div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>            }</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>            <span class="keywordflow">if</span> (temp-&gt;right != <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>                nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/push.html">push</a>(temp-&gt;right);  <span class="comment">///&lt; Insert right node</span></div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>            }</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>        }  <span class="comment">/// Add nodes while Tree is not empty</span></div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  121</span>                                         {</div>
+<div class="line"><span class="lineno">  122</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;  <span class="comment">///&lt; Result vector of int</span></div>
+<div class="line"><span class="lineno">  123</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#ab6a17a04aa93aaaef71e038e8cc2edeb">root</a> == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  124</span>            <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;  <span class="comment">///&lt; Return empty vector if root is Invalid</span></div>
+<div class="line"><span class="lineno">  125</span>        }</div>
+<div class="line"><span class="lineno">  126</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue&lt;Node*&gt;</a> nodes;  <span class="comment">///&lt; Queue of the nodes in the tree</span></div>
+<div class="line"><span class="lineno">  127</span>        nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/push.html">push</a>(<a class="code hl_variable" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#ab6a17a04aa93aaaef71e038e8cc2edeb">root</a>);         <span class="comment">///&lt; Insert root into the queue</span></div>
+<div class="line"><span class="lineno">  128</span>        <span class="keywordflow">while</span> (!nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/empty.html">empty</a>()) {</div>
+<div class="line"><span class="lineno">  129</span>            <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>* temp = nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/front.html">front</a>();  <span class="comment">///&lt; Copy the first element</span></div>
+<div class="line"><span class="lineno">  130</span>            <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>.push_back(temp-&gt;data);  <span class="comment">///&lt; Add the element to the data</span></div>
+<div class="line"><span class="lineno">  131</span>            nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/pop.html">pop</a>();                 <span class="comment">///&lt; Remove element</span></div>
+<div class="line"><span class="lineno">  132</span>            <span class="keywordflow">if</span> (temp-&gt;left != <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">  133</span>                nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/push.html">push</a>(temp-&gt;left);  <span class="comment">///&lt; Insert left node</span></div>
+<div class="line"><span class="lineno">  134</span>            }</div>
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+<div class="line"><span class="lineno">  136</span>                nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/push.html">push</a>(temp-&gt;right);  <span class="comment">///&lt; Insert right node</span></div>
+<div class="line"><span class="lineno">  137</span>            }</div>
+<div class="line"><span class="lineno">  138</span>        }  <span class="comment">/// Add nodes while Tree is not empty</span></div>
+<div class="line"><span class="lineno">  139</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
+<div class="line"><span class="lineno">  140</span>    }</div>
 <div class="ttc" id="aempty_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue/empty.html">std::queue::empty</a></div><div class="ttdeci">T empty(T... args)</div></div>
 <div class="ttc" id="afront_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue/front.html">std::queue::front</a></div><div class="ttdeci">T front(T... args)</div></div>
 <div class="ttc" id="apop_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue/pop.html">std::queue::pop</a></div><div class="ttdeci">T pop(T... args)</div></div>
 <div class="ttc" id="apush_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue/push.html">std::queue::push</a></div><div class="ttdeci">T push(T... args)</div></div>
 <div class="ttc" id="aqueue_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue</a></div></div>
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 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -360,19 +360,19 @@ Here is the call graph for this function:</div>
 <p >&lt; Create new node</p>
 <p >&lt; Insert <a class="el" href="../../d8/dfd/structoperations__on__datastructures_1_1reverse__binary__tree_1_1_node.html" title="A Node struct that represents a single node in a Binary Tree.">Node</a> to the left</p>
 <p >&lt; Insert node to the right</p>
-<div class="fragment"><div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>                                            {</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="keywordflow">if</span> (pivot == <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>            <span class="keywordflow">return</span> <span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);  <span class="comment">///&lt; Create new node</span></div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        }</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        <span class="keywordflow">if</span> (data &lt;= pivot-&gt;<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>) {</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>            pivot-&gt;left =</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>                <a class="code hl_function" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#adb2b6be741b0500ee75d89b6d06b5d50">insert</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, pivot-&gt;left);  <span class="comment">///&lt; Insert Node to the left</span></div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>            pivot-&gt;right =</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>                <a class="code hl_function" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#adb2b6be741b0500ee75d89b6d06b5d50">insert</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, pivot-&gt;right);  <span class="comment">///&lt; Insert node to the right</span></div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>        }</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        <span class="keywordflow">return</span> pivot;</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   65</span>                                            {</div>
+<div class="line"><span class="lineno">   66</span>        <span class="keywordflow">if</span> (pivot == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">   67</span>            <span class="keywordflow">return</span> <span class="keyword">new</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);  <span class="comment">///&lt; Create new node</span></div>
+<div class="line"><span class="lineno">   68</span>        }</div>
+<div class="line"><span class="lineno">   69</span>        <span class="keywordflow">if</span> (data &lt;= pivot-&gt;<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>) {</div>
+<div class="line"><span class="lineno">   70</span>            pivot-&gt;left =</div>
+<div class="line"><span class="lineno">   71</span>                <a class="code hl_function" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#adb2b6be741b0500ee75d89b6d06b5d50">insert</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, pivot-&gt;left);  <span class="comment">///&lt; Insert Node to the left</span></div>
+<div class="line"><span class="lineno">   72</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   73</span>            pivot-&gt;right =</div>
+<div class="line"><span class="lineno">   74</span>                <a class="code hl_function" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#adb2b6be741b0500ee75d89b6d06b5d50">insert</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, pivot-&gt;right);  <span class="comment">///&lt; Insert node to the right</span></div>
+<div class="line"><span class="lineno">   75</span>        }</div>
+<div class="line"><span class="lineno">   76</span>        <span class="keywordflow">return</span> pivot;</div>
+<div class="line"><span class="lineno">   77</span>    }</div>
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 Here is the call graph for this function:</div>
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@@ -409,12 +409,12 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
 <p >Print each element in the tree</p>
 <p >Print newline</p>
-<div class="fragment"><div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>                 {</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i : <a class="code hl_function" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#a2e683b271d8d5cd63e0d09cf8aaa325c">get_level_order</a>()) {</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;  <span class="comment">/// Print each element in the tree</span></div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>        }</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;  <span class="comment">/// Print newline</span></div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  146</span>                 {</div>
+<div class="line"><span class="lineno">  147</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i : <a class="code hl_function" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#a2e683b271d8d5cd63e0d09cf8aaa325c">get_level_order</a>()) {</div>
+<div class="line"><span class="lineno">  148</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;  <span class="comment">/// Print each element in the tree</span></div>
+<div class="line"><span class="lineno">  149</span>        }</div>
+<div class="line"><span class="lineno">  150</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;  <span class="comment">/// Print newline</span></div>
+<div class="line"><span class="lineno">  151</span>    }</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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 </div><!-- fragment --><div class="dynheader">
@@ -449,7 +449,7 @@ Here is the call graph for this function:</div>
 </table>
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 <p >Reverses the Binary Tree </p>
-<div class="fragment"><div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>{ <a class="code hl_variable" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#ab6a17a04aa93aaaef71e038e8cc2edeb">root</a> = <a class="code hl_function" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#af6f974381f523fdb981fc2d843bbf4a1">reverseBinaryTree</a>(<a class="code hl_variable" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#ab6a17a04aa93aaaef71e038e8cc2edeb">root</a>); }</div>
+<div class="fragment"><div class="line"><span class="lineno">  110</span>{ <a class="code hl_variable" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#ab6a17a04aa93aaaef71e038e8cc2edeb">root</a> = <a class="code hl_function" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#af6f974381f523fdb981fc2d843bbf4a1">reverseBinaryTree</a>(<a class="code hl_variable" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#ab6a17a04aa93aaaef71e038e8cc2edeb">root</a>); }</div>
 <div class="ttc" id="aclassoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree_html_af6f974381f523fdb981fc2d843bbf4a1"><div class="ttname"><a href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#af6f974381f523fdb981fc2d843bbf4a1">operations_on_datastructures::reverse_binary_tree::BinaryTree::reverseBinaryTree</a></div><div class="ttdeci">Node * reverseBinaryTree(Node *pivot)</div><div class="ttdoc">Reverses a Binary Tree recursively by swapping the left and right subtrees and their children.</div><div class="ttdef"><b>Definition:</b> reverse_binary_tree.cpp:84</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -496,15 +496,15 @@ Here is the call graph for this function:</div>
 <p >&lt; pointer to the left subtree</p>
 <p >&lt; Swap</p>
 <p >&lt; Swap</p>
-<div class="fragment"><div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>                                         {</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>        <span class="keywordflow">if</span> (pivot == <span class="keyword">nullptr</span>) {</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>            <span class="keywordflow">return</span> pivot;  <span class="comment">///&lt; Base case</span></div>
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-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>* temp = pivot-&gt;left;  <span class="comment">///&lt; pointer to the left subtree</span></div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        pivot-&gt;left = <a class="code hl_function" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#af6f974381f523fdb981fc2d843bbf4a1">reverseBinaryTree</a>(pivot-&gt;right);  <span class="comment">///&lt; Swap</span></div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>        pivot-&gt;right = <a class="code hl_function" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#af6f974381f523fdb981fc2d843bbf4a1">reverseBinaryTree</a>(temp);         <span class="comment">///&lt; Swap</span></div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>        <span class="keywordflow">return</span> pivot;</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   84</span>                                         {</div>
+<div class="line"><span class="lineno">   85</span>        <span class="keywordflow">if</span> (pivot == <span class="keyword">nullptr</span>) {</div>
+<div class="line"><span class="lineno">   86</span>            <span class="keywordflow">return</span> pivot;  <span class="comment">///&lt; Base case</span></div>
+<div class="line"><span class="lineno">   87</span>        }</div>
+<div class="line"><span class="lineno">   88</span>        <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a>* temp = pivot-&gt;left;  <span class="comment">///&lt; pointer to the left subtree</span></div>
+<div class="line"><span class="lineno">   89</span>        pivot-&gt;left = <a class="code hl_function" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#af6f974381f523fdb981fc2d843bbf4a1">reverseBinaryTree</a>(pivot-&gt;right);  <span class="comment">///&lt; Swap</span></div>
+<div class="line"><span class="lineno">   90</span>        pivot-&gt;right = <a class="code hl_function" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html#af6f974381f523fdb981fc2d843bbf4a1">reverseBinaryTree</a>(temp);         <span class="comment">///&lt; Swap</span></div>
+<div class="line"><span class="lineno">   91</span>        <span class="keywordflow">return</span> pivot;</div>
+<div class="line"><span class="lineno">   92</span>    }</div>
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@@ -523,7 +523,7 @@ Here is the call graph for this function:</div>
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   <ul>
     <li class="navelem"><a class="el" href="../../da/d6d/namespaceoperations__on__datastructures.html">operations_on_datastructures</a></li><li class="navelem"><b>reverse_binary_tree</b></li><li class="navelem"><a class="el" href="../../de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html">BinaryTree</a></li>
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+<div class="line"><span class="lineno">  257</span>    <span class="keywordflow">return</span> 0;</div>
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 Here is the call graph for this function:</div>
@@ -215,25 +215,25 @@ Here is the call graph for this function:</div>
   /     |     \
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+<div class="line"><span class="lineno">  237</span><span class="comment">     *          /     |     \</span></div>
+<div class="line"><span class="lineno">  238</span><span class="comment">     *        1       6       4</span></div>
+<div class="line"><span class="lineno">  239</span><span class="comment">     *      / |     /   \       \</span></div>
+<div class="line"><span class="lineno">  240</span><span class="comment">     *    7   5   2       8       0</span></div>
+<div class="line"><span class="lineno">  241</span><span class="comment">     *            |</span></div>
+<div class="line"><span class="lineno">  242</span><span class="comment">     *            9</span></div>
+<div class="line"><span class="lineno">  243</span><span class="comment">     */</span></div>
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+<div class="line"><span class="lineno">  245</span>        {7, 1}, {1, 5}, {1, 3}, {3, 6}, {6, 2}, {2, 9}, {6, 8}, {4, 3}, {0, 4}};</div>
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+<div class="line"><span class="lineno">  247</span>    <a class="code hl_class" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html">graph::LowestCommonAncestor</a> lca(t);</div>
+<div class="line"><span class="lineno">  248</span>    assert(lca.lowest_common_ancestor(7, 4) == 3);</div>
+<div class="line"><span class="lineno">  249</span>    assert(lca.lowest_common_ancestor(9, 6) == 6);</div>
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-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter N: &quot;</span>;</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>;</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>    }</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span> </div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>    clock_t start_time = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <a class="code hl_class" href="../../db/d82/classlarge__number.html">large_number</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../de/de4/fibonacci__large_8cpp.html#adf3e906875ab257f7fab3bc1370aa2db">fib</a>(N);</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    clock_t end_time = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    <span class="keywordtype">double</span> time_taken = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(end_time - start_time) /</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>                        <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(CLOCKS_PER_SEC);</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span> </div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>              &lt;&lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> &lt;&lt; <span class="stringliteral">&quot;^th Fibonacci number: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>              &lt;&lt; <span class="stringliteral">&quot;Number of digits: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.num_digits() &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>              &lt;&lt; <span class="stringliteral">&quot;Time taken: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/fixed.html">std::scientific</a> &lt;&lt; time_taken &lt;&lt; <span class="stringliteral">&quot; s&quot;</span></div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span> </div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 5000;</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <span class="keywordflow">if</span> (<a class="code hl_function" href="../../de/de4/fibonacci__large_8cpp.html#adf3e906875ab257f7fab3bc1370aa2db">fib</a>(N) ==</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        <a class="code hl_class" href="../../db/d82/classlarge__number.html">large_number</a>(</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>            <span class="stringliteral">&quot;387896845438832563370191630832590531208212771464624510616059721489&quot;</span></div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>            <span class="stringliteral">&quot;555013904403709701082291646221066947929345285888297381348310200895&quot;</span></div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>            <span class="stringliteral">&quot;498294036143015691147893836421656394410691021450563413370655865623&quot;</span></div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>            <span class="stringliteral">&quot;825465670071252592990385493381392883637834751890876297071203333705&quot;</span></div>
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-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>            <span class="stringliteral">&quot;035290330450584270114763524227021093463769910400671417488329842289&quot;</span></div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>            <span class="stringliteral">&quot;149127310405432875329804427367682297724498774987455569190770388063&quot;</span></div>
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-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>            <span class="stringliteral">&quot;0360311370547754724604639987588046985178408674382863125&quot;</span>))</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test for &quot;</span> &lt;&lt; N &lt;&lt; <span class="stringliteral">&quot;^th Fibonacci number passed!&quot;</span></div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>                  &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    <span class="keywordflow">else</span></div>
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-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>                  &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span> </div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   38</span>                                 {</div>
+<div class="line"><span class="lineno">   39</span>    uint64_t <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>;</div>
+<div class="line"><span class="lineno">   40</span>    <span class="keywordflow">if</span> (argc == 2) {</div>
+<div class="line"><span class="lineno">   41</span>        <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/strtoul.html">strtoull</a>(argv[1], NULL, 10);</div>
+<div class="line"><span class="lineno">   42</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   43</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter N: &quot;</span>;</div>
+<div class="line"><span class="lineno">   44</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>;</div>
+<div class="line"><span class="lineno">   45</span>    }</div>
+<div class="line"><span class="lineno">   46</span> </div>
+<div class="line"><span class="lineno">   47</span>    clock_t start_time = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">   48</span>    <a class="code hl_class" href="../../db/d82/classlarge__number.html">large_number</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../de/de4/fibonacci__large_8cpp.html#adf3e906875ab257f7fab3bc1370aa2db">fib</a>(N);</div>
+<div class="line"><span class="lineno">   49</span>    clock_t end_time = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><span class="lineno">   50</span>    <span class="keywordtype">double</span> time_taken = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(end_time - start_time) /</div>
+<div class="line"><span class="lineno">   51</span>                        <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(CLOCKS_PER_SEC);</div>
+<div class="line"><span class="lineno">   52</span> </div>
+<div class="line"><span class="lineno">   53</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
+<div class="line"><span class="lineno">   54</span>              &lt;&lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> &lt;&lt; <span class="stringliteral">&quot;^th Fibonacci number: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
+<div class="line"><span class="lineno">   55</span>              &lt;&lt; <span class="stringliteral">&quot;Number of digits: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.num_digits() &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
+<div class="line"><span class="lineno">   56</span>              &lt;&lt; <span class="stringliteral">&quot;Time taken: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/fixed.html">std::scientific</a> &lt;&lt; time_taken &lt;&lt; <span class="stringliteral">&quot; s&quot;</span></div>
+<div class="line"><span class="lineno">   57</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   58</span> </div>
+<div class="line"><span class="lineno">   59</span>    <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 5000;</div>
+<div class="line"><span class="lineno">   60</span>    <span class="keywordflow">if</span> (<a class="code hl_function" href="../../de/de4/fibonacci__large_8cpp.html#adf3e906875ab257f7fab3bc1370aa2db">fib</a>(N) ==</div>
+<div class="line"><span class="lineno">   61</span>        <a class="code hl_class" href="../../db/d82/classlarge__number.html">large_number</a>(</div>
+<div class="line"><span class="lineno">   62</span>            <span class="stringliteral">&quot;387896845438832563370191630832590531208212771464624510616059721489&quot;</span></div>
+<div class="line"><span class="lineno">   63</span>            <span class="stringliteral">&quot;555013904403709701082291646221066947929345285888297381348310200895&quot;</span></div>
+<div class="line"><span class="lineno">   64</span>            <span class="stringliteral">&quot;498294036143015691147893836421656394410691021450563413370655865623&quot;</span></div>
+<div class="line"><span class="lineno">   65</span>            <span class="stringliteral">&quot;825465670071252592990385493381392883637834751890876297071203333705&quot;</span></div>
+<div class="line"><span class="lineno">   66</span>            <span class="stringliteral">&quot;292310769300851809384980180384781399674888176555465378829164426891&quot;</span></div>
+<div class="line"><span class="lineno">   67</span>            <span class="stringliteral">&quot;298038461377896902150229308247566634622492307188332480328037503913&quot;</span></div>
+<div class="line"><span class="lineno">   68</span>            <span class="stringliteral">&quot;035290330450584270114763524227021093463769910400671417488329842289&quot;</span></div>
+<div class="line"><span class="lineno">   69</span>            <span class="stringliteral">&quot;149127310405432875329804427367682297724498774987455569190770388063&quot;</span></div>
+<div class="line"><span class="lineno">   70</span>            <span class="stringliteral">&quot;704683279481135897373999311010621930814901857081539785437919530561&quot;</span></div>
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+<div class="line"><span class="lineno">   72</span>            <span class="stringliteral">&quot;784902798823435102359984466393485325641195222185956306047536464547&quot;</span></div>
+<div class="line"><span class="lineno">   73</span>            <span class="stringliteral">&quot;076033090242080638258492915645287629157575914234380914230291749108&quot;</span></div>
+<div class="line"><span class="lineno">   74</span>            <span class="stringliteral">&quot;898415520985443248659407979357131684169286803954530954538869811466&quot;</span></div>
+<div class="line"><span class="lineno">   75</span>            <span class="stringliteral">&quot;508206686289742063932343848846524098874239587380197699382031717420&quot;</span></div>
+<div class="line"><span class="lineno">   76</span>            <span class="stringliteral">&quot;893226546887936400263079778005875912967138963421425257911687275560&quot;</span></div>
+<div class="line"><span class="lineno">   77</span>            <span class="stringliteral">&quot;0360311370547754724604639987588046985178408674382863125&quot;</span>))</div>
+<div class="line"><span class="lineno">   78</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test for &quot;</span> &lt;&lt; N &lt;&lt; <span class="stringliteral">&quot;^th Fibonacci number passed!&quot;</span></div>
+<div class="line"><span class="lineno">   79</span>                  &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   80</span>    <span class="keywordflow">else</span></div>
+<div class="line"><span class="lineno">   81</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Test for &quot;</span> &lt;&lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> &lt;&lt; <span class="stringliteral">&quot;^th Fibonacci number failed!&quot;</span></div>
+<div class="line"><span class="lineno">   82</span>                  &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   83</span> </div>
+<div class="line"><span class="lineno">   84</span>    <span class="keywordflow">return</span> 0;</div>
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@@ -249,7 +249,7 @@ Functions</h2></td></tr>
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+<div class="line"><span class="lineno">  173</span> </div>
+<div class="line"><span class="lineno">  174</span>    <span class="comment">// Get user input (by the command line parameters or the console after</span></div>
+<div class="line"><span class="lineno">  175</span>    <span class="comment">// displaying messages)</span></div>
+<div class="line"><span class="lineno">  176</span>    <span class="keywordflow">if</span> (argc == 4) {</div>
+<div class="line"><span class="lineno">  177</span>        <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">std::atoi</a>(argv[1]);</div>
+<div class="line"><span class="lineno">  178</span>        a = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a>(argv[2]);</div>
+<div class="line"><span class="lineno">  179</span>        b = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a>(argv[3]);</div>
+<div class="line"><span class="lineno">  180</span>        <span class="comment">// Check if a&lt;b else abort</span></div>
+<div class="line"><span class="lineno">  181</span>        assert(a &lt; b &amp;&amp; <span class="stringliteral">&quot;a has to be less than b&quot;</span>);</div>
+<div class="line"><span class="lineno">  182</span>        assert(N &gt; 0 &amp;&amp; <span class="stringliteral">&quot;N has to be &gt; 0&quot;</span>);</div>
+<div class="line"><span class="lineno">  183</span>        <span class="keywordflow">if</span> (N &lt; 4 || a != 1 || b != 3) {</div>
+<div class="line"><span class="lineno">  184</span>            used_argv_parameters = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  185</span>        }</div>
+<div class="line"><span class="lineno">  186</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;You selected N=&quot;</span> &lt;&lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> &lt;&lt; <span class="stringliteral">&quot;, a=&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, b=&quot;</span> &lt;&lt; b</div>
+<div class="line"><span class="lineno">  187</span>                  &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  188</span>    } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  189</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Default N=&quot;</span> &lt;&lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> &lt;&lt; <span class="stringliteral">&quot;, a=&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, b=&quot;</span> &lt;&lt; b</div>
+<div class="line"><span class="lineno">  190</span>                  &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  191</span>    }</div>
+<div class="line"><span class="lineno">  192</span> </div>
+<div class="line"><span class="lineno">  193</span>    <span class="comment">// Find the step</span></div>
+<div class="line"><span class="lineno">  194</span>    <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> = (b - a) / N;</div>
+<div class="line"><span class="lineno">  195</span> </div>
+<div class="line"><span class="lineno">  196</span>    <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#a2ae48a41e43dc6ab11b962742349646e">test</a>(N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, b, used_argv_parameters);  <span class="comment">// run self-test implementations</span></div>
+<div class="line"><span class="lineno">  197</span> </div>
+<div class="line"><span class="lineno">  198</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  199</span>}</div>
 <div class="ttc" id="aatof_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a></div><div class="ttdeci">T atof(T... args)</div></div>
 <div class="ttc" id="aatoi_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">std::atoi</a></div><div class="ttdeci">T atoi(T... args)</div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
@@ -437,37 +437,37 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>the result of the integration </dd></dl>
-<div class="fragment"><div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>                                                         {</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map&lt;int, double&gt;</a></div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>        data_table;  <span class="comment">// Contains the data points, key: i, value: f(xi)</span></div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    <span class="keywordtype">double</span> xi = a;   <span class="comment">// Initialize xi to the starting point x0 = a</span></div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span> </div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <span class="comment">// Create the data table</span></div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <span class="comment">// Loop from x0 to xN-1</span></div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <span class="keywordtype">double</span> temp = NAN;</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    <span class="keywordflow">for</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int32_t</a> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        temp = func(xi + <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> / 2);  <span class="comment">// find f(xi+h/2)</span></div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        data_table.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map/insert.html">insert</a>(</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;std::int32_t, double&gt;</a>(i, temp));  <span class="comment">// add i and f(xi)</span></div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        xi += <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>;  <span class="comment">// Get the next point xi for the next iteration</span></div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    }</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span> </div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <span class="comment">// Evaluate the integral.</span></div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    <span class="comment">// Remember: {f(x0+h/2) + f(x1+h/2) + ... + f(xN-1+h/2)}</span></div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>    <span class="keywordtype">double</span> evaluate_integral = 0;</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    <span class="keywordflow">for</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int32_t</a> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) evaluate_integral += data_table.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map/at.html">at</a>(i);</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span> </div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <span class="comment">// Multiply by the coefficient h</span></div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    evaluate_integral *= <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>;</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span> </div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>    <span class="comment">// If the result calculated is nan, then the user has given wrong input</span></div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <span class="comment">// interval.</span></div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    assert(!<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/isnan.html">std::isnan</a>(evaluate_integral) &amp;&amp;</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>           <span class="stringliteral">&quot;The definite integral can&#39;t be evaluated. Check the validity of &quot;</span></div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>           <span class="stringliteral">&quot;your input.\n&quot;</span>);</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    <span class="comment">// Else return</span></div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <span class="keywordflow">return</span> evaluate_integral;</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   53</span>                                                         {</div>
+<div class="line"><span class="lineno">   54</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map&lt;int, double&gt;</a></div>
+<div class="line"><span class="lineno">   55</span>        data_table;  <span class="comment">// Contains the data points, key: i, value: f(xi)</span></div>
+<div class="line"><span class="lineno">   56</span>    <span class="keywordtype">double</span> xi = a;   <span class="comment">// Initialize xi to the starting point x0 = a</span></div>
+<div class="line"><span class="lineno">   57</span> </div>
+<div class="line"><span class="lineno">   58</span>    <span class="comment">// Create the data table</span></div>
+<div class="line"><span class="lineno">   59</span>    <span class="comment">// Loop from x0 to xN-1</span></div>
+<div class="line"><span class="lineno">   60</span>    <span class="keywordtype">double</span> temp = NAN;</div>
+<div class="line"><span class="lineno">   61</span>    <span class="keywordflow">for</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int32_t</a> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
+<div class="line"><span class="lineno">   62</span>        temp = func(xi + <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> / 2);  <span class="comment">// find f(xi+h/2)</span></div>
+<div class="line"><span class="lineno">   63</span>        data_table.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map/insert.html">insert</a>(</div>
+<div class="line"><span class="lineno">   64</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;std::int32_t, double&gt;</a>(i, temp));  <span class="comment">// add i and f(xi)</span></div>
+<div class="line"><span class="lineno">   65</span>        xi += <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>;  <span class="comment">// Get the next point xi for the next iteration</span></div>
+<div class="line"><span class="lineno">   66</span>    }</div>
+<div class="line"><span class="lineno">   67</span> </div>
+<div class="line"><span class="lineno">   68</span>    <span class="comment">// Evaluate the integral.</span></div>
+<div class="line"><span class="lineno">   69</span>    <span class="comment">// Remember: {f(x0+h/2) + f(x1+h/2) + ... + f(xN-1+h/2)}</span></div>
+<div class="line"><span class="lineno">   70</span>    <span class="keywordtype">double</span> evaluate_integral = 0;</div>
+<div class="line"><span class="lineno">   71</span>    <span class="keywordflow">for</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int32_t</a> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) evaluate_integral += data_table.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map/at.html">at</a>(i);</div>
+<div class="line"><span class="lineno">   72</span> </div>
+<div class="line"><span class="lineno">   73</span>    <span class="comment">// Multiply by the coefficient h</span></div>
+<div class="line"><span class="lineno">   74</span>    evaluate_integral *= <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>;</div>
+<div class="line"><span class="lineno">   75</span> </div>
+<div class="line"><span class="lineno">   76</span>    <span class="comment">// If the result calculated is nan, then the user has given wrong input</span></div>
+<div class="line"><span class="lineno">   77</span>    <span class="comment">// interval.</span></div>
+<div class="line"><span class="lineno">   78</span>    assert(!<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/isnan.html">std::isnan</a>(evaluate_integral) &amp;&amp;</div>
+<div class="line"><span class="lineno">   79</span>           <span class="stringliteral">&quot;The definite integral can&#39;t be evaluated. Check the validity of &quot;</span></div>
+<div class="line"><span class="lineno">   80</span>           <span class="stringliteral">&quot;your input.\n&quot;</span>);</div>
+<div class="line"><span class="lineno">   81</span>    <span class="comment">// Else return</span></div>
+<div class="line"><span class="lineno">   82</span>    <span class="keywordflow">return</span> evaluate_integral;</div>
+<div class="line"><span class="lineno">   83</span>}</div>
 <div class="ttc" id="aat_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/map/at.html">std::map::at</a></div><div class="ttdeci">T at(T... args)</div></div>
 <div class="ttc" id="ainsert_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/map/insert.html">std::map::insert</a></div><div class="ttdeci">T insert(T... args)</div></div>
 <div class="ttc" id="aisnan_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/isnan.html">std::isnan</a></div><div class="ttdeci">T isnan(T... args)</div></div>
@@ -545,37 +545,37 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>                                            {</div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>    <span class="comment">// Call midpoint() for each of the test functions f, g, k, l</span></div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    <span class="comment">// Assert with two decimal point precision</span></div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    <span class="keywordtype">double</span> result_f = <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>        N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::f);</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    assert((used_argv_parameters || (result_f &gt;= 4.09 &amp;&amp; result_f &lt;= 4.10)) &amp;&amp;</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>           <span class="stringliteral">&quot;The result of f(x) is wrong&quot;</span>);</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The result of integral f(x) on interval [&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; b</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>              &lt;&lt; <span class="stringliteral">&quot;] is equal to: &quot;</span> &lt;&lt; result_f &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span> </div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    <span class="keywordtype">double</span> result_g = <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>        N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::g);</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    assert((used_argv_parameters || (result_g &gt;= 0.27 &amp;&amp; result_g &lt;= 0.28)) &amp;&amp;</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>           <span class="stringliteral">&quot;The result of g(x) is wrong&quot;</span>);</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The result of integral g(x) on interval [&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; b</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>              &lt;&lt; <span class="stringliteral">&quot;] is equal to: &quot;</span> &lt;&lt; result_g &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span> </div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    <span class="keywordtype">double</span> result_k = <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>        N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::k);</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    assert((used_argv_parameters || (result_k &gt;= 9.06 &amp;&amp; result_k &lt;= 9.07)) &amp;&amp;</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>           <span class="stringliteral">&quot;The result of k(x) is wrong&quot;</span>);</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The result of integral k(x) on interval [&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; b</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>              &lt;&lt; <span class="stringliteral">&quot;] is equal to: &quot;</span> &lt;&lt; result_k &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span> </div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>    <span class="keywordtype">double</span> result_l = <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>        N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::l);</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    assert((used_argv_parameters || (result_l &gt;= 7.16 &amp;&amp; result_l &lt;= 7.17)) &amp;&amp;</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>           <span class="stringliteral">&quot;The result of l(x) is wrong&quot;</span>);</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The result of integral l(x) on interval [&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; b</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>              &lt;&lt; <span class="stringliteral">&quot;] is equal to: &quot;</span> &lt;&lt; result_l &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  124</span>                                            {</div>
+<div class="line"><span class="lineno">  125</span>    <span class="comment">// Call midpoint() for each of the test functions f, g, k, l</span></div>
+<div class="line"><span class="lineno">  126</span>    <span class="comment">// Assert with two decimal point precision</span></div>
+<div class="line"><span class="lineno">  127</span>    <span class="keywordtype">double</span> result_f = <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
+<div class="line"><span class="lineno">  128</span>        N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::f);</div>
+<div class="line"><span class="lineno">  129</span>    assert((used_argv_parameters || (result_f &gt;= 4.09 &amp;&amp; result_f &lt;= 4.10)) &amp;&amp;</div>
+<div class="line"><span class="lineno">  130</span>           <span class="stringliteral">&quot;The result of f(x) is wrong&quot;</span>);</div>
+<div class="line"><span class="lineno">  131</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The result of integral f(x) on interval [&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; b</div>
+<div class="line"><span class="lineno">  132</span>              &lt;&lt; <span class="stringliteral">&quot;] is equal to: &quot;</span> &lt;&lt; result_f &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  133</span> </div>
+<div class="line"><span class="lineno">  134</span>    <span class="keywordtype">double</span> result_g = <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
+<div class="line"><span class="lineno">  135</span>        N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::g);</div>
+<div class="line"><span class="lineno">  136</span>    assert((used_argv_parameters || (result_g &gt;= 0.27 &amp;&amp; result_g &lt;= 0.28)) &amp;&amp;</div>
+<div class="line"><span class="lineno">  137</span>           <span class="stringliteral">&quot;The result of g(x) is wrong&quot;</span>);</div>
+<div class="line"><span class="lineno">  138</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The result of integral g(x) on interval [&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; b</div>
+<div class="line"><span class="lineno">  139</span>              &lt;&lt; <span class="stringliteral">&quot;] is equal to: &quot;</span> &lt;&lt; result_g &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  140</span> </div>
+<div class="line"><span class="lineno">  141</span>    <span class="keywordtype">double</span> result_k = <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
+<div class="line"><span class="lineno">  142</span>        N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::k);</div>
+<div class="line"><span class="lineno">  143</span>    assert((used_argv_parameters || (result_k &gt;= 9.06 &amp;&amp; result_k &lt;= 9.07)) &amp;&amp;</div>
+<div class="line"><span class="lineno">  144</span>           <span class="stringliteral">&quot;The result of k(x) is wrong&quot;</span>);</div>
+<div class="line"><span class="lineno">  145</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The result of integral k(x) on interval [&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; b</div>
+<div class="line"><span class="lineno">  146</span>              &lt;&lt; <span class="stringliteral">&quot;] is equal to: &quot;</span> &lt;&lt; result_k &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  147</span> </div>
+<div class="line"><span class="lineno">  148</span>    <span class="keywordtype">double</span> result_l = <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
+<div class="line"><span class="lineno">  149</span>        N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::l);</div>
+<div class="line"><span class="lineno">  150</span>    assert((used_argv_parameters || (result_l &gt;= 7.16 &amp;&amp; result_l &lt;= 7.17)) &amp;&amp;</div>
+<div class="line"><span class="lineno">  151</span>           <span class="stringliteral">&quot;The result of l(x) is wrong&quot;</span>);</div>
+<div class="line"><span class="lineno">  152</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The result of integral l(x) on interval [&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; b</div>
+<div class="line"><span class="lineno">  153</span>              &lt;&lt; <span class="stringliteral">&quot;] is equal to: &quot;</span> &lt;&lt; result_l &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  154</span>}</div>
 <div class="ttc" id="amidpoint__integral__method_8cpp_html_a7072493d1f0f8a91b2a71d4cc456c09c"><div class="ttname"><a href="../../df/d11/midpoint__integral__method_8cpp.html#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a></div><div class="ttdeci">double midpoint(const std::int32_t N, const double h, const double a, const std::function&lt; double(double)&gt; &amp;func)</div><div class="ttdoc">Main function for implementing the Midpoint Integral Method implementation.</div><div class="ttdef"><b>Definition:</b> midpoint_integral_method.cpp:52</div></div>
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-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
+  <td id="projectalign">
    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
    </div>
    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
 </table>
 </div>
 <!-- end header part -->
-<!-- Generated by Doxygen 1.9.2 -->
+<!-- Generated by Doxygen 1.9.3 -->
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@@ -129,7 +129,8 @@ Functions</h2></td></tr>
 </table>
 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
 <div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Disjoint-set-data_structure" target="_blank">DSU (Disjoint sets)</a> </p>
-<p >dsu : It is a very powerful data structure which keeps track of different clusters(sets) of elements, these sets are disjoint(doesnot have a common element). Disjoint sets uses cases : for finding connected components in a graph, used in Kruskal's algorithm for finding <a class="el" href="../../d4/d12/namespace_minimum.html" title="Implementation of Minimum Edit Distance algorithm.">Minimum</a> Spanning tree. Operations that can be performed: 1) UnionSet(i,j): add(element i and j to the set) 2) findSet(i): returns the representative of the set to which i belogngs to. 3) getParents(i): prints the parent of i and so on and so forth. Below is the class-based approach which uses the heuristic of union-ranks. Using union-rank in findSet(i),we are able to get to the representative of i in slightly delayed O(logN) time but it allows us to keep tracks of the parent of i. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/AayushVyasKIIT" target="_blank">AayushVyasKIIT</a> </dd></dl>
+<p >dsu : It is a very powerful data structure which keeps track of different clusters(sets) of elements, these sets are disjoint(doesnot have a common
+element). Disjoint sets uses cases : for finding connected components in a graph, used in Kruskal's algorithm for finding <a class="el" href="../../d4/d12/namespace_minimum.html" title="Implementation of Minimum Edit Distance algorithm.">Minimum</a> Spanning tree. Operations that can be performed: 1) UnionSet(i,j): add(element i and j to the set) 2) findSet(i): returns the representative of the set to which i belogngs to. 3) getParents(i): prints the parent of i and so on and so forth. Below is the class-based approach which uses the heuristic of union-ranks. Using union-rank in findSet(i),we are able to get to the representative of i in slightly delayed O(logN) time but it allows us to keep tracks of the parent of i. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/AayushVyasKIIT" target="_blank">AayushVyasKIIT</a> </dd></dl>
 <dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d3/dae/dsu__path__compression_8cpp.html" title="DSU (Disjoint sets)">dsu_path_compression.cpp</a> </dd></dl>
 </div><h2 class="groupheader">Function Documentation</h2>
 <a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
@@ -150,18 +151,18 @@ Functions</h2></td></tr>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>           {</div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>    <a class="code hl_function" href="../../df/d28/dsu__union__rank_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a>();  <span class="comment">// run 1st test case</span></div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>    <a class="code hl_function" href="../../df/d28/dsu__union__rank_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a>();  <span class="comment">// run 2nd test case</span></div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span> </div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  182</span>           {</div>
+<div class="line"><span class="lineno">  183</span>    <a class="code hl_function" href="../../df/d28/dsu__union__rank_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a>();  <span class="comment">// run 1st test case</span></div>
+<div class="line"><span class="lineno">  184</span>    <a class="code hl_function" href="../../df/d28/dsu__union__rank_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a>();  <span class="comment">// run 2nd test case</span></div>
+<div class="line"><span class="lineno">  185</span> </div>
+<div class="line"><span class="lineno">  186</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  187</span>}</div>
 <div class="ttc" id="adsu__union__rank_8cpp_html_a45d94ead4cf4e1ff9f87c38bc99f59ae"><div class="ttname"><a href="../../df/d28/dsu__union__rank_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a></div><div class="ttdeci">static void test2()</div><div class="ttdoc">Self-implementations, 2nd test.</div><div class="ttdef"><b>Definition:</b> dsu_union_rank.cpp:157</div></div>
 <div class="ttc" id="adsu__union__rank_8cpp_html_ae7880ce913f3058a35ff106d5be9e243"><div class="ttname"><a href="../../df/d28/dsu__union__rank_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a></div><div class="ttdeci">static void test1()</div><div class="ttdoc">Self-implementations, 1st test.</div><div class="ttdef"><b>Definition:</b> dsu_union_rank.cpp:133</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/d28/dsu__union__rank_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="606" height="207"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/d28/dsu__union__rank_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="606" height="230"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
 </div>
 </div>
 
