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<p><a href="https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods">Runge Kutta fourth order</a> method implementation
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
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Include dependency graph for rungekutta.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:d1/de0/namespacenumerical__methods"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a></td></tr>
<tr class="memdesc:d1/de0/namespacenumerical__methods"><td class="mdescLeft">&#160;</td><td class="mdescRight">for io operations <br /></td></tr>
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<tr class="memitem:d2/de7/namespacerunge__kutta"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/de7/namespacerunge__kutta.html">runge_kutta</a></td></tr>
<tr class="memdesc:d2/de7/namespacerunge__kutta"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for <a href="https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods">Runge Kutta fourth order</a> method. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a7b9f40c7b5e9749cc550f19be3dc8856"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/da6/rungekutta_8cpp.html#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a> (double init_x, const double &amp;init_y, const double &amp;x, const double &amp;<a class="el" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>)</td></tr>
<tr class="memdesc:a7b9f40c7b5e9749cc550f19be3dc8856"><td class="mdescLeft">&#160;</td><td class="mdescRight">the Runge Kutta method finds the value of integration of a function in the given limits. the lower limit of integration as the initial value and the upper limit is the given x <a href="../../d1/da6/rungekutta_8cpp.html#a7b9f40c7b5e9749cc550f19be3dc8856">More...</a><br /></td></tr>
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<tr><td colspan="2"><div class="groupHeader"></div></td></tr>
<tr class="memitem:a450497475f5607333f9aca8f88901579"><td class="memItemLeft" align="right" valign="top">static double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a> (double x, double y)</td></tr>
<tr class="memdesc:a450497475f5607333f9aca8f88901579"><td class="mdescLeft">&#160;</td><td class="mdescRight">asserting the test functions <a href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">More...</a><br /></td></tr>
<tr class="separator:a450497475f5607333f9aca8f88901579"><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="../../d1/da6/rungekutta_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Tests to check algorithm implementation. <a href="../../d1/da6/rungekutta_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/da6/rungekutta_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d1/da6/rungekutta_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></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://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods">Runge Kutta fourth order</a> method implementation </p>
<dl class="section author"><dt>Author</dt><dd><a href="http://github.com/rudra697">Rudra Prasad Das</a></dd></dl>
<p>It solves the unknown value of y for a given value of x only first order differential equations can be solved </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a450497475f5607333f9aca8f88901579"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a450497475f5607333f9aca8f88901579">&#9670;&nbsp;</a></span>change()</h2>
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<td class="memname">static double change </td>
<td>(</td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>y</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">static</span></span> </td>
</tr>
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<p>asserting the test functions </p>
<p>for io operations for using the vector container</p>
<p>The <a class="el" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579" title="asserting the test functions">change()</a> function is used to return the updated iterative value corresponding to the given function </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>is the value corresponding to the x coordinate </td></tr>
<tr><td class="paramname">y</td><td>is the value corresponding to the y coordinate </td></tr>
</table>
</dd>
</dl>
<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 name="l00032"></a><span class="lineno"> 32</span>&#160;{ </div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; <span class="keywordflow">return</span> ((x - y)/2.0); </div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; </div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160;} </div>
</div><!-- fragment -->
</div>
</div>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<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"><a name="l00131"></a><span class="lineno"> 131</span>&#160;{ </div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160; </div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160; <a class="code" href="../../d1/da6/rungekutta_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// Execute the tests</span></div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160; <span class="keywordflow">return</span> 0; </div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160;} </div>
</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a7b9f40c7b5e9749cc550f19be3dc8856">&#9670;&nbsp;</a></span>rungeKutta()</h2>
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<td class="memname">double numerical_methods::runge_kutta::rungeKutta </td>
<td>(</td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>init_x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const double &amp;&#160;</td>
<td class="paramname"><em>init_y</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const double &amp;&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const double &amp;&#160;</td>
<td class="paramname"><em>h</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>the Runge Kutta method finds the value of integration of a function in the given limits. the lower limit of integration as the initial value and the upper limit is the given x </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">init_x</td><td>is the value of initial x and is updated after each call </td></tr>
<tr><td class="paramname">init_y</td><td>is the value of initial x and is updated after each call </td></tr>
<tr><td class="paramname">x</td><td>is current iteration at which the function needs to be evaluated </td></tr>
<tr><td class="paramname">h</td><td>is the step value </td></tr>
</table>
</dd>
</dl>