@@ -195,26 +196,26 @@ Here is the call graph for this function:</div>
 <p >&lt; number of elements</p>
 <p >&lt; object of class disjoint sets</p>
 <p >&lt; performs union operation on 1 and 2</p>
-<div class="fragment"><div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>                    {</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    <span class="comment">/* checks the parents in the resultant structures */</span></div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    uint64_t n = 10;   <span class="comment">///&lt; number of elements</span></div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1);      <span class="comment">///&lt; object of class disjoint sets</span></div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    d.unionSet(2, 1);  <span class="comment">///&lt; performs union operation on 1 and 2</span></div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    d.unionSet(1, 4);</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>    d.unionSet(8, 1);</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>    d.unionSet(3, 5);</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    d.unionSet(5, 6);</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    d.unionSet(5, 7);</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    d.unionSet(9, 10);</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    d.unionSet(2, 10);</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <span class="comment">// keeping track of the changes using parent pointers</span></div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = {7, 5};</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.size(); i++) {</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>        assert(d.getParents(7).at(i) ==</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>               <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>[i]);  <span class="comment">// makes sure algorithm works fine</span></div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    }</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test passed!&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  133</span>                    {</div>
+<div class="line"><span class="lineno">  134</span>    <span class="comment">/* checks the parents in the resultant structures */</span></div>
+<div class="line"><span class="lineno">  135</span>    uint64_t n = 10;   <span class="comment">///&lt; number of elements</span></div>
+<div class="line"><span class="lineno">  136</span>    <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1);      <span class="comment">///&lt; object of class disjoint sets</span></div>
+<div class="line"><span class="lineno">  137</span>    d.unionSet(2, 1);  <span class="comment">///&lt; performs union operation on 1 and 2</span></div>
+<div class="line"><span class="lineno">  138</span>    d.unionSet(1, 4);</div>
+<div class="line"><span class="lineno">  139</span>    d.unionSet(8, 1);</div>
+<div class="line"><span class="lineno">  140</span>    d.unionSet(3, 5);</div>
+<div class="line"><span class="lineno">  141</span>    d.unionSet(5, 6);</div>
+<div class="line"><span class="lineno">  142</span>    d.unionSet(5, 7);</div>
+<div class="line"><span class="lineno">  143</span>    d.unionSet(9, 10);</div>
+<div class="line"><span class="lineno">  144</span>    d.unionSet(2, 10);</div>
+<div class="line"><span class="lineno">  145</span>    <span class="comment">// keeping track of the changes using parent pointers</span></div>
+<div class="line"><span class="lineno">  146</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = {7, 5};</div>
+<div class="line"><span class="lineno">  147</span>    <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.size(); i++) {</div>
+<div class="line"><span class="lineno">  148</span>        assert(d.getParents(7).at(i) ==</div>
+<div class="line"><span class="lineno">  149</span>               <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>[i]);  <span class="comment">// makes sure algorithm works fine</span></div>
+<div class="line"><span class="lineno">  150</span>    }</div>
+<div class="line"><span class="lineno">  151</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test passed!&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
+<div class="line"><span class="lineno">  152</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aclassdsu_html"><div class="ttname"><a href="../../dd/d1f/classdsu.html">dsu</a></div><div class="ttdoc">Disjoint sets union data structure, class based representation.</div><div class="ttdef"><b>Definition:</b> dsu_path_compression.cpp:33</div></div>
 <div class="ttc" id="amatrix__exponentiation_8cpp_html_a600eaf353befc174637855795f12d258"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a></div><div class="ttdeci">#define endl</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:36</div></div>
@@ -223,7 +224,7 @@ Here is the call graph for this function:</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/d28/dsu__union__rank_8cpp_ae7880ce913f3058a35ff106d5be9e243_cgraph.svg" width="507" height="190"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/d28/dsu__union__rank_8cpp_ae7880ce913f3058a35ff106d5be9e243_cgraph.svg" width="507" height="215"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
 </div>
 </div>
 
@@ -259,31 +260,31 @@ Here is the call graph for this function:</div>
 <p >performs union operation on 1 and 2</p>
 <p >keeping track of the changes using parent pointers</p>
 <p >makes sure algorithm works fine</p>
-<div class="fragment"><div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>                    {</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    <span class="comment">// checks the parents in the resultant structures</span></div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>    uint64_t n = 10;   <span class="comment">///&lt; number of elements</span></div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>    <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1);      <span class="comment">///&lt; object of class disjoint sets</span></div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>    d.unionSet(2, 1);  <span class="comment">/// performs union operation on 1 and 2</span></div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>    d.unionSet(1, 4);</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>    d.unionSet(8, 1);</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>    d.unionSet(3, 5);</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>    d.unionSet(5, 6);</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    d.unionSet(5, 7);</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>    d.unionSet(9, 10);</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    d.unionSet(2, 10);</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span><span class="comment"></span> </div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span><span class="comment">    /// keeping track of the changes using parent pointers</span></div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = {2, 1, 10};</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>    <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.size(); i++) {</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>        assert(d.getParents(2).at(i) ==</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>               <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>[i]);  <span class="comment">/// makes sure algorithm works fine</span></div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>    }</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test passed!&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  157</span>                    {</div>
+<div class="line"><span class="lineno">  158</span>    <span class="comment">// checks the parents in the resultant structures</span></div>
+<div class="line"><span class="lineno">  159</span>    uint64_t n = 10;   <span class="comment">///&lt; number of elements</span></div>
+<div class="line"><span class="lineno">  160</span>    <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1);      <span class="comment">///&lt; object of class disjoint sets</span></div>
+<div class="line"><span class="lineno">  161</span>    d.unionSet(2, 1);  <span class="comment">/// performs union operation on 1 and 2</span></div>
+<div class="line"><span class="lineno">  162</span>    d.unionSet(1, 4);</div>
+<div class="line"><span class="lineno">  163</span>    d.unionSet(8, 1);</div>
+<div class="line"><span class="lineno">  164</span>    d.unionSet(3, 5);</div>
+<div class="line"><span class="lineno">  165</span>    d.unionSet(5, 6);</div>
+<div class="line"><span class="lineno">  166</span>    d.unionSet(5, 7);</div>
+<div class="line"><span class="lineno">  167</span>    d.unionSet(9, 10);</div>
+<div class="line"><span class="lineno">  168</span>    d.unionSet(2, 10);</div>
+<div class="line"><span class="lineno">  169</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  170</span><span class="comment">    /// keeping track of the changes using parent pointers</span></div>
+<div class="line"><span class="lineno">  171</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = {2, 1, 10};</div>
+<div class="line"><span class="lineno">  172</span>    <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.size(); i++) {</div>
+<div class="line"><span class="lineno">  173</span>        assert(d.getParents(2).at(i) ==</div>
+<div class="line"><span class="lineno">  174</span>               <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>[i]);  <span class="comment">/// makes sure algorithm works fine</span></div>
+<div class="line"><span class="lineno">  175</span>    }</div>
+<div class="line"><span class="lineno">  176</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test passed!&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
+<div class="line"><span class="lineno">  177</span>}</div>
 </div><!-- fragment --><div class="dynheader">
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-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
+  <td id="projectalign">
    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
    </div>
    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
 </table>
 </div>
 <!-- end header part -->
-<!-- Generated by Doxygen 1.9.2 -->
+<!-- Generated by Doxygen 1.9.3 -->
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 /* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
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@@ -178,12 +178,12 @@ Functions</h2></td></tr>
 
 <p>Main function. </p>
 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>           {</div>
-<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>    <a class="code hl_function" href="../../df/d2c/elliptic__curve__key__exchange_8cpp.html#a8800c8a84d77dadadb05ad5e83b77ef4">uint128_t_tests</a>();  <span class="comment">// running predefined 128-bit unsigned integer tests</span></div>
-<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>    <a class="code hl_function" href="../../df/d2c/elliptic__curve__key__exchange_8cpp.html#a37775d1724ffe404c088dabbc8da91ae">uint256_t_tests</a>();  <span class="comment">// running predefined 256-bit unsigned integer tests</span></div>
-<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>    <a class="code hl_function" href="../../df/d2c/elliptic__curve__key__exchange_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();             <span class="comment">// running self-test implementations</span></div>
-<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  320</span>           {</div>
+<div class="line"><span class="lineno">  321</span>    <a class="code hl_function" href="../../df/d2c/elliptic__curve__key__exchange_8cpp.html#a8800c8a84d77dadadb05ad5e83b77ef4">uint128_t_tests</a>();  <span class="comment">// running predefined 128-bit unsigned integer tests</span></div>
+<div class="line"><span class="lineno">  322</span>    <a class="code hl_function" href="../../df/d2c/elliptic__curve__key__exchange_8cpp.html#a37775d1724ffe404c088dabbc8da91ae">uint256_t_tests</a>();  <span class="comment">// running predefined 256-bit unsigned integer tests</span></div>
+<div class="line"><span class="lineno">  323</span>    <a class="code hl_function" href="../../df/d2c/elliptic__curve__key__exchange_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();             <span class="comment">// running self-test implementations</span></div>
+<div class="line"><span class="lineno">  324</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  325</span>}</div>
 <div class="ttc" id="aelliptic__curve__key__exchange_8cpp_html_a37775d1724ffe404c088dabbc8da91ae"><div class="ttname"><a href="../../df/d2c/elliptic__curve__key__exchange_8cpp.html#a37775d1724ffe404c088dabbc8da91ae">uint256_t_tests</a></div><div class="ttdeci">static void uint256_t_tests()</div><div class="ttdoc">Function to test the uint256_t header.</div><div class="ttdef"><b>Definition:</b> elliptic_curve_key_exchange.cpp:230</div></div>
 <div class="ttc" id="aelliptic__curve__key__exchange_8cpp_html_a8800c8a84d77dadadb05ad5e83b77ef4"><div class="ttname"><a href="../../df/d2c/elliptic__curve__key__exchange_8cpp.html#a8800c8a84d77dadadb05ad5e83b77ef4">uint128_t_tests</a></div><div class="ttdeci">static void uint128_t_tests()</div><div class="ttdoc">Function to test the uint128_t header.</div><div class="ttdef"><b>Definition:</b> elliptic_curve_key_exchange.cpp:197</div></div>
 <div class="ttc" id="aelliptic__curve__key__exchange_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../df/d2c/elliptic__curve__key__exchange_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Function to test the provided algorithm above.</div><div class="ttdef"><b>Definition:</b> elliptic_curve_key_exchange.cpp:267</div></div>
@@ -221,54 +221,54 @@ Here is the call graph for this function:</div>
 
 <p>Function to test the provided algorithm above. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>                   {</div>
-<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>    <span class="comment">// demonstration of key exchange using curve secp112r1</span></div>
-<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span> </div>
-<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>    <span class="comment">// Equation of the form y^2 = (x^3 + ax + b) % P (here p is mod)</span></div>
-<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>    <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> a(<span class="stringliteral">&quot;4451685225093714772084598273548424&quot;</span>),</div>
-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>        b(<span class="stringliteral">&quot;2061118396808653202902996166388514&quot;</span>),</div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>        mod(<span class="stringliteral">&quot;4451685225093714772084598273548427&quot;</span>);</div>
-<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span> </div>
-<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>    <span class="comment">// Generator value: is pre-defined for the given curve</span></div>
-<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>    <a class="code hl_struct" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">ciphers::elliptic_curve_key_exchange::Point</a> ptr = {</div>
-<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;188281465057972534892223778713752&quot;</span>),</div>
-<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;3419875491033170827167861896082688&quot;</span>)};</div>
-<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span> </div>
-<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>    <span class="comment">// Shared key generation.</span></div>
-<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>    <span class="comment">// For alice</span></div>
-<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;For alice:\n&quot;</span>;</div>
-<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>    <span class="comment">// Alice&#39;s private key (can be generated randomly)</span></div>
-<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>    <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> alice_private_key(<span class="stringliteral">&quot;164330438812053169644452143505618&quot;</span>);</div>
-<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>    <a class="code hl_struct" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">ciphers::elliptic_curve_key_exchange::Point</a> alice_public_key =</div>
-<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>        <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#a17f3d667241b88115a95282cdd719cb2">multiply</a>(ptr, a, alice_private_key, mod);</div>
-<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPrivate key: &quot;</span> &lt;&lt; alice_private_key &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPublic Key: &quot;</span> &lt;&lt; alice_public_key &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span> </div>
-<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>    <span class="comment">// For Bob</span></div>
-<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;For Bob:\n&quot;</span>;</div>
-<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>    <span class="comment">// Bob&#39;s private key (can be generated randomly)</span></div>
-<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>    <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> bob_private_key(<span class="stringliteral">&quot;1959473333748537081510525763478373&quot;</span>);</div>
-<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>    <a class="code hl_struct" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">ciphers::elliptic_curve_key_exchange::Point</a> bob_public_key =</div>
-<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span>        <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#a17f3d667241b88115a95282cdd719cb2">multiply</a>(ptr, a, bob_private_key, mod);</div>
-<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPrivate key: &quot;</span> &lt;&lt; bob_private_key &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPublic Key: &quot;</span> &lt;&lt; bob_public_key &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span> </div>
-<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>    <span class="comment">// After public key exchange, create a shared key for communication.</span></div>
-<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span>    <span class="comment">// create shared key:</span></div>
-<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span>    <a class="code hl_struct" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">ciphers::elliptic_curve_key_exchange::Point</a> alice_shared_key = <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#a17f3d667241b88115a95282cdd719cb2">multiply</a>(</div>
-<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span>                                                    bob_public_key, a,</div>
-<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span>                                                    alice_private_key, mod),</div>
-<div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span>                                                bob_shared_key = <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#a17f3d667241b88115a95282cdd719cb2">multiply</a>(</div>
-<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span>                                                    alice_public_key, a,</div>
-<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>                                                    bob_private_key, mod);</div>
-<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span> </div>
-<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Shared keys:\n&quot;</span>;</div>
-<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; alice_shared_key &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; bob_shared_key &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span> </div>
-<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>    <span class="comment">// Check whether shared keys are equal</span></div>
-<div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span>    assert(alice_shared_key == bob_shared_key);</div>
-<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  267</span>                   {</div>
+<div class="line"><span class="lineno">  268</span>    <span class="comment">// demonstration of key exchange using curve secp112r1</span></div>
+<div class="line"><span class="lineno">  269</span> </div>
+<div class="line"><span class="lineno">  270</span>    <span class="comment">// Equation of the form y^2 = (x^3 + ax + b) % P (here p is mod)</span></div>
+<div class="line"><span class="lineno">  271</span>    <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> a(<span class="stringliteral">&quot;4451685225093714772084598273548424&quot;</span>),</div>
+<div class="line"><span class="lineno">  272</span>        b(<span class="stringliteral">&quot;2061118396808653202902996166388514&quot;</span>),</div>
+<div class="line"><span class="lineno">  273</span>        mod(<span class="stringliteral">&quot;4451685225093714772084598273548427&quot;</span>);</div>
+<div class="line"><span class="lineno">  274</span> </div>
+<div class="line"><span class="lineno">  275</span>    <span class="comment">// Generator value: is pre-defined for the given curve</span></div>
+<div class="line"><span class="lineno">  276</span>    <a class="code hl_struct" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">ciphers::elliptic_curve_key_exchange::Point</a> ptr = {</div>
+<div class="line"><span class="lineno">  277</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;188281465057972534892223778713752&quot;</span>),</div>
+<div class="line"><span class="lineno">  278</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;3419875491033170827167861896082688&quot;</span>)};</div>
+<div class="line"><span class="lineno">  279</span> </div>
+<div class="line"><span class="lineno">  280</span>    <span class="comment">// Shared key generation.</span></div>
+<div class="line"><span class="lineno">  281</span>    <span class="comment">// For alice</span></div>
+<div class="line"><span class="lineno">  282</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;For alice:\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  283</span>    <span class="comment">// Alice&#39;s private key (can be generated randomly)</span></div>
+<div class="line"><span class="lineno">  284</span>    <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> alice_private_key(<span class="stringliteral">&quot;164330438812053169644452143505618&quot;</span>);</div>
+<div class="line"><span class="lineno">  285</span>    <a class="code hl_struct" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">ciphers::elliptic_curve_key_exchange::Point</a> alice_public_key =</div>
+<div class="line"><span class="lineno">  286</span>        <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#a17f3d667241b88115a95282cdd719cb2">multiply</a>(ptr, a, alice_private_key, mod);</div>
+<div class="line"><span class="lineno">  287</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPrivate key: &quot;</span> &lt;&lt; alice_private_key &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  288</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPublic Key: &quot;</span> &lt;&lt; alice_public_key &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  289</span> </div>
+<div class="line"><span class="lineno">  290</span>    <span class="comment">// For Bob</span></div>
+<div class="line"><span class="lineno">  291</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;For Bob:\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  292</span>    <span class="comment">// Bob&#39;s private key (can be generated randomly)</span></div>
+<div class="line"><span class="lineno">  293</span>    <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> bob_private_key(<span class="stringliteral">&quot;1959473333748537081510525763478373&quot;</span>);</div>
+<div class="line"><span class="lineno">  294</span>    <a class="code hl_struct" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">ciphers::elliptic_curve_key_exchange::Point</a> bob_public_key =</div>
+<div class="line"><span class="lineno">  295</span>        <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#a17f3d667241b88115a95282cdd719cb2">multiply</a>(ptr, a, bob_private_key, mod);</div>
+<div class="line"><span class="lineno">  296</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPrivate key: &quot;</span> &lt;&lt; bob_private_key &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  297</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPublic Key: &quot;</span> &lt;&lt; bob_public_key &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  298</span> </div>
+<div class="line"><span class="lineno">  299</span>    <span class="comment">// After public key exchange, create a shared key for communication.</span></div>
+<div class="line"><span class="lineno">  300</span>    <span class="comment">// create shared key:</span></div>
+<div class="line"><span class="lineno">  301</span>    <a class="code hl_struct" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">ciphers::elliptic_curve_key_exchange::Point</a> alice_shared_key = <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#a17f3d667241b88115a95282cdd719cb2">multiply</a>(</div>
+<div class="line"><span class="lineno">  302</span>                                                    bob_public_key, a,</div>
+<div class="line"><span class="lineno">  303</span>                                                    alice_private_key, mod),</div>
+<div class="line"><span class="lineno">  304</span>                                                bob_shared_key = <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#a17f3d667241b88115a95282cdd719cb2">multiply</a>(</div>
+<div class="line"><span class="lineno">  305</span>                                                    alice_public_key, a,</div>
+<div class="line"><span class="lineno">  306</span>                                                    bob_private_key, mod);</div>
+<div class="line"><span class="lineno">  307</span> </div>
+<div class="line"><span class="lineno">  308</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Shared keys:\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  309</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; alice_shared_key &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  310</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; bob_shared_key &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  311</span> </div>
+<div class="line"><span class="lineno">  312</span>    <span class="comment">// Check whether shared keys are equal</span></div>
+<div class="line"><span class="lineno">  313</span>    assert(alice_shared_key == bob_shared_key);</div>
+<div class="line"><span class="lineno">  314</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aclassuint256__t_html"><div class="ttname"><a href="../../d1/d83/classuint256__t.html">uint256_t</a></div><div class="ttdoc">class for 256-bit unsigned integer</div><div class="ttdef"><b>Definition:</b> uint256_t.hpp:33</div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
@@ -308,33 +308,33 @@ Here is the call graph for this function:</div>
 
 <p>Function to test the <a class="el" href="../../db/d9a/classuint128__t.html" title="class for 128-bit unsigned integer">uint128_t</a> header. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>                              {</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>    <span class="comment">// 1st test: Operations test</span></div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>    <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> a(<span class="stringliteral">&quot;122&quot;</span>), b(<span class="stringliteral">&quot;2312&quot;</span>);</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    assert(a + b == 2434);</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>    assert(b - a == 2190);</div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>    assert(a * b == 282064);</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>    assert(b / a == 18);</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>    assert(b % a == 116);</div>
-<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    assert((a &amp; b) == 8);</div>
-<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    assert((a | b) == 2426);</div>
-<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>    assert((a ^ b) == 2418);</div>
-<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    assert((a &lt;&lt; 64) == <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(<span class="stringliteral">&quot;2250502776992565297152&quot;</span>));</div>
-<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>    assert((b &gt;&gt; 7) == 18);</div>
-<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span> </div>
-<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>    <span class="comment">// 2nd test: Operations test</span></div>
-<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>    a = <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(<span class="stringliteral">&quot;12321421424232142122&quot;</span>);</div>
-<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>    b = <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(<span class="stringliteral">&quot;23123212&quot;</span>);</div>
-<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>    assert(a + b == <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(<span class="stringliteral">&quot;12321421424255265334&quot;</span>));</div>
-<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>    assert(a - b == <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(<span class="stringliteral">&quot;12321421424209018910&quot;</span>));</div>
-<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>    assert(a * b == <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(<span class="stringliteral">&quot;284910839733861759501135864&quot;</span>));</div>
-<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>    assert(a / b == 532859423865LL);</div>
-<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>    assert(a % b == 3887742);</div>
-<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>    assert((a &amp; b) == 18912520);</div>
-<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>    assert((a | b) == <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(<span class="stringliteral">&quot;12321421424236352814&quot;</span>));</div>
-<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>    assert((a ^ b) == <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(<span class="stringliteral">&quot;12321421424217440294&quot;</span>));</div>
-<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>    assert((a &lt;&lt; 64) == <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(<span class="stringliteral">&quot;227290107637132170748078080907806769152&quot;</span>));</div>
-<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  197</span>                              {</div>
+<div class="line"><span class="lineno">  198</span>    <span class="comment">// 1st test: Operations test</span></div>
+<div class="line"><span class="lineno">  199</span>    <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> a(<span class="stringliteral">&quot;122&quot;</span>), b(<span class="stringliteral">&quot;2312&quot;</span>);</div>
+<div class="line"><span class="lineno">  200</span>    assert(a + b == 2434);</div>
+<div class="line"><span class="lineno">  201</span>    assert(b - a == 2190);</div>
+<div class="line"><span class="lineno">  202</span>    assert(a * b == 282064);</div>
+<div class="line"><span class="lineno">  203</span>    assert(b / a == 18);</div>
+<div class="line"><span class="lineno">  204</span>    assert(b % a == 116);</div>
+<div class="line"><span class="lineno">  205</span>    assert((a &amp; b) == 8);</div>
+<div class="line"><span class="lineno">  206</span>    assert((a | b) == 2426);</div>
+<div class="line"><span class="lineno">  207</span>    assert((a ^ b) == 2418);</div>
+<div class="line"><span class="lineno">  208</span>    assert((a &lt;&lt; 64) == <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(<span class="stringliteral">&quot;2250502776992565297152&quot;</span>));</div>
+<div class="line"><span class="lineno">  209</span>    assert((b &gt;&gt; 7) == 18);</div>
+<div class="line"><span class="lineno">  210</span> </div>
+<div class="line"><span class="lineno">  211</span>    <span class="comment">// 2nd test: Operations test</span></div>
+<div class="line"><span class="lineno">  212</span>    a = <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(<span class="stringliteral">&quot;12321421424232142122&quot;</span>);</div>
+<div class="line"><span class="lineno">  213</span>    b = <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(<span class="stringliteral">&quot;23123212&quot;</span>);</div>
+<div class="line"><span class="lineno">  214</span>    assert(a + b == <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(<span class="stringliteral">&quot;12321421424255265334&quot;</span>));</div>
+<div class="line"><span class="lineno">  215</span>    assert(a - b == <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(<span class="stringliteral">&quot;12321421424209018910&quot;</span>));</div>
+<div class="line"><span class="lineno">  216</span>    assert(a * b == <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(<span class="stringliteral">&quot;284910839733861759501135864&quot;</span>));</div>
+<div class="line"><span class="lineno">  217</span>    assert(a / b == 532859423865LL);</div>
+<div class="line"><span class="lineno">  218</span>    assert(a % b == 3887742);</div>
+<div class="line"><span class="lineno">  219</span>    assert((a &amp; b) == 18912520);</div>
+<div class="line"><span class="lineno">  220</span>    assert((a | b) == <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(<span class="stringliteral">&quot;12321421424236352814&quot;</span>));</div>
+<div class="line"><span class="lineno">  221</span>    assert((a ^ b) == <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(<span class="stringliteral">&quot;12321421424217440294&quot;</span>));</div>
+<div class="line"><span class="lineno">  222</span>    assert((a &lt;&lt; 64) == <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a>(<span class="stringliteral">&quot;227290107637132170748078080907806769152&quot;</span>));</div>
+<div class="line"><span class="lineno">  223</span>}</div>
 <div class="ttc" id="aclassuint128__t_html"><div class="ttname"><a href="../../db/d9a/classuint128__t.html">uint128_t</a></div><div class="ttdoc">class for 128-bit unsigned integer</div><div class="ttdef"><b>Definition:</b> uint128_t.hpp:59</div></div>
 </div><!-- fragment -->
 </div>
@@ -364,37 +364,37 @@ Here is the call graph for this function:</div>
 
 <p>Function to test the <a class="el" href="../../d1/d83/classuint256__t.html" title="class for 256-bit unsigned integer">uint256_t</a> header. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>                              {</div>
-<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>    <span class="comment">// 1st test: Operations test</span></div>
-<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>    <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> a(<span class="stringliteral">&quot;122&quot;</span>), b(<span class="stringliteral">&quot;2312&quot;</span>);</div>
-<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>    assert(a + b == 2434);</div>
-<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>    assert(b - a == 2190);</div>
-<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>    assert(a * b == 282064);</div>
-<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>    assert(b / a == 18);</div>
-<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>    assert(b % a == 116);</div>
-<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>    assert((a &amp; b) == 8);</div>
-<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>    assert((a | b) == 2426);</div>
-<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>    assert((a ^ b) == 2418);</div>
-<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>    assert((a &lt;&lt; 64) == <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;2250502776992565297152&quot;</span>));</div>
-<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>    assert((b &gt;&gt; 7) == 18);</div>
-<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span> </div>
-<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>    <span class="comment">// 2nd test: Operations test</span></div>
-<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>    a = <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;12321423124513251424232142122&quot;</span>);</div>
-<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>    b = <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;23124312431243243215354315132413213212&quot;</span>);</div>
-<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>    assert(a + b == <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;23124312443564666339867566556645355334&quot;</span>));</div>
-<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>    <span class="comment">// Since a &lt; b, the value is greater</span></div>
-<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>    assert(a - b == <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;115792089237316195423570985008687907853246860353&quot;</span></div>
-<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>                              <span class="stringliteral">&quot;221642219366742944204948568846&quot;</span>));</div>
-<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>    assert(a * b == <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;284924437928789743312147393953938013677909398222&quot;</span></div>
-<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>                              <span class="stringliteral">&quot;169728183872115864&quot;</span>));</div>
-<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>    assert(b / a == <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;1876756621&quot;</span>));</div>
-<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>    assert(b % a == <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;2170491202688962563936723450&quot;</span>));</div>
-<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>    assert((a &amp; b) == <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;3553901085693256462344&quot;</span>));</div>
-<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>    assert((a | b) == <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;23124312443564662785966480863388892990&quot;</span>));</div>
-<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>    assert((a ^ b) == <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;23124312443564659232065395170132430646&quot;</span>));</div>
-<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>    assert((a &lt;&lt; 128) == <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;4192763024643754272961909047609369343091683&quot;</span></div>
-<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>                                   <span class="stringliteral">&quot;376561852756163540549632&quot;</span>));</div>
-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  230</span>                              {</div>
+<div class="line"><span class="lineno">  231</span>    <span class="comment">// 1st test: Operations test</span></div>
+<div class="line"><span class="lineno">  232</span>    <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> a(<span class="stringliteral">&quot;122&quot;</span>), b(<span class="stringliteral">&quot;2312&quot;</span>);</div>
+<div class="line"><span class="lineno">  233</span>    assert(a + b == 2434);</div>
+<div class="line"><span class="lineno">  234</span>    assert(b - a == 2190);</div>
+<div class="line"><span class="lineno">  235</span>    assert(a * b == 282064);</div>
+<div class="line"><span class="lineno">  236</span>    assert(b / a == 18);</div>
+<div class="line"><span class="lineno">  237</span>    assert(b % a == 116);</div>
+<div class="line"><span class="lineno">  238</span>    assert((a &amp; b) == 8);</div>
+<div class="line"><span class="lineno">  239</span>    assert((a | b) == 2426);</div>
+<div class="line"><span class="lineno">  240</span>    assert((a ^ b) == 2418);</div>
+<div class="line"><span class="lineno">  241</span>    assert((a &lt;&lt; 64) == <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;2250502776992565297152&quot;</span>));</div>
+<div class="line"><span class="lineno">  242</span>    assert((b &gt;&gt; 7) == 18);</div>
+<div class="line"><span class="lineno">  243</span> </div>
+<div class="line"><span class="lineno">  244</span>    <span class="comment">// 2nd test: Operations test</span></div>
+<div class="line"><span class="lineno">  245</span>    a = <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;12321423124513251424232142122&quot;</span>);</div>
+<div class="line"><span class="lineno">  246</span>    b = <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;23124312431243243215354315132413213212&quot;</span>);</div>
+<div class="line"><span class="lineno">  247</span>    assert(a + b == <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;23124312443564666339867566556645355334&quot;</span>));</div>
+<div class="line"><span class="lineno">  248</span>    <span class="comment">// Since a &lt; b, the value is greater</span></div>
+<div class="line"><span class="lineno">  249</span>    assert(a - b == <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(<span class="stringliteral">&quot;115792089237316195423570985008687907853246860353&quot;</span></div>
+<div class="line"><span class="lineno">  250</span>                              <span class="stringliteral">&quot;221642219366742944204948568846&quot;</span>));</div>
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-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span><span class="comment"></span> </div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span><span class="comment">        /// Find the (first) position of the value we want to erase, and erase</span></div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span><span class="comment">        /// it</span></div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span><span class="comment"></span>        <span class="keyword">const</span> <span class="keyword">auto</span> it = <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#aacd76f078632faee1a8788d031e6c2de">_sortedValues</a>.find(value);  <span class="comment">// O(logN)</span></div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>        <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#aacd76f078632faee1a8788d031e6c2de">_sortedValues</a>.erase(it);                    <span class="comment">// O(logN)</span></div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">   95</span>                                    {</div>
+<div class="line"><span class="lineno">   96</span>        <span class="keyword">const</span> <span class="keyword">auto</span> sz = <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#aacd76f078632faee1a8788d031e6c2de">_sortedValues</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/multiset/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   97</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   98</span><span class="comment">        /// If the erased value is on the left branch or the median itself and</span></div>
+<div class="line"><span class="lineno">   99</span><span class="comment">        /// the number of elements is even, the new median will be the right</span></div>
+<div class="line"><span class="lineno">  100</span><span class="comment">        /// child of the current one</span></div>
+<div class="line"><span class="lineno">  101</span><span class="comment"></span>        <span class="keywordflow">if</span> (value &lt;= *<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a> &amp;&amp; sz % 2 == 0) {</div>
+<div class="line"><span class="lineno">  102</span>            ++<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a>;  <span class="comment">/// O(1) - traversing one step to the right child</span></div>
+<div class="line"><span class="lineno">  103</span>        }</div>
+<div class="line"><span class="lineno">  104</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  105</span><span class="comment">        /// However, if the erased value is on the right branch or the median</span></div>
+<div class="line"><span class="lineno">  106</span><span class="comment">        /// itself, and the number of elements is odd, the new median will be</span></div>
+<div class="line"><span class="lineno">  107</span><span class="comment">        /// the left child of the current one</span></div>
+<div class="line"><span class="lineno">  108</span><span class="comment"></span>        <span class="keywordflow">else</span> <span class="keywordflow">if</span> (value &gt;= *<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a> &amp;&amp; sz % 2 != 0) {</div>
+<div class="line"><span class="lineno">  109</span>            --<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a>;  <span class="comment">// O(1) - traversing one step to the left child</span></div>
+<div class="line"><span class="lineno">  110</span>        }</div>
+<div class="line"><span class="lineno">  111</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  112</span><span class="comment">        /// Find the (first) position of the value we want to erase, and erase</span></div>
+<div class="line"><span class="lineno">  113</span><span class="comment">        /// it</span></div>
+<div class="line"><span class="lineno">  114</span><span class="comment"></span>        <span class="keyword">const</span> <span class="keyword">auto</span> it = <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#aacd76f078632faee1a8788d031e6c2de">_sortedValues</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/multiset/find.html">find</a>(value);  <span class="comment">// O(logN)</span></div>
+<div class="line"><span class="lineno">  115</span>        <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#aacd76f078632faee1a8788d031e6c2de">_sortedValues</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/multiset/erase.html">erase</a>(it);                    <span class="comment">// O(logN)</span></div>
+<div class="line"><span class="lineno">  116</span>    }</div>
 <div class="ttc" id="aclassprobability_1_1windowed__median_1_1_windowed_median_html_a55ae3543a76045dffcb5ec7904a32a20"><div class="ttname"><a href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">probability::windowed_median::WindowedMedian::_itMedian</a></div><div class="ttdeci">std::multiset&lt; int &gt;::const_iterator _itMedian</div><div class="ttdef"><b>Definition:</b> windowed_median.cpp:62</div></div>
 <div class="ttc" id="aclassprobability_1_1windowed__median_1_1_windowed_median_html_aacd76f078632faee1a8788d031e6c2de"><div class="ttname"><a href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#aacd76f078632faee1a8788d031e6c2de">probability::windowed_median::WindowedMedian::_sortedValues</a></div><div class="ttdeci">std::multiset&lt; int &gt; _sortedValues</div><div class="ttdef"><b>Definition:</b> windowed_median.cpp:59</div></div>
-</div><!-- fragment -->
+<div class="ttc" id="aerase_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/multiset/erase.html">std::multiset::erase</a></div><div class="ttdeci">T erase(T... args)</div></div>
+<div class="ttc" id="afind_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/multiset/find.html">std::multiset::find</a></div><div class="ttdeci">T find(T... args)</div></div>
+<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/multiset/size.html">std::multiset::size</a></div><div class="ttdeci">T size(T... args)</div></div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median_af544e271ea19a6fd69a6b3ed6816453e_cgraph.svg" width="376" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
 </div>
 </div>
 <a id="a938cafbdf70dc01e86e9bb12d29ec65d" name="a938cafbdf70dc01e86e9bb12d29ec65d"></a>
@@ -275,14 +284,20 @@ const size_type&#160;</td><td class="memItemRight" valign="bottom"><b>_windowSiz
 <p>Gets the median of the values in the sliding window. </p>
 <dl class="section return"><dt>Returns</dt><dd>Median of sliding window. For even window size return the average between the two values in the middle </dd></dl>
 <p >O(1)</p>
-<div class="fragment"><div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>                            {</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#aacd76f078632faee1a8788d031e6c2de">_sortedValues</a>.size() % 2 != 0) {</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>            <span class="keywordflow">return</span> *<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a>;  <span class="comment">// O(1)</span></div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>        }</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>        <span class="keywordflow">return</span> 0.5f * *<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a> + 0.5f * *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a>(<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a>);  <span class="comment">/// O(1)</span></div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  148</span>                            {</div>
+<div class="line"><span class="lineno">  149</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#aacd76f078632faee1a8788d031e6c2de">_sortedValues</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/multiset/size.html">size</a>() % 2 != 0) {</div>
+<div class="line"><span class="lineno">  150</span>            <span class="keywordflow">return</span> *<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a>;  <span class="comment">// O(1)</span></div>
+<div class="line"><span class="lineno">  151</span>        }</div>
+<div class="line"><span class="lineno">  152</span>        <span class="keywordflow">return</span> 0.5f * *<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a> + 0.5f * *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a>(<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a>);  <span class="comment">/// O(1)</span></div>
+<div class="line"><span class="lineno">  153</span>    }</div>
 <div class="ttc" id="anext_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/next.html">std::next</a></div><div class="ttdeci">T next(T... args)</div></div>
-</div><!-- fragment -->
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median_a938cafbdf70dc01e86e9bb12d29ec65d_cgraph.svg" width="368" height="67"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
 </div>
 </div>
 <a id="a61804988fcb1a6caf640f8291979aaa6" name="a61804988fcb1a6caf640f8291979aaa6"></a>
@@ -313,18 +328,18 @@ const size_type&#160;</td><td class="memItemRight" valign="bottom"><b>_windowSiz
 <p >Sort window - O(NlogN)</p>
 <p >Find value in the middle - O(N)</p>
 <p >O(N)</p>
-<div class="fragment"><div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>                                 {</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>        <span class="keyword">auto</span> window = <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a825a7aaef844c9f743a27b268e8569b2">_window</a>;</div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>        window.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/sort.html">sort</a>();  <span class="comment">/// Sort window - O(NlogN)</span></div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>        <span class="keyword">auto</span> median =</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>            *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a>(window.begin(),</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>                  window.size() / 2);  <span class="comment">/// Find value in the middle - O(N)</span></div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>        <span class="keywordflow">if</span> (window.size() % 2 != 0) {</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>            <span class="keywordflow">return</span> median;</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>        }</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>        <span class="keywordflow">return</span> 0.5f * median +</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>               0.5f * *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a>(window.begin(), window.size() / 2 - 1);  <span class="comment">/// O(N)</span></div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  161</span>                                 {</div>
+<div class="line"><span class="lineno">  162</span>        <span class="keyword">auto</span> window = <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a825a7aaef844c9f743a27b268e8569b2">_window</a>;</div>
+<div class="line"><span class="lineno">  163</span>        window.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/sort.html">sort</a>();  <span class="comment">/// Sort window - O(NlogN)</span></div>
+<div class="line"><span class="lineno">  164</span>        <span class="keyword">auto</span> median =</div>
+<div class="line"><span class="lineno">  165</span>            *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a>(window.begin(),</div>
+<div class="line"><span class="lineno">  166</span>                  window.size() / 2);  <span class="comment">/// Find value in the middle - O(N)</span></div>
+<div class="line"><span class="lineno">  167</span>        <span class="keywordflow">if</span> (window.size() % 2 != 0) {</div>
+<div class="line"><span class="lineno">  168</span>            <span class="keywordflow">return</span> median;</div>
+<div class="line"><span class="lineno">  169</span>        }</div>
+<div class="line"><span class="lineno">  170</span>        <span class="keywordflow">return</span> 0.5f * median +</div>
+<div class="line"><span class="lineno">  171</span>               0.5f * *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a>(window.begin(), window.size() / 2 - 1);  <span class="comment">/// O(N)</span></div>
+<div class="line"><span class="lineno">  172</span>    }</div>
 <div class="ttc" id="aclassprobability_1_1windowed__median_1_1_windowed_median_html_a825a7aaef844c9f743a27b268e8569b2"><div class="ttname"><a href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a825a7aaef844c9f743a27b268e8569b2">probability::windowed_median::WindowedMedian::_window</a></div><div class="ttdeci">Window _window</div><div class="ttdoc">a sliding window of values along the stream</div><div class="ttdef"><b>Definition:</b> windowed_median.cpp:58</div></div>
 <div class="ttc" id="asort_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list/sort.html">std::list::sort</a></div><div class="ttdeci">T sort(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -371,29 +386,28 @@ Here is the call graph for this function:</div>
 <p >If exceeding size of window, pop from its left side</p>
 <p >Erase from the multi-value BST the window left side value</p>
 <p >Pop the left side value from the window - O(1)</p>
-<div class="fragment"><div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>                           {<span class="comment"></span></div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span><span class="comment">        /// Push new value to the back of the sliding window - O(1)</span></div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span><span class="comment"></span>        <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a825a7aaef844c9f743a27b268e8569b2">_window</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/push_back.html">push_back</a>(value);</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>        <a class="code hl_function" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a3a7f57679e9cd6c9f042dfd0612b2b24">insertToSorted</a>(value);  <span class="comment">// Insert value to the multi-value BST - O(logN)</span></div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a825a7aaef844c9f743a27b268e8569b2">_window</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/size.html">size</a>() &gt; <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#aafda847b152684578dab891e5268d750">_windowSize</a>) {  <span class="comment">/// If exceeding size of window,</span><span class="comment"></span></div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span><span class="comment">                                             /// pop from its left side</span></div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span><span class="comment"></span>            <a class="code hl_function" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#af544e271ea19a6fd69a6b3ed6816453e">eraseFromSorted</a>(</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>                <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a825a7aaef844c9f743a27b268e8569b2">_window</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/front.html">front</a>());  <span class="comment">/// Erase from the multi-value BST</span><span class="comment"></span></div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span><span class="comment">                                   /// the window left side value</span></div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span><span class="comment"></span>            <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a825a7aaef844c9f743a27b268e8569b2">_window</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/pop_front.html">pop_front</a>();   <span class="comment">/// Pop the left side value from the window -</span><span class="comment"></span></div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span><span class="comment">                                   /// O(1)</span></div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span><span class="comment"></span>        }</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    }</div>
+<div class="fragment"><div class="line"><span class="lineno">  129</span>                           {<span class="comment"></span></div>
+<div class="line"><span class="lineno">  130</span><span class="comment">        /// Push new value to the back of the sliding window - O(1)</span></div>
+<div class="line"><span class="lineno">  131</span><span class="comment"></span>        <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a825a7aaef844c9f743a27b268e8569b2">_window</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/push_back.html">push_back</a>(value);</div>
+<div class="line"><span class="lineno">  132</span>        <a class="code hl_function" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a3a7f57679e9cd6c9f042dfd0612b2b24">insertToSorted</a>(value);  <span class="comment">// Insert value to the multi-value BST - O(logN)</span></div>
+<div class="line"><span class="lineno">  133</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a825a7aaef844c9f743a27b268e8569b2">_window</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/size.html">size</a>() &gt; <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#aafda847b152684578dab891e5268d750">_windowSize</a>) {  <span class="comment">/// If exceeding size of window,</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  134</span><span class="comment">                                             /// pop from its left side</span></div>
+<div class="line"><span class="lineno">  135</span><span class="comment"></span>            <a class="code hl_function" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#af544e271ea19a6fd69a6b3ed6816453e">eraseFromSorted</a>(</div>
+<div class="line"><span class="lineno">  136</span>                <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a825a7aaef844c9f743a27b268e8569b2">_window</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/front.html">front</a>());  <span class="comment">/// Erase from the multi-value BST</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  137</span><span class="comment">                                   /// the window left side value</span></div>
+<div class="line"><span class="lineno">  138</span><span class="comment"></span>            <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a825a7aaef844c9f743a27b268e8569b2">_window</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list/pop_front.html">pop_front</a>();   <span class="comment">/// Pop the left side value from the window -</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  139</span><span class="comment">                                   /// O(1)</span></div>
+<div class="line"><span class="lineno">  140</span><span class="comment"></span>        }</div>
+<div class="line"><span class="lineno">  141</span>    }</div>
 <div class="ttc" id="aclassprobability_1_1windowed__median_1_1_windowed_median_html_a3a7f57679e9cd6c9f042dfd0612b2b24"><div class="ttname"><a href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a3a7f57679e9cd6c9f042dfd0612b2b24">probability::windowed_median::WindowedMedian::insertToSorted</a></div><div class="ttdeci">void insertToSorted(int value)</div><div class="ttdoc">Inserts a value to a sorted multi-value BST.</div><div class="ttdef"><b>Definition:</b> windowed_median.cpp:69</div></div>
 <div class="ttc" id="aclassprobability_1_1windowed__median_1_1_windowed_median_html_af544e271ea19a6fd69a6b3ed6816453e"><div class="ttname"><a href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#af544e271ea19a6fd69a6b3ed6816453e">probability::windowed_median::WindowedMedian::eraseFromSorted</a></div><div class="ttdeci">void eraseFromSorted(int value)</div><div class="ttdoc">Erases a value from a sorted multi-value BST.</div><div class="ttdef"><b>Definition:</b> windowed_median.cpp:95</div></div>
 <div class="ttc" id="afront_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list/front.html">std::list::front</a></div><div class="ttdeci">T front(T... args)</div></div>
 <div class="ttc" id="apop_front_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list/pop_front.html">std::list::pop_front</a></div><div class="ttdeci">T pop_front(T... args)</div></div>
 <div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list/push_back.html">std::list::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
-<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list/size.html">std::list::size</a></div><div class="ttdeci">T size(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median_a6b52b7851750f28d53508e63c52a69f7_cgraph.svg" width="424" height="350"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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 </div>
 </div>
 
@@ -435,28 +449,36 @@ Here is the call graph for this function:</div>
 <p >If new value goes to left tree branch, and number of elements is even, the new median in the balanced tree is the left child of the median before the insertion</p>
 <p >However, if the new value goes to the right branch, the previous median's right child is the new median in the balanced tree</p>
 <p >O(1) - traversing one step to the right child</p>
-<div class="fragment"><div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>                                   {</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#aacd76f078632faee1a8788d031e6c2de">_sortedValues</a>.insert(value);  <span class="comment">/// Insert value to BST - O(logN)</span></div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        <span class="keyword">const</span> <span class="keyword">auto</span> sz = <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#aacd76f078632faee1a8788d031e6c2de">_sortedValues</a>.size();</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>        <span class="keywordflow">if</span> (sz == 1) {  <span class="comment">/// For the first value, set median iterator to BST root</span></div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>            <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a> = <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#aacd76f078632faee1a8788d031e6c2de">_sortedValues</a>.begin();</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>            <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>        }</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span><span class="comment"></span> </div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span><span class="comment">        /// If new value goes to left tree branch, and number of elements is</span></div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span><span class="comment">        /// even, the new median in the balanced tree is the left child of the</span></div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span><span class="comment">        /// median before the insertion</span></div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span><span class="comment"></span>        <span class="keywordflow">if</span> (value &lt; *<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a> &amp;&amp; sz % 2 == 0) {</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>            --<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a>;  <span class="comment">// O(1) - traversing one step to the left child</span></div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        }</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span><span class="comment"></span> </div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span><span class="comment">        /// However, if the new value goes to the right branch, the previous</span></div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span><span class="comment">        /// median&#39;s right child is the new median in the balanced tree</span></div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span><span class="comment"></span>        <span class="keywordflow">else</span> <span class="keywordflow">if</span> (value &gt;= *<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a> &amp;&amp; sz % 2 != 0) {</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>            ++<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a>;  <span class="comment">/// O(1) - traversing one step to the right child</span></div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        }</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    }</div>
-</div><!-- fragment -->
+<div class="fragment"><div class="line"><span class="lineno">   69</span>                                   {</div>
+<div class="line"><span class="lineno">   70</span>        <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#aacd76f078632faee1a8788d031e6c2de">_sortedValues</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/multiset/insert.html">insert</a>(value);  <span class="comment">/// Insert value to BST - O(logN)</span></div>
+<div class="line"><span class="lineno">   71</span>        <span class="keyword">const</span> <span class="keyword">auto</span> sz = <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#aacd76f078632faee1a8788d031e6c2de">_sortedValues</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/multiset/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   72</span>        <span class="keywordflow">if</span> (sz == 1) {  <span class="comment">/// For the first value, set median iterator to BST root</span></div>
+<div class="line"><span class="lineno">   73</span>            <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a> = <a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#aacd76f078632faee1a8788d031e6c2de">_sortedValues</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/multiset/begin.html">begin</a>();</div>
+<div class="line"><span class="lineno">   74</span>            <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">   75</span>        }</div>
+<div class="line"><span class="lineno">   76</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   77</span><span class="comment">        /// If new value goes to left tree branch, and number of elements is</span></div>
+<div class="line"><span class="lineno">   78</span><span class="comment">        /// even, the new median in the balanced tree is the left child of the</span></div>
+<div class="line"><span class="lineno">   79</span><span class="comment">        /// median before the insertion</span></div>
+<div class="line"><span class="lineno">   80</span><span class="comment"></span>        <span class="keywordflow">if</span> (value &lt; *<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a> &amp;&amp; sz % 2 == 0) {</div>
+<div class="line"><span class="lineno">   81</span>            --<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a>;  <span class="comment">// O(1) - traversing one step to the left child</span></div>
+<div class="line"><span class="lineno">   82</span>        }</div>
+<div class="line"><span class="lineno">   83</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   84</span><span class="comment">        /// However, if the new value goes to the right branch, the previous</span></div>
+<div class="line"><span class="lineno">   85</span><span class="comment">        /// median&#39;s right child is the new median in the balanced tree</span></div>
+<div class="line"><span class="lineno">   86</span><span class="comment"></span>        <span class="keywordflow">else</span> <span class="keywordflow">if</span> (value &gt;= *<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a> &amp;&amp; sz % 2 != 0) {</div>
+<div class="line"><span class="lineno">   87</span>            ++<a class="code hl_variable" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#a55ae3543a76045dffcb5ec7904a32a20">_itMedian</a>;  <span class="comment">/// O(1) - traversing one step to the right child</span></div>
+<div class="line"><span class="lineno">   88</span>        }</div>
+<div class="line"><span class="lineno">   89</span>    }</div>
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+Here is the call graph for this function:</div>
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 <h2 class="groupheader">Member Data Documentation</h2>
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     <li class="navelem"><a class="el" href="../../d4/ded/namespaceprobability.html">probability</a></li><li class="navelem"><b>windowed_median</b></li><li class="navelem"><a class="el" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html">WindowedMedian</a></li>
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+++ b/df/d39/interpolation__search2_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.md5
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+++ b/df/d39/interpolation__search2_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg
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index b4377ffdd..c71e20b2e 100644
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@@ -3,7 +3,7 @@
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@@ -30,8 +30,8 @@ MathJax.Hub.Config({
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  <tbody>
- <tr style="height: 56px;">
-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
+  <td id="projectalign">
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+<!-- Generated by Doxygen 1.9.3 -->
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@@ -168,16 +168,16 @@ Functions</h2></td></tr>
         </tr>
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-<div class="fragment"><div class="line"><a id="l00555" name="l00555"></a><span class="lineno">  555</span>           {</div>
-<div class="line"><a id="l00556" name="l00556"></a><span class="lineno">  556</span>    <a class="code hl_function" href="../../df/d42/binary__search__tree2_8cpp.html#a8c882f43e1e52948a7841a8bfb091350">test_insert</a>();</div>
-<div class="line"><a id="l00557" name="l00557"></a><span class="lineno">  557</span>    <a class="code hl_function" href="../../df/d42/binary__search__tree2_8cpp.html#ab1333c3ea06dcad896ee204bbd407c4e">test_remove</a>();</div>
-<div class="line"><a id="l00558" name="l00558"></a><span class="lineno">  558</span>    <a class="code hl_function" href="../../df/d42/binary__search__tree2_8cpp.html#a1d42876440ac5346e2850a32497385c3">test_contains</a>();</div>
-<div class="line"><a id="l00559" name="l00559"></a><span class="lineno">  559</span>    <a class="code hl_function" href="../../df/d42/binary__search__tree2_8cpp.html#a9856b68e2cba50d2e26a1cbe374e0365">test_find_max</a>();</div>
-<div class="line"><a id="l00560" name="l00560"></a><span class="lineno">  560</span>    <a class="code hl_function" href="../../df/d42/binary__search__tree2_8cpp.html#af2847a901160fd45b4044550e9921cb4">test_find_min</a>();</div>
-<div class="line"><a id="l00561" name="l00561"></a><span class="lineno">  561</span>    <a class="code hl_function" href="../../df/d42/binary__search__tree2_8cpp.html#a06f35064850e891d6fda0093c0d9ee6e">test_get_elements_inorder</a>();</div>
-<div class="line"><a id="l00562" name="l00562"></a><span class="lineno">  562</span>    <a class="code hl_function" href="../../df/d42/binary__search__tree2_8cpp.html#ab00b8d0f21aeb5fbddb6decf3bcb640a">test_get_elements_preorder</a>();</div>
-<div class="line"><a id="l00563" name="l00563"></a><span class="lineno">  563</span>    <a class="code hl_function" href="../../df/d42/binary__search__tree2_8cpp.html#a94b76f781fcbe1ad0e3397ace6bb1965">test_get_elements_postorder</a>();</div>
-<div class="line"><a id="l00564" name="l00564"></a><span class="lineno">  564</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  555</span>           {</div>
+<div class="line"><span class="lineno">  556</span>    <a class="code hl_function" href="../../df/d42/binary__search__tree2_8cpp.html#a8c882f43e1e52948a7841a8bfb091350">test_insert</a>();</div>
+<div class="line"><span class="lineno">  557</span>    <a class="code hl_function" href="../../df/d42/binary__search__tree2_8cpp.html#ab1333c3ea06dcad896ee204bbd407c4e">test_remove</a>();</div>
+<div class="line"><span class="lineno">  558</span>    <a class="code hl_function" href="../../df/d42/binary__search__tree2_8cpp.html#a1d42876440ac5346e2850a32497385c3">test_contains</a>();</div>
+<div class="line"><span class="lineno">  559</span>    <a class="code hl_function" href="../../df/d42/binary__search__tree2_8cpp.html#a9856b68e2cba50d2e26a1cbe374e0365">test_find_max</a>();</div>
+<div class="line"><span class="lineno">  560</span>    <a class="code hl_function" href="../../df/d42/binary__search__tree2_8cpp.html#af2847a901160fd45b4044550e9921cb4">test_find_min</a>();</div>
+<div class="line"><span class="lineno">  561</span>    <a class="code hl_function" href="../../df/d42/binary__search__tree2_8cpp.html#a06f35064850e891d6fda0093c0d9ee6e">test_get_elements_inorder</a>();</div>
+<div class="line"><span class="lineno">  562</span>    <a class="code hl_function" href="../../df/d42/binary__search__tree2_8cpp.html#ab00b8d0f21aeb5fbddb6decf3bcb640a">test_get_elements_preorder</a>();</div>
+<div class="line"><span class="lineno">  563</span>    <a class="code hl_function" href="../../df/d42/binary__search__tree2_8cpp.html#a94b76f781fcbe1ad0e3397ace6bb1965">test_get_elements_postorder</a>();</div>
+<div class="line"><span class="lineno">  564</span>}</div>
 <div class="ttc" id="abinary__search__tree2_8cpp_html_a06f35064850e891d6fda0093c0d9ee6e"><div class="ttname"><a href="../../df/d42/binary__search__tree2_8cpp.html#a06f35064850e891d6fda0093c0d9ee6e">test_get_elements_inorder</a></div><div class="ttdeci">static void test_get_elements_inorder()</div><div class="ttdoc">Function for testing get_elements_inorder().</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:497</div></div>
 <div class="ttc" id="abinary__search__tree2_8cpp_html_a1d42876440ac5346e2850a32497385c3"><div class="ttname"><a href="../../df/d42/binary__search__tree2_8cpp.html#a1d42876440ac5346e2850a32497385c3">test_contains</a></div><div class="ttdeci">static void test_contains()</div><div class="ttdoc">Function for testing contains().</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:428</div></div>
 <div class="ttc" id="abinary__search__tree2_8cpp_html_a8c882f43e1e52948a7841a8bfb091350"><div class="ttname"><a href="../../df/d42/binary__search__tree2_8cpp.html#a8c882f43e1e52948a7841a8bfb091350">test_insert</a></div><div class="ttdeci">static void test_insert()</div><div class="ttdoc">Function for testing insert().</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:357</div></div>
@@ -214,23 +214,23 @@ Functions</h2></td></tr>
 
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 <dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
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-<div class="line"><a id="l00431" name="l00431"></a><span class="lineno">  431</span>    <a class="code hl_class" href="../../d9/dde/classbinary__search__tree.html">binary_search_tree&lt;int&gt;</a> tree;</div>
-<div class="line"><a id="l00432" name="l00432"></a><span class="lineno">  432</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(5);</div>
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-<div class="line"><a id="l00438" name="l00438"></a><span class="lineno">  438</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#aa4f84b2eec9b9201af1840868ddb5fb2">contains</a>(4));</div>
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+<div class="line"><span class="lineno">  430</span> </div>
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+<div class="line"><span class="lineno">  439</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#aa4f84b2eec9b9201af1840868ddb5fb2">contains</a>(3));</div>
+<div class="line"><span class="lineno">  440</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#aa4f84b2eec9b9201af1840868ddb5fb2">contains</a>(6));</div>
+<div class="line"><span class="lineno">  441</span>    assert(!tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#aa4f84b2eec9b9201af1840868ddb5fb2">contains</a>(999));</div>
+<div class="line"><span class="lineno">  442</span> </div>
+<div class="line"><span class="lineno">  443</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ok&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  444</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aclassbinary__search__tree_html"><div class="ttname"><a href="../../d9/dde/classbinary__search__tree.html">binary_search_tree</a></div><div class="ttdoc">The Binary Search Tree class.</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:19</div></div>
 <div class="ttc" id="aclassbinary__search__tree_html_a9d1e7e10efa74d741bf48cf032df3778"><div class="ttname"><a href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">binary_search_tree::insert</a></div><div class="ttdeci">bool insert(std::unique_ptr&lt; bst_node &gt; &amp;node, T new_value)</div><div class="ttdoc">Recursive function to insert a value into the BST.</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:89</div></div>
@@ -270,23 +270,23 @@ Here is the call graph for this function:</div>
 
 <p>Function for testing find_max(). </p>
 <dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00474" name="l00474"></a><span class="lineno">  474</span>                            {</div>
-<div class="line"><a id="l00475" name="l00475"></a><span class="lineno">  475</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testing BST find_max...&quot;</span>;</div>
-<div class="line"><a id="l00476" name="l00476"></a><span class="lineno">  476</span> </div>
-<div class="line"><a id="l00477" name="l00477"></a><span class="lineno">  477</span>    <span class="keywordtype">int</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">max</a> = 0;</div>
-<div class="line"><a id="l00478" name="l00478"></a><span class="lineno">  478</span>    <a class="code hl_class" href="../../d9/dde/classbinary__search__tree.html">binary_search_tree&lt;int&gt;</a> tree;</div>
-<div class="line"><a id="l00479" name="l00479"></a><span class="lineno">  479</span>    assert(!tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a75f897af6aa732a9901454401c869bcb">find_max</a>(max));</div>
-<div class="line"><a id="l00480" name="l00480"></a><span class="lineno">  480</span> </div>
-<div class="line"><a id="l00481" name="l00481"></a><span class="lineno">  481</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(5);</div>
-<div class="line"><a id="l00482" name="l00482"></a><span class="lineno">  482</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(4);</div>
-<div class="line"><a id="l00483" name="l00483"></a><span class="lineno">  483</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(3);</div>
-<div class="line"><a id="l00484" name="l00484"></a><span class="lineno">  484</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(6);</div>
-<div class="line"><a id="l00485" name="l00485"></a><span class="lineno">  485</span> </div>
-<div class="line"><a id="l00486" name="l00486"></a><span class="lineno">  486</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a75f897af6aa732a9901454401c869bcb">find_max</a>(max));</div>
-<div class="line"><a id="l00487" name="l00487"></a><span class="lineno">  487</span>    assert(max == 6);</div>
-<div class="line"><a id="l00488" name="l00488"></a><span class="lineno">  488</span> </div>
-<div class="line"><a id="l00489" name="l00489"></a><span class="lineno">  489</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ok&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00490" name="l00490"></a><span class="lineno">  490</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  474</span>                            {</div>
+<div class="line"><span class="lineno">  475</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testing BST find_max...&quot;</span>;</div>
+<div class="line"><span class="lineno">  476</span> </div>
+<div class="line"><span class="lineno">  477</span>    <span class="keywordtype">int</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">max</a> = 0;</div>
+<div class="line"><span class="lineno">  478</span>    <a class="code hl_class" href="../../d9/dde/classbinary__search__tree.html">binary_search_tree&lt;int&gt;</a> tree;</div>
+<div class="line"><span class="lineno">  479</span>    assert(!tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a75f897af6aa732a9901454401c869bcb">find_max</a>(max));</div>
+<div class="line"><span class="lineno">  480</span> </div>
+<div class="line"><span class="lineno">  481</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(5);</div>
+<div class="line"><span class="lineno">  482</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(4);</div>
+<div class="line"><span class="lineno">  483</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(3);</div>
+<div class="line"><span class="lineno">  484</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(6);</div>
+<div class="line"><span class="lineno">  485</span> </div>
+<div class="line"><span class="lineno">  486</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a75f897af6aa732a9901454401c869bcb">find_max</a>(max));</div>
+<div class="line"><span class="lineno">  487</span>    assert(max == 6);</div>
+<div class="line"><span class="lineno">  488</span> </div>
+<div class="line"><span class="lineno">  489</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ok&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  490</span>}</div>
 <div class="ttc" id="aclassbinary__search__tree_html_a75f897af6aa732a9901454401c869bcb"><div class="ttname"><a href="../../d9/dde/classbinary__search__tree.html#a75f897af6aa732a9901454401c869bcb">binary_search_tree::find_max</a></div><div class="ttdeci">bool find_max(std::unique_ptr&lt; bst_node &gt; &amp;node, T &amp;ret_value)</div><div class="ttdoc">Recursive function to find the maximum value in the BST.</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:52</div></div>
 <div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -323,23 +323,23 @@ Here is the call graph for this function:</div>
 
 <p>Function for testing find_min(). </p>
 <dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00451" name="l00451"></a><span class="lineno">  451</span>                            {</div>
-<div class="line"><a id="l00452" name="l00452"></a><span class="lineno">  452</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testing BST find_min...&quot;</span>;</div>
-<div class="line"><a id="l00453" name="l00453"></a><span class="lineno">  453</span> </div>
-<div class="line"><a id="l00454" name="l00454"></a><span class="lineno">  454</span>    <span class="keywordtype">int</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a> = 0;</div>
-<div class="line"><a id="l00455" name="l00455"></a><span class="lineno">  455</span>    <a class="code hl_class" href="../../d9/dde/classbinary__search__tree.html">binary_search_tree&lt;int&gt;</a> tree;</div>
-<div class="line"><a id="l00456" name="l00456"></a><span class="lineno">  456</span>    assert(!tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af9a2c7c187a7ca3142c77ce342ef3153">find_min</a>(min));</div>
-<div class="line"><a id="l00457" name="l00457"></a><span class="lineno">  457</span> </div>
-<div class="line"><a id="l00458" name="l00458"></a><span class="lineno">  458</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(5);</div>
-<div class="line"><a id="l00459" name="l00459"></a><span class="lineno">  459</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(4);</div>
-<div class="line"><a id="l00460" name="l00460"></a><span class="lineno">  460</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(3);</div>
-<div class="line"><a id="l00461" name="l00461"></a><span class="lineno">  461</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(6);</div>
-<div class="line"><a id="l00462" name="l00462"></a><span class="lineno">  462</span> </div>
-<div class="line"><a id="l00463" name="l00463"></a><span class="lineno">  463</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af9a2c7c187a7ca3142c77ce342ef3153">find_min</a>(min));</div>
-<div class="line"><a id="l00464" name="l00464"></a><span class="lineno">  464</span>    assert(min == 3);</div>
-<div class="line"><a id="l00465" name="l00465"></a><span class="lineno">  465</span> </div>
-<div class="line"><a id="l00466" name="l00466"></a><span class="lineno">  466</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ok&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00467" name="l00467"></a><span class="lineno">  467</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  451</span>                            {</div>
+<div class="line"><span class="lineno">  452</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testing BST find_min...&quot;</span>;</div>
+<div class="line"><span class="lineno">  453</span> </div>
+<div class="line"><span class="lineno">  454</span>    <span class="keywordtype">int</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a> = 0;</div>
+<div class="line"><span class="lineno">  455</span>    <a class="code hl_class" href="../../d9/dde/classbinary__search__tree.html">binary_search_tree&lt;int&gt;</a> tree;</div>
+<div class="line"><span class="lineno">  456</span>    assert(!tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af9a2c7c187a7ca3142c77ce342ef3153">find_min</a>(min));</div>
+<div class="line"><span class="lineno">  457</span> </div>
+<div class="line"><span class="lineno">  458</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(5);</div>
+<div class="line"><span class="lineno">  459</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(4);</div>
+<div class="line"><span class="lineno">  460</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(3);</div>
+<div class="line"><span class="lineno">  461</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(6);</div>
+<div class="line"><span class="lineno">  462</span> </div>
+<div class="line"><span class="lineno">  463</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af9a2c7c187a7ca3142c77ce342ef3153">find_min</a>(min));</div>
+<div class="line"><span class="lineno">  464</span>    assert(min == 3);</div>
+<div class="line"><span class="lineno">  465</span> </div>
+<div class="line"><span class="lineno">  466</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ok&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  467</span>}</div>
 <div class="ttc" id="aclassbinary__search__tree_html_af9a2c7c187a7ca3142c77ce342ef3153"><div class="ttname"><a href="../../d9/dde/classbinary__search__tree.html#af9a2c7c187a7ca3142c77ce342ef3153">binary_search_tree::find_min</a></div><div class="ttdeci">bool find_min(std::unique_ptr&lt; bst_node &gt; &amp;node, T &amp;ret_value)</div><div class="ttdoc">Recursive function to find the minimum value in the BST.</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:70</div></div>
 <div class="ttc" id="amin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a></div><div class="ttdeci">T min(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -376,23 +376,23 @@ Here is the call graph for this function:</div>
 
 <p>Function for testing get_elements_inorder(). </p>
 <dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00497" name="l00497"></a><span class="lineno">  497</span>                                        {</div>
-<div class="line"><a id="l00498" name="l00498"></a><span class="lineno">  498</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testing BST get_elements_inorder...&quot;</span>;</div>
-<div class="line"><a id="l00499" name="l00499"></a><span class="lineno">  499</span> </div>
-<div class="line"><a id="l00500" name="l00500"></a><span class="lineno">  500</span>    <a class="code hl_class" href="../../d9/dde/classbinary__search__tree.html">binary_search_tree&lt;int&gt;</a> tree;</div>
-<div class="line"><a id="l00501" name="l00501"></a><span class="lineno">  501</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(5);</div>
-<div class="line"><a id="l00502" name="l00502"></a><span class="lineno">  502</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(4);</div>
-<div class="line"><a id="l00503" name="l00503"></a><span class="lineno">  503</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(3);</div>
-<div class="line"><a id="l00504" name="l00504"></a><span class="lineno">  504</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(6);</div>
-<div class="line"><a id="l00505" name="l00505"></a><span class="lineno">  505</span> </div>
-<div class="line"><a id="l00506" name="l00506"></a><span class="lineno">  506</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> expected = {3, 4, 5, 6};</div>
-<div class="line"><a id="l00507" name="l00507"></a><span class="lineno">  507</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> actual = tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a1f23830316204664514f396a4eb5275a">get_elements_inorder</a>();</div>
-<div class="line"><a id="l00508" name="l00508"></a><span class="lineno">  508</span>    assert(actual == expected);</div>
-<div class="line"><a id="l00509" name="l00509"></a><span class="lineno">  509</span> </div>
-<div class="line"><a id="l00510" name="l00510"></a><span class="lineno">  510</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ok&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00511" name="l00511"></a><span class="lineno">  511</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  497</span>                                        {</div>
+<div class="line"><span class="lineno">  498</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testing BST get_elements_inorder...&quot;</span>;</div>
+<div class="line"><span class="lineno">  499</span> </div>
+<div class="line"><span class="lineno">  500</span>    <a class="code hl_class" href="../../d9/dde/classbinary__search__tree.html">binary_search_tree&lt;int&gt;</a> tree;</div>
+<div class="line"><span class="lineno">  501</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(5);</div>
+<div class="line"><span class="lineno">  502</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(4);</div>
+<div class="line"><span class="lineno">  503</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(3);</div>
+<div class="line"><span class="lineno">  504</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(6);</div>
+<div class="line"><span class="lineno">  505</span> </div>
+<div class="line"><span class="lineno">  506</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> expected = {3, 4, 5, 6};</div>
+<div class="line"><span class="lineno">  507</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> actual = tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a1f23830316204664514f396a4eb5275a">get_elements_inorder</a>();</div>
+<div class="line"><span class="lineno">  508</span>    assert(actual == expected);</div>
+<div class="line"><span class="lineno">  509</span> </div>
+<div class="line"><span class="lineno">  510</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ok&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  511</span>}</div>
 <div class="ttc" id="aclassbinary__search__tree_html_a1f23830316204664514f396a4eb5275a"><div class="ttname"><a href="../../d9/dde/classbinary__search__tree.html#a1f23830316204664514f396a4eb5275a">binary_search_tree::get_elements_inorder</a></div><div class="ttdeci">std::vector&lt; T &gt; get_elements_inorder()</div><div class="ttdoc">Get all values of the BST in in-order order.</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:320</div></div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int &gt;</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -427,21 +427,21 @@ Here is the call graph for this function:</div>
 