<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 name="l00057"></a><span class="lineno"> 57</span>&#160;{ </div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; </div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="comment">// Count number of iterations </span></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="comment">// using step size or </span></div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <span class="comment">// step height h </span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; </div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; </div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <span class="comment">// n calucates the number of iterations</span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; <span class="comment">// k1, k2, k3, k4 are the Runge Kutta variables </span></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="comment">// used for calculation of y at each iteration</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; </div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <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" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>); </div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <span class="comment">// used a vector container for the variables</span></div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> k(4,0.0);</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; </div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; </div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <span class="comment">// Iterate for number of iterations </span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; </div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <span class="keywordtype">double</span> y = init_y; </div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=1; i&lt;=n; ++i) </div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; { </div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; </div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; <span class="comment">// Apply Runge Kutta Formulas </span></div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="comment">// to find next value of y </span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; k[0] = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>*<a class="code" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a>(init_x, y); </div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; k[1] = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>*<a class="code" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a>(init_x + 0.5*<a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, y + 0.5*k[0]); </div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; k[2] = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>*<a class="code" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a>(init_x + 0.5*<a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, y + 0.5*k[1]); </div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; k[3] = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>*<a class="code" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a>(init_x + <a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, y + k[2]); </div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; </div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; </div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; <span class="comment">// Update next value of y </span></div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; </div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; y += (1.0/6.0)*(k[0] + 2*k[1] + 2*k[2] + k[3]);</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; </div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; <span class="comment">// Update next value of x </span></div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; </div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; init_x += <a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>; </div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; } </div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; </div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160;} </div>
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Here is the call graph for this function:</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&nbsp;</a></span>test()</h2>
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<td class="memname">static void test </td>
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<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 name="l00106"></a><span class="lineno"> 106</span>&#160; {</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; <a class="codeRef" 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 precomputed values\n&quot;</span>;</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; </div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; <a class="codeRef" 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; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; <span class="keywordtype">double</span> valfirst=<a class="code" href="../../d1/da6/rungekutta_8cpp.html#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a>(2,3,4,0.2); <span class="comment">// Tests the function with pre calculated values</span></div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; assert(valfirst==3.10363932323749570);</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; <a class="codeRef" 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 name="l00113"></a><span class="lineno"> 113</span>&#160; </div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160; <a class="codeRef" 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; <span class="stringliteral">&quot;\n&quot;</span>;</div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160; assert(valsec==3.40600589380261409);</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160; <a class="codeRef" 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"><a name="l00118"></a><span class="lineno"> 118</span>&#160; </div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160; <a class="codeRef" 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; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160; <span class="keywordtype">double</span> valthird=<a class="code" href="../../d1/da6/rungekutta_8cpp.html#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a>(-1,3,4,0.1); <span class="comment">// Tested with negative value</span></div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160; assert(valthird==2.49251005860244268);</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160; <a class="codeRef" 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"><a name="l00123"></a><span class="lineno"> 123</span>&#160; }</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; double &gt;</a></div></div>
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<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">asserting the test functions</div><div class="ttdef"><b>Definition:</b> rungekutta.cpp:31</div></div>
<div class="ttc" id="arungekutta_8cpp_html_a7b9f40c7b5e9749cc550f19be3dc8856"><div class="ttname"><a href="../../d1/da6/rungekutta_8cpp.html#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a></div><div class="ttdeci">double rungeKutta(double init_x, const double &amp;init_y, const double &amp;x, const double &amp;h)</div><div class="ttdoc">the Runge Kutta method finds the value of integration of a function in the given limits....</div><div class="ttdef"><b>Definition:</b> rungekutta.cpp:56</div></div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>for io operations </p>
<p>Numerical Methods.</p>
<p>for math operations</p>
<p>Numerical methods </p>
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<dl class="section return"><dt>Returns</dt><dd>hash value for <code>key</code> </dd></dl>
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<p>Functions for <a href="https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods">Runge Kutta fourth order</a> method.