 <p>Function for testing get_elements_postorder(). </p>
 <dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00539" name="l00539"></a><span class="lineno">  539</span>                                          {</div>
-<div class="line"><a id="l00540" name="l00540"></a><span class="lineno">  540</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testing BST get_elements_postorder...&quot;</span>;</div>
-<div class="line"><a id="l00541" name="l00541"></a><span class="lineno">  541</span> </div>
-<div class="line"><a id="l00542" name="l00542"></a><span class="lineno">  542</span>    <a class="code hl_class" href="../../d9/dde/classbinary__search__tree.html">binary_search_tree&lt;int&gt;</a> tree;</div>
-<div class="line"><a id="l00543" name="l00543"></a><span class="lineno">  543</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(5);</div>
-<div class="line"><a id="l00544" name="l00544"></a><span class="lineno">  544</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(4);</div>
-<div class="line"><a id="l00545" name="l00545"></a><span class="lineno">  545</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(3);</div>
-<div class="line"><a id="l00546" name="l00546"></a><span class="lineno">  546</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(6);</div>
-<div class="line"><a id="l00547" name="l00547"></a><span class="lineno">  547</span> </div>
-<div class="line"><a id="l00548" name="l00548"></a><span class="lineno">  548</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> expected = {3, 4, 6, 5};</div>
-<div class="line"><a id="l00549" name="l00549"></a><span class="lineno">  549</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> actual = tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a5c011e1b0863d79c3a7c11a0426bdcff">get_elements_postorder</a>();</div>
-<div class="line"><a id="l00550" name="l00550"></a><span class="lineno">  550</span>    assert(actual == expected);</div>
-<div class="line"><a id="l00551" name="l00551"></a><span class="lineno">  551</span> </div>
-<div class="line"><a id="l00552" name="l00552"></a><span class="lineno">  552</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ok&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00553" name="l00553"></a><span class="lineno">  553</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  539</span>                                          {</div>
+<div class="line"><span class="lineno">  540</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testing BST get_elements_postorder...&quot;</span>;</div>
+<div class="line"><span class="lineno">  541</span> </div>
+<div class="line"><span class="lineno">  542</span>    <a class="code hl_class" href="../../d9/dde/classbinary__search__tree.html">binary_search_tree&lt;int&gt;</a> tree;</div>
+<div class="line"><span class="lineno">  543</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(5);</div>
+<div class="line"><span class="lineno">  544</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(4);</div>
+<div class="line"><span class="lineno">  545</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(3);</div>
+<div class="line"><span class="lineno">  546</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(6);</div>
+<div class="line"><span class="lineno">  547</span> </div>
+<div class="line"><span class="lineno">  548</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> expected = {3, 4, 6, 5};</div>
+<div class="line"><span class="lineno">  549</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> actual = tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a5c011e1b0863d79c3a7c11a0426bdcff">get_elements_postorder</a>();</div>
+<div class="line"><span class="lineno">  550</span>    assert(actual == expected);</div>
+<div class="line"><span class="lineno">  551</span> </div>
+<div class="line"><span class="lineno">  552</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ok&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  553</span>}</div>
 <div class="ttc" id="aclassbinary__search__tree_html_a5c011e1b0863d79c3a7c11a0426bdcff"><div class="ttname"><a href="../../d9/dde/classbinary__search__tree.html#a5c011e1b0863d79c3a7c11a0426bdcff">binary_search_tree::get_elements_postorder</a></div><div class="ttdeci">std::vector&lt; T &gt; get_elements_postorder()</div><div class="ttdoc">Get all values of the BST in post-order order.</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:344</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -477,21 +477,21 @@ Here is the call graph for this function:</div>
 
 <p>Function for testing get_elements_preorder(). </p>
 <dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00518" name="l00518"></a><span class="lineno">  518</span>                                         {</div>
-<div class="line"><a id="l00519" name="l00519"></a><span class="lineno">  519</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testing BST get_elements_preorder...&quot;</span>;</div>
-<div class="line"><a id="l00520" name="l00520"></a><span class="lineno">  520</span> </div>
-<div class="line"><a id="l00521" name="l00521"></a><span class="lineno">  521</span>    <a class="code hl_class" href="../../d9/dde/classbinary__search__tree.html">binary_search_tree&lt;int&gt;</a> tree;</div>
-<div class="line"><a id="l00522" name="l00522"></a><span class="lineno">  522</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(5);</div>
-<div class="line"><a id="l00523" name="l00523"></a><span class="lineno">  523</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(4);</div>
-<div class="line"><a id="l00524" name="l00524"></a><span class="lineno">  524</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(3);</div>
-<div class="line"><a id="l00525" name="l00525"></a><span class="lineno">  525</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(6);</div>
-<div class="line"><a id="l00526" name="l00526"></a><span class="lineno">  526</span> </div>
-<div class="line"><a id="l00527" name="l00527"></a><span class="lineno">  527</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> expected = {5, 4, 3, 6};</div>
-<div class="line"><a id="l00528" name="l00528"></a><span class="lineno">  528</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> actual = tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a5764c1cf848f84a5b77462036a6d8c13">get_elements_preorder</a>();</div>
-<div class="line"><a id="l00529" name="l00529"></a><span class="lineno">  529</span>    assert(actual == expected);</div>
-<div class="line"><a id="l00530" name="l00530"></a><span class="lineno">  530</span> </div>
-<div class="line"><a id="l00531" name="l00531"></a><span class="lineno">  531</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ok&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00532" name="l00532"></a><span class="lineno">  532</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  518</span>                                         {</div>
+<div class="line"><span class="lineno">  519</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testing BST get_elements_preorder...&quot;</span>;</div>
+<div class="line"><span class="lineno">  520</span> </div>
+<div class="line"><span class="lineno">  521</span>    <a class="code hl_class" href="../../d9/dde/classbinary__search__tree.html">binary_search_tree&lt;int&gt;</a> tree;</div>
+<div class="line"><span class="lineno">  522</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(5);</div>
+<div class="line"><span class="lineno">  523</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(4);</div>
+<div class="line"><span class="lineno">  524</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(3);</div>
+<div class="line"><span class="lineno">  525</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(6);</div>
+<div class="line"><span class="lineno">  526</span> </div>
+<div class="line"><span class="lineno">  527</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> expected = {5, 4, 3, 6};</div>
+<div class="line"><span class="lineno">  528</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> actual = tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a5764c1cf848f84a5b77462036a6d8c13">get_elements_preorder</a>();</div>
+<div class="line"><span class="lineno">  529</span>    assert(actual == expected);</div>
+<div class="line"><span class="lineno">  530</span> </div>
+<div class="line"><span class="lineno">  531</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ok&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  532</span>}</div>
 <div class="ttc" id="aclassbinary__search__tree_html_a5764c1cf848f84a5b77462036a6d8c13"><div class="ttname"><a href="../../d9/dde/classbinary__search__tree.html#a5764c1cf848f84a5b77462036a6d8c13">binary_search_tree::get_elements_preorder</a></div><div class="ttdeci">std::vector&lt; T &gt; get_elements_preorder()</div><div class="ttdoc">Get all values of the BST in pre-order order.</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:332</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -527,34 +527,34 @@ Here is the call graph for this function:</div>
 
 <p>Function for testing <a class="el" href="../../d8/dee/avltree_8cpp.html#a2473fe7416332495b2678ebe89652e4b">insert()</a>. </p>
 <dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00357" name="l00357"></a><span class="lineno">  357</span>                          {</div>
-<div class="line"><a id="l00358" name="l00358"></a><span class="lineno">  358</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testing BST insert...&quot;</span>;</div>
-<div class="line"><a id="l00359" name="l00359"></a><span class="lineno">  359</span> </div>
-<div class="line"><a id="l00360" name="l00360"></a><span class="lineno">  360</span>    <a class="code hl_class" href="../../d9/dde/classbinary__search__tree.html">binary_search_tree&lt;int&gt;</a> tree;</div>
-<div class="line"><a id="l00361" name="l00361"></a><span class="lineno">  361</span>    <span class="keywordtype">bool</span> res = tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(5);</div>
-<div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span>    <span class="keywordtype">int</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a> = -1, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">max</a> = -1;</div>
-<div class="line"><a id="l00363" name="l00363"></a><span class="lineno">  363</span>    assert(res);</div>
-<div class="line"><a id="l00364" name="l00364"></a><span class="lineno">  364</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a75f897af6aa732a9901454401c869bcb">find_max</a>(max));</div>
-<div class="line"><a id="l00365" name="l00365"></a><span class="lineno">  365</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af9a2c7c187a7ca3142c77ce342ef3153">find_min</a>(min));</div>
-<div class="line"><a id="l00366" name="l00366"></a><span class="lineno">  366</span>    assert(max == 5);</div>
-<div class="line"><a id="l00367" name="l00367"></a><span class="lineno">  367</span>    assert(min == 5);</div>
-<div class="line"><a id="l00368" name="l00368"></a><span class="lineno">  368</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a564fe43e7e8f7ecb6f10667a70fbc6f3">size</a>() == 1);</div>
-<div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span> </div>
-<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(4);</div>
-<div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(3);</div>
-<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(6);</div>
-<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a75f897af6aa732a9901454401c869bcb">find_max</a>(max));</div>
-<div class="line"><a id="l00374" name="l00374"></a><span class="lineno">  374</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af9a2c7c187a7ca3142c77ce342ef3153">find_min</a>(min));</div>
-<div class="line"><a id="l00375" name="l00375"></a><span class="lineno">  375</span>    assert(max == 6);</div>
-<div class="line"><a id="l00376" name="l00376"></a><span class="lineno">  376</span>    assert(min == 3);</div>
-<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a564fe43e7e8f7ecb6f10667a70fbc6f3">size</a>() == 4);</div>
-<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span> </div>
-<div class="line"><a id="l00379" name="l00379"></a><span class="lineno">  379</span>    <span class="keywordtype">bool</span> fail_res = tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(4);</div>
-<div class="line"><a id="l00380" name="l00380"></a><span class="lineno">  380</span>    assert(!fail_res);</div>
-<div class="line"><a id="l00381" name="l00381"></a><span class="lineno">  381</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a564fe43e7e8f7ecb6f10667a70fbc6f3">size</a>() == 4);</div>
-<div class="line"><a id="l00382" name="l00382"></a><span class="lineno">  382</span> </div>
-<div class="line"><a id="l00383" name="l00383"></a><span class="lineno">  383</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ok&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00384" name="l00384"></a><span class="lineno">  384</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  357</span>                          {</div>
+<div class="line"><span class="lineno">  358</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testing BST insert...&quot;</span>;</div>
+<div class="line"><span class="lineno">  359</span> </div>
+<div class="line"><span class="lineno">  360</span>    <a class="code hl_class" href="../../d9/dde/classbinary__search__tree.html">binary_search_tree&lt;int&gt;</a> tree;</div>
+<div class="line"><span class="lineno">  361</span>    <span class="keywordtype">bool</span> res = tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(5);</div>
+<div class="line"><span class="lineno">  362</span>    <span class="keywordtype">int</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a> = -1, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">max</a> = -1;</div>
+<div class="line"><span class="lineno">  363</span>    assert(res);</div>
+<div class="line"><span class="lineno">  364</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a75f897af6aa732a9901454401c869bcb">find_max</a>(max));</div>
+<div class="line"><span class="lineno">  365</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af9a2c7c187a7ca3142c77ce342ef3153">find_min</a>(min));</div>
+<div class="line"><span class="lineno">  366</span>    assert(max == 5);</div>
+<div class="line"><span class="lineno">  367</span>    assert(min == 5);</div>
+<div class="line"><span class="lineno">  368</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a564fe43e7e8f7ecb6f10667a70fbc6f3">size</a>() == 1);</div>
+<div class="line"><span class="lineno">  369</span> </div>
+<div class="line"><span class="lineno">  370</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(4);</div>
+<div class="line"><span class="lineno">  371</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(3);</div>
+<div class="line"><span class="lineno">  372</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(6);</div>
+<div class="line"><span class="lineno">  373</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a75f897af6aa732a9901454401c869bcb">find_max</a>(max));</div>
+<div class="line"><span class="lineno">  374</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af9a2c7c187a7ca3142c77ce342ef3153">find_min</a>(min));</div>
+<div class="line"><span class="lineno">  375</span>    assert(max == 6);</div>
+<div class="line"><span class="lineno">  376</span>    assert(min == 3);</div>
+<div class="line"><span class="lineno">  377</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a564fe43e7e8f7ecb6f10667a70fbc6f3">size</a>() == 4);</div>
+<div class="line"><span class="lineno">  378</span> </div>
+<div class="line"><span class="lineno">  379</span>    <span class="keywordtype">bool</span> fail_res = tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(4);</div>
+<div class="line"><span class="lineno">  380</span>    assert(!fail_res);</div>
+<div class="line"><span class="lineno">  381</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a564fe43e7e8f7ecb6f10667a70fbc6f3">size</a>() == 4);</div>
+<div class="line"><span class="lineno">  382</span> </div>
+<div class="line"><span class="lineno">  383</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ok&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  384</span>}</div>
 <div class="ttc" id="aclassbinary__search__tree_html_a564fe43e7e8f7ecb6f10667a70fbc6f3"><div class="ttname"><a href="../../d9/dde/classbinary__search__tree.html#a564fe43e7e8f7ecb6f10667a70fbc6f3">binary_search_tree::size</a></div><div class="ttdeci">std::size_t size()</div><div class="ttdoc">Get the number of values in the BST.</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:313</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -590,37 +590,37 @@ Here is the call graph for this function:</div>
 
 <p>Function for testing <a class="el" href="../../d0/d65/namespacedouble__hashing.html#a28083ecac6eb94b643281875c8665931">remove()</a>. </p>
 <dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
-<div class="fragment"><div class="line"><a id="l00391" name="l00391"></a><span class="lineno">  391</span>                          {</div>
-<div class="line"><a id="l00392" name="l00392"></a><span class="lineno">  392</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testing BST remove...&quot;</span>;</div>
-<div class="line"><a id="l00393" name="l00393"></a><span class="lineno">  393</span> </div>
-<div class="line"><a id="l00394" name="l00394"></a><span class="lineno">  394</span>    <a class="code hl_class" href="../../d9/dde/classbinary__search__tree.html">binary_search_tree&lt;int&gt;</a> tree;</div>
-<div class="line"><a id="l00395" name="l00395"></a><span class="lineno">  395</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(5);</div>
-<div class="line"><a id="l00396" name="l00396"></a><span class="lineno">  396</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(4);</div>
-<div class="line"><a id="l00397" name="l00397"></a><span class="lineno">  397</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(3);</div>
-<div class="line"><a id="l00398" name="l00398"></a><span class="lineno">  398</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(6);</div>
-<div class="line"><a id="l00399" name="l00399"></a><span class="lineno">  399</span> </div>
-<div class="line"><a id="l00400" name="l00400"></a><span class="lineno">  400</span>    <span class="keywordtype">bool</span> res = tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">remove</a>(5);</div>
-<div class="line"><a id="l00401" name="l00401"></a><span class="lineno">  401</span>    <span class="keywordtype">int</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a> = -1, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">max</a> = -1;</div>
-<div class="line"><a id="l00402" name="l00402"></a><span class="lineno">  402</span>    assert(res);</div>
-<div class="line"><a id="l00403" name="l00403"></a><span class="lineno">  403</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a75f897af6aa732a9901454401c869bcb">find_max</a>(max));</div>
-<div class="line"><a id="l00404" name="l00404"></a><span class="lineno">  404</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af9a2c7c187a7ca3142c77ce342ef3153">find_min</a>(min));</div>
-<div class="line"><a id="l00405" name="l00405"></a><span class="lineno">  405</span>    assert(max == 6);</div>
-<div class="line"><a id="l00406" name="l00406"></a><span class="lineno">  406</span>    assert(min == 3);</div>
-<div class="line"><a id="l00407" name="l00407"></a><span class="lineno">  407</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a564fe43e7e8f7ecb6f10667a70fbc6f3">size</a>() == 3);</div>
-<div class="line"><a id="l00408" name="l00408"></a><span class="lineno">  408</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#aa4f84b2eec9b9201af1840868ddb5fb2">contains</a>(5) == <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00409" name="l00409"></a><span class="lineno">  409</span> </div>
-<div class="line"><a id="l00410" name="l00410"></a><span class="lineno">  410</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">remove</a>(4);</div>
-<div class="line"><a id="l00411" name="l00411"></a><span class="lineno">  411</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">remove</a>(3);</div>
-<div class="line"><a id="l00412" name="l00412"></a><span class="lineno">  412</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">remove</a>(6);</div>
-<div class="line"><a id="l00413" name="l00413"></a><span class="lineno">  413</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a564fe43e7e8f7ecb6f10667a70fbc6f3">size</a>() == 0);</div>
-<div class="line"><a id="l00414" name="l00414"></a><span class="lineno">  414</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#aa4f84b2eec9b9201af1840868ddb5fb2">contains</a>(6) == <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00415" name="l00415"></a><span class="lineno">  415</span> </div>
-<div class="line"><a id="l00416" name="l00416"></a><span class="lineno">  416</span>    <span class="keywordtype">bool</span> fail_res = tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">remove</a>(5);</div>
-<div class="line"><a id="l00417" name="l00417"></a><span class="lineno">  417</span>    assert(!fail_res);</div>
-<div class="line"><a id="l00418" name="l00418"></a><span class="lineno">  418</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a564fe43e7e8f7ecb6f10667a70fbc6f3">size</a>() == 0);</div>
-<div class="line"><a id="l00419" name="l00419"></a><span class="lineno">  419</span> </div>
-<div class="line"><a id="l00420" name="l00420"></a><span class="lineno">  420</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ok&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00421" name="l00421"></a><span class="lineno">  421</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  391</span>                          {</div>
+<div class="line"><span class="lineno">  392</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testing BST remove...&quot;</span>;</div>
+<div class="line"><span class="lineno">  393</span> </div>
+<div class="line"><span class="lineno">  394</span>    <a class="code hl_class" href="../../d9/dde/classbinary__search__tree.html">binary_search_tree&lt;int&gt;</a> tree;</div>
+<div class="line"><span class="lineno">  395</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(5);</div>
+<div class="line"><span class="lineno">  396</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(4);</div>
+<div class="line"><span class="lineno">  397</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(3);</div>
+<div class="line"><span class="lineno">  398</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a9d1e7e10efa74d741bf48cf032df3778">insert</a>(6);</div>
+<div class="line"><span class="lineno">  399</span> </div>
+<div class="line"><span class="lineno">  400</span>    <span class="keywordtype">bool</span> res = tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">remove</a>(5);</div>
+<div class="line"><span class="lineno">  401</span>    <span class="keywordtype">int</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a> = -1, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">max</a> = -1;</div>
+<div class="line"><span class="lineno">  402</span>    assert(res);</div>
+<div class="line"><span class="lineno">  403</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a75f897af6aa732a9901454401c869bcb">find_max</a>(max));</div>
+<div class="line"><span class="lineno">  404</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af9a2c7c187a7ca3142c77ce342ef3153">find_min</a>(min));</div>
+<div class="line"><span class="lineno">  405</span>    assert(max == 6);</div>
+<div class="line"><span class="lineno">  406</span>    assert(min == 3);</div>
+<div class="line"><span class="lineno">  407</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a564fe43e7e8f7ecb6f10667a70fbc6f3">size</a>() == 3);</div>
+<div class="line"><span class="lineno">  408</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#aa4f84b2eec9b9201af1840868ddb5fb2">contains</a>(5) == <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  409</span> </div>
+<div class="line"><span class="lineno">  410</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">remove</a>(4);</div>
+<div class="line"><span class="lineno">  411</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">remove</a>(3);</div>
+<div class="line"><span class="lineno">  412</span>    tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">remove</a>(6);</div>
+<div class="line"><span class="lineno">  413</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a564fe43e7e8f7ecb6f10667a70fbc6f3">size</a>() == 0);</div>
+<div class="line"><span class="lineno">  414</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#aa4f84b2eec9b9201af1840868ddb5fb2">contains</a>(6) == <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  415</span> </div>
+<div class="line"><span class="lineno">  416</span>    <span class="keywordtype">bool</span> fail_res = tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">remove</a>(5);</div>
+<div class="line"><span class="lineno">  417</span>    assert(!fail_res);</div>
+<div class="line"><span class="lineno">  418</span>    assert(tree.<a class="code hl_function" href="../../d9/dde/classbinary__search__tree.html#a564fe43e7e8f7ecb6f10667a70fbc6f3">size</a>() == 0);</div>
+<div class="line"><span class="lineno">  419</span> </div>
+<div class="line"><span class="lineno">  420</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ok&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  421</span>}</div>
 <div class="ttc" id="aclassbinary__search__tree_html_af4a865ce5244608819b169fc78a41153"><div class="ttname"><a href="../../d9/dde/classbinary__search__tree.html#af4a865ce5244608819b169fc78a41153">binary_search_tree::remove</a></div><div class="ttdeci">bool remove(std::unique_ptr&lt; bst_node &gt; &amp;parent, std::unique_ptr&lt; bst_node &gt; &amp;node, T rm_value)</div><div class="ttdoc">Recursive function to remove a value from the BST.</div><div class="ttdef"><b>Definition:</b> binary_search_tree2.cpp:124</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -637,7 +637,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_2e746e9d06bf2d8ff842208bcc6ebcfc.html">data_structures</a></li><li class="navelem"><a class="el" href="../../df/d42/binary__search__tree2_8cpp.html">binary_search_tree2.cpp</a></li>
-    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.2 </li>
+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
   </ul>
 </div>
 </body>
diff --git a/df/d42/binary__search__tree2_8cpp_a06f35064850e891d6fda0093c0d9ee6e_cgraph.map b/df/d42/binary__search__tree2_8cpp_a06f35064850e891d6fda0093c0d9ee6e_cgraph.map
index 8235419ae..b7ccc81af 100644
--- a/df/d42/binary__search__tree2_8cpp_a06f35064850e891d6fda0093c0d9ee6e_cgraph.map
+++ b/df/d42/binary__search__tree2_8cpp_a06f35064850e891d6fda0093c0d9ee6e_cgraph.map
@@ -1,6 +1,6 @@
 <map id="test_get_elements_inorder" name="test_get_elements_inorder">
 <area shape="rect" id="node1" title="Function for testing get_elements_inorder()." alt="" coords="5,64,180,91"/>
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 <area shape="rect" id="node4" href="$d9/dde/classbinary__search__tree.html#a2fcf37549bd002c174a45b0b4203c2bd" title="Recursive function to traverse the tree in in&#45;order order." alt="" coords="431,57,563,98"/>
diff --git a/df/d42/binary__search__tree2_8cpp_a06f35064850e891d6fda0093c0d9ee6e_cgraph.md5 b/df/d42/binary__search__tree2_8cpp_a06f35064850e891d6fda0093c0d9ee6e_cgraph.md5
index 228950989..fd8aae55f 100644
--- a/df/d42/binary__search__tree2_8cpp_a06f35064850e891d6fda0093c0d9ee6e_cgraph.md5
+++ b/df/d42/binary__search__tree2_8cpp_a06f35064850e891d6fda0093c0d9ee6e_cgraph.md5
@@ -1 +1 @@
-5e5607f8fbb296358816e10f8aabd958
\ No newline at end of file
+559cd5a858cacf8b9879d59eecfa5a85
\ No newline at end of file
diff --git a/df/d42/binary__search__tree2_8cpp_a06f35064850e891d6fda0093c0d9ee6e_cgraph.svg b/df/d42/binary__search__tree2_8cpp_a06f35064850e891d6fda0093c0d9ee6e_cgraph.svg
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+++ b/df/d42/binary__search__tree2_8cpp_a06f35064850e891d6fda0093c0d9ee6e_cgraph.svg
@@ -21,7 +21,7 @@
 <!-- Node2 -->
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@@ -320,32 +320,32 @@ false if t1 and t2 are in the INCORRECT order </dd></dl>
 
 <p>Self-test implementations. </p>
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-<div class="fragment"><div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>                   {</div>
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-<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>        <a class="code hl_class" href="../../dd/dca/class_f_c_f_s.html">FCFS&lt;uint32_t, uint32_t, uint32_t&gt;</a> readyQueue;</div>
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-<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span> </div>
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-<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>            <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">time</a>(<span class="keyword">nullptr</span>));</div>
-<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>            get&lt;2&gt;(input[i]) = 1 + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">rand</a>() % 10000;</div>
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-<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>            readyQueue.<a class="code hl_function" href="../../dd/dca/class_f_c_f_s.html#a8fbfe4d85f7576b4a7aade07d29fbd69">addProcess</a>(get&lt;0&gt;(input[i]), get&lt;1&gt;(input[i]),</div>
-<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>                                  get&lt;2&gt;(input[i]));</div>
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+<div class="line"><span class="lineno">  271</span>        <span class="keywordflow">for</span> (uint32_t i{}; i &lt; n; i++) {</div>
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+<div class="line"><span class="lineno">  273</span>                                  get&lt;2&gt;(input[i]));</div>
+<div class="line"><span class="lineno">  274</span>        }</div>
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+<div class="line"><span class="lineno">  277</span>        assert(res == readyQueue.<a class="code hl_function" href="../../dd/dca/class_f_c_f_s.html#aa25dbe30ba9930b5a7c1a6d11758bd91">scheduleForFcfs</a>());</div>
+<div class="line"><span class="lineno">  278</span>        <span class="comment">// readyQueue.printResult();</span></div>
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+<div class="line"><span class="lineno">  280</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;All the tests have successfully passed!&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
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 <div class="ttc" id="aclass_f_c_f_s_html_a8fbfe4d85f7576b4a7aade07d29fbd69"><div class="ttname"><a href="../../dd/dca/class_f_c_f_s.html#a8fbfe4d85f7576b4a7aade07d29fbd69">FCFS::addProcess</a></div><div class="ttdeci">void addProcess(S id, T arrival, E burst)</div><div class="ttdoc">Adds the process to the ready queue if it isn't already there.</div><div class="ttdef"><b>Definition:</b> fcfs_scheduling.cpp:129</div></div>
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 <p >Performs the cross product as shown in @algorithm.</p>
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-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a> product;<span class="comment"></span></div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span><span class="comment">            /// Performs the cross product as shown in @algorithm.</span></div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span><span class="comment"></span>            product[0] = (A[1] * B[2]) - (A[2] * B[1]);</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>            product[1] = -((A[0] * B[2]) - (A[2] * B[0]));</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>            product[2] = (A[0] * B[1]) - (A[1] * B[0]);</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>            <span class="keywordflow">return</span> product;</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        }</div>
+<div class="fragment"><div class="line"><span class="lineno">   69</span>                                                                                              {</div>
+<div class="line"><span class="lineno">   70</span>            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a> product;<span class="comment"></span></div>
+<div class="line"><span class="lineno">   71</span><span class="comment">            /// Performs the cross product as shown in @algorithm.</span></div>
+<div class="line"><span class="lineno">   72</span><span class="comment"></span>            product[0] = (A[1] * B[2]) - (A[2] * B[1]);</div>
+<div class="line"><span class="lineno">   73</span>            product[1] = -((A[0] * B[2]) - (A[2] * B[0]));</div>
+<div class="line"><span class="lineno">   74</span>            product[2] = (A[0] * B[1]) - (A[1] * B[0]);</div>
+<div class="line"><span class="lineno">   75</span>            <span class="keywordflow">return</span> product;</div>
+<div class="line"><span class="lineno">   76</span>        }</div>
 <div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -228,10 +228,10 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>type: double description: the magnitude of the mathematical vector from the given direction ratios. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>                                                   {</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>            <span class="keywordtype">double</span> magnitude = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">sqrt</a>((vec[0] * vec[0]) + (vec[1] * vec[1]) + (vec[2] * vec[2]));</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>            <span class="keywordflow">return</span> magnitude;</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>        }</div>
+<div class="fragment"><div class="line"><span class="lineno">   83</span>                                                   {</div>
+<div class="line"><span class="lineno">   84</span>            <span class="keywordtype">double</span> magnitude = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">sqrt</a>((vec[0] * vec[0]) + (vec[1] * vec[1]) + (vec[2] * vec[2]));</div>
+<div class="line"><span class="lineno">   85</span>            <span class="keywordflow">return</span> magnitude;</div>
+<div class="line"><span class="lineno">   86</span>        }</div>
 <div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -265,31 +265,31 @@ Here is the call graph for this function:</div>
 <p >Gets the values for the second vector.</p>
 <p >Displays the output out.</p>
 <p >Displays the magnitude of the cross product.</p>
-<div class="fragment"><div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>           {</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span><span class="comment"></span> </div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span><span class="comment">    /// Tests the functions with sample input before asking for user input.</span></div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span><span class="comment"></span>    <a class="code hl_function" href="../../df/d66/vector__cross__product_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span> </div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a> vec1;</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a> vec2;</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span><span class="comment"></span> </div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span><span class="comment">    /// Gets the values for the first vector.</span></div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPass the first Vector: &quot;</span>;</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; vec1[0] &gt;&gt; vec1[1] &gt;&gt; vec1[2];</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span><span class="comment"></span> </div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span><span class="comment">    /// Gets the values for the second vector.</span></div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPass the second Vector: &quot;</span>;</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; vec2[0] &gt;&gt; vec2[1] &gt;&gt; vec2[2];</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span><span class="comment"></span> </div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span><span class="comment">    /// Displays the output out.</span></div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a> product = <a class="code hl_function" href="../../df/d66/vector__cross__product_8cpp.html#a225732399c5c076976eae5b180a9f8c9">math::vector_cross::cross</a>(vec1, vec2);</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nThe cross product is: &quot;</span> &lt;&lt; product[0] &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; product[1] &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; product[2] &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span><span class="comment"></span> </div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span><span class="comment">    /// Displays the magnitude of the cross product.</span></div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Magnitude: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8">math::vector_cross::mag</a>(product) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span> </div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  109</span>           {</div>
+<div class="line"><span class="lineno">  110</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  111</span><span class="comment">    /// Tests the functions with sample input before asking for user input.</span></div>
+<div class="line"><span class="lineno">  112</span><span class="comment"></span>    <a class="code hl_function" href="../../df/d66/vector__cross__product_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
+<div class="line"><span class="lineno">  113</span> </div>
+<div class="line"><span class="lineno">  114</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a> vec1;</div>
+<div class="line"><span class="lineno">  115</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a> vec2;</div>
+<div class="line"><span class="lineno">  116</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  117</span><span class="comment">    /// Gets the values for the first vector.</span></div>
+<div class="line"><span class="lineno">  118</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPass the first Vector: &quot;</span>;</div>
+<div class="line"><span class="lineno">  119</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; vec1[0] &gt;&gt; vec1[1] &gt;&gt; vec1[2];</div>
+<div class="line"><span class="lineno">  120</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  121</span><span class="comment">    /// Gets the values for the second vector.</span></div>
+<div class="line"><span class="lineno">  122</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nPass the second Vector: &quot;</span>;</div>
+<div class="line"><span class="lineno">  123</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; vec2[0] &gt;&gt; vec2[1] &gt;&gt; vec2[2];</div>
+<div class="line"><span class="lineno">  124</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  125</span><span class="comment">    /// Displays the output out.</span></div>
+<div class="line"><span class="lineno">  126</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a> product = <a class="code hl_function" href="../../df/d66/vector__cross__product_8cpp.html#a225732399c5c076976eae5b180a9f8c9">math::vector_cross::cross</a>(vec1, vec2);</div>
+<div class="line"><span class="lineno">  127</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nThe cross product is: &quot;</span> &lt;&lt; product[0] &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; product[1] &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; product[2] &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  128</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  129</span><span class="comment">    /// Displays the magnitude of the cross product.</span></div>
+<div class="line"><span class="lineno">  130</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Magnitude: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8">math::vector_cross::mag</a>(product) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  131</span> </div>
+<div class="line"><span class="lineno">  132</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  133</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
@@ -333,15 +333,15 @@ Here is the call graph for this function:</div>
 <p >test the <a class="el" href="../../df/d66/vector__cross__product_8cpp.html#a225732399c5c076976eae5b180a9f8c9" title="Function to calculate the cross product of the passed arrays containing the direction ratios of the t...">cross()</a> and the <a class="el" href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8" title="Calculates the magnitude of the mathematical vector from it&#39;s direction ratios.">mag()</a> functions. </p>
 <p >Tests the <a class="el" href="../../df/d66/vector__cross__product_8cpp.html#a225732399c5c076976eae5b180a9f8c9" title="Function to calculate the cross product of the passed arrays containing the direction ratios of the t...">cross()</a> function.</p>
 <p >Tests the <a class="el" href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8" title="Calculates the magnitude of the mathematical vector from it&#39;s direction ratios.">mag()</a> function.</p>
-<div class="fragment"><div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>                   {<span class="comment"></span></div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span><span class="comment">    /// Tests the cross() function.</span></div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a> t_vec = <a class="code hl_function" href="../../df/d66/vector__cross__product_8cpp.html#a225732399c5c076976eae5b180a9f8c9">math::vector_cross::cross</a>({1, 2, 3}, {4, 5, 6});</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    assert(t_vec[0] == -3 &amp;&amp; t_vec[1] == 6 &amp;&amp; t_vec[2] == -3);</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span><span class="comment"></span> </div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span><span class="comment">    /// Tests the mag() function.</span></div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span><span class="comment"></span>    <span class="keywordtype">double</span> t_mag = <a class="code hl_function" href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8">math::vector_cross::mag</a>({6, 8, 0});</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    assert(t_mag == 10);</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   94</span>                   {<span class="comment"></span></div>
+<div class="line"><span class="lineno">   95</span><span class="comment">    /// Tests the cross() function.</span></div>
+<div class="line"><span class="lineno">   96</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a> t_vec = <a class="code hl_function" href="../../df/d66/vector__cross__product_8cpp.html#a225732399c5c076976eae5b180a9f8c9">math::vector_cross::cross</a>({1, 2, 3}, {4, 5, 6});</div>
+<div class="line"><span class="lineno">   97</span>    assert(t_vec[0] == -3 &amp;&amp; t_vec[1] == 6 &amp;&amp; t_vec[2] == -3);</div>
+<div class="line"><span class="lineno">   98</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   99</span><span class="comment">    /// Tests the mag() function.</span></div>
+<div class="line"><span class="lineno">  100</span><span class="comment"></span>    <span class="keywordtype">double</span> t_mag = <a class="code hl_function" href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8">math::vector_cross::mag</a>({6, 8, 0});</div>
+<div class="line"><span class="lineno">  101</span>    assert(t_mag == 10);</div>
+<div class="line"><span class="lineno">  102</span>}</div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -351,7 +351,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../df/d66/vector__cross__product_8cpp.html">vector_cross_product.cpp</a></li>
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diff --git a/df/d66/vector__cross__product_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.md5 b/df/d66/vector__cross__product_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.md5
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@@ -200,48 +200,48 @@ Functions</h2></td></tr>
 <p >value zero</p>
 <p >slope when the line is tangent to curve. This operation is performed while doubling. Taking derivative of <code>y^2 = x^3 + ax + b</code> =&gt; <code>2y dy = (3 * x^2 + a)dx</code> =&gt; <code>(dy/dx) = (3x^2 + a)/(2y)</code></p>
 <p >if y co-ordinate is zero, the slope is infinite, return inf. else calculate the slope (here % mod and store in lambda)</p>
-<div class="fragment"><div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>                              {</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> lambda(0);  <span class="comment">/// Slope</span></div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> zero(0);    <span class="comment">/// value zero</span></div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    lambda = zero = 0;</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> inf = ~zero;</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    <span class="keywordflow">if</span> (a.x != b.x || a.y != b.y) {</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>        <span class="comment">// Slope being infinite.</span></div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>        <span class="keywordflow">if</span> (b.x == a.x) {</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>            <span class="keywordflow">return</span> {inf, inf};</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        }</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> num = (b.y - a.y + mod), den = (b.x - a.x + mod);</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>        lambda = (num * (<a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#ac00616a4e40d3cd5cfb4da87d9ff9af0">exp</a>(den, mod - 2, mod))) % mod;</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    } <span class="keywordflow">else</span> {<span class="comment"></span></div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span><span class="comment">        /**</span></div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span><span class="comment">         *  slope when the line is tangent to curve. This operation is performed</span></div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span><span class="comment">         * while doubling. Taking derivative of `y^2 = x^3 + ax + b`</span></div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span><span class="comment">         * =&gt; `2y dy = (3 * x^2 + a)dx`</span></div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span><span class="comment">         * =&gt; `(dy/dx) = (3x^2 + a)/(2y)`</span></div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span><span class="comment">         */</span><span class="comment"></span></div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span><span class="comment">        /**</span></div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span><span class="comment">         * if y co-ordinate is zero, the slope is infinite, return inf.</span></div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span><span class="comment">         * else calculate the slope (here % mod and store in lambda)</span></div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span><span class="comment">         */</span></div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>        <span class="keywordflow">if</span> (!a.y) {</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>            <span class="keywordflow">return</span> {inf, inf};</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>        }</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> axsq = ((a.x * a.x)) % mod;</div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>        <span class="comment">// Mulitply by 3 adjustment</span></div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        axsq += (axsq &lt;&lt; 1);</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>        axsq %= mod;</div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>        <span class="comment">// Mulitply by 2 adjustment</span></div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> a_2 = (a.y &lt;&lt; 1);</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>        lambda =</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>            (((axsq + curve_a_coeff) % mod) * <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#ac00616a4e40d3cd5cfb4da87d9ff9af0">exp</a>(a_2, mod - 2, mod)) % mod;</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    }</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    <a class="code hl_struct" href="../../d8/dc8/struct_point.html">Point</a> c;</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    <span class="comment">// new point: x = ((lambda^2) - x1 - x2)</span></div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>    <span class="comment">// y = (lambda * (x1 - x)) - y1</span></div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>    c.x = ((lambda * lambda) % mod + (mod &lt;&lt; 1) - a.x - b.x) % mod;</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    c.<a class="code hl_variable" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> = (((lambda * (a.x + mod - c.x)) % mod) + mod - a.y) % mod;</div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    <span class="keywordflow">return</span> c;</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  111</span>                              {</div>
+<div class="line"><span class="lineno">  112</span>    <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> lambda(0);  <span class="comment">/// Slope</span></div>
+<div class="line"><span class="lineno">  113</span>    <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> zero(0);    <span class="comment">/// value zero</span></div>
+<div class="line"><span class="lineno">  114</span>    lambda = zero = 0;</div>
+<div class="line"><span class="lineno">  115</span>    <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> inf = ~zero;</div>
+<div class="line"><span class="lineno">  116</span>    <span class="keywordflow">if</span> (a.x != b.x || a.y != b.y) {</div>
+<div class="line"><span class="lineno">  117</span>        <span class="comment">// Slope being infinite.</span></div>
+<div class="line"><span class="lineno">  118</span>        <span class="keywordflow">if</span> (b.x == a.x) {</div>
+<div class="line"><span class="lineno">  119</span>            <span class="keywordflow">return</span> {inf, inf};</div>
+<div class="line"><span class="lineno">  120</span>        }</div>
+<div class="line"><span class="lineno">  121</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> num = (b.y - a.y + mod), den = (b.x - a.x + mod);</div>
+<div class="line"><span class="lineno">  122</span>        lambda = (num * (<a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#ac00616a4e40d3cd5cfb4da87d9ff9af0">exp</a>(den, mod - 2, mod))) % mod;</div>
+<div class="line"><span class="lineno">  123</span>    } <span class="keywordflow">else</span> {<span class="comment"></span></div>
+<div class="line"><span class="lineno">  124</span><span class="comment">        /**</span></div>
+<div class="line"><span class="lineno">  125</span><span class="comment">         *  slope when the line is tangent to curve. This operation is performed</span></div>
+<div class="line"><span class="lineno">  126</span><span class="comment">         * while doubling. Taking derivative of `y^2 = x^3 + ax + b`</span></div>
+<div class="line"><span class="lineno">  127</span><span class="comment">         * =&gt; `2y dy = (3 * x^2 + a)dx`</span></div>
+<div class="line"><span class="lineno">  128</span><span class="comment">         * =&gt; `(dy/dx) = (3x^2 + a)/(2y)`</span></div>
+<div class="line"><span class="lineno">  129</span><span class="comment">         */</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">  130</span><span class="comment">        /**</span></div>
+<div class="line"><span class="lineno">  131</span><span class="comment">         * if y co-ordinate is zero, the slope is infinite, return inf.</span></div>
+<div class="line"><span class="lineno">  132</span><span class="comment">         * else calculate the slope (here % mod and store in lambda)</span></div>
+<div class="line"><span class="lineno">  133</span><span class="comment">         */</span></div>
+<div class="line"><span class="lineno">  134</span>        <span class="keywordflow">if</span> (!a.y) {</div>
+<div class="line"><span class="lineno">  135</span>            <span class="keywordflow">return</span> {inf, inf};</div>
+<div class="line"><span class="lineno">  136</span>        }</div>
+<div class="line"><span class="lineno">  137</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> axsq = ((a.x * a.x)) % mod;</div>
+<div class="line"><span class="lineno">  138</span>        <span class="comment">// Mulitply by 3 adjustment</span></div>
+<div class="line"><span class="lineno">  139</span>        axsq += (axsq &lt;&lt; 1);</div>
+<div class="line"><span class="lineno">  140</span>        axsq %= mod;</div>
+<div class="line"><span class="lineno">  141</span>        <span class="comment">// Mulitply by 2 adjustment</span></div>
+<div class="line"><span class="lineno">  142</span>        <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> a_2 = (a.y &lt;&lt; 1);</div>
+<div class="line"><span class="lineno">  143</span>        lambda =</div>
+<div class="line"><span class="lineno">  144</span>            (((axsq + curve_a_coeff) % mod) * <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#ac00616a4e40d3cd5cfb4da87d9ff9af0">exp</a>(a_2, mod - 2, mod)) % mod;</div>
+<div class="line"><span class="lineno">  145</span>    }</div>
+<div class="line"><span class="lineno">  146</span>    <a class="code hl_struct" href="../../d8/dc8/struct_point.html">Point</a> c;</div>
+<div class="line"><span class="lineno">  147</span>    <span class="comment">// new point: x = ((lambda^2) - x1 - x2)</span></div>
+<div class="line"><span class="lineno">  148</span>    <span class="comment">// y = (lambda * (x1 - x)) - y1</span></div>
+<div class="line"><span class="lineno">  149</span>    c.x = ((lambda * lambda) % mod + (mod &lt;&lt; 1) - a.x - b.x) % mod;</div>
+<div class="line"><span class="lineno">  150</span>    c.<a class="code hl_variable" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> = (((lambda * (a.x + mod - c.x)) % mod) + mod - a.y) % mod;</div>
+<div class="line"><span class="lineno">  151</span>    <span class="keywordflow">return</span> c;</div>
+<div class="line"><span class="lineno">  152</span>}</div>
 <div class="ttc" id="aclassuint256__t_html"><div class="ttname"><a href="../../d1/d83/classuint256__t.html">uint256_t</a></div><div class="ttdoc">class for 256-bit unsigned integer</div><div class="ttdef"><b>Definition:</b> uint256_t.hpp:33</div></div>
 <div class="ttc" id="anamespaceciphers_1_1elliptic__curve__key__exchange_html_ac00616a4e40d3cd5cfb4da87d9ff9af0"><div class="ttname"><a href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#ac00616a4e40d3cd5cfb4da87d9ff9af0">ciphers::elliptic_curve_key_exchange::exp</a></div><div class="ttdeci">uint256_t exp(uint256_t number, uint256_t power, const uint256_t &amp;mod)</div><div class="ttdoc">This function calculates number raised to exponent power under modulo mod using Modular Exponentiatio...</div><div class="ttdef"><b>Definition:</b> elliptic_curve_key_exchange.cpp:78</div></div>
 <div class="ttc" id="astruct_point_html"><div class="ttname"><a href="../../d8/dc8/struct_point.html">Point</a></div><div class="ttdef"><b>Definition:</b> line_segment_intersection.cpp:12</div></div>
@@ -297,23 +297,23 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>number raised to power modulo mod </dd></dl>
-<div class="fragment"><div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>                                                                       {</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <span class="keywordflow">if</span> (!power) {</div>
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-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    number = number % mod;</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    <span class="keywordflow">while</span> (power) {</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>        <span class="keywordflow">if</span> ((power &amp; 1)) {</div>
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-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>        }</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    }</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   78</span>                                                                       {</div>
+<div class="line"><span class="lineno">   79</span>    <span class="keywordflow">if</span> (!power) {</div>
+<div class="line"><span class="lineno">   80</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(1);</div>
+<div class="line"><span class="lineno">   81</span>    }</div>
+<div class="line"><span class="lineno">   82</span>    <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>(1);</div>
+<div class="line"><span class="lineno">   83</span>    number = number % mod;</div>
+<div class="line"><span class="lineno">   84</span>    <span class="keywordflow">while</span> (power) {</div>
+<div class="line"><span class="lineno">   85</span>        <span class="keywordflow">if</span> ((power &amp; 1)) {</div>
+<div class="line"><span class="lineno">   86</span>            <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = (<a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> * number) % mod;</div>
+<div class="line"><span class="lineno">   87</span>        }</div>
+<div class="line"><span class="lineno">   88</span>        power &gt;&gt;= 1;</div>
+<div class="line"><span class="lineno">   89</span>        <span class="keywordflow">if</span> (power) {</div>
+<div class="line"><span class="lineno">   90</span>            number = (number * number) % mod;</div>
+<div class="line"><span class="lineno">   91</span>        }</div>
+<div class="line"><span class="lineno">   92</span>    }</div>
+<div class="line"><span class="lineno">   93</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
+<div class="line"><span class="lineno">   94</span>}</div>
 <div class="ttc" id="amatrix__exponentiation_8cpp_html_ad8389ed58fd0ec66df248014775ad1fa"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a></div><div class="ttdeci">ll ans(ll n)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:91</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -373,29 +373,29 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>the resultant point </dd></dl>
-<div class="fragment"><div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>                                     {</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>    <a class="code hl_struct" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">Point</a> N = a;</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    N.x %= mod;</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>    N.y %= mod;</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>    <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> inf{};</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>    inf = <a class="code hl_class" href="../../d1/d83/classuint256__t.html">~uint256_t</a>(0);</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>    <a class="code hl_struct" href="../../d8/dc8/struct_point.html">Point</a> Q = {inf, inf};</div>
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-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>        <span class="keywordflow">if</span> ((p &amp; 1)) {</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>            <span class="keywordflow">if</span> (Q.x == inf &amp;&amp; Q.<a class="code hl_variable" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> == inf) {</div>
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-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>            }</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>        }</div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>        p &gt;&gt;= 1;</div>
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-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>    <span class="keywordflow">return</span> Q;</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  166</span>                                     {</div>
+<div class="line"><span class="lineno">  167</span>    <a class="code hl_struct" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">Point</a> N = a;</div>
+<div class="line"><span class="lineno">  168</span>    N.x %= mod;</div>
+<div class="line"><span class="lineno">  169</span>    N.y %= mod;</div>
+<div class="line"><span class="lineno">  170</span>    <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> inf{};</div>
+<div class="line"><span class="lineno">  171</span>    inf = <a class="code hl_class" href="../../d1/d83/classuint256__t.html">~uint256_t</a>(0);</div>
+<div class="line"><span class="lineno">  172</span>    <a class="code hl_struct" href="../../d8/dc8/struct_point.html">Point</a> Q = {inf, inf};</div>
+<div class="line"><span class="lineno">  173</span>    <span class="keywordflow">while</span> (p) {</div>
+<div class="line"><span class="lineno">  174</span>        <span class="keywordflow">if</span> ((p &amp; 1)) {</div>
+<div class="line"><span class="lineno">  175</span>            <span class="keywordflow">if</span> (Q.x == inf &amp;&amp; Q.<a class="code hl_variable" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> == inf) {</div>
+<div class="line"><span class="lineno">  176</span>                Q.x = N.x;</div>
+<div class="line"><span class="lineno">  177</span>                Q.<a class="code hl_variable" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> = N.y;</div>
+<div class="line"><span class="lineno">  178</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">  179</span>                Q = <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#acc5fe9c2032fb7582c38a20d1fa69bcf">addition</a>(Q, N, curve_a_coeff, mod);</div>
+<div class="line"><span class="lineno">  180</span>            }</div>
+<div class="line"><span class="lineno">  181</span>        }</div>
+<div class="line"><span class="lineno">  182</span>        p &gt;&gt;= 1;</div>
+<div class="line"><span class="lineno">  183</span>        <span class="keywordflow">if</span> (p) {</div>
+<div class="line"><span class="lineno">  184</span>            <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#acc5fe9c2032fb7582c38a20d1fa69bcf">addition</a>(N, N, curve_a_coeff, mod);</div>
+<div class="line"><span class="lineno">  185</span>        }</div>
+<div class="line"><span class="lineno">  186</span>    }</div>
+<div class="line"><span class="lineno">  187</span>    <span class="keywordflow">return</span> Q;</div>
+<div class="line"><span class="lineno">  188</span>}</div>
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 <div class="ttc" id="anamespaceciphers_1_1elliptic__curve__key__exchange_html_acc5fe9c2032fb7582c38a20d1fa69bcf"><div class="ttname"><a href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#acc5fe9c2032fb7582c38a20d1fa69bcf">ciphers::elliptic_curve_key_exchange::addition</a></div><div class="ttdeci">Point addition(Point a, Point b, const uint256_t &amp;curve_a_coeff, uint256_t mod)</div><div class="ttdoc">Addition of points.</div><div class="ttdef"><b>Definition:</b> elliptic_curve_key_exchange.cpp:110</div></div>
 <div class="ttc" id="astructciphers_1_1elliptic__curve__key__exchange_1_1_point_html"><div class="ttname"><a href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">ciphers::elliptic_curve_key_exchange::Point</a></div><div class="ttdoc">Definition of struct Point.</div><div class="ttdef"><b>Definition:</b> elliptic_curve_key_exchange.cpp:46</div></div>
@@ -414,7 +414,7 @@ Here is the call graph for this function:</div>
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diff --git a/df/d72/modular__division_8cpp.html b/df/d72/modular__division_8cpp.html
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    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
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    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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-<!-- Generated by Doxygen 1.9.2 -->
+<!-- Generated by Doxygen 1.9.3 -->
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@@ -171,10 +171,10 @@ Functions</h2></td></tr>
   </dd>
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 <dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
-<div class="fragment"><div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>                                 {</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    <a class="code hl_function" href="../../df/d72/modular__division_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// execute the tests</span></div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  112</span>                                 {</div>
+<div class="line"><span class="lineno">  113</span>    <a class="code hl_function" href="../../df/d72/modular__division_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// execute the tests</span></div>
+<div class="line"><span class="lineno">  114</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  115</span>}</div>
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 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -229,12 +229,12 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd>a/b modulo c </dd></dl>
 <p >Calculate the inverse of b</p>
 <p >Calculate the final result</p>
-<div class="fragment"><div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>                                                          {</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    uint64_t inverse = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">power</a>(b, p - 2, p) % p;  <span class="comment">/// Calculate the inverse of b</span></div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>    uint64_t <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> =</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>        ((a % p) * (inverse % p)) % p;  <span class="comment">/// Calculate the final result</span></div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   74</span>                                                          {</div>
+<div class="line"><span class="lineno">   75</span>    uint64_t inverse = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">power</a>(b, p - 2, p) % p;  <span class="comment">/// Calculate the inverse of b</span></div>
+<div class="line"><span class="lineno">   76</span>    uint64_t <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> =</div>
+<div class="line"><span class="lineno">   77</span>        ((a % p) * (inverse % p)) % p;  <span class="comment">/// Calculate the final result</span></div>
+<div class="line"><span class="lineno">   78</span>    <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
+<div class="line"><span class="lineno">   79</span>}</div>
 <div class="ttc" id="afibonacci__sum_8cpp_html_a7cf5feaf168b88e74544da59ed830311"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">math::fibonacci_sum::power</a></div><div class="ttdeci">math::fibonacci_sum::matrix power(math::fibonacci_sum::matrix T, uint64_t ex)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:57</div></div>
 <div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
 </div><!-- fragment --><div class="dynheader">
@@ -294,23 +294,23 @@ Here is the call graph for this function:</div>
 <p >If b is odd, multiply a with answer</p>
 <p >b must be even now</p>
 <p >b = b/2</p>
-<div class="fragment"><div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>                                                   {</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    uint64_t <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = 1;  <span class="comment">/// Initialize the answer to be returned</span></div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    a = a % c;         <span class="comment">/// Update a if it is more than or equal to c</span></div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    <span class="keywordflow">if</span> (a == 0) {</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>        <span class="keywordflow">return</span> 0;  <span class="comment">/// In case a is divisible by c;</span></div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>    }</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <span class="keywordflow">while</span> (b &gt; 0) {<span class="comment"></span></div>
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-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>}</div>
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+<div class="line"><span class="lineno">   50</span>    uint64_t <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = 1;  <span class="comment">/// Initialize the answer to be returned</span></div>
+<div class="line"><span class="lineno">   51</span>    a = a % c;         <span class="comment">/// Update a if it is more than or equal to c</span></div>
+<div class="line"><span class="lineno">   52</span>    <span class="keywordflow">if</span> (a == 0) {</div>
+<div class="line"><span class="lineno">   53</span>        <span class="keywordflow">return</span> 0;  <span class="comment">/// In case a is divisible by c;</span></div>
+<div class="line"><span class="lineno">   54</span>    }</div>
+<div class="line"><span class="lineno">   55</span>    <span class="keywordflow">while</span> (b &gt; 0) {<span class="comment"></span></div>
+<div class="line"><span class="lineno">   56</span><span class="comment">        /// If b is odd, multiply a with answer</span></div>
+<div class="line"><span class="lineno">   57</span><span class="comment"></span>        <span class="keywordflow">if</span> (b &amp; 1) {</div>
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-<g id="a_node1"><a xlink:title="&lt;a href=&quot;https://en.wikipedia.org/wiki/Component_(graph_theory)&quot;">
+<g id="a_node1"><a xlink:title="[Graph Connected Components (Connected Components)] (https://en.wikipedia.org/wiki/Component_(graph_t...">
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- <tr style="height: 56px;">
-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
+  <td id="projectalign">
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    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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+<!-- Generated by Doxygen 1.9.3 -->
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@@ -199,28 +199,28 @@ template&lt;size_t V&gt; </div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>                                                  {</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    <span class="comment">// base case:</span></div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    <span class="comment">// If all vertices are assigned a color then return true</span></div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>    <span class="keywordflow">if</span> (v == V) {</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>        printSolution&lt;V&gt;(color);</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        <span class="keywordflow">return</span>;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    }</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span> </div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    <span class="comment">// Consider this vertex v and try different colors</span></div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> c = 1; c &lt;= m; c++) {</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>        <span class="comment">// Check if assignment of color c to v is fine</span></div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>        <span class="keywordflow">if</span> (isSafe&lt;V&gt;(v, <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>, color, c)) {</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>            color[v] = c;</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span> </div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>            <span class="comment">// recur to assign colors to rest of the vertices</span></div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>            graphColoring&lt;V&gt;(<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>, m, color, v + 1);</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span> </div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>            <span class="comment">// If assigning color c doesn&#39;t lead to a solution then remove it</span></div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>            color[v] = 0;</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>        }</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    }</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   83</span>                                                  {</div>
+<div class="line"><span class="lineno">   84</span>    <span class="comment">// base case:</span></div>
+<div class="line"><span class="lineno">   85</span>    <span class="comment">// If all vertices are assigned a color then return true</span></div>
+<div class="line"><span class="lineno">   86</span>    <span class="keywordflow">if</span> (v == V) {</div>
+<div class="line"><span class="lineno">   87</span>        printSolution&lt;V&gt;(color);</div>
+<div class="line"><span class="lineno">   88</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><span class="lineno">   89</span>    }</div>
+<div class="line"><span class="lineno">   90</span> </div>
+<div class="line"><span class="lineno">   91</span>    <span class="comment">// Consider this vertex v and try different colors</span></div>
+<div class="line"><span class="lineno">   92</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> c = 1; c &lt;= m; c++) {</div>
+<div class="line"><span class="lineno">   93</span>        <span class="comment">// Check if assignment of color c to v is fine</span></div>
+<div class="line"><span class="lineno">   94</span>        <span class="keywordflow">if</span> (isSafe&lt;V&gt;(v, <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>, color, c)) {</div>
+<div class="line"><span class="lineno">   95</span>            color[v] = c;</div>
+<div class="line"><span class="lineno">   96</span> </div>
+<div class="line"><span class="lineno">   97</span>            <span class="comment">// recur to assign colors to rest of the vertices</span></div>
+<div class="line"><span class="lineno">   98</span>            graphColoring&lt;V&gt;(<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>, m, color, v + 1);</div>
+<div class="line"><span class="lineno">   99</span> </div>
+<div class="line"><span class="lineno">  100</span>            <span class="comment">// If assigning color c doesn&#39;t lead to a solution then remove it</span></div>
+<div class="line"><span class="lineno">  101</span>            color[v] = 0;</div>
+<div class="line"><span class="lineno">  102</span>        }</div>
+<div class="line"><span class="lineno">  103</span>    }</div>
+<div class="line"><span class="lineno">  104</span>}</div>
 <div class="ttc" id="anamespacegraph_html"><div class="ttname"><a href="../../df/dce/namespacegraph.html">graph</a></div><div class="ttdoc">Graph Algorithms.</div></div>
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@@ -290,14 +290,14 @@ template&lt;size_t V&gt; </div>
 <dl class="section return"><dt>Returns</dt><dd><code>true</code> if the color is safe to be assigned to the node </dd>
 <dd>
 <code>false</code> if the color is not safe to be assigned to the node </dd></dl>
-<div class="fragment"><div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>                                                  {</div>
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-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        <span class="keywordflow">if</span> (<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>[v][i] &amp;&amp; c == color[i]) {</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    }</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   63</span>                                                  {</div>
+<div class="line"><span class="lineno">   64</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; V; i++) {</div>
+<div class="line"><span class="lineno">   65</span>        <span class="keywordflow">if</span> (<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>[v][i] &amp;&amp; c == color[i]) {</div>
+<div class="line"><span class="lineno">   66</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   67</span>        }</div>
+<div class="line"><span class="lineno">   68</span>    }</div>
+<div class="line"><span class="lineno">   69</span>    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   70</span>}</div>
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 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -328,25 +328,25 @@ Here is the call graph for this function:</div>
 <p>Driver Code </p>
 <dl class="section examples"><dt>Examples</dt><dd><a class="el" href="../../dc/dc4/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2numerical_methods_2rungekutta_8cpp-example.html#a7">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp</a>, and <a class="el" href="../../dd/db0/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2sorting_2wiggle_sort_8cpp-example.html#a11">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/sorting/wiggle_sort.cpp</a>.</dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>           {</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    <span class="comment">// Create following graph and test whether it is 3 colorable</span></div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    <span class="comment">// (3)---(2)</span></div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    <span class="comment">// |   / |</span></div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    <span class="comment">// |  /  |</span></div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    <span class="comment">// | /   |</span></div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    <span class="comment">// (0)---(1)</span></div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span> </div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> V = 4;  <span class="comment">// number of vertices in the graph</span></div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;int, V&gt;</a>, V&gt; <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a> = {</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>({0, 1, 1, 1}), <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>({1, 0, 1, 0}),</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>({1, 1, 0, 1}), <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>({1, 0, 1, 0})};</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span> </div>
-<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>    <span class="keywordtype">int</span> m = 3;  <span class="comment">// Number of colors</span></div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a> color{};</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span> </div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    backtracking::graph_coloring::graphColoring&lt;V&gt;(<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>, m, color, 0);</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  112</span>           {</div>
+<div class="line"><span class="lineno">  113</span>    <span class="comment">// Create following graph and test whether it is 3 colorable</span></div>
+<div class="line"><span class="lineno">  114</span>    <span class="comment">// (3)---(2)</span></div>
+<div class="line"><span class="lineno">  115</span>    <span class="comment">// |   / |</span></div>
+<div class="line"><span class="lineno">  116</span>    <span class="comment">// |  /  |</span></div>
+<div class="line"><span class="lineno">  117</span>    <span class="comment">// | /   |</span></div>
+<div class="line"><span class="lineno">  118</span>    <span class="comment">// (0)---(1)</span></div>
+<div class="line"><span class="lineno">  119</span> </div>
+<div class="line"><span class="lineno">  120</span>    <span class="keyword">const</span> <span class="keywordtype">int</span> V = 4;  <span class="comment">// number of vertices in the graph</span></div>
+<div class="line"><span class="lineno">  121</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;int, V&gt;</a>, V&gt; <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a> = {</div>
+<div class="line"><span class="lineno">  122</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>({0, 1, 1, 1}), <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>({1, 0, 1, 0}),</div>
+<div class="line"><span class="lineno">  123</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>({1, 1, 0, 1}), <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>({1, 0, 1, 0})};</div>
+<div class="line"><span class="lineno">  124</span> </div>
+<div class="line"><span class="lineno">  125</span>    <span class="keywordtype">int</span> m = 3;  <span class="comment">// Number of colors</span></div>
+<div class="line"><span class="lineno">  126</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a> color{};</div>
+<div class="line"><span class="lineno">  127</span> </div>
+<div class="line"><span class="lineno">  128</span>    backtracking::graph_coloring::graphColoring&lt;V&gt;(<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>, m, color, 0);</div>
+<div class="line"><span class="lineno">  129</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  130</span>}</div>
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@@ -382,13 +382,13 @@ template&lt;size_t V&gt; </div>
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+<div class="line"><span class="lineno">   43</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Following are the assigned colors\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   44</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span>&amp; col : color) {</div>
+<div class="line"><span class="lineno">   45</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; col;</div>
+<div class="line"><span class="lineno">   46</span>    }</div>
+<div class="line"><span class="lineno">   47</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   48</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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@@ -405,7 +405,7 @@ Here is the call graph for this function:</div>
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 <title>Algorithms_in_C++: graph/breadth_first_search.cpp File Reference</title>
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@@ -30,8 +30,8 @@ MathJax.Hub.Config({
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- <tr style="height: 56px;">
-  <td id="projectalign" style="padding-left: 0.5em;">
+ <tr id="projectrow">
+  <td id="projectalign">
    <div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
    </div>
    <div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
 </table>
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+<!-- Generated by Doxygen 1.9.3 -->
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 var searchBox = new SearchBox("searchBox", "../../search",'Search','.html');
@@ -175,25 +175,25 @@ Functions</h2></td></tr>
       </table>
 </div><div class="memdoc">
 <p >Main function </p>
-<div class="fragment"><div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>           {</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>    <a class="code hl_function" href="../../df/d82/breadth__first__search_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>();</div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>    <span class="keywordtype">size_t</span> edges = 0;</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number of edges: &quot;</span>;</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; edges;</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span> </div>
-<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>    <a class="code hl_class" href="../../dc/d61/classgraph_1_1_graph.html">graph::Graph&lt;int&gt;</a> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>;</div>
-<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span> </div>
-<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter space-separated pairs of vertices that form edges: &quot;</span></div>
-<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>    <span class="keywordflow">while</span> (edges--) {</div>
-<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>        <span class="keywordtype">int</span> u = 0, v = 0;</div>
-<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; u &gt;&gt; v;</div>
-<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>        <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>.add_edge(u, v);</div>
-<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    }</div>
-<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span> </div>
-<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>    <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>.breadth_first_search(0);</div>
-<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  186</span>           {</div>
+<div class="line"><span class="lineno">  187</span>    <a class="code hl_function" href="../../df/d82/breadth__first__search_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>();</div>
+<div class="line"><span class="lineno">  188</span>    <span class="keywordtype">size_t</span> edges = 0;</div>
+<div class="line"><span class="lineno">  189</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number of edges: &quot;</span>;</div>
+<div class="line"><span class="lineno">  190</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; edges;</div>
+<div class="line"><span class="lineno">  191</span> </div>
+<div class="line"><span class="lineno">  192</span>    <a class="code hl_class" href="../../dc/d61/classgraph_1_1_graph.html">graph::Graph&lt;int&gt;</a> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>;</div>
+<div class="line"><span class="lineno">  193</span> </div>
+<div class="line"><span class="lineno">  194</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter space-separated pairs of vertices that form edges: &quot;</span></div>
+<div class="line"><span class="lineno">  195</span>              &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  196</span>    <span class="keywordflow">while</span> (edges--) {</div>
+<div class="line"><span class="lineno">  197</span>        <span class="keywordtype">int</span> u = 0, v = 0;</div>
+<div class="line"><span class="lineno">  198</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; u &gt;&gt; v;</div>
+<div class="line"><span class="lineno">  199</span>        <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>.add_edge(u, v);</div>
+<div class="line"><span class="lineno">  200</span>    }</div>
+<div class="line"><span class="lineno">  201</span> </div>
+<div class="line"><span class="lineno">  202</span>    <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>.breadth_first_search(0);</div>
+<div class="line"><span class="lineno">  203</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  204</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="abreadth__first__search_8cpp_html_a483bb8ccf42aaf7375a83e91490eda1e"><div class="ttname"><a href="../../df/d82/breadth__first__search_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a></div><div class="ttdeci">static void tests()</div><div class="ttdef"><b>Definition:</b> breadth_first_search.cpp:139</div></div>
@@ -235,51 +235,51 @@ Here is the call graph for this function:</div>
 <p >Test 1 Begin</p>
 <p >Test 2 Begin</p>
 <p >Test 3 Begins</p>
-<div class="fragment"><div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>                    {<span class="comment"></span></div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span><span class="comment">    /// Test 1 Begin</span></div>
-<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span><span class="comment"></span>    <a class="code hl_class" href="../../dc/d61/classgraph_1_1_graph.html">graph::Graph&lt;int&gt;</a> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>;</div>
-<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map&lt;int, bool&gt;</a> correct_result;</div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>.add_edge(0, 1);</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>.add_edge(1, 2);</div>
-<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>.add_edge(2, 3);</div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    correct_result[0] = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    correct_result[1] = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>    correct_result[2] = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>    correct_result[3] = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span> </div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map&lt;int, bool&gt;</a> returned_result = <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>.breadth_first_search(2);</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span> </div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>    assert(returned_result == correct_result);</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span><span class="comment"></span> </div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span><span class="comment">    /// Test 2 Begin</span></div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span><span class="comment"></span>    returned_result = <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>.breadth_first_search(0);</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span> </div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>    assert(returned_result == correct_result);</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span><span class="comment"></span> </div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span><span class="comment">    /// Test 3 Begins</span></div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span><span class="comment"></span>    <a class="code hl_class" href="../../dc/d61/classgraph_1_1_graph.html">graph::Graph&lt;std::string&gt;</a> g2;</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span> </div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>    g2.<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a877b2cba40d8d46dde6fb4209effed19">add_edge</a>(<span class="stringliteral">&quot;Gorakhpur&quot;</span>, <span class="stringliteral">&quot;Lucknow&quot;</span>, <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    g2.<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a877b2cba40d8d46dde6fb4209effed19">add_edge</a>(<span class="stringliteral">&quot;Gorakhpur&quot;</span>, <span class="stringliteral">&quot;Kanpur&quot;</span>, <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>    g2.<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a877b2cba40d8d46dde6fb4209effed19">add_edge</a>(<span class="stringliteral">&quot;Lucknow&quot;</span>, <span class="stringliteral">&quot;Agra&quot;</span>, <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    g2.<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a877b2cba40d8d46dde6fb4209effed19">add_edge</a>(<span class="stringliteral">&quot;Kanpur&quot;</span>, <span class="stringliteral">&quot;Agra&quot;</span>, <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>    g2.<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a877b2cba40d8d46dde6fb4209effed19">add_edge</a>(<span class="stringliteral">&quot;Lucknow&quot;</span>, <span class="stringliteral">&quot;Prayagraj&quot;</span>, <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>    g2.<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a877b2cba40d8d46dde6fb4209effed19">add_edge</a>(<span class="stringliteral">&quot;Agra&quot;</span>, <span class="stringliteral">&quot;Noida&quot;</span>, <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span> </div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map&lt;std::string, bool&gt;</a> correct_res;</div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map&lt;std::string, bool&gt;</a> returned_res =</div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>        g2.<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a3755ec9e6a842238c7f4aac10b661981">breadth_first_search</a>(<span class="stringliteral">&quot;Kanpur&quot;</span>);</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>    correct_res[<span class="stringliteral">&quot;Gorakhpur&quot;</span>] = <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>    correct_res[<span class="stringliteral">&quot;Lucknow&quot;</span>] = <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>    correct_res[<span class="stringliteral">&quot;Kanpur&quot;</span>] = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>    correct_res[<span class="stringliteral">&quot;Agra&quot;</span>] = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>    correct_res[<span class="stringliteral">&quot;Prayagraj&quot;</span>] = <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>    correct_res[<span class="stringliteral">&quot;Noida&quot;</span>] = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>    assert(correct_res == returned_res);</div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  139</span>                    {<span class="comment"></span></div>
+<div class="line"><span class="lineno">  140</span><span class="comment">    /// Test 1 Begin</span></div>
+<div class="line"><span class="lineno">  141</span><span class="comment"></span>    <a class="code hl_class" href="../../dc/d61/classgraph_1_1_graph.html">graph::Graph&lt;int&gt;</a> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>;</div>
+<div class="line"><span class="lineno">  142</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map&lt;int, bool&gt;</a> correct_result;</div>
+<div class="line"><span class="lineno">  143</span>    <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>.add_edge(0, 1);</div>
+<div class="line"><span class="lineno">  144</span>    <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>.add_edge(1, 2);</div>
+<div class="line"><span class="lineno">  145</span>    <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>.add_edge(2, 3);</div>
+<div class="line"><span class="lineno">  146</span>    correct_result[0] = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  147</span>    correct_result[1] = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  148</span>    correct_result[2] = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  149</span>    correct_result[3] = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  150</span> </div>
+<div class="line"><span class="lineno">  151</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map&lt;int, bool&gt;</a> returned_result = <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>.breadth_first_search(2);</div>
+<div class="line"><span class="lineno">  152</span> </div>
+<div class="line"><span class="lineno">  153</span>    assert(returned_result == correct_result);</div>
+<div class="line"><span class="lineno">  154</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  155</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  156</span><span class="comment">    /// Test 2 Begin</span></div>
+<div class="line"><span class="lineno">  157</span><span class="comment"></span>    returned_result = <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a>.breadth_first_search(0);</div>
+<div class="line"><span class="lineno">  158</span> </div>
+<div class="line"><span class="lineno">  159</span>    assert(returned_result == correct_result);</div>
+<div class="line"><span class="lineno">  160</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  161</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">  162</span><span class="comment">    /// Test 3 Begins</span></div>
+<div class="line"><span class="lineno">  163</span><span class="comment"></span>    <a class="code hl_class" href="../../dc/d61/classgraph_1_1_graph.html">graph::Graph&lt;std::string&gt;</a> g2;</div>
+<div class="line"><span class="lineno">  164</span> </div>
+<div class="line"><span class="lineno">  165</span>    g2.<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a877b2cba40d8d46dde6fb4209effed19">add_edge</a>(<span class="stringliteral">&quot;Gorakhpur&quot;</span>, <span class="stringliteral">&quot;Lucknow&quot;</span>, <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  166</span>    g2.<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a877b2cba40d8d46dde6fb4209effed19">add_edge</a>(<span class="stringliteral">&quot;Gorakhpur&quot;</span>, <span class="stringliteral">&quot;Kanpur&quot;</span>, <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  167</span>    g2.<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a877b2cba40d8d46dde6fb4209effed19">add_edge</a>(<span class="stringliteral">&quot;Lucknow&quot;</span>, <span class="stringliteral">&quot;Agra&quot;</span>, <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  168</span>    g2.<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a877b2cba40d8d46dde6fb4209effed19">add_edge</a>(<span class="stringliteral">&quot;Kanpur&quot;</span>, <span class="stringliteral">&quot;Agra&quot;</span>, <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  169</span>    g2.<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a877b2cba40d8d46dde6fb4209effed19">add_edge</a>(<span class="stringliteral">&quot;Lucknow&quot;</span>, <span class="stringliteral">&quot;Prayagraj&quot;</span>, <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  170</span>    g2.<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a877b2cba40d8d46dde6fb4209effed19">add_edge</a>(<span class="stringliteral">&quot;Agra&quot;</span>, <span class="stringliteral">&quot;Noida&quot;</span>, <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  171</span> </div>
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+<div class="line"><span class="lineno">  173</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map&lt;std::string, bool&gt;</a> returned_res =</div>
+<div class="line"><span class="lineno">  174</span>        g2.<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a3755ec9e6a842238c7f4aac10b661981">breadth_first_search</a>(<span class="stringliteral">&quot;Kanpur&quot;</span>);</div>
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+<div class="line"><span class="lineno">  176</span>    correct_res[<span class="stringliteral">&quot;Lucknow&quot;</span>] = <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  177</span>    correct_res[<span class="stringliteral">&quot;Kanpur&quot;</span>] = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  178</span>    correct_res[<span class="stringliteral">&quot;Agra&quot;</span>] = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  179</span>    correct_res[<span class="stringliteral">&quot;Prayagraj&quot;</span>] = <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">  180</span>    correct_res[<span class="stringliteral">&quot;Noida&quot;</span>] = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">  181</span>    assert(correct_res == returned_res);</div>
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+<div class="line"><span class="lineno">   40</span>    int64_t count_of_subset = 0;</div>
+<div class="line"><span class="lineno">   41</span>    int64_t current_sum = 0;</div>
+<div class="line"><span class="lineno">   42</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map.html">std::unordered_map&lt;int64_t, int64_t&gt;</a></div>
+<div class="line"><span class="lineno">   43</span>        sumarray;  <span class="comment">// to store the subarrays count</span></div>
+<div class="line"><span class="lineno">   44</span>                   <span class="comment">// frequency having some sum value</span></div>
+<div class="line"><span class="lineno">   45</span> </div>
+<div class="line"><span class="lineno">   46</span>    <span class="keywordflow">for</span> (int64_t i = 0; i &lt; nelement; i++) {</div>
+<div class="line"><span class="lineno">   47</span>        current_sum += in_arr[i];</div>
+<div class="line"><span class="lineno">   48</span> </div>
+<div class="line"><span class="lineno">   49</span>        <span class="keywordflow">if</span> (current_sum == <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>) {</div>
+<div class="line"><span class="lineno">   50</span>            count_of_subset++;</div>
+<div class="line"><span class="lineno">   51</span>        }</div>
+<div class="line"><span class="lineno">   52</span>        <span class="comment">// If in case current_sum is greater than the required sum</span></div>
+<div class="line"><span class="lineno">   53</span>        <span class="keywordflow">if</span> (sumarray.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/find.html">find</a>(current_sum - <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>) != sumarray.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map/end.html">end</a>()) {</div>
+<div class="line"><span class="lineno">   54</span>            count_of_subset += (sumarray[current_sum - <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>]);</div>
+<div class="line"><span class="lineno">   55</span>        }</div>
+<div class="line"><span class="lineno">   56</span>        sumarray[current_sum]++;</div>
+<div class="line"><span class="lineno">   57</span>    }</div>
+<div class="line"><span class="lineno">   58</span>    <span class="keywordflow">return</span> count_of_subset;</div>
+<div class="line"><span class="lineno">   59</span>}</div>
 <div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/unordered_map/end.html">std::unordered_map::end</a></div><div class="ttdeci">T end(T... args)</div></div>
 <div class="ttc" id="afind_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/unordered_map/find.html">std::unordered_map::find</a></div><div class="ttdeci">T find(T... args)</div></div>
 <div class="ttc" id="anamespacemachine__learning_html_a6f1c98c016ad34ff3d9f39372161bd35"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">machine_learning::sum</a></div><div class="ttdeci">T sum(const std::vector&lt; std::valarray&lt; T &gt; &gt; &amp;A)</div><div class="ttdef"><b>Definition:</b> vector_ops.hpp:232</div></div>
@@ -264,51 +264,51 @@ Here is the call graph for this function:</div>
 