<a href="../../d2/de7/namespacerunge__kutta.html#details">More...</a></p>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Functions for <a href="https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods">Runge Kutta fourth order</a> method. </p>
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@@ -154,7 +154,7 @@ Functions</h2></td></tr>
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<p>Main function</p>
<p>Driver Code </p>
<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#a11">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/sorting/wiggle_sort.cpp</a>.</dd>
<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#a6">/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>
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<div class="fragment"><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; {</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; <span class="comment">// Create following graph and test whether it is 3 colorable</span></div>
@@ -218,6 +218,7 @@ Functions</h2></td></tr>
<div class="ttc" id="agroup__sorting_html_ga29d28b140174dbdde7c9f5157758435f"><div class="ttname"><a href="../../d5/d4c/group__sorting.html#ga29d28b140174dbdde7c9f5157758435f">heapSort</a></div><div class="ttdeci">void heapSort(T *arr, int n)</div><div class="ttdef"><b>Definition:</b> heap_sort.cpp:84</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>
<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>
<div class="ttc" id="anamespacenumerical__methods_html"><div class="ttname"><a href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a></div><div class="ttdoc">for io operations</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 class="ttc" id="abinomial__dist_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d6/db0/binomial__dist_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> binomial_dist.cpp:84</div></div>
<div class="ttc" id="aaddition__rule_8cpp_html_a565ffcbbdbe496ced37250bc8dc36bc0"><div class="ttname"><a href="../../d6/d4a/addition__rule_8cpp.html#a565ffcbbdbe496ced37250bc8dc36bc0">addition_rule_dependent</a></div><div class="ttdeci">double addition_rule_dependent(double A, double B, double B_given_A)</div><div class="ttdef"><b>Definition:</b> addition_rule.cpp:25</div></div>
@@ -234,7 +235,7 @@ Functions</h2></td></tr>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_s_g_html_a3c75bf5770790f8eba8cc92227b5400c"><div class="ttname"><a href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#a3c75bf5770790f8eba8cc92227b5400c">range_queries::heavy_light_decomposition::SG::update</a></div><div class="ttdeci">void update(int p, X v)</div><div class="ttdoc">Update the value at a node.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:293</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_a835fb2bbb27307b8cacad9b287968bc1"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a835fb2bbb27307b8cacad9b287968bc1">range_queries::heavy_light_decomposition::Tree::Tree</a></div><div class="ttdeci">Tree(int nodes)</div><div class="ttdoc">Class parameterized constructor, resizes the and initializes the data members.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:140</div></div>
<div class="ttc" id="afibonacci__search_8cpp_html_a2aa09bef74ee063c1331de0883af4f4f"><div class="ttname"><a href="../../de/d0d/fibonacci__search_8cpp.html#a2aa09bef74ee063c1331de0883af4f4f">random_tests</a></div><div class="ttdeci">bool random_tests()</div><div class="ttdoc">random tests which cover cases when we have one, multiple or zero occurences of the value we're looki...</div><div class="ttdef"><b>Definition:</b> fibonacci_search.cpp:96</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 class="ttdoc">STL class.</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 class="ttc" id="afind_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/find.html">std::find</a></div><div class="ttdeci">T find(T... args)</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>
<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>
@@ -364,6 +365,7 @@ Functions</h2></td></tr>
<div class="ttc" id="aparanthesis__matching_8cpp_html_ade525d33459755a32ba21e1b6910ff21"><div class="ttname"><a href="../../dc/dc5/paranthesis__matching_8cpp.html#ade525d33459755a32ba21e1b6910ff21">opening</a></div><div class="ttdeci">char opening(char ch)</div><div class="ttdef"><b>Definition:</b> paranthesis_matching.cpp:36</div></div>