 <p>Self-test implementations. </p>
 <dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
-<div class="fragment"><div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>                   {</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <span class="comment">// 1st test</span></div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test &quot;</span>;</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array1 = {-7, -3, -2, 5, 8};  <span class="comment">// input array</span></div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    assert(</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>        backtracking::subarray_sum::subarray_sum(0, array1) ==</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>        1);  <span class="comment">// first argument in subarray_sum function is the required sum and</span></div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>             <span class="comment">// second is the input array, answer is the subarray {(-3,-2,5)}</span></div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span> </div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <span class="comment">// 2nd test</span></div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test &quot;</span>;</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array2 = {1, 2, 3, 3};</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    assert(backtracking::subarray_sum::subarray_sum(6, array2) ==</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>           2);  <span class="comment">// here we are expecting 2 subsets which sum up to 6 i.e.</span></div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>                <span class="comment">// {(1,2,3),(3,3)}</span></div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span> </div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    <span class="comment">// 3rd test</span></div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3rd test &quot;</span>;</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array3 = {1, 1, 1, 1};</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    assert(backtracking::subarray_sum::subarray_sum(1, array3) ==</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>           4);  <span class="comment">// here we are expecting 4 subsets which sum up to 1 i.e.</span></div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>                <span class="comment">// {(1),(1),(1),(1)}</span></div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span> </div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    <span class="comment">// 4rd test</span></div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4th test &quot;</span>;</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array4 = {3, 3, 3, 3};</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    assert(backtracking::subarray_sum::subarray_sum(6, array4) ==</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>           3);  <span class="comment">// here we are expecting 3 subsets which sum up to 6 i.e.</span></div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>                <span class="comment">// {(3,3),(3,3),(3,3)}</span></div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span> </div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <span class="comment">// 5th test</span></div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;5th test &quot;</span>;</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array5 = {};</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    assert(backtracking::subarray_sum::subarray_sum(6, array5) ==</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>           0);  <span class="comment">// here we are expecting 0 subsets which sum up to 6 i.e. we</span></div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>                <span class="comment">// cannot select anything from an empty array</span></div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   67</span>                   {</div>
+<div class="line"><span class="lineno">   68</span>    <span class="comment">// 1st test</span></div>
+<div class="line"><span class="lineno">   69</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test &quot;</span>;</div>
+<div class="line"><span class="lineno">   70</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array1 = {-7, -3, -2, 5, 8};  <span class="comment">// input array</span></div>
+<div class="line"><span class="lineno">   71</span>    assert(</div>
+<div class="line"><span class="lineno">   72</span>        backtracking::subarray_sum::subarray_sum(0, array1) ==</div>
+<div class="line"><span class="lineno">   73</span>        1);  <span class="comment">// first argument in subarray_sum function is the required sum and</span></div>
+<div class="line"><span class="lineno">   74</span>             <span class="comment">// second is the input array, answer is the subarray {(-3,-2,5)}</span></div>
+<div class="line"><span class="lineno">   75</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   76</span> </div>
+<div class="line"><span class="lineno">   77</span>    <span class="comment">// 2nd test</span></div>
+<div class="line"><span class="lineno">   78</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test &quot;</span>;</div>
+<div class="line"><span class="lineno">   79</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array2 = {1, 2, 3, 3};</div>
+<div class="line"><span class="lineno">   80</span>    assert(backtracking::subarray_sum::subarray_sum(6, array2) ==</div>
+<div class="line"><span class="lineno">   81</span>           2);  <span class="comment">// here we are expecting 2 subsets which sum up to 6 i.e.</span></div>
+<div class="line"><span class="lineno">   82</span>                <span class="comment">// {(1,2,3),(3,3)}</span></div>
+<div class="line"><span class="lineno">   83</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   84</span> </div>
+<div class="line"><span class="lineno">   85</span>    <span class="comment">// 3rd test</span></div>
+<div class="line"><span class="lineno">   86</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3rd test &quot;</span>;</div>
+<div class="line"><span class="lineno">   87</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array3 = {1, 1, 1, 1};</div>
+<div class="line"><span class="lineno">   88</span>    assert(backtracking::subarray_sum::subarray_sum(1, array3) ==</div>
+<div class="line"><span class="lineno">   89</span>           4);  <span class="comment">// here we are expecting 4 subsets which sum up to 1 i.e.</span></div>
+<div class="line"><span class="lineno">   90</span>                <span class="comment">// {(1),(1),(1),(1)}</span></div>
+<div class="line"><span class="lineno">   91</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   92</span> </div>
+<div class="line"><span class="lineno">   93</span>    <span class="comment">// 4rd test</span></div>
+<div class="line"><span class="lineno">   94</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4th test &quot;</span>;</div>
+<div class="line"><span class="lineno">   95</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array4 = {3, 3, 3, 3};</div>
+<div class="line"><span class="lineno">   96</span>    assert(backtracking::subarray_sum::subarray_sum(6, array4) ==</div>
+<div class="line"><span class="lineno">   97</span>           3);  <span class="comment">// here we are expecting 3 subsets which sum up to 6 i.e.</span></div>
+<div class="line"><span class="lineno">   98</span>                <span class="comment">// {(3,3),(3,3),(3,3)}</span></div>
+<div class="line"><span class="lineno">   99</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  100</span> </div>
+<div class="line"><span class="lineno">  101</span>    <span class="comment">// 5th test</span></div>
+<div class="line"><span class="lineno">  102</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;5th test &quot;</span>;</div>
+<div class="line"><span class="lineno">  103</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array5 = {};</div>
+<div class="line"><span class="lineno">  104</span>    assert(backtracking::subarray_sum::subarray_sum(6, array5) ==</div>
+<div class="line"><span class="lineno">  105</span>           0);  <span class="comment">// here we are expecting 0 subsets which sum up to 6 i.e. we</span></div>
+<div class="line"><span class="lineno">  106</span>                <span class="comment">// cannot select anything from an empty array</span></div>
+<div class="line"><span class="lineno">  107</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  108</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int64_t &gt;</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
@@ -324,7 +324,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_c11585dfcef32a26e29098facab6c144.html">backtracking</a></li><li class="navelem"><a class="el" href="../../df/d94/subarray__sum_8cpp.html">subarray_sum.cpp</a></li>
-    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.2 </li>
+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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diff --git a/df/d94/subarray__sum_8cpp_aa8dca7b867074164d5f45b0f3851269d_cgraph.map b/df/d94/subarray__sum_8cpp_aa8dca7b867074164d5f45b0f3851269d_cgraph.map
index 4aada47a7..437744541 100644
--- a/df/d94/subarray__sum_8cpp_aa8dca7b867074164d5f45b0f3851269d_cgraph.map
+++ b/df/d94/subarray__sum_8cpp_aa8dca7b867074164d5f45b0f3851269d_cgraph.map
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+ <div class="fragment"><div class="line"><span class="lineno">   12</span>{ <span class="keywordflow">return</span> (3 * y) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">cos</a>(y) - 2; }</div>
 <div class="ttc" id="acos_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a></div><div class="ttdeci">T cos(T... args)</div></div>
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 </div>
@@ -176,7 +176,7 @@ Functions</h2></td></tr>
 <p >equation 2 </p><p class="formulaDsp">
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 </p>
- <div class="fragment"><div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span>{ <span class="keywordflow">return</span> 0.5 * (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">cos</a>(y) + 2); }</div>
+ <div class="fragment"><div class="line"><span class="lineno">   17</span>{ <span class="keywordflow">return</span> 0.5 * (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">cos</a>(y) + 2); }</div>
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@@ -196,27 +196,27 @@ Functions</h2></td></tr>
       </table>
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 <p >Main function </p>
-<div class="fragment"><div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span>           {</div>
-<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>    <span class="keywordtype">float</span> y, x1, x2, x3, <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>, s, a, f1, f2, gd;</div>
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-<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span>    <span class="keywordflow">for</span> (i = 0; i &lt; 10; i++) {</div>
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-<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;value of equation at &quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>        y++;</div>
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-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; x1;</div>
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-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
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-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>        x1 = x2;</div>
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-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   20</span>           {</div>
+<div class="line"><span class="lineno">   21</span>    <span class="keywordtype">float</span> y, x1, x2, x3, <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>, s, a, f1, f2, gd;</div>
+<div class="line"><span class="lineno">   22</span>    <span class="keywordtype">int</span> i, n;</div>
+<div class="line"><span class="lineno">   23</span> </div>
+<div class="line"><span class="lineno">   24</span>    <span class="keywordflow">for</span> (i = 0; i &lt; 10; i++) {</div>
+<div class="line"><span class="lineno">   25</span>        <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a> = <a class="code hl_function" href="../../df/dc8/successive__approximation_8cpp.html#a79c1d08919ff7780a5d7723172602389">eq</a>(y);</div>
+<div class="line"><span class="lineno">   26</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;value of equation at &quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   27</span>        y++;</div>
+<div class="line"><span class="lineno">   28</span>    }</div>
+<div class="line"><span class="lineno">   29</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;enter the x1-&gt;&quot;</span>;</div>
+<div class="line"><span class="lineno">   30</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; x1;</div>
+<div class="line"><span class="lineno">   31</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;enter the no iteration to perform-&gt;\n&quot;</span>;</div>
+<div class="line"><span class="lineno">   32</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
+<div class="line"><span class="lineno">   33</span> </div>
+<div class="line"><span class="lineno">   34</span>    <span class="keywordflow">for</span> (i = 0; i &lt;= n; i++) {</div>
+<div class="line"><span class="lineno">   35</span>        x2 = <a class="code hl_function" href="../../df/dc8/successive__approximation_8cpp.html#ae89c36add7c55298c5195d0a83de1456">eqd</a>(x1);</div>
+<div class="line"><span class="lineno">   36</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nenter the x2-&gt;&quot;</span> &lt;&lt; x2;</div>
+<div class="line"><span class="lineno">   37</span>        x1 = x2;</div>
+<div class="line"><span class="lineno">   38</span>    }</div>
+<div class="line"><span class="lineno">   39</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">   40</span>}</div>
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@@ -237,7 +237,7 @@ Here is the call graph for this function:</div>
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@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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+<!-- Generated by Doxygen 1.9.3 -->
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+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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@@ -201,10 +201,10 @@ Functions</h2></td></tr>
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-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   46</span>                                                           {</div>
+<div class="line"><span class="lineno">   47</span>    (*adj)[u - 1].push_back(v - 1);</div>
+<div class="line"><span class="lineno">   48</span>    (*adj)[v - 1].push_back(u - 1);</div>
+<div class="line"><span class="lineno">   49</span>}</div>
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@@ -249,17 +249,17 @@ Functions</h2></td></tr>
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-<div class="fragment"><div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>                                                                    {</div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    <span class="comment">/*</span></div>
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-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    (*adj)[u - 1].push_back(v - 1);</div>
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-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   56</span>                                                                    {</div>
+<div class="line"><span class="lineno">   57</span>    <span class="comment">/*</span></div>
+<div class="line"><span class="lineno">   58</span><span class="comment">     *</span></div>
+<div class="line"><span class="lineno">   59</span><span class="comment">     * Here we are considering undirected graph that&#39;s the</span></div>
+<div class="line"><span class="lineno">   60</span><span class="comment">     * reason we are adding v to the adjacency list representation of u</span></div>
+<div class="line"><span class="lineno">   61</span><span class="comment">     * and also adding u to the adjacency list representation of v</span></div>
+<div class="line"><span class="lineno">   62</span><span class="comment">     *</span></div>
+<div class="line"><span class="lineno">   63</span><span class="comment">     */</span></div>
+<div class="line"><span class="lineno">   64</span>    (*adj)[u - 1].push_back(v - 1);</div>
+<div class="line"><span class="lineno">   65</span>    (*adj)[v - 1].push_back(u - 1);</div>
+<div class="line"><span class="lineno">   66</span>}</div>
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-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    <span class="comment">// (*adj)[v - 1].push_back(std::make_pair(u - 1, w));</span></div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   49</span>                    {</div>
+<div class="line"><span class="lineno">   50</span>    (*adj)[u - 1].push_back(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(v - 1, w));</div>
+<div class="line"><span class="lineno">   51</span>    <span class="comment">// (*adj)[v - 1].push_back(std::make_pair(u - 1, w));</span></div>
+<div class="line"><span class="lineno">   52</span>}</div>
 <div class="ttc" id="amake_pair_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a></div><div class="ttdeci">T make_pair(T... args)</div></div>
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 <p >insert the neighbouring node into the queue</p>
 <p >if both the current node and its neighbour has the same state then it is not a bipartite graph</p>
 <p >return true when all the connected nodes of the current nodes are travelled and satisify all the above conditions</p>
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-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>        int64_t u = q.front();</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>        q.pop();</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>        <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>[u].size(); i++) {</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>            int64_t v =</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>                <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>[u][i];     <span class="comment">///&lt; stores the neighbour of the current node</span></div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>            <span class="keywordflow">if</span> (!(*visited)[v])  <span class="comment">/// check whether the neighbour node is</span><span class="comment"></span></div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span><span class="comment">                                 /// travelled already or not</span></div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span><span class="comment"></span>            {</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>                (*visited)[v] =</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>                    ((*visited)[u] == 1)</div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>                        ? -1</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>                        : 1;  <span class="comment">/// colour the neighbouring node with</span><span class="comment"></span></div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span><span class="comment">                              /// different colour than the current node</span></div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span><span class="comment"></span>                q.push(v);    <span class="comment">/// insert the neighbouring node into the queue</span></div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> ((*visited)[v] ==</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>                       (*visited)[u])  <span class="comment">/// if both the current node and its</span><span class="comment"></span></div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span><span class="comment">                                       /// neighbour has the same state then it</span></div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span><span class="comment">                                       /// is not a bipartite graph</span></div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span><span class="comment"></span>            {</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>                <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>            }</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        }</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    }</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <span class="keywordflow">return</span> <span class="keyword">true</span>;  <span class="comment">/// return true when all the connected nodes of the current</span><span class="comment"></span></div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span><span class="comment">                  /// nodes are travelled and satisify all the above conditions</span></div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span><span class="comment"></span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   37</span>                                                                {</div>
+<div class="line"><span class="lineno">   38</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue&lt;int64_t&gt;</a> q;  <span class="comment">///&lt; stores the neighbouring node indexes in squence</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">   39</span><span class="comment">                            /// of being reached</span></div>
+<div class="line"><span class="lineno">   40</span><span class="comment"></span>    q.push(index);          <span class="comment">/// insert the current node into the queue</span></div>
+<div class="line"><span class="lineno">   41</span>    (*visited)[index] = 1;  <span class="comment">/// mark the current node as travelled</span></div>
+<div class="line"><span class="lineno">   42</span>    <span class="keywordflow">while</span> (q.size()) {</div>
+<div class="line"><span class="lineno">   43</span>        int64_t u = q.front();</div>
+<div class="line"><span class="lineno">   44</span>        q.pop();</div>
+<div class="line"><span class="lineno">   45</span>        <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>[u].size(); i++) {</div>
+<div class="line"><span class="lineno">   46</span>            int64_t v =</div>
+<div class="line"><span class="lineno">   47</span>                <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>[u][i];     <span class="comment">///&lt; stores the neighbour of the current node</span></div>
+<div class="line"><span class="lineno">   48</span>            <span class="keywordflow">if</span> (!(*visited)[v])  <span class="comment">/// check whether the neighbour node is</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">   49</span><span class="comment">                                 /// travelled already or not</span></div>
+<div class="line"><span class="lineno">   50</span><span class="comment"></span>            {</div>
+<div class="line"><span class="lineno">   51</span>                (*visited)[v] =</div>
+<div class="line"><span class="lineno">   52</span>                    ((*visited)[u] == 1)</div>
+<div class="line"><span class="lineno">   53</span>                        ? -1</div>
+<div class="line"><span class="lineno">   54</span>                        : 1;  <span class="comment">/// colour the neighbouring node with</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">   55</span><span class="comment">                              /// different colour than the current node</span></div>
+<div class="line"><span class="lineno">   56</span><span class="comment"></span>                q.push(v);    <span class="comment">/// insert the neighbouring node into the queue</span></div>
+<div class="line"><span class="lineno">   57</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> ((*visited)[v] ==</div>
+<div class="line"><span class="lineno">   58</span>                       (*visited)[u])  <span class="comment">/// if both the current node and its</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">   59</span><span class="comment">                                       /// neighbour has the same state then it</span></div>
+<div class="line"><span class="lineno">   60</span><span class="comment">                                       /// is not a bipartite graph</span></div>
+<div class="line"><span class="lineno">   61</span><span class="comment"></span>            {</div>
+<div class="line"><span class="lineno">   62</span>                <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><span class="lineno">   63</span>            }</div>
+<div class="line"><span class="lineno">   64</span>        }</div>
+<div class="line"><span class="lineno">   65</span>    }</div>
+<div class="line"><span class="lineno">   66</span>    <span class="keywordflow">return</span> <span class="keyword">true</span>;  <span class="comment">/// return true when all the connected nodes of the current</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">   67</span><span class="comment">                  /// nodes are travelled and satisify all the above conditions</span></div>
+<div class="line"><span class="lineno">   68</span><span class="comment"></span>}</div>
 <div class="ttc" id="anamespacegraph_html"><div class="ttname"><a href="../../df/dce/namespacegraph.html">graph</a></div><div class="ttdoc">Graph Algorithms.</div></div>
-<div class="ttc" id="aqueue_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue</a></div></div>
+<div class="ttc" id="aqueue_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue&lt; int64_t &gt;</a></div></div>
 </div><!-- fragment -->
 </div>
 </div>
@@ -445,18 +445,19 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>                                      {</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <span class="keywordtype">size_t</span> vertices = adj.size();</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span> </div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> visited(vertices, <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a64c1db5aad7502c6f08e4652f6edd463">explore</a>(adj, start, &amp;visited);</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  100</span>                                      {</div>
+<div class="line"><span class="lineno">  101</span>    <span class="keywordtype">size_t</span> vertices = adj.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">  102</span> </div>
+<div class="line"><span class="lineno">  103</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> visited(vertices, <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  104</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a64c1db5aad7502c6f08e4652f6edd463">explore</a>(adj, start, &amp;visited);</div>
+<div class="line"><span class="lineno">  105</span>}</div>
 <div class="ttc" id="anamespacegraph_html_a64c1db5aad7502c6f08e4652f6edd463"><div class="ttname"><a href="../../df/dce/namespacegraph.html#a64c1db5aad7502c6f08e4652f6edd463">graph::explore</a></div><div class="ttdeci">void explore(const std::vector&lt; std::vector&lt; size_t &gt; &gt; &amp;adj, size_t v, std::vector&lt; bool &gt; *visited)</div><div class="ttdoc">Explores the given vertex, exploring a vertex means traversing over all the vertices which are connec...</div><div class="ttdef"><b>Definition:</b> depth_first_search.cpp:80</div></div>
-<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
+<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; bool &gt;</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/dce/namespacegraph_ab5428a3519267a28bba4b4310cfbb6ae_cgraph.svg" width="286" height="70"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/dce/namespacegraph_ab5428a3519267a28bba4b4310cfbb6ae_cgraph.svg" width="298" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
 </div>
 </div>
 
@@ -513,50 +514,50 @@ Here is the call graph for this function:</div>
 <p >first element of pair denotes the distance</p>
 <p >for all the reachable vertex from the currently exploring vertex we will try to minimize the distance</p>
 <p >minimizing distances</p>
-<div class="fragment"><div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>                                                                         {<span class="comment"></span></div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span><span class="comment">    /// n denotes the number of vertices in graph</span></div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span><span class="comment"></span>    <span class="keywordtype">int</span> n = adj-&gt;size();</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span><span class="comment"></span> </div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span><span class="comment">    /// setting all the distances initially to INF</span></div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> dist(n, INF);</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span><span class="comment"></span> </div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span><span class="comment">    /// creating a min heap using priority queue</span></div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span><span class="comment">    /// first element of pair contains the distance</span></div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span><span class="comment">    /// second element of pair contains the vertex</span></div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue.html">std::priority_queue&lt;std::pair&lt;int, int&gt;</a>, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::pair&lt;int, int&gt;</a>&gt;,</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>                        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/greater.html">std::greater&lt;std::pair&lt;int, int&gt;</a>&gt;&gt;</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        pq;</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span><span class="comment"></span> </div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span><span class="comment">    /// pushing the source vertex &#39;s&#39; with 0 distance in min heap</span></div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span><span class="comment"></span>    pq.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/push.html">push</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(0, s));</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span><span class="comment"></span> </div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span><span class="comment">    /// marking the distance of source as 0</span></div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span><span class="comment"></span>    dist[s] = 0;</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span> </div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>    <span class="keywordflow">while</span> (!pq.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/empty.html">empty</a>()) {<span class="comment"></span></div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span><span class="comment">        /// second element of pair denotes the node / vertex</span></div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span><span class="comment"></span>        <span class="keywordtype">int</span> currentNode = pq.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/top.html">top</a>().second;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span><span class="comment"></span> </div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span><span class="comment">        /// first element of pair denotes the distance</span></div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span><span class="comment"></span>        <span class="keywordtype">int</span> currentDist = pq.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/top.html">top</a>().first;</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span> </div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>        pq.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/pop.html">pop</a>();</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span><span class="comment"></span> </div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span><span class="comment">        /// for all the reachable vertex from the currently exploring vertex</span></div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span><span class="comment">        /// we will try to minimize the distance</span></div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span><span class="comment"></span>        <span class="keywordflow">for</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;int, int&gt;</a> edge : (*adj)[currentNode]) {<span class="comment"></span></div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span><span class="comment">            /// minimizing distances</span></div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span><span class="comment"></span>            <span class="keywordflow">if</span> (currentDist + edge.second &lt; dist[edge.first]) {</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>                dist[edge.first] = currentDist + edge.second;</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>                pq.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/push.html">push</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(dist[edge.first], edge.first));</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>            }</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        }</div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    }</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <span class="keywordflow">if</span> (dist[t] != INF) {</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>        <span class="keywordflow">return</span> dist[t];</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    }</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    <span class="keywordflow">return</span> -1;</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   66</span>                                                                         {<span class="comment"></span></div>
+<div class="line"><span class="lineno">   67</span><span class="comment">    /// n denotes the number of vertices in graph</span></div>
+<div class="line"><span class="lineno">   68</span><span class="comment"></span>    <span class="keywordtype">int</span> n = adj-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   69</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   70</span><span class="comment">    /// setting all the distances initially to INF</span></div>
+<div class="line"><span class="lineno">   71</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> dist(n, INF);</div>
+<div class="line"><span class="lineno">   72</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   73</span><span class="comment">    /// creating a min heap using priority queue</span></div>
+<div class="line"><span class="lineno">   74</span><span class="comment">    /// first element of pair contains the distance</span></div>
+<div class="line"><span class="lineno">   75</span><span class="comment">    /// second element of pair contains the vertex</span></div>
+<div class="line"><span class="lineno">   76</span><span class="comment"></span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue.html">std::priority_queue&lt;std::pair&lt;int, int&gt;</a>, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::pair&lt;int, int&gt;</a>&gt;,</div>
+<div class="line"><span class="lineno">   77</span>                        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/greater.html">std::greater&lt;std::pair&lt;int, int&gt;</a>&gt;&gt;</div>
+<div class="line"><span class="lineno">   78</span>        pq;</div>
+<div class="line"><span class="lineno">   79</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   80</span><span class="comment">    /// pushing the source vertex &#39;s&#39; with 0 distance in min heap</span></div>
+<div class="line"><span class="lineno">   81</span><span class="comment"></span>    pq.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/push.html">push</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(0, s));</div>
+<div class="line"><span class="lineno">   82</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   83</span><span class="comment">    /// marking the distance of source as 0</span></div>
+<div class="line"><span class="lineno">   84</span><span class="comment"></span>    dist[s] = 0;</div>
+<div class="line"><span class="lineno">   85</span> </div>
+<div class="line"><span class="lineno">   86</span>    <span class="keywordflow">while</span> (!pq.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/empty.html">empty</a>()) {<span class="comment"></span></div>
+<div class="line"><span class="lineno">   87</span><span class="comment">        /// second element of pair denotes the node / vertex</span></div>
+<div class="line"><span class="lineno">   88</span><span class="comment"></span>        <span class="keywordtype">int</span> currentNode = pq.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/top.html">top</a>().second;</div>
+<div class="line"><span class="lineno">   89</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   90</span><span class="comment">        /// first element of pair denotes the distance</span></div>
+<div class="line"><span class="lineno">   91</span><span class="comment"></span>        <span class="keywordtype">int</span> currentDist = pq.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/top.html">top</a>().first;</div>
+<div class="line"><span class="lineno">   92</span> </div>
+<div class="line"><span class="lineno">   93</span>        pq.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/pop.html">pop</a>();</div>
+<div class="line"><span class="lineno">   94</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   95</span><span class="comment">        /// for all the reachable vertex from the currently exploring vertex</span></div>
+<div class="line"><span class="lineno">   96</span><span class="comment">        /// we will try to minimize the distance</span></div>
+<div class="line"><span class="lineno">   97</span><span class="comment"></span>        <span class="keywordflow">for</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;int, int&gt;</a> edge : (*adj)[currentNode]) {<span class="comment"></span></div>
+<div class="line"><span class="lineno">   98</span><span class="comment">            /// minimizing distances</span></div>
+<div class="line"><span class="lineno">   99</span><span class="comment"></span>            <span class="keywordflow">if</span> (currentDist + edge.second &lt; dist[edge.first]) {</div>
+<div class="line"><span class="lineno">  100</span>                dist[edge.first] = currentDist + edge.second;</div>
+<div class="line"><span class="lineno">  101</span>                pq.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/push.html">push</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(dist[edge.first], edge.first));</div>
+<div class="line"><span class="lineno">  102</span>            }</div>
+<div class="line"><span class="lineno">  103</span>        }</div>
+<div class="line"><span class="lineno">  104</span>    }</div>
+<div class="line"><span class="lineno">  105</span>    <span class="keywordflow">if</span> (dist[t] != INF) {</div>
+<div class="line"><span class="lineno">  106</span>        <span class="keywordflow">return</span> dist[t];</div>
+<div class="line"><span class="lineno">  107</span>    }</div>
+<div class="line"><span class="lineno">  108</span>    <span class="keywordflow">return</span> -1;</div>
+<div class="line"><span class="lineno">  109</span>}</div>
 <div class="ttc" id="aempty_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/priority_queue/empty.html">std::priority_queue::empty</a></div><div class="ttdeci">T empty(T... args)</div></div>
 <div class="ttc" id="agreater_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/functional/greater.html">std::greater</a></div></div>
 <div class="ttc" id="apair_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a></div></div>
@@ -564,7 +565,13 @@ Here is the call graph for this function:</div>
 <div class="ttc" id="apriority_queue_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/priority_queue.html">std::priority_queue</a></div></div>
 <div class="ttc" id="apush_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/priority_queue/push.html">std::priority_queue::push</a></div><div class="ttdeci">T push(T... args)</div></div>
 <div class="ttc" id="atop_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/priority_queue/top.html">std::priority_queue::top</a></div><div class="ttdeci">T top(T... args)</div></div>
-</div><!-- fragment -->
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/dce/namespacegraph_adc68cbc8ba09eb1142265935c0d45b84_cgraph.svg" width="279" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
 </div>
 </div>
 <a id="a3ae80bc4c6a79d041b4f3a6589eb7fb8" name="a3ae80bc4c6a79d041b4f3a6589eb7fb8"></a>
@@ -608,14 +615,14 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>                                       {</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    (*visited)[u] = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> v : (*adj)[u]) {</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        <span class="keywordflow">if</span> (!(*visited)[v]) {</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>            <a class="code hl_function" href="../../df/dce/namespacegraph.html#a3ae80bc4c6a79d041b4f3a6589eb7fb8">explore</a>(adj, v, visited);</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        }</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    }</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   60</span>                                       {</div>
+<div class="line"><span class="lineno">   61</span>    (*visited)[u] = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   62</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> v : (*adj)[u]) {</div>
+<div class="line"><span class="lineno">   63</span>        <span class="keywordflow">if</span> (!(*visited)[v]) {</div>
+<div class="line"><span class="lineno">   64</span>            <a class="code hl_function" href="../../df/dce/namespacegraph.html#a3ae80bc4c6a79d041b4f3a6589eb7fb8">explore</a>(adj, v, visited);</div>
+<div class="line"><span class="lineno">   65</span>        }</div>
+<div class="line"><span class="lineno">   66</span>    }</div>
+<div class="line"><span class="lineno">   67</span>}</div>
 <div class="ttc" id="anamespacegraph_html_a3ae80bc4c6a79d041b4f3a6589eb7fb8"><div class="ttname"><a href="../../df/dce/namespacegraph.html#a3ae80bc4c6a79d041b4f3a6589eb7fb8">graph::explore</a></div><div class="ttdeci">void explore(const std::vector&lt; std::vector&lt; int &gt; &gt; *adj, int u, std::vector&lt; bool &gt; *visited)</div><div class="ttdoc">Utility function for depth first seach algorithm this function explores the vertex which is passed in...</div><div class="ttdef"><b>Definition:</b> connected_components.cpp:59</div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -667,15 +674,15 @@ Here is the call graph for this function:</div>
   </table>
   </dd>
 </dl>
-<div class="fragment"><div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>                                       {</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; v + 1 &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    (*visited)[v] = <span class="keyword">true</span>;</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> x : adj[v]) {</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>        <span class="keywordflow">if</span> (!(*visited)[x]) {</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>            <a class="code hl_function" href="../../df/dce/namespacegraph.html#a64c1db5aad7502c6f08e4652f6edd463">explore</a>(adj, x, visited);</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>        }</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    }</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   81</span>                                       {</div>
+<div class="line"><span class="lineno">   82</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; v + 1 &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><span class="lineno">   83</span>    (*visited)[v] = <span class="keyword">true</span>;</div>
+<div class="line"><span class="lineno">   84</span>    <span class="keywordflow">for</span> (<span class="keyword">auto</span> x : adj[v]) {</div>
+<div class="line"><span class="lineno">   85</span>        <span class="keywordflow">if</span> (!(*visited)[x]) {</div>
+<div class="line"><span class="lineno">   86</span>            <a class="code hl_function" href="../../df/dce/namespacegraph.html#a64c1db5aad7502c6f08e4652f6edd463">explore</a>(adj, x, visited);</div>
+<div class="line"><span class="lineno">   87</span>        }</div>
+<div class="line"><span class="lineno">   88</span>    }</div>
+<div class="line"><span class="lineno">   89</span>}</div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
@@ -710,23 +717,23 @@ Here is the call graph for this function:</div>
   </dd>
 </dl>
 <dl class="section return"><dt>Returns</dt><dd>connected_components number of connected components in graph. </dd></dl>
-<div class="fragment"><div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>                                                                 {</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    <span class="keywordtype">int</span> n = adj-&gt;size();</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <span class="keywordtype">int</span> connected_components = 0;</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> visited(n, <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span> </div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>        <span class="keywordflow">if</span> (!visited[i]) {</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>            <a class="code hl_function" href="../../df/dce/namespacegraph.html#a3ae80bc4c6a79d041b4f3a6589eb7fb8">explore</a>(adj, i, &amp;visited);</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>            connected_components++;</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>        }</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    }</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    <span class="keywordflow">return</span> connected_components;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   77</span>                                                                 {</div>
+<div class="line"><span class="lineno">   78</span>    <span class="keywordtype">int</span> n = adj-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><span class="lineno">   79</span>    <span class="keywordtype">int</span> connected_components = 0;</div>
+<div class="line"><span class="lineno">   80</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> visited(n, <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">   81</span> </div>
+<div class="line"><span class="lineno">   82</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
+<div class="line"><span class="lineno">   83</span>        <span class="keywordflow">if</span> (!visited[i]) {</div>
+<div class="line"><span class="lineno">   84</span>            <a class="code hl_function" href="../../df/dce/namespacegraph.html#a3ae80bc4c6a79d041b4f3a6589eb7fb8">explore</a>(adj, i, &amp;visited);</div>
+<div class="line"><span class="lineno">   85</span>            connected_components++;</div>
+<div class="line"><span class="lineno">   86</span>        }</div>
+<div class="line"><span class="lineno">   87</span>    }</div>
+<div class="line"><span class="lineno">   88</span>    <span class="keywordflow">return</span> connected_components;</div>
+<div class="line"><span class="lineno">   89</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/dce/namespacegraph_a83ab16e96cec644109a58dfc9329bc2b_cgraph.svg" width="380" height="62"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/dce/namespacegraph_a83ab16e96cec644109a58dfc9329bc2b_cgraph.svg" width="392" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
 </div>
 </div>
 