<div class="ttc" id="ac_str_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/c_str.html">std::string::c_str</a></div><div class="ttdeci">T c_str(T... args)</div></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="anamespacerunge__kutta_html"><div class="ttname"><a href="../../d2/de7/namespacerunge__kutta.html">runge_kutta</a></div><div class="ttdoc">Functions for Runge Kutta fourth order method.</div></div>
<div class="ttc" id="ahappy__number_8cpp_html_a00ccdb1166a7c83ac3c33ac67a2532b7"><div class="ttname"><a href="../../db/df3/happy__number_8cpp.html#a00ccdb1166a7c83ac3c33ac67a2532b7">is_happy</a></div><div class="ttdeci">bool is_happy(T n)</div><div class="ttdef"><b>Definition:</b> happy_number.cpp:14</div></div>
<div class="ttc" id="anamespacestring__search_html_aebe07cea289a13142503d98be7df11fd"><div class="ttname"><a href="../../d9/d03/namespacestring__search.html#aebe07cea289a13142503d98be7df11fd">string_search::check_if_equal</a></div><div class="ttdeci">bool check_if_equal(const std::string &amp;str1, const std::string &amp;str2, int start1, int end1, int start2, int end2)</div><div class="ttdef"><b>Definition:</b> rabin_karp.cpp:60</div></div>
<div class="ttc" id="agroup__sorting_html_ga135e4c638e3bcf548bd122b5f49a3e72"><div class="ttname"><a href="../../d5/d4c/group__sorting.html#ga135e4c638e3bcf548bd122b5f49a3e72">displayElements</a></div><div class="ttdeci">static void displayElements(const std::vector&lt; T &gt; &amp;arr)</div><div class="ttdoc">Utility function used for printing the elements. Prints elements of the array after they're sorted us...</div><div class="ttdef"><b>Definition:</b> wiggle_sort.cpp:84</div></div>
@@ -472,6 +474,7 @@ Functions</h2></td></tr>
<div class="ttc" id="aspiral__print_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../db/d07/spiral__print_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> spiral_print.cpp:69</div></div>
<div class="ttc" id="aparanthesis__matching_8cpp_html_a392fb874e547e582e9c66a08a1f23326"><div class="ttname"><a href="../../dc/dc5/paranthesis__matching_8cpp.html#a392fb874e547e582e9c66a08a1f23326">MAX</a></div><div class="ttdeci">#define MAX</div><div class="ttdef"><b>Definition:</b> paranthesis_matching.cpp:16</div></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="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">asserting the test functions</div><div class="ttdef"><b>Definition:</b> rungekutta.cpp:31</div></div>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_a5769b745458157ef2679949155684f3b"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a5769b745458157ef2679949155684f3b">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="amerge__insertion__sort_8cpp_html_a0cba4fbf287ab8cb978ed7f8fef886b1"><div class="ttname"><a href="../../de/d7b/merge__insertion__sort_8cpp.html#a0cba4fbf287ab8cb978ed7f8fef886b1">sorting::merge_insertion::InsertionSort</a></div><div class="ttdeci">static void InsertionSort(std::array&lt; T, N &gt; *A, size_t start, size_t end)</div><div class="ttdoc">Insertion merge algorithm.</div><div class="ttdef"><b>Definition:</b> merge_insertion_sort.cpp:37</div></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>
@@ -506,6 +509,7 @@ Functions</h2></td></tr>
<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 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="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="arungekutta_8cpp_html_a7b9f40c7b5e9749cc550f19be3dc8856"><div class="ttname"><a href="../../d1/da6/rungekutta_8cpp.html#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a></div><div class="ttdeci">double rungeKutta(double init_x, const double &amp;init_y, const double &amp;x, const double &amp;h)</div><div class="ttdoc">the Runge Kutta method finds the value of integration of a function in the given limits....</div><div class="ttdef"><b>Definition:</b> rungekutta.cpp:56</div></div>
<div class="ttc" id="aparanthesis__matching_8cpp_html_aa37d24a036d239b3b528f13b9de880c7"><div class="ttname"><a href="../../dc/dc5/paranthesis__matching_8cpp.html#aa37d24a036d239b3b528f13b9de880c7">stack</a></div><div class="ttdeci">char stack[MAX]</div><div class="ttdef"><b>Definition:</b> paranthesis_matching.cpp:20</div></div>
<div class="ttc" id="abayes__theorem_8cpp_html_a655bfe51252468d232dc639a340656ba"><div class="ttname"><a href="../../d5/d67/bayes__theorem_8cpp.html#a655bfe51252468d232dc639a340656ba">bayes_AgivenB</a></div><div class="ttdeci">double bayes_AgivenB(double BgivenA, double A, double B)</div><div class="ttdef"><b>Definition:</b> bayes_theorem.cpp:14</div></div>
<div class="ttc" id="aclass_fenwick_tree_html_ade1d6a3d49af9d9df33e2fb26cab1699"><div class="ttname"><a href="../../dd/d91/class_fenwick_tree.html#ade1d6a3d49af9d9df33e2fb26cab1699">FenwickTree::sum</a></div><div class="ttdeci">int sum(int id)</div><div class="ttdef"><b>Definition:</b> fenwick_tree.cpp:54</div></div>
@@ -515,6 +519,7 @@ Functions</h2></td></tr>
<div class="ttc" id="amerge__insertion__sort_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../de/d7b/merge__insertion__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Function to test code using random arrays.</div><div class="ttdef"><b>Definition:</b> merge_insertion_sort.cpp:132</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_ab916d554afa8ca5230b4310c2c69fae0"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab916d554afa8ca5230b4310c2c69fae0">range_queries::heavy_light_decomposition::Tree::change_root</a></div><div class="ttdeci">void change_root(int new_root)</div><div class="ttdoc">Set the root for the tree.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:167</div></div>
<div class="ttc" id="aclass_fenwick_tree_html_a70f8c261393ca09ec1ad716ac806ead6"><div class="ttname"><a href="../../dd/d91/class_fenwick_tree.html#a70f8c261393ca09ec1ad716ac806ead6">FenwickTree::FenwickTree</a></div><div class="ttdeci">FenwickTree(int x)</div><div class="ttdef"><b>Definition:</b> fenwick_tree.cpp:39</div></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:105</div></div>
<div class="ttc" id="astruct_point_html_ae2d6fb1b3fd3a96169d963d62e37130a"><div class="ttname"><a href="../../d8/dc8/struct_point.html#ae2d6fb1b3fd3a96169d963d62e37130a">Point::Point</a></div><div class="ttdeci">Point(double a=0.f, double b=0.f)</div><div class="ttdef"><b>Definition:</b> smallest_circle.cpp:23</div></div>
<div class="ttc" id="aprimality__test_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../da/d7b/primality__test_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> primality_test.cpp:31</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>
@@ -523,6 +528,7 @@ Functions</h2></td></tr>
<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>
<div class="ttc" id="atower__of__hanoi_8cpp_html_ab037f72a5eac476535a6cfbbcb965417"><div class="ttname"><a href="../../db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">TH</a></div><div class="ttdeci">void TH(int n, tower *From, tower *Using, tower *To)</div><div class="ttdef"><b>Definition:</b> tower_of_hanoi.cpp:52</div></div>
<div class="ttc" id="ainterpolation__search_8cpp_html_a9805865b5c5ca6b0fdf95fd86132625a"><div class="ttname"><a href="../../d9/dd7/interpolation__search_8cpp.html#a9805865b5c5ca6b0fdf95fd86132625a">interpolation_search</a></div><div class="ttdeci">int interpolation_search(int arr[], int value, int len)</div><div class="ttdef"><b>Definition:</b> interpolation_search.cpp:15</div></div>
<div class="ttc" id="arungekutta_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d1/da6/rungekutta_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition:</b> rungekutta.cpp:130</div></div>
<div class="ttc" id="aparanthesis__matching_8cpp_html_aae41c72130114bf31204cde6873b6095"><div class="ttname"><a href="../../dc/dc5/paranthesis__matching_8cpp.html#aae41c72130114bf31204cde6873b6095">push</a></div><div class="ttdeci">void push(char ch)</div><div class="ttdoc">push byte to stack variable</div><div class="ttdef"><b>Definition:</b> paranthesis_matching.cpp:26</div></div>
<div class="ttc" id="abogo__sort_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d5/ddb/bogo__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> bogo_sort.cpp:104</div></div>
<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>

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@@ -296,6 +296,7 @@ Numerical Methods</h1>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/qr_decompose.h">Qr Decompose</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/qr_decomposition.cpp">Qr Decomposition</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/qr_eigen_values.cpp">Qr Eigen Values</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/rungekutta.cpp">Rungekutta</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/successive_approximation.cpp">Successive Approximation</a></li>