@@ -758,24 +765,24 @@ Here is the call graph for this function:</div>
 <dl class="section return"><dt>Returns</dt><dd>booleans </dd></dl>
 <p >&lt; stores boolean values which signify whether that node had been visited or not</p>
 <p >if the current node is not visited then check whether the sub-graph of that node is a bipartite or not</p>
-<div class="fragment"><div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>                                                             {</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> visited(</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>        <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.size());  <span class="comment">///&lt; stores boolean values</span><span class="comment"></span></div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span><span class="comment">                        /// which signify whether that node had been visited or</span></div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span><span class="comment">                        /// not</span></div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span><span class="comment"></span> </div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.size(); i++) {</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        <span class="keywordflow">if</span> (!visited[i])  <span class="comment">/// if the current node is not visited then check</span><span class="comment"></span></div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span><span class="comment">                          /// whether the sub-graph of that node is a bipartite</span></div>
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-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span><span class="comment"></span>        {</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>            <span class="keywordflow">if</span> (!<a class="code hl_function" href="../../df/dce/namespacegraph.html#a8e1b547cd407c0774e63f0dc95cda9e7">checkBipartite</a>(<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>, i, &amp;visited)) {</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>                <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   75</span>                                                             {</div>
+<div class="line"><span class="lineno">   76</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> visited(</div>
+<div class="line"><span class="lineno">   77</span>        <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.size());  <span class="comment">///&lt; stores boolean values</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">   78</span><span class="comment">                        /// which signify whether that node had been visited or</span></div>
+<div class="line"><span class="lineno">   79</span><span class="comment">                        /// not</span></div>
+<div class="line"><span class="lineno">   80</span><span class="comment"></span> </div>
+<div class="line"><span class="lineno">   81</span>    <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.size(); i++) {</div>
+<div class="line"><span class="lineno">   82</span>        <span class="keywordflow">if</span> (!visited[i])  <span class="comment">/// if the current node is not visited then check</span><span class="comment"></span></div>
+<div class="line"><span class="lineno">   83</span><span class="comment">                          /// whether the sub-graph of that node is a bipartite</span></div>
+<div class="line"><span class="lineno">   84</span><span class="comment">                          /// or not</span></div>
+<div class="line"><span class="lineno">   85</span><span class="comment"></span>        {</div>
+<div class="line"><span class="lineno">   86</span>            <span class="keywordflow">if</span> (!<a class="code hl_function" href="../../df/dce/namespacegraph.html#a8e1b547cd407c0774e63f0dc95cda9e7">checkBipartite</a>(<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>, i, &amp;visited)) {</div>
+<div class="line"><span class="lineno">   87</span>                <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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+<div class="line"><span class="lineno">   89</span>        }</div>
+<div class="line"><span class="lineno">   90</span>    }</div>
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-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    que.push(5);</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    que.push(0);</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    assert(que.peek() == 2);</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    assert(que.pop() == 2);</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    assert(que.peek() == 5);</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    assert(que.pop() == 5);</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    assert(que.peek() == 0);</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    assert(que.pop() == 0);</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    assert(que.empty() == <span class="keyword">true</span>);</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;PASSED\n&quot;</span>;</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span> </div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test #2\n&quot;</span>;</div>
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-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    assert(que.empty() == <span class="keyword">false</span>);</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    assert(que.peek() == -1);</div>
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-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test #3\n&quot;</span>;</div>
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+<div class="line"><span class="lineno">  102</span>    MyQueue&lt;int&gt; que;</div>
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+<div class="line"><span class="lineno">  104</span>    que.push(2);</div>
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+<div class="line"><span class="lineno">  107</span>    assert(que.peek() == 2);</div>
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+<div class="line"><span class="lineno">  109</span>    assert(que.peek() == 5);</div>
+<div class="line"><span class="lineno">  110</span>    assert(que.pop() == 5);</div>
+<div class="line"><span class="lineno">  111</span>    assert(que.peek() == 0);</div>
+<div class="line"><span class="lineno">  112</span>    assert(que.pop() == 0);</div>
+<div class="line"><span class="lineno">  113</span>    assert(que.empty() == <span class="keyword">true</span>);</div>
+<div class="line"><span class="lineno">  114</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;PASSED\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  115</span> </div>
+<div class="line"><span class="lineno">  116</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test #2\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  117</span>    que.push(-1);</div>
+<div class="line"><span class="lineno">  118</span>    assert(que.empty() == <span class="keyword">false</span>);</div>
+<div class="line"><span class="lineno">  119</span>    assert(que.peek() == -1);</div>
+<div class="line"><span class="lineno">  120</span>    assert(que.pop() == -1);</div>
+<div class="line"><span class="lineno">  121</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;PASSED\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  122</span> </div>
+<div class="line"><span class="lineno">  123</span>    MyQueue&lt;double&gt; que2;</div>
+<div class="line"><span class="lineno">  124</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test #3\n&quot;</span>;</div>
+<div class="line"><span class="lineno">  125</span>    que2.push(2.31223);</div>
+<div class="line"><span class="lineno">  126</span>    que2.push(3.1415926);</div>
+<div class="line"><span class="lineno">  127</span>    que2.push(2.92);</div>
+<div class="line"><span class="lineno">  128</span> </div>
+<div class="line"><span class="lineno">  129</span>    assert(que2.peek() == 2.31223);</div>
+<div class="line"><span class="lineno">  130</span>    assert(que2.pop() == 2.31223);</div>
+<div class="line"><span class="lineno">  131</span>    assert(que2.peek() == 3.1415926);</div>
+<div class="line"><span class="lineno">  132</span>    assert(que2.pop() == 3.1415926);</div>
+<div class="line"><span class="lineno">  133</span>    assert(que2.peek() == 2.92);</div>
+<div class="line"><span class="lineno">  134</span>    assert(que2.pop() == 2.92);</div>
+<div class="line"><span class="lineno">  135</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;PASSED\n&quot;</span>;</div>
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diff --git a/df/ddd/connected__components_8cpp.html b/df/ddd/connected__components_8cpp.html
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-<p>&lt;a href="https://en.wikipedia.org/wiki/Component_(graph_theory)"  
+<p>[<a class="el" href="../../da/d9a/class_graph.html">Graph</a> Connected Components (Connected Components)] (<a href="https://en.wikipedia.org/wiki/Component_(graph_theory)">https://en.wikipedia.org/wiki/Component_(graph_theory)</a>)  
 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
 <code>#include &lt;cassert&gt;</code><br />
@@ -133,8 +133,7 @@ Functions</h2></td></tr>
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 </table>
 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
-<div class="textblock"><p >&lt;a href="https://en.wikipedia.org/wiki/Component_(graph_theory)" </p>
-<p >target="_blank" &gt;<a class="el" href="../../da/d9a/class_graph.html">Graph</a> Connected Components (Connected Components)</p>
+<div class="textblock"><p >[<a class="el" href="../../da/d9a/class_graph.html">Graph</a> Connected Components (Connected Components)] (<a href="https://en.wikipedia.org/wiki/Component_(graph_theory)">https://en.wikipedia.org/wiki/Component_(graph_theory)</a>) </p>
 <dl class="section author"><dt>Author</dt><dd><a href="http://github.com/ayaankhan98" target="_blank">Ayaan Khan</a></dd></dl>
 <p>A graph is a collection of nodes also called vertices and these vertices are connected by edges. A connected component in a graph refers to a set of vertices which are reachable form one another.</p>
 <pre>
@@ -164,28 +163,28 @@ Example - Here is graph with 3 connected components
 </div><div class="memdoc">
 <p >Main function </p>
 <p >running predefined tests</p>
-<div class="fragment"><div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>           {<span class="comment"></span></div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span><span class="comment">    /// running predefined tests</span></div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span><span class="comment"></span>    <a class="code hl_function" href="../../df/ddd/connected__components_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span> </div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    <span class="keywordtype">int</span> vertices = int(), edges = int();</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number of vertices : &quot;</span>;</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; vertices;</div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number of edges : &quot;</span>;</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; edges;</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span> </div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a>&gt; adj(vertices, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>());</div>
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-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">  127</span>           {<span class="comment"></span></div>
+<div class="line"><span class="lineno">  128</span><span class="comment">    /// running predefined tests</span></div>
+<div class="line"><span class="lineno">  129</span><span class="comment"></span>    <a class="code hl_function" href="../../df/ddd/connected__components_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
+<div class="line"><span class="lineno">  130</span> </div>
+<div class="line"><span class="lineno">  131</span>    <span class="keywordtype">int</span> vertices = int(), edges = int();</div>
+<div class="line"><span class="lineno">  132</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number of vertices : &quot;</span>;</div>
+<div class="line"><span class="lineno">  133</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; vertices;</div>
+<div class="line"><span class="lineno">  134</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number of edges : &quot;</span>;</div>
+<div class="line"><span class="lineno">  135</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; edges;</div>
+<div class="line"><span class="lineno">  136</span> </div>
+<div class="line"><span class="lineno">  137</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a>&gt; adj(vertices, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>());</div>
+<div class="line"><span class="lineno">  138</span> </div>
+<div class="line"><span class="lineno">  139</span>    <span class="keywordtype">int</span> u = int(), v = int();</div>
+<div class="line"><span class="lineno">  140</span>    <span class="keywordflow">while</span> (edges--) {</div>
+<div class="line"><span class="lineno">  141</span>        <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; u &gt;&gt; v;</div>
+<div class="line"><span class="lineno">  142</span>        <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj, u, v);</div>
+<div class="line"><span class="lineno">  143</span>    }</div>
+<div class="line"><span class="lineno">  144</span> </div>
+<div class="line"><span class="lineno">  145</span>    <span class="keywordtype">int</span> cc = <a class="code hl_function" href="../../df/dce/namespacegraph.html#a83ab16e96cec644109a58dfc9329bc2b">graph::getConnectedComponents</a>(&amp;adj);</div>
+<div class="line"><span class="lineno">  146</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; cc &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  147</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  148</span>}</div>
 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
 <div class="ttc" id="aconnected__components_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="../../df/ddd/connected__components_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdef"><b>Definition:</b> connected_components.cpp:93</div></div>
@@ -196,7 +195,7 @@ Example - Here is graph with 3 connected components
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/ddd/connected__components_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="578" height="163"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/ddd/connected__components_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="590" height="188"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
 </div>
 </div>
 
@@ -217,42 +216,42 @@ Here is the call graph for this function:</div>
       </table>
 </div><div class="memdoc">
 <p >Function to test the algorithm </p>
-<div class="fragment"><div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>             {</div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Running predefined tests...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiating Test 1...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a>&gt; adj1(9, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>());</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 1, 2);</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 1, 3);</div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 3, 4);</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 5, 7);</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 5, 6);</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 8, 9);</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span> </div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#a83ab16e96cec644109a58dfc9329bc2b">graph::getConnectedComponents</a>(&amp;adj1) == 3);</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span> </div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Innitiating Test 2...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a>&gt; adj2(10, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>());</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 1, 2);</div>
-<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 1, 3);</div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 1, 4);</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 2, 3);</div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 3, 4);</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 4, 8);</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 4, 10);</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 8, 10);</div>
-<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 8, 9);</div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 5, 7);</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 5, 6);</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 6, 7);</div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span> </div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#a83ab16e96cec644109a58dfc9329bc2b">graph::getConnectedComponents</a>(&amp;adj2) == 2);</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   93</span>             {</div>
+<div class="line"><span class="lineno">   94</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Running predefined tests...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   95</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiating Test 1...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">   96</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a>&gt; adj1(9, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>());</div>
+<div class="line"><span class="lineno">   97</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 1, 2);</div>
+<div class="line"><span class="lineno">   98</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 1, 3);</div>
+<div class="line"><span class="lineno">   99</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 3, 4);</div>
+<div class="line"><span class="lineno">  100</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 5, 7);</div>
+<div class="line"><span class="lineno">  101</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 5, 6);</div>
+<div class="line"><span class="lineno">  102</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 8, 9);</div>
+<div class="line"><span class="lineno">  103</span> </div>
+<div class="line"><span class="lineno">  104</span>    assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#a83ab16e96cec644109a58dfc9329bc2b">graph::getConnectedComponents</a>(&amp;adj1) == 3);</div>
+<div class="line"><span class="lineno">  105</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  106</span> </div>
+<div class="line"><span class="lineno">  107</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Innitiating Test 2...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  108</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a>&gt; adj2(10, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>());</div>
+<div class="line"><span class="lineno">  109</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 1, 2);</div>
+<div class="line"><span class="lineno">  110</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 1, 3);</div>
+<div class="line"><span class="lineno">  111</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 1, 4);</div>
+<div class="line"><span class="lineno">  112</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 2, 3);</div>
+<div class="line"><span class="lineno">  113</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 3, 4);</div>
+<div class="line"><span class="lineno">  114</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 4, 8);</div>
+<div class="line"><span class="lineno">  115</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 4, 10);</div>
+<div class="line"><span class="lineno">  116</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 8, 10);</div>
+<div class="line"><span class="lineno">  117</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 8, 9);</div>
+<div class="line"><span class="lineno">  118</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 5, 7);</div>
+<div class="line"><span class="lineno">  119</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 5, 6);</div>
+<div class="line"><span class="lineno">  120</span>    <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 6, 7);</div>
+<div class="line"><span class="lineno">  121</span> </div>
+<div class="line"><span class="lineno">  122</span>    assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#a83ab16e96cec644109a58dfc9329bc2b">graph::getConnectedComponents</a>(&amp;adj2) == 2);</div>
+<div class="line"><span class="lineno">  123</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><span class="lineno">  124</span>}</div>
 </div><!-- fragment --><div class="dynheader">
 Here is the call graph for this function:</div>
 <div class="dyncontent">
-<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/ddd/connected__components_8cpp_a88ec9ad42717780d6caaff9d3d6977f9_cgraph.svg" width="479" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/ddd/connected__components_8cpp_a88ec9ad42717780d6caaff9d3d6977f9_cgraph.svg" width="491" height="164"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
 </div>
 </div>
 