</ul>
<h1><a class="anchor" id="autotoc_md41"></a>

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@@ -294,7 +294,7 @@ Here is the call graph for this function:</div>
<p>Test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></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#a7">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/sorting/wiggle_sort.cpp</a>.</dd>
<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>, 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#a7">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/sorting/wiggle_sort.cpp</a>.</dd>
</dl>
<div class="fragment"><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; {</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> size = 4;</div>

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<div class="title">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp</div> </div>
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<p>it solves \frac{\mathrm{d} y}{\mathrm{d} x}= \frac{\left ( x-y \right )}{2} given x for given initial conditions There can be many such equations</p>
<div class="fragment"><div class="line"><span class="comment">/**</span></div>
<div class="line"><span class="comment"> * @{</span></div>
<div class="line"><span class="comment"> * \file</span></div>
<div class="line"><span class="comment"> * \brief [Runge Kutta fourth order](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods) method implementation</span></div>
<div class="line"><span class="comment"> *</span></div>
<div class="line"><span class="comment"> * \author [Rudra Prasad Das](http://github.com/rudra697)</span></div>
<div class="line"><span class="comment"> *</span></div>
<div class="line"><span class="comment"> * \details</span></div>
<div class="line"><span class="comment"> * It solves the unknown value of y </span></div>
<div class="line"><span class="comment"> * for a given value of x</span></div>
<div class="line"><span class="comment"> * only first order differential equations</span></div>
<div class="line"><span class="comment"> * can be solved</span></div>
<div class="line"><span class="comment"> * \example</span></div>
<div class="line"><span class="comment"> * it solves \frac{\mathrm{d} y}{\mathrm{d} x}= \frac{\left ( x-y \right )}{2}</span></div>
<div class="line"><span class="comment"> * given x for given initial </span></div>
<div class="line"><span class="comment"> * conditions</span></div>
<div class="line"><span class="comment"> * There can be many such equations </span></div>
<div class="line"><span class="comment"> */</span></div>
<div class="line"><span class="preprocessor">#include &lt;iostream&gt;</span> <span class="comment">/// for io operations</span></div>
<div class="line"><span class="comment"></span><span class="preprocessor">#include &lt;vector&gt;</span> <span class="comment">/// for using the vector container</span></div>
<div class="line"><span class="comment"></span><span class="preprocessor">#include &lt;cassert&gt;</span> <span class="comment">/// asserting the test functions</span></div>
<div class="line"><span class="comment"></span><span class="comment"></span> </div>
<div class="line"><span class="comment">/**</span></div>
<div class="line"><span class="comment"> * @brief The change() function is used </span></div>
<div class="line"><span class="comment"> * to return the updated iterative value corresponding </span></div>
<div class="line"><span class="comment"> * to the given function</span></div>
<div class="line"><span class="comment"> * @param x is the value corresponding to the x coordinate</span></div>
<div class="line"><span class="comment"> * @param y is the value corresponding to the y coordinate </span></div>
<div class="line"><span class="comment"> * @returns the computed function value at that call</span></div>
<div class="line"><span class="comment"> */</span></div>
<div class="line"><span class="keyword">static</span> <span class="keywordtype">double</span> <a name="a0"></a><a class="code" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a>(<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y) </div>
<div class="line">{ </div>
<div class="line"> <span class="keywordflow">return</span> ((x - y)/2.0); </div>
<div class="line"> </div>
<div class="line">} </div>
<div class="line"><span class="comment"></span> </div>
<div class="line"><span class="comment">/**</span></div>
<div class="line"><span class="comment"> * @namespace numerical_methods</span></div>
<div class="line"><span class="comment"> * @brief Numerical Methods</span></div>
<div class="line"><span class="comment"> */</span></div>
<div class="line"><span class="keyword">namespace </span><a class="code" href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a> {<span class="comment"></span></div>
<div class="line"><span class="comment">/**</span></div>
<div class="line"><span class="comment"> * @namespace runge_kutta</span></div>
<div class="line"><span class="comment"> * @brief Functions for [Runge Kutta fourth order](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods) method</span></div>
<div class="line"><span class="comment"> */</span></div>
<div class="line"><span class="keyword">namespace </span><a class="code" href="../../d2/de7/namespacerunge__kutta.html">runge_kutta</a> {<span class="comment"></span></div>
<div class="line"><span class="comment">/**</span></div>
<div class="line"><span class="comment"> * @brief the Runge Kutta method finds the value of integration of a function in the given limits.</span></div>
<div class="line"><span class="comment"> * the lower limit of integration as the initial value and the upper limit is the given x</span></div>
<div class="line"><span class="comment"> * @param init_x is the value of initial x and is updated after each call</span></div>
<div class="line"><span class="comment"> * @param init_y is the value of initial x and is updated after each call</span></div>
<div class="line"><span class="comment"> * @param x is current iteration at which the function needs to be evaluated</span></div>
<div class="line"><span class="comment"> * @param h is the step value </span></div>
<div class="line"><span class="comment"> * @returns the value of y at thr required value of x from the initial conditions</span></div>
<div class="line"><span class="comment"> */</span></div>
<div class="line"><span class="keywordtype">double</span> <a name="a1"></a><a class="code" href="../../d1/da6/rungekutta_8cpp.html#a7b9f40c7b5e9749cc550f19be3dc8856">rungeKutta</a>(<span class="keywordtype">double</span> init_x, <span class="keyword">const</span> <span class="keywordtype">double</span> &amp;init_y, <span class="keyword">const</span> <span class="keywordtype">double</span> &amp;x, <span class="keyword">const</span> <span class="keywordtype">double</span> &amp;<a name="a2"></a><a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>) </div>
<div class="line">{ </div>
<div class="line"> </div>
<div class="line"> <span class="comment">// Count number of iterations </span></div>
<div class="line"> <span class="comment">// using step size or </span></div>
<div class="line"> <span class="comment">// step height h </span></div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> <span class="comment">// n calucates the number of iterations</span></div>
<div class="line"> <span class="comment">// k1, k2, k3, k4 are the Runge Kutta variables </span></div>
<div class="line"> <span class="comment">// used for calculation of y at each iteration</span></div>
<div class="line"> </div>
<div class="line"> <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" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>); </div>
<div class="line"> <span class="comment">// used a vector container for the variables</span></div>
<div class="line"> <a name="_a3"></a><a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> k(4,0.0);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> <span class="comment">// Iterate for number of iterations </span></div>
<div class="line"> </div>
<div class="line"> <span class="keywordtype">double</span> y = init_y; </div>
<div class="line"> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=1; i&lt;=n; ++i) </div>
<div class="line"> { </div>
<div class="line"> </div>
<div class="line"> <span class="comment">// Apply Runge Kutta Formulas </span></div>
<div class="line"> <span class="comment">// to find next value of y </span></div>
<div class="line"> k[0] = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>*<a class="code" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a>(init_x, y); </div>
<div class="line"> k[1] = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>*<a class="code" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a>(init_x + 0.5*<a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, y + 0.5*k[0]); </div>