@@ -264,7 +263,7 @@ Here is the call graph for this function:</div>
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="../../dir_12552d7fa429bf94a2e32e5cf39f7e69.html">graph</a></li><li class="navelem"><a class="el" href="../../df/ddd/connected__components_8cpp.html">connected_components.cpp</a></li>
-    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.2 </li>
+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
   </ul>
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 </body>
diff --git a/df/ddd/connected__components_8cpp_a88ec9ad42717780d6caaff9d3d6977f9_cgraph.map b/df/ddd/connected__components_8cpp_a88ec9ad42717780d6caaff9d3d6977f9_cgraph.map
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-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>}</div>
+<div class="fragment"><div class="line"><span class="lineno">   25</span>                                             {</div>
+<div class="line"><span class="lineno">   26</span>    <span class="comment">// Initialize carry</span></div>
+<div class="line"><span class="lineno">   27</span>    <span class="keywordtype">int</span> carry = 0;</div>
+<div class="line"><span class="lineno">   28</span> </div>
+<div class="line"><span class="lineno">   29</span>    <span class="comment">// One by one multiply n with</span></div>
+<div class="line"><span class="lineno">   30</span>    <span class="comment">// individual digits of res[]</span></div>
+<div class="line"><span class="lineno">   31</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; res_size; i++) {</div>
+<div class="line"><span class="lineno">   32</span>        <span class="keywordtype">int</span> prod = res[i] * x + carry;</div>
+<div class="line"><span class="lineno">   33</span> </div>
+<div class="line"><span class="lineno">   34</span>        <span class="comment">// Store last digit of</span></div>
+<div class="line"><span class="lineno">   35</span>        <span class="comment">// &#39;prod&#39; in res[]</span></div>
+<div class="line"><span class="lineno">   36</span>        res[i] = prod % 10;</div>
+<div class="line"><span class="lineno">   37</span> </div>
+<div class="line"><span class="lineno">   38</span>        <span class="comment">// Put rest in carry</span></div>
+<div class="line"><span class="lineno">   39</span>        carry = prod / 10;</div>
+<div class="line"><span class="lineno">   40</span>    }</div>
+<div class="line"><span class="lineno">   41</span> </div>
+<div class="line"><span class="lineno">   42</span>    <span class="comment">// Put carry in res and</span></div>
+<div class="line"><span class="lineno">   43</span>    <span class="comment">// increase result size</span></div>
+<div class="line"><span class="lineno">   44</span>    <span class="keywordflow">while</span> (carry) {</div>
+<div class="line"><span class="lineno">   45</span>        res[res_size] = carry % 10;</div>
+<div class="line"><span class="lineno">   46</span>        carry = carry / 10;</div>
+<div class="line"><span class="lineno">   47</span>        res_size++;</div>
+<div class="line"><span class="lineno">   48</span>    }</div>
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+<div class="line"><span class="lineno">   57</span>    <span class="comment">// printing value &quot;1&quot; for power = 0</span></div>
+<div class="line"><span class="lineno">   58</span>    <span class="keywordflow">if</span> (n == 0) {</div>
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+<div class="line"><span class="lineno">   64</span>    <span class="keywordtype">int</span> res_size = 0;</div>
+<div class="line"><span class="lineno">   65</span>    <span class="keywordtype">int</span> temp = x;</div>
+<div class="line"><span class="lineno">   66</span> </div>
+<div class="line"><span class="lineno">   67</span>    <span class="comment">// Initialize result</span></div>
+<div class="line"><span class="lineno">   68</span>    <span class="keywordflow">while</span> (temp != 0) {</div>
+<div class="line"><span class="lineno">   69</span>        res[res_size++] = temp % 10;</div>
+<div class="line"><span class="lineno">   70</span>        temp = temp / 10;</div>
+<div class="line"><span class="lineno">   71</span>    }</div>
+<div class="line"><span class="lineno">   72</span> </div>
+<div class="line"><span class="lineno">   73</span>    <span class="comment">// Multiply x n times</span></div>
+<div class="line"><span class="lineno">   74</span>    <span class="comment">// (x^n = x*x*x....n times)</span></div>
+<div class="line"><span class="lineno">   75</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 2; i &lt;= n; i++) res_size = <a class="code hl_function" href="../../df/def/power__for__huge__numbers_8cpp.html#aa141a7904f0c4668bac112d652a3acf9">multiply</a>(x, res, res_size);</div>
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+<div class="line"><span class="lineno">   78</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = res_size - 1; i &gt;= 0; i--) <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; res[i];</div>
+<div class="line"><span class="lineno">   79</span>}</div>
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@@ -140,7 +141,7 @@ solve-a-rat-in-a-maze-c-java-pytho/" </td></tr>
 <tr id="row_4_9_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d3/dce/linkedlist__implentation__usingarray_8cpp.html" target="_self">linkedlist_implentation_usingarray.cpp</a></td><td class="desc">Linked list implementation using Arrays </td></tr>
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@@ -153,12 +154,12 @@ solve-a-rat-in-a-maze-c-java-pytho/" </td></tr>
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 <tr id="row_6_2_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d9/d31/coin__change__topdown_8cpp.html" target="_self">coin_change_topdown.cpp</a></td><td class="desc"><a href="https://leetcode.com/problems/coin-change/" target="_blank">Minimum coins</a> change problem is a problem used to find the minimum number of coins required to completely reach a target amount </td></tr>
 <tr id="row_6_3_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d6/d10/cut__rod_8cpp.html" target="_self">cut_rod.cpp</a></td><td class="desc">Implementation of cutting a rod problem </td></tr>
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@@ -170,18 +171,18 @@ solve-a-rat-in-a-maze-c-java-pytho/" </td></tr>
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@@ -199,9 +200,9 @@ solve-a-rat-in-a-maze-c-java-pytho/" </td></tr>
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 <tr id="row_13_1_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/def/kohonen__som__topology_8cpp.html" target="_self">kohonen_som_topology.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Self-organizing_map" target="_blank">Kohonen self organizing map</a> (topological map) </td></tr>
 <tr id="row_13_2_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d9/d49/kohonen__som__trace_8cpp.html" target="_self">kohonen_som_trace.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Self-organizing_map" target="_blank">Kohonen self organizing map</a> (data tracing) </td></tr>
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+<tr id="row_13_3_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d2/d58/neural__network_8cpp.html" target="_self">neural_network.cpp</a></td><td class="desc">Implementation of [Multilayer Perceptron] (<a href="https://en.wikipedia.org/wiki/Multilayer_perceptron">https://en.wikipedia.org/wiki/Multilayer_perceptron</a>) </td></tr>
 <tr id="row_13_4_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html" target="_self">ordinary_least_squares_regressor.cpp</a></td><td class="desc">Linear regression example using <a href="https://en.wikipedia.org/wiki/Ordinary_least_squares" target="_blank">Ordinary least squares</a> </td></tr>
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+<tr id="row_13_5_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><a href="d8/d95/vector__ops_8hpp_source.html"><span class="icondoc"></span></a><a class="el" href="d8/d95/vector__ops_8hpp.html" target="_self">vector_ops.hpp</a></td><td class="desc">Various functions for vectors associated with [NeuralNetwork (aka Multilayer Perceptron)] (<a href="https://en.wikipedia.org/wiki/Multilayer_perceptron">https://en.wikipedia.org/wiki/Multilayer_perceptron</a>) </td></tr>
 <tr id="row_14_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_14_" class="arrow" onclick="toggleFolder('14_')">&#9658;</span><span id="img_14_" class="iconfclosed" onclick="toggleFolder('14_')">&#160;</span><a class="el" href="dir_296d53ceaeaa7e099814a6def439fe8a.html" target="_self">math</a></td><td class="desc"></td></tr>
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@@ -213,7 +214,7 @@ solve-a-rat-in-a-maze-c-java-pytho/" </td></tr>
 <tr id="row_14_7_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d5/d67/complex__numbers_8cpp.html" target="_self">complex_numbers.cpp</a></td><td class="desc">An implementation of <a class="el" href="da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> Number as Objects </td></tr>
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+<tr id="row_14_10_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d9/d5d/extended__euclid__algorithm_8cpp.html" target="_self">extended_euclid_algorithm.cpp</a></td><td class="desc">GCD using [extended Euclid's algorithm] (<a href="https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm">https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm</a>) </td></tr>
 <tr id="row_14_11_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d9/d00/factorial_8cpp.html" target="_self">factorial.cpp</a></td><td class="desc">C++ program to find factorial of given number </td></tr>
 <tr id="row_14_12_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d2/d0b/fast__power_8cpp.html" target="_self">fast_power.cpp</a></td><td class="desc">Faster computation for \(a^b\) </td></tr>
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@@ -294,7 +295,7 @@ solve-a-rat-in-a-maze-c-java-pytho/" </td></tr>
 <tr id="row_17_3_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="de/d85/decimal__to__roman__numeral_8cpp.html" target="_self">decimal_to_roman_numeral.cpp</a></td><td class="desc">This Programme Converts a given decimal number in the range [0,4000) to both Lower case and Upper case Roman Numeral </td></tr>
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 <tr id="row_17_5_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="db/df3/happy__number_8cpp.html" target="_self">happy_number.cpp</a></td><td class="desc">A happy number is a number whose sum of digits is calculated until the sum is a single digit, and this sum turns out to be 1 </td></tr>
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+<tr id="row_17_6_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d8/d90/iterative__tree__traversals_8cpp.html" target="_self">iterative_tree_traversals.cpp</a></td><td class="desc">Iterative version of Preorder, Postorder, and preorder [Traversal of the Tree] (<a href="https://en.wikipedia.org/wiki/Tree_traversal">https://en.wikipedia.org/wiki/Tree_traversal</a>) </td></tr>
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 <tr id="row_17_8_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d3/db3/lru__cache_8cpp.html" target="_self">lru_cache.cpp</a></td><td class="desc">An implementation of <a href="https://en.wikipedia.org/wiki/Cache_replacement_policies#Least_recently_used_(LRU)" target="_blank">LRU Cache</a>. Lru is a part of cache algorithms (also frequently called cache replacement algorithms or cache replacement policies) </td></tr>
 <tr id="row_17_9_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d7/d35/matrix__exponentiation_8cpp.html" target="_self">matrix_exponentiation.cpp</a></td><td class="desc">Matrix Exponentiation </td></tr>
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 <tr id="row_17_12_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="dc/d1a/pascal__triangle_8cpp.html" target="_self">pascal_triangle.cpp</a></td><td class="desc">Pascal's triangle implementation </td></tr>
 <tr id="row_17_13_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d7/d75/postfix__evaluation_8cpp.html" target="_self">postfix_evaluation.cpp</a></td><td class="desc">Evaluation of <a href="https://en.wikipedia.org/wiki/Reverse_Polish_notation" target="_blank">Postfix Expression</a> </td></tr>
 <tr id="row_17_14_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="da/d7b/primality__test_8cpp.html" target="_self">primality_test.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Primality_test" target="_blank">Primality test</a> implementation </td></tr>
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+<tr id="row_17_15_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="dc/de1/recursive__tree__traversal_8cpp.html" target="_self">recursive_tree_traversal.cpp</a></td><td class="desc">Recursive version of Inorder, Preorder, and Postorder [Traversal of the Tree] (<a href="https://en.wikipedia.org/wiki/Tree_traversal">https://en.wikipedia.org/wiki/Tree_traversal</a>) </td></tr>
 <tr id="row_17_16_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d0/d01/smallest__circle_8cpp.html" target="_self">smallest_circle.cpp</a></td><td class="desc">Get centre and radius of the <a href="https://en.wikipedia.org/wiki/Smallest-circle_problem" target="_blank">smallest circle</a> that circumscribes given set of points </td></tr>
 <tr id="row_17_17_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d3/d19/sparse__matrix_8cpp.html" target="_self">sparse_matrix.cpp</a></td><td class="desc"></td></tr>
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 <tr id="row_19_2_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d5/d58/persistent__seg__tree__lazy__prop_8cpp.html" target="_self">persistent_seg_tree_lazy_prop.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Persistent_data_structure" target="_blank">Persistent segment tree with range updates (lazy propagation)</a> </td></tr>
 <tr id="row_19_3_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d1/d9e/prefix__sum__array_8cpp.html" target="_self">prefix_sum_array.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Prefix_sum" target="_blank">Prefix Sum Array</a> data structure implementation </td></tr>
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 <tr id="row_19_5_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d96/range__queries_2sparse__table_8cpp.html" target="_self">sparse_table.cpp</a></td><td class="desc">Implementation of <a href="https://en.wikipedia.org/wiki/Range_minimum_query" target="_blank">Sparse Table</a> data structure </td></tr>
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@@ -352,7 +353,7 @@ solve-a-rat-in-a-maze-c-java-pytho/" </td></tr>
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 <tr id="row_21_13_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d3/d92/pancake__sort_8cpp.html" target="_self">pancake_sort.cpp</a></td><td class="desc">Pancake sort sorts a disordered stack of pancakes by flipping any number of pancakes using a spatula using minimum number of flips </td></tr>
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+<tr id="row_21_14_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="dd/da8/pigeonhole__sort_8cpp.html" target="_self">pigeonhole_sort.cpp</a></td><td class="desc">Implementation of [Pigeonhole Sort algorithm] (<a href="https://en.wikipedia.org/wiki/Pigeonhole_sort">https://en.wikipedia.org/wiki/Pigeonhole_sort</a>) </td></tr>
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 <h3><a id="index_t" name="index_t"></a>- t -</h3><ul>
 <li>ternary_search()&#160;:&#160;<a class="el" href="dc/dfe/ternary__search_8cpp.html#aef655a27eb82efa299bf9d0becf6e9c8">ternary_search.cpp</a></li>
-<li>test()&#160;:&#160;<a class="el" href="dc/d5a/rat__maze_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">rat_maze.cpp</a>, <a class="el" href="df/d94/subarray__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">subarray_sum.cpp</a>, <a class="el" href="d2/d5a/subset__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">subset_sum.cpp</a>, <a class="el" href="dc/d14/wildcard__matching_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">wildcard_matching.cpp</a>, <a class="el" href="d7/d56/count__bits__flip_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">count_bits_flip.cpp</a>, <a class="el" href="da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">count_of_trailing_ciphers_in_factorial_n.cpp</a>, <a class="el" href="d4/d48/hamming__distance_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">hamming_distance.cpp</a>, <a class="el" href="de/db6/a1z26__cipher_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">a1z26_cipher.cpp</a>, <a class="el" href="dc/dfb/atbash__cipher_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">atbash_cipher.cpp</a>, <a class="el" href="d6/d2c/caesar__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">caesar_cipher.cpp</a>, <a class="el" href="df/d2c/elliptic__curve__key__exchange_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">elliptic_curve_key_exchange.cpp</a>, <a class="el" href="d8/d76/morse__code_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">morse_code.cpp</a>, <a class="el" href="dd/d12/vigenere__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">vigenere_cipher.cpp</a>, <a class="el" href="d3/d4c/xor__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">xor_cipher.cpp</a>, <a class="el" href="df/d47/fcfs__scheduling_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">fcfs_scheduling.cpp</a>, <a class="el" href="d7/d00/list__array_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">list_array.cpp</a>, <a class="el" href="d6/d05/reverse__a__linked__list_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">reverse_a_linked_list.cpp</a>, <a class="el" href="d6/d42/data__structures_2sparse__table_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">sparse_table.cpp</a>, <a class="el" href="d7/d83/trie__tree_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">trie_tree.cpp</a>, <a class="el" href="d5/d8a/trie__using__hashmap_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">trie_using_hashmap.cpp</a>, <a class="el" href="da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">karatsuba_algorithm_for_fast_multiplication.cpp</a>, <a class="el" href="db/d16/0__1__knapsack_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">0_1_knapsack.cpp</a>, <a class="el" href="d7/d73/abbreviation_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">abbreviation.cpp</a>, <a class="el" href="d9/d31/coin__change__topdown_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">coin_change_topdown.cpp</a>, <a class="el" href="d6/d10/cut__rod_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">cut_rod.cpp</a>, <a class="el" href="d6/d26/house__robber_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">house_robber.cpp</a>, <a class="el" href="d7/d57/longest__increasing__subsequence_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">longest_increasing_subsequence.cpp</a>, <a class="el" href="d0/d77/longest__palindromic__subsequence_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">longest_palindromic_subsequence.cpp</a>, <a class="el" href="da/d52/minimum__edit__distance_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">minimum_edit_distance.cpp</a>, <a class="el" href="d5/d90/palindrome__partitioning_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">palindrome_partitioning.cpp</a>, <a class="el" href="d7/d65/shortest__common__supersequence_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">shortest_common_supersequence.cpp</a>, <a class="el" href="d3/d84/word__break_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">word_break.cpp</a>, <a class="el" href="d4/d8d/jarvis__algorithm_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">jarvis_algorithm.cpp</a>, <a class="el" href="d8/d99/connected__components__with__dsu_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">connected_components_with_dsu.cpp</a>, <a class="el" href="d6/dd8/is__graph__bipartite_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">is_graph_bipartite.cpp</a>, <a class="el" href="df/d64/jumpgame_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">jumpgame.cpp</a>, <a class="el" href="d5/d96/md5_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">md5.cpp</a>, <a class="el" href="d8/d7a/sha1_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">sha1.cpp</a>, <a class="el" href="d5/d33/gram__schmidt_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">gram_schmidt.cpp</a>, <a class="el" href="d2/d58/neural__network_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">neural_network.cpp</a>, <a class="el" href="dc/d82/area_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">area.cpp</a>, <a class="el" href="d4/d5d/math_2armstrong__number_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">armstrong_number.cpp</a>, <a class="el" href="d5/df6/check__amicable__pair_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">check_amicable_pair.cpp</a>, <a class="el" href="d7/d89/double__factorial_8cpp.html#abbbcebf3a2d0c67f4c3cfb5511a97981">double_factorial.cpp</a>, <a class="el" href="d9/d89/fibonacci_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">fibonacci.cpp</a>, <a class="el" href="da/dc9/fibonacci__matrix__exponentiation_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">fibonacci_matrix_exponentiation.cpp</a>, <a class="el" href="de/dc3/fibonacci__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">fibonacci_sum.cpp</a>, <a class="el" href="d0/d46/finding__number__of__digits__in__a__number_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">finding_number_of_digits_in_a_number.cpp</a>, <a class="el" href="db/d40/integral__approximation2_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">integral_approximation2.cpp</a>, <a class="el" href="d6/db8/inv__sqrt_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">inv_sqrt.cpp</a>, <a class="el" href="d5/d7a/largest__power_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">largest_power.cpp</a>, <a class="el" href="d5/d83/lcm__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">lcm_sum.cpp</a>, <a class="el" href="df/d72/modular__division_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">modular_division.cpp</a>, <a class="el" href="d0/d6d/modular__exponentiation_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">modular_exponentiation.cpp</a>, <a class="el" href="db/d27/n__bonacci_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">n_bonacci.cpp</a>, <a class="el" href="d1/dbb/n__choose__r_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">n_choose_r.cpp</a>, <a class="el" href="d4/d9d/sum__of__binomial__coefficient_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">sum_of_binomial_coefficient.cpp</a>, <a class="el" href="d4/d83/sum__of__digits_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">sum_of_digits.cpp</a>, <a class="el" href="df/d66/vector__cross__product_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">vector_cross_product.cpp</a>, <a class="el" href="da/d39/volume_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">volume.cpp</a>, <a class="el" href="dc/d9c/babylonian__method_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">babylonian_method.cpp</a>, <a class="el" href="d4/d18/composite__simpson__rule_8cpp.html#a2ae48a41e43dc6ab11b962742349646e">composite_simpson_rule.cpp</a>, <a class="el" href="d8/d9a/fast__fourier__transform_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">fast_fourier_transform.cpp</a>, <a class="el" href="d9/d37/inverse__fast__fourier__transform_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">inverse_fast_fourier_transform.cpp</a>, <a class="el" href="df/d11/midpoint__integral__method_8cpp.html#a2ae48a41e43dc6ab11b962742349646e">midpoint_integral_method.cpp</a>, <a class="el" href="d1/da6/rungekutta_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">rungekutta.cpp</a>, <a class="el" href="d9/d14/array__left__rotation_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">array_left_rotation.cpp</a>, <a class="el" href="d6/d57/array__right__rotation_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">array_right_rotation.cpp</a>, <a class="el" href="de/d33/circular__linked__list_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">circular_linked_list.cpp</a>, <a class="el" href="d4/d32/inorder__successor__of__bst_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">inorder_successor_of_bst.cpp</a>, <a class="el" href="de/dc5/intersection__of__two__arrays_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">intersection_of_two_arrays.cpp</a>, <a class="el" href="d4/db6/reverse__binary__tree_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">reverse_binary_tree.cpp</a>, <a class="el" href="d7/def/trie__multiple__search_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">trie_multiple_search.cpp</a>, <a class="el" href="d8/d9c/union__of__two__arrays_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">union_of_two_arrays.cpp</a>, <a class="el" href="de/dcd/kadanes3_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">kadanes3.cpp</a>, <a class="el" href="d0/d01/smallest__circle_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">smallest_circle.cpp</a>, <a class="el" href="de/d72/geometric__dist_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">geometric_dist.cpp</a>, <a class="el" href="d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">windowed_median.cpp</a>, <a class="el" href="d5/d58/persistent__seg__tree__lazy__prop_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">persistent_seg_tree_lazy_prop.cpp</a>, <a class="el" href="d1/d9e/prefix__sum__array_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">prefix_sum_array.cpp</a>, <a class="el" href="d2/d45/segtree_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">segtree.cpp</a>, <a class="el" href="db/dc4/floyd__cycle__detection__algo_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">floyd_cycle_detection_algo.cpp</a>, <a class="el" href="d9/d69/median__search_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">median_search.cpp</a>, <a class="el" href="d3/d22/saddleback__search_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">saddleback_search.cpp</a>, <a class="el" href="d5/d45/sublist__search_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">sublist_search.cpp</a>, <a class="el" href="dc/db5/text__search_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">text_search.cpp</a>, <a class="el" href="d8/dcc/binary__insertion__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">binary_insertion_sort.cpp</a>, <a class="el" href="d5/ddb/bogo__sort_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">bogo_sort.cpp</a>, <a class="el" href="d2/d26/count__inversions_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">count_inversions.cpp</a>, <a class="el" href="de/d07/cycle__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">cycle_sort.cpp</a>, <a class="el" href="d6/d1a/dnf__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">dnf_sort.cpp</a>, <a class="el" href="d2/d21/gnome__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">gnome_sort.cpp</a>, <a class="el" href="d2/d52/heap__sort_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">heap_sort.cpp</a>, <a class="el" href="de/d7b/merge__insertion__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">merge_insertion_sort.cpp</a>, <a class="el" href="d3/d92/pancake__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">pancake_sort.cpp</a>, <a class="el" href="d1/daa/random__pivot__quick__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">random_pivot_quick_sort.cpp</a>, <a class="el" href="d3/df9/recursive__bubble__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">recursive_bubble_sort.cpp</a>, <a class="el" href="d4/d9f/selection__sort__recursive_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">selection_sort_recursive.cpp</a>, <a class="el" href="dc/dd9/strand__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">strand_sort.cpp</a>, <a class="el" href="db/d3f/wave__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">wave_sort.cpp</a>, <a class="el" href="d5/d4c/group__sorting.html#gaa8dca7b867074164d5f45b0f3851269d">wiggle_sort.cpp</a>, <a class="el" href="d3/dfe/horspool_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">horspool.cpp</a>, <a class="el" href="d3/d39/manacher__algorithm_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">manacher_algorithm.cpp</a>, <a class="el" href="d3/d80/z__function_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">z_function.cpp</a></li>
+<li>test()&#160;:&#160;<a class="el" href="dc/d5a/rat__maze_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">rat_maze.cpp</a>, <a class="el" href="df/d94/subarray__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">subarray_sum.cpp</a>, <a class="el" href="d2/d5a/subset__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">subset_sum.cpp</a>, <a class="el" href="dc/d14/wildcard__matching_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">wildcard_matching.cpp</a>, <a class="el" href="d7/d56/count__bits__flip_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">count_bits_flip.cpp</a>, <a class="el" href="da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">count_of_trailing_ciphers_in_factorial_n.cpp</a>, <a class="el" href="d4/d48/hamming__distance_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">hamming_distance.cpp</a>, <a class="el" href="d5/db5/set__kth__bit_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">set_kth_bit.cpp</a>, <a class="el" href="de/db6/a1z26__cipher_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">a1z26_cipher.cpp</a>, <a class="el" href="dc/dfb/atbash__cipher_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">atbash_cipher.cpp</a>, <a class="el" href="d6/d2c/caesar__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">caesar_cipher.cpp</a>, <a class="el" href="df/d2c/elliptic__curve__key__exchange_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">elliptic_curve_key_exchange.cpp</a>, <a class="el" href="d8/d76/morse__code_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">morse_code.cpp</a>, <a class="el" href="dd/d12/vigenere__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">vigenere_cipher.cpp</a>, <a class="el" href="d3/d4c/xor__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">xor_cipher.cpp</a>, <a class="el" href="df/d47/fcfs__scheduling_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">fcfs_scheduling.cpp</a>, <a class="el" href="d7/d00/list__array_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">list_array.cpp</a>, <a class="el" href="d6/d05/reverse__a__linked__list_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">reverse_a_linked_list.cpp</a>, <a class="el" href="d6/d42/data__structures_2sparse__table_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">sparse_table.cpp</a>, <a class="el" href="d7/d83/trie__tree_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">trie_tree.cpp</a>, <a class="el" href="d5/d8a/trie__using__hashmap_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">trie_using_hashmap.cpp</a>, <a class="el" href="da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">karatsuba_algorithm_for_fast_multiplication.cpp</a>, <a class="el" href="db/d16/0__1__knapsack_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">0_1_knapsack.cpp</a>, <a class="el" href="d7/d73/abbreviation_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">abbreviation.cpp</a>, <a class="el" href="d9/d31/coin__change__topdown_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">coin_change_topdown.cpp</a>, <a class="el" href="d6/d10/cut__rod_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">cut_rod.cpp</a>, <a class="el" href="d6/d26/house__robber_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">house_robber.cpp</a>, <a class="el" href="d7/d57/longest__increasing__subsequence_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">longest_increasing_subsequence.cpp</a>, <a class="el" href="d0/d77/longest__palindromic__subsequence_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">longest_palindromic_subsequence.cpp</a>, <a class="el" href="da/d52/minimum__edit__distance_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">minimum_edit_distance.cpp</a>, <a class="el" href="d5/d90/palindrome__partitioning_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">palindrome_partitioning.cpp</a>, <a class="el" href="d7/d65/shortest__common__supersequence_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">shortest_common_supersequence.cpp</a>, <a class="el" href="d3/d84/word__break_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">word_break.cpp</a>, <a class="el" href="d4/d8d/jarvis__algorithm_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">jarvis_algorithm.cpp</a>, <a class="el" href="d8/d99/connected__components__with__dsu_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">connected_components_with_dsu.cpp</a>, <a class="el" href="d6/dd8/is__graph__bipartite_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">is_graph_bipartite.cpp</a>, <a class="el" href="df/d64/jumpgame_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">jumpgame.cpp</a>, <a class="el" href="d5/d96/md5_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">md5.cpp</a>, <a class="el" href="d8/d7a/sha1_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">sha1.cpp</a>, <a class="el" href="d5/d33/gram__schmidt_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">gram_schmidt.cpp</a>, <a class="el" href="d2/d58/neural__network_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">neural_network.cpp</a>, <a class="el" href="dc/d82/area_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">area.cpp</a>, <a class="el" href="d4/d5d/math_2armstrong__number_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">armstrong_number.cpp</a>, <a class="el" href="d5/df6/check__amicable__pair_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">check_amicable_pair.cpp</a>, <a class="el" href="d7/d89/double__factorial_8cpp.html#abbbcebf3a2d0c67f4c3cfb5511a97981">double_factorial.cpp</a>, <a class="el" href="d9/d89/fibonacci_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">fibonacci.cpp</a>, <a class="el" href="da/dc9/fibonacci__matrix__exponentiation_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">fibonacci_matrix_exponentiation.cpp</a>, <a class="el" href="de/dc3/fibonacci__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">fibonacci_sum.cpp</a>, <a class="el" href="d0/d46/finding__number__of__digits__in__a__number_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">finding_number_of_digits_in_a_number.cpp</a>, <a class="el" href="db/d40/integral__approximation2_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">integral_approximation2.cpp</a>, <a class="el" href="d6/db8/inv__sqrt_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">inv_sqrt.cpp</a>, <a class="el" href="d5/d7a/largest__power_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">largest_power.cpp</a>, <a class="el" href="d5/d83/lcm__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">lcm_sum.cpp</a>, <a class="el" href="df/d72/modular__division_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">modular_division.cpp</a>, <a class="el" href="d0/d6d/modular__exponentiation_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">modular_exponentiation.cpp</a>, <a class="el" href="db/d27/n__bonacci_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">n_bonacci.cpp</a>, <a class="el" href="d1/dbb/n__choose__r_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">n_choose_r.cpp</a>, <a class="el" href="d4/d9d/sum__of__binomial__coefficient_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">sum_of_binomial_coefficient.cpp</a>, <a class="el" href="d4/d83/sum__of__digits_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">sum_of_digits.cpp</a>, <a class="el" href="df/d66/vector__cross__product_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">vector_cross_product.cpp</a>, <a class="el" href="da/d39/volume_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">volume.cpp</a>, <a class="el" href="dc/d9c/babylonian__method_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">babylonian_method.cpp</a>, <a class="el" href="d4/d18/composite__simpson__rule_8cpp.html#a2ae48a41e43dc6ab11b962742349646e">composite_simpson_rule.cpp</a>, <a class="el" href="d8/d9a/fast__fourier__transform_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">fast_fourier_transform.cpp</a>, <a class="el" href="d9/d37/inverse__fast__fourier__transform_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">inverse_fast_fourier_transform.cpp</a>, <a class="el" href="df/d11/midpoint__integral__method_8cpp.html#a2ae48a41e43dc6ab11b962742349646e">midpoint_integral_method.cpp</a>, <a class="el" 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href="db/dc4/floyd__cycle__detection__algo_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">floyd_cycle_detection_algo.cpp</a>, <a class="el" href="d9/d69/median__search_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">median_search.cpp</a>, <a class="el" href="d3/d22/saddleback__search_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">saddleback_search.cpp</a>, <a class="el" href="d5/d45/sublist__search_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">sublist_search.cpp</a>, <a class="el" href="dc/db5/text__search_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">text_search.cpp</a>, <a class="el" href="d8/dcc/binary__insertion__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">binary_insertion_sort.cpp</a>, <a class="el" href="d5/ddb/bogo__sort_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">bogo_sort.cpp</a>, <a class="el" href="d2/d26/count__inversions_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">count_inversions.cpp</a>, <a class="el" href="de/d07/cycle__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">cycle_sort.cpp</a>, <a class="el" href="d6/d1a/dnf__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">dnf_sort.cpp</a>, <a class="el" href="d2/d21/gnome__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">gnome_sort.cpp</a>, <a class="el" href="d2/d52/heap__sort_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">heap_sort.cpp</a>, <a class="el" href="de/d7b/merge__insertion__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">merge_insertion_sort.cpp</a>, <a class="el" href="d3/d92/pancake__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">pancake_sort.cpp</a>, <a class="el" href="d1/daa/random__pivot__quick__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">random_pivot_quick_sort.cpp</a>, <a class="el" href="d3/df9/recursive__bubble__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">recursive_bubble_sort.cpp</a>, <a class="el" href="d4/d9f/selection__sort__recursive_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">selection_sort_recursive.cpp</a>, <a class="el" href="dc/dd9/strand__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">strand_sort.cpp</a>, <a class="el" href="db/d3f/wave__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">wave_sort.cpp</a>, <a class="el" href="d5/d4c/group__sorting.html#gaa8dca7b867074164d5f45b0f3851269d">wiggle_sort.cpp</a>, <a class="el" href="d3/dfe/horspool_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">horspool.cpp</a>, <a class="el" href="d3/d39/manacher__algorithm_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">manacher_algorithm.cpp</a>, <a class="el" href="d3/d80/z__function_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">z_function.cpp</a></li>
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 <li>test3()&#160;:&#160;<a class="el" href="dd/d0c/hamiltons__cycle_8cpp.html#a0cc94918b6831f308d4fe4fa27f08299">hamiltons_cycle.cpp</a>, <a class="el" href="d5/db0/adaline__learning_8cpp.html#a992bdf1fdb0b9d414bcf7981d2d87aa9">adaline_learning.cpp</a>, <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">kohonen_som_topology.cpp</a>, <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">kohonen_som_trace.cpp</a>, <a class="el" href="db/d01/brent__method__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">brent_method_extrema.cpp</a>, <a class="el" href="d6/d7a/golden__search__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">golden_search_extrema.cpp</a>, <a class="el" href="d8/d90/iterative__tree__traversals_8cpp.html#a425c4c8520991999ee6dbe13d99b87f4">iterative_tree_traversals.cpp</a>, <a class="el" href="dc/de1/recursive__tree__traversal_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">recursive_tree_traversal.cpp</a>, <a class="el" href="d0/d01/smallest__circle_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">smallest_circle.cpp</a></li>
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+<tr id="row_66_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d9/d5a/structgeometry_1_1jarvis_1_1_point.html" target="_self">geometry::jarvis::Point</a></td><td class="desc"></td></tr>
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+<tr id="row_70_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="dc/db5/struct_queue.html" target="_self">Queue</a></td><td class="desc"></td></tr>
+<tr id="row_71_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d6/d04/classdata__structures_1_1queue__using__array_1_1_queue___array.html" target="_self">data_structures::queue_using_array::Queue_Array</a></td><td class="desc"><a class="el" href="d6/d04/classdata__structures_1_1queue__using__array_1_1_queue___array.html" title="Queue_Array class containing the main data and also index of head and tail of the array.">Queue_Array</a> class containing the main data and also index of head and tail of the array </td></tr>
+<tr id="row_72_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d8/d72/class_r_btree.html" target="_self">RBtree</a></td><td class="desc"></td></tr>
+<tr id="row_73_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d4/db4/struct_segment_intersection.html" target="_self">SegmentIntersection</a></td><td class="desc"></td></tr>
+<tr id="row_74_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_74_" class="arrow" onclick="toggleFolder('74_')">&#9658;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html" target="_self">range_queries::heavy_light_decomposition::SG&lt; X &gt;</a></td><td class="desc">Segment <a class="el" href="d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html" title="A Basic Tree, which supports binary lifting.">Tree</a>, to store heavy chains </td></tr>
+<tr id="row_74_0_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html" target="_self">range_queries::heavy_light_decomposition::HLD&lt; X &gt;</a></td><td class="desc">The Heavy-Light Decomposition class </td></tr>
+<tr id="row_75_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d4/d90/classdata__structures_1_1_skip_list.html" target="_self">data_structures::SkipList</a></td><td class="desc"></td></tr>
+<tr id="row_76_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="dd/d4f/class_solution.html" target="_self">Solution</a></td><td class="desc"></td></tr>
+<tr id="row_77_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html" target="_self">data_structures::sparse_table::Sparse_table</a></td><td class="desc"></td></tr>
+<tr id="row_78_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="db/d5b/structdata__structures_1_1stack__using__queue_1_1_stack.html" target="_self">data_structures::stack_using_queue::Stack</a></td><td class="desc"><a class="el" href="db/d5b/structdata__structures_1_1stack__using__queue_1_1_stack.html" title="Stack Class implementation for basic methods of Stack Data Structure.">Stack</a> Class implementation for basic methods of <a class="el" href="db/d5b/structdata__structures_1_1stack__using__queue_1_1_stack.html" title="Stack Class implementation for basic methods of Stack Data Structure.">Stack</a> Data Structure </td></tr>
+<tr id="row_79_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d5/d8a/classothers_1_1postfix__expression_1_1_stack.html" target="_self">others::postfix_expression::Stack</a></td><td class="desc">Creates an array to be used as stack for storing values </td></tr>
+<tr id="row_80_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d1/dc2/classstack.html" target="_self">stack&lt; Type &gt;</a></td><td class="desc"></td></tr>
+<tr id="row_81_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d2/dc4/classstack__linked_list.html" target="_self">stack_linkedList</a></td><td class="desc"></td></tr>
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+<tr id="row_83_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d8/dab/classstatistics_1_1stats__computer2.html" target="_self">statistics::stats_computer2&lt; T &gt;</a></td><td class="desc"></td></tr>
+<tr id="row_84_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d5/d58/class_test_cases.html" target="_self">TestCases</a></td><td class="desc">Class encapsulating the necessary test cases </td></tr>
+<tr id="row_85_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html" target="_self">operations_on_datastructures::trie_operations::Tnode</a></td><td class="desc">Class defining the structure of trie node and containing the methods to perform operations on them </td></tr>
+<tr id="row_86_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d2/d2c/structtower.html" target="_self">tower</a></td><td class="desc"></td></tr>
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+<tr id="row_87_0_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html" target="_self">range_queries::heavy_light_decomposition::HLD&lt; X &gt;</a></td><td class="desc">The Heavy-Light Decomposition class </td></tr>
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index dba73ff39..b50204837 100644
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 <tr id="row_29_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/dc9/namespacefibonacci__sum.html" target="_self">fibonacci_sum</a></td><td class="desc">Functions for the sum of the Fibonacci Sequence: \(\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\) </td></tr>
 <tr id="row_30_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dd/d8a/namespacegeometric__dist.html" target="_self">geometric_dist</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Geometric_distribution" target="_blank">Geometric Distribution</a> algorithm implementation </td></tr>
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 <tr id="row_68_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d1/d64/namespacemodular__division.html" target="_self">modular_division</a></td><td class="desc">Functions for <a href="https://www.geeksforgeeks.org/modular-division" target="_blank">Modular Division</a> implementation </td></tr>
 <tr id="row_69_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d0/da4/namespacemonte__carlo.html" target="_self">monte_carlo</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Monte_Carlo_integration" target="_blank">Monte Carlo Integration</a> implementation </td></tr>
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+<tr id="row_70_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/d8d/namespacemorse.html" target="_self">morse</a></td><td class="desc">Functions for [Morse Code] (<a href="https://en.wikipedia.org/wiki/Morse_code">https://en.wikipedia.org/wiki/Morse_code</a>) </td></tr>
 <tr id="row_71_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/d36/namespacen__bonacci.html" target="_self">n_bonacci</a></td><td class="desc">Functions for the <a href="http://oeis.org/wiki/N-bonacci_numbers" target="_blank">N-bonacci</a> implementation </td></tr>
 <tr id="row_72_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/da1/namespacen__queens.html" target="_self">n_queens</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" target="_blank">Eight Queens</a> puzzle </td></tr>
 <tr id="row_73_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d44/namespacen__queens__all__solutions.html" target="_self">n_queens_all_solutions</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" target="_blank">Eight Queens</a> puzzle with all solutions </td></tr>
@@ -273,7 +273,7 @@ $(document).ready(function(){initNavTree('namespaces.html',''); initResizable();
 <tr id="row_85_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d2/d3b/namespaceqr__algorithm.html" target="_self">qr_algorithm</a></td><td class="desc">Functions to compute <a href="https://en.wikipedia.org/wiki/QR_decomposition" target="_blank">QR decomposition</a> of any rectangular matrix </td></tr>
 <tr id="row_86_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_86_" class="arrow" onclick="toggleFolder('86_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/dd2/namespacequadratic__probing.html" target="_self">quadratic_probing</a></td><td class="desc">An implementation of hash table using <a href="https://en.wikipedia.org/wiki/Quadratic_probing" target="_blank">quadratic probing</a> algorithm </td></tr>
 <tr id="row_86_0_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="da/dd1/structquadratic__probing_1_1_entry.html" target="_self">Entry</a></td><td class="desc"></td></tr>
-<tr id="row_87_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d70/namespacequeue__using__array.html" target="_self">queue_using_array</a></td><td class="desc">Functions for <a href="https://www.geeksforgeeks.org/array-implementation-of-queue-simple/" target="_blank">Queue using Array</a> implementation </td></tr>
+<tr id="row_87_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d70/namespacequeue__using__array.html" target="_self">queue_using_array</a></td><td class="desc">Functions for [<a class="el" href="dc/db5/struct_queue.html">Queue</a> using Array] (<a href="https://www.geeksforgeeks.org/array-implementation-of-queue-simple/">https://www.geeksforgeeks.org/array-implementation-of-queue-simple/</a>) implementation </td></tr>
 <tr id="row_88_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="da/dda/namespaceradix__sort.html" target="_self">radix_sort</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Radix_sort" target="_blank">Radix sort</a> algorithm </td></tr>
 <tr id="row_89_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/d6b/namespacerandom__pivot__quick__sort.html" target="_self">random_pivot_quick_sort</a></td><td class="desc">Functions for the <a href="https://www.sanfoundry.com/cpp-program-implement-quick-sort-using-randomisation" target="_blank">Random Pivot Quick Sort</a> implementation </td></tr>
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@@ -297,47 +297,48 @@ solve-a-rat-in-a-maze-c-java-pytho/" </td></tr>
 <tr id="row_95_3_" class="even" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_95_3_" class="arrow" onclick="toggleFolder('95_3_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>sublist_search</b></td><td class="desc"></td></tr>
 <tr id="row_95_3_0_" class="even" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="da/d61/structsearch_1_1sublist__search_1_1_node.html" target="_self">Node</a></td><td class="desc">A <a class="el" href="da/d61/structsearch_1_1sublist__search_1_1_node.html" title="A Node structure representing a single link Node in a linked list.">Node</a> structure representing a single link <a class="el" href="da/d61/structsearch_1_1sublist__search_1_1_node.html" title="A Node structure representing a single link Node in a linked list.">Node</a> in a linked list </td></tr>
 <tr id="row_96_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d4a/namespaceselection__sort__recursive.html" target="_self">selection_sort_recursive</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Selection_sort" target="_blank">Selection sort</a> implementation using recursion </td></tr>
-<tr id="row_97_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/dd3/namespace_s_h_a.html" target="_self">SHA</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/SHA-1" target="_blank">SHA-1</a> algorithm implementation </td></tr>
-<tr id="row_98_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/deb/namespaceshortest__common__supersequence.html" target="_self">shortest_common_supersequence</a></td><td class="desc">Shortest Common Super Sequence algorithm </td></tr>
-<tr id="row_99_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/d6d/namespacesimpson__method.html" target="_self">simpson_method</a></td><td class="desc">Contains the Simpson's method implementation </td></tr>
-<tr id="row_100_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d5/d91/namespacesorting.html" target="_self">sorting</a></td><td class="desc">For working with vectors </td></tr>
-<tr id="row_101_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d55/namespacesparse__table.html" target="_self">sparse_table</a></td><td class="desc">Functions for Implementation of <a href="https://brilliant.org/wiki/sparse-table/" target="_blank">Sparse Table</a> </td></tr>
-<tr id="row_102_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="da/dd3/namespacespirograph.html" target="_self">spirograph</a></td><td class="desc"></td></tr>
-<tr id="row_103_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d1c/namespacestack__using__queue.html" target="_self">stack_using_queue</a></td><td class="desc">Functions for the <a href="https://www.studytonight.com/data-structures/stack-using-queue" target="_blank">Stack Using Queue</a> implementation </td></tr>
-<tr id="row_104_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_104_" class="arrow" onclick="toggleFolder('104_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d2/dcf/namespacestatistics.html" target="_self">statistics</a></td><td class="desc">Statistical algorithms </td></tr>
-<tr id="row_104_0_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d7/d7c/classstatistics_1_1stats__computer1.html" target="_self">stats_computer1</a></td><td class="desc"></td></tr>
-<tr id="row_104_1_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d8/dab/classstatistics_1_1stats__computer2.html" target="_self">stats_computer2</a></td><td class="desc"></td></tr>
-<tr id="row_105_"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_105_" class="arrow" onclick="toggleFolder('105_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/dcc/namespacestd.html" target="_self">std</a></td><td class="desc">STL namespace </td></tr>
-<tr id="row_105_0_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>chrono</b></td><td class="desc"></td></tr>
-<tr id="row_105_1_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>experimental</b></td><td class="desc"></td></tr>
-<tr id="row_105_2_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>rel_ops</b></td><td class="desc"></td></tr>
-<tr id="row_105_3_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>this_thread</b></td><td class="desc"></td></tr>
-<tr id="row_105_4_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d2/dfc/structstd_1_1is__arithmetic_3_01uint128__t_01_4.html" target="_self">is_arithmetic&lt; uint128_t &gt;</a></td><td class="desc"></td></tr>
-<tr id="row_105_5_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="dc/d6d/structstd_1_1is__arithmetic_3_01uint256__t_01_4.html" target="_self">is_arithmetic&lt; uint256_t &gt;</a></td><td class="desc"></td></tr>
-<tr id="row_105_6_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d2/dd4/structstd_1_1is__integral_3_01uint128__t_01_4.html" target="_self">is_integral&lt; uint128_t &gt;</a></td><td class="desc"></td></tr>
-<tr id="row_105_7_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d7/d47/structstd_1_1is__integral_3_01uint256__t_01_4.html" target="_self">is_integral&lt; uint256_t &gt;</a></td><td class="desc"></td></tr>
-<tr id="row_105_8_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d5/d25/structstd_1_1is__unsigned_3_01uint128__t_01_4.html" target="_self">is_unsigned&lt; uint128_t &gt;</a></td><td class="desc"></td></tr>
-<tr id="row_105_9_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="df/d99/structstd_1_1is__unsigned_3_01uint256__t_01_4.html" target="_self">is_unsigned&lt; uint256_t &gt;</a></td><td class="desc"></td></tr>
-<tr id="row_106_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d1d/namespacestrand.html" target="_self">strand</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Strand_sort" target="_blank">Strand Sort</a> algorithm </td></tr>
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-<tr id="row_108_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/dcb/namespacestrings.html" target="_self">strings</a></td><td class="desc">Algorithms with strings </td></tr>
-<tr id="row_109_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d74/namespacesubarray__sum.html" target="_self">subarray_sum</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Subset_sum_problem" target="_blank">Subset sum</a> implementation </td></tr>
-<tr id="row_110_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/def/namespacesublist__search.html" target="_self">sublist_search</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/sublist-search-search-a-linked-list-in-another-list" target="_blank">Sublist Search</a> implementation </td></tr>
-<tr id="row_111_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/d95/namespace_subsets.html" target="_self">Subsets</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Subset_sum_problem" target="_blank">Subset Sum</a> problem </td></tr>
-<tr id="row_112_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d9f/namespacesudoku__solver.html" target="_self">sudoku_solver</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Sudoku" target="_blank">Sudoku Solver</a> implementation </td></tr>
-<tr id="row_113_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/df4/namespacetests.html" target="_self">tests</a></td><td class="desc">Testcases to check Union of Two Arrays </td></tr>
-<tr id="row_114_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/dab/namespacetree__234.html" target="_self">tree_234</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/2%E2%80%933%E2%80%934_tree" target="_blank">2–3–4 tree</a> </td></tr>
-<tr id="row_115_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d8e/namespacetrie__operations.html" target="_self">trie_operations</a></td><td class="desc">Functions for <a href="https://iq.opengenus.org/autocomplete-using-trie-data-structure/" target="_blank">Trie datastructure</a> implementation </td></tr>
-<tr id="row_116_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d7/d0a/namespacetrie__using__hashmap.html" target="_self">trie_using_hashmap</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Trie" target="_blank">Trie</a> data structure using hashmap implementation </td></tr>
-<tr id="row_117_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/d17/namespaceutil__functions.html" target="_self">util_functions</a></td><td class="desc">Various utility functions used in Neural network </td></tr>
-<tr id="row_118_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/d91/namespacevector__cross.html" target="_self">vector_cross</a></td><td class="desc">Functions for Vector Cross Product algorithms </td></tr>
-<tr id="row_119_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/da2/namespacevigenere.html" target="_self">vigenere</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher" target="_blank">vigenère cipher</a> algorithm </td></tr>
-<tr id="row_120_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d21/namespacewave__sort.html" target="_self">wave_sort</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/sort-array-wave-form-2/" target="_blank">Wave sort</a> implementation </td></tr>
-<tr id="row_121_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d0/d52/namespacewiggle__sort.html" target="_self">wiggle_sort</a></td><td class="desc">Functions for <a href="https://leetcode.com/problems/wiggle-sort-ii/" target="_blank">Wiggle Sort</a> algorithm </td></tr>
-<tr id="row_122_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="db/d03/namespacewildcard__matching.html" target="_self">wildcard_matching</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/wildcard-pattern-matching/" target="_blank">Wildcard Matching</a> problem </td></tr>
-<tr id="row_123_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dd/d21/namespacewindowed__median.html" target="_self">windowed_median</a></td><td class="desc">Functions for the Windowed Median algorithm implementation </td></tr>
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-<tr id="row_125_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d7/d47/namespace_x_o_r.html" target="_self">XOR</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/XOR_cipher" target="_blank">XOR cipher</a> algorithm </td></tr>
+<tr id="row_97_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d88/namespaceset_kth_bit.html" target="_self">setKthBit</a></td><td class="desc">Functions for the [From the right, set the Kth bit in the binary representation of N] (<a href="https://practice.geeksforgeeks.org/problems/set-kth-bit3724/1/">https://practice.geeksforgeeks.org/problems/set-kth-bit3724/1/</a>) implementation </td></tr>
+<tr id="row_98_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/dd3/namespace_s_h_a.html" target="_self">SHA</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/SHA-1" target="_blank">SHA-1</a> algorithm implementation </td></tr>
+<tr id="row_99_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/deb/namespaceshortest__common__supersequence.html" target="_self">shortest_common_supersequence</a></td><td class="desc">Shortest Common Super Sequence algorithm </td></tr>
+<tr id="row_100_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/d6d/namespacesimpson__method.html" target="_self">simpson_method</a></td><td class="desc">Contains the Simpson's method implementation </td></tr>
+<tr id="row_101_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d5/d91/namespacesorting.html" target="_self">sorting</a></td><td class="desc">For working with vectors </td></tr>
+<tr id="row_102_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d55/namespacesparse__table.html" target="_self">sparse_table</a></td><td class="desc">Functions for Implementation of <a href="https://brilliant.org/wiki/sparse-table/" target="_blank">Sparse Table</a> </td></tr>
+<tr id="row_103_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="da/dd3/namespacespirograph.html" target="_self">spirograph</a></td><td class="desc"></td></tr>
+<tr id="row_104_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d1c/namespacestack__using__queue.html" target="_self">stack_using_queue</a></td><td class="desc">Functions for the <a href="https://www.studytonight.com/data-structures/stack-using-queue" target="_blank">Stack Using Queue</a> implementation </td></tr>
+<tr id="row_105_"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_105_" class="arrow" onclick="toggleFolder('105_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d2/dcf/namespacestatistics.html" target="_self">statistics</a></td><td class="desc">Statistical algorithms </td></tr>
+<tr id="row_105_0_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d7/d7c/classstatistics_1_1stats__computer1.html" target="_self">stats_computer1</a></td><td class="desc"></td></tr>
+<tr id="row_105_1_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d8/dab/classstatistics_1_1stats__computer2.html" target="_self">stats_computer2</a></td><td class="desc"></td></tr>
+<tr id="row_106_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_106_" class="arrow" onclick="toggleFolder('106_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/dcc/namespacestd.html" target="_self">std</a></td><td class="desc">STL namespace </td></tr>
+<tr id="row_106_0_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>chrono</b></td><td class="desc"></td></tr>
+<tr id="row_106_1_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>experimental</b></td><td class="desc"></td></tr>
+<tr id="row_106_2_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>rel_ops</b></td><td class="desc"></td></tr>
+<tr id="row_106_3_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>this_thread</b></td><td class="desc"></td></tr>
+<tr id="row_106_4_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d2/dfc/structstd_1_1is__arithmetic_3_01uint128__t_01_4.html" target="_self">is_arithmetic&lt; uint128_t &gt;</a></td><td class="desc"></td></tr>
+<tr id="row_106_5_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="dc/d6d/structstd_1_1is__arithmetic_3_01uint256__t_01_4.html" target="_self">is_arithmetic&lt; uint256_t &gt;</a></td><td class="desc"></td></tr>
+<tr id="row_106_6_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d2/dd4/structstd_1_1is__integral_3_01uint128__t_01_4.html" target="_self">is_integral&lt; uint128_t &gt;</a></td><td class="desc"></td></tr>
+<tr id="row_106_7_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d7/d47/structstd_1_1is__integral_3_01uint256__t_01_4.html" target="_self">is_integral&lt; uint256_t &gt;</a></td><td class="desc"></td></tr>
+<tr id="row_106_8_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d5/d25/structstd_1_1is__unsigned_3_01uint128__t_01_4.html" target="_self">is_unsigned&lt; uint128_t &gt;</a></td><td class="desc"></td></tr>
+<tr id="row_106_9_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="df/d99/structstd_1_1is__unsigned_3_01uint256__t_01_4.html" target="_self">is_unsigned&lt; uint256_t &gt;</a></td><td class="desc"></td></tr>
+<tr id="row_107_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d1d/namespacestrand.html" target="_self">strand</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Strand_sort" target="_blank">Strand Sort</a> algorithm </td></tr>
+<tr id="row_108_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d03/namespacestring__search.html" target="_self">string_search</a></td><td class="desc">String search algorithms </td></tr>
+<tr id="row_109_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/dcb/namespacestrings.html" target="_self">strings</a></td><td class="desc">Algorithms with strings </td></tr>
+<tr id="row_110_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d74/namespacesubarray__sum.html" target="_self">subarray_sum</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Subset_sum_problem" target="_blank">Subset sum</a> implementation </td></tr>
+<tr id="row_111_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/def/namespacesublist__search.html" target="_self">sublist_search</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/sublist-search-search-a-linked-list-in-another-list" target="_blank">Sublist Search</a> implementation </td></tr>
+<tr id="row_112_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/d95/namespace_subsets.html" target="_self">Subsets</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Subset_sum_problem" target="_blank">Subset Sum</a> problem </td></tr>
+<tr id="row_113_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d9f/namespacesudoku__solver.html" target="_self">sudoku_solver</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Sudoku" target="_blank">Sudoku Solver</a> implementation </td></tr>
+<tr id="row_114_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/df4/namespacetests.html" target="_self">tests</a></td><td class="desc">Testcases to check Union of Two Arrays </td></tr>
+<tr id="row_115_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/dab/namespacetree__234.html" target="_self">tree_234</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/2%E2%80%933%E2%80%934_tree" target="_blank">2–3–4 tree</a> </td></tr>
+<tr id="row_116_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d8e/namespacetrie__operations.html" target="_self">trie_operations</a></td><td class="desc">Functions for <a href="https://iq.opengenus.org/autocomplete-using-trie-data-structure/" target="_blank">Trie datastructure</a> implementation </td></tr>
+<tr id="row_117_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d7/d0a/namespacetrie__using__hashmap.html" target="_self">trie_using_hashmap</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Trie" target="_blank">Trie</a> data structure using hashmap implementation </td></tr>
+<tr id="row_118_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/d17/namespaceutil__functions.html" target="_self">util_functions</a></td><td class="desc">Various utility functions used in Neural network </td></tr>
+<tr id="row_119_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/d91/namespacevector__cross.html" target="_self">vector_cross</a></td><td class="desc">Functions for Vector Cross Product algorithms </td></tr>
+<tr id="row_120_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/da2/namespacevigenere.html" target="_self">vigenere</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher" target="_blank">vigenère cipher</a> algorithm </td></tr>
+<tr id="row_121_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d21/namespacewave__sort.html" target="_self">wave_sort</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/sort-array-wave-form-2/" target="_blank">Wave sort</a> implementation </td></tr>
+<tr id="row_122_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d0/d52/namespacewiggle__sort.html" target="_self">wiggle_sort</a></td><td class="desc">Functions for <a href="https://leetcode.com/problems/wiggle-sort-ii/" target="_blank">Wiggle Sort</a> algorithm </td></tr>
+<tr id="row_123_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="db/d03/namespacewildcard__matching.html" target="_self">wildcard_matching</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/wildcard-pattern-matching/" target="_blank">Wildcard Matching</a> problem </td></tr>
+<tr id="row_124_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dd/d21/namespacewindowed__median.html" target="_self">windowed_median</a></td><td class="desc">Functions for the Windowed Median algorithm implementation </td></tr>
+<tr id="row_125_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/d53/namespaceword__break.html" target="_self">word_break</a></td><td class="desc">Functions for <a href="https://leetcode.com/problems/word-break/" target="_blank">Word Break</a> problem </td></tr>
+<tr id="row_126_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d7/d47/namespace_x_o_r.html" target="_self">XOR</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/XOR_cipher" target="_blank">XOR cipher</a> algorithm </td></tr>
 </table>
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