<div class="line"> k[2] = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>*<a class="code" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a>(init_x + 0.5*<a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, y + 0.5*k[1]); </div>
<div class="line"> k[3] = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>*<a class="code" href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a>(init_x + <a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, y + k[2]); </div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> <span class="comment">// Update next value of y </span></div>
<div class="line"> </div>
<div class="line"> y += (1.0/6.0)*(k[0] + 2*k[1] + 2*k[2] + k[3]);</div>
<div class="line"> </div>
<div class="line"> <span class="comment">// Update next value of x </span></div>
<div class="line"> </div>
<div class="line"> init_x += <a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>; </div>
<div class="line"> } </div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">return</span> y; </div>
<div class="line">} </div>
<div class="line">} <span class="comment">// namespace runge_kutta</span></div>
<div class="line">} <span class="comment">// namespace numerical_methods</span></div>
<div class="line"><span class="comment"></span> </div>
<div class="line"><span class="comment">/**</span></div>
<div class="line"><span class="comment"> * @brief Tests to check algorithm implementation.</span></div>
<div class="line"><span class="comment"> * @returns void </span></div>
<div class="line"><span class="comment"> */</span></div>
<div class="line"> <span class="keyword">static</span> <span class="keywordtype">void</span> <a name="a4"></a><a class="code" href="../../dc/d5a/rat__maze_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>()</div>
<div class="line"> {</div>
<div class="line"> <a name="_a5"></a><a class="codeRef" 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 precomputed values\n&quot;</span>;</div>
<div class="line"> </div>
<div class="line"> <a class="codeRef" 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; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"> <span class="keywordtype">double</span> valfirst=<a class="code" href="../../d1/da6/rungekutta_8cpp.html#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a>(2,3,4,0.2); <span class="comment">// Tests the function with pre calculated values</span></div>
<div class="line"> assert(valfirst==3.10363932323749570);</div>
<div class="line"> <a class="codeRef" 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"> </div>
<div class="line"> <a class="codeRef" 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; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"> <span class="keywordtype">double</span> valsec=<a class="code" href="../../d1/da6/rungekutta_8cpp.html#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a>(1,2,5,0.1); <span class="comment">// The value of step changed</span></div>
<div class="line"> assert(valsec==3.40600589380261409);</div>
<div class="line"> <a class="codeRef" 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"> </div>
<div class="line"> <a class="codeRef" 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; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"> <span class="keywordtype">double</span> valthird=<a class="code" href="../../d1/da6/rungekutta_8cpp.html#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a>(-1,3,4,0.1); <span class="comment">// Tested with negative value</span></div>
<div class="line"> assert(valthird==2.49251005860244268);</div>
<div class="line"> <a class="codeRef" 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"> }</div>
<div class="line"> </div>
<div class="line"> <span class="comment"></span></div>
<div class="line"><span class="comment">/**</span></div>
<div class="line"><span class="comment"> * @brief Main function</span></div>
<div class="line"><span class="comment"> * @returns 0 on exit </span></div>
<div class="line"><span class="comment"> */</span></div>
<div class="line"><span class="keywordtype">int</span> <a name="a6"></a><a class="code" href="../../d3/d40/graph__coloring_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() </div>
<div class="line">{ </div>
<div class="line"> </div>
<div class="line"> <a class="code" href="../../dc/d5a/rat__maze_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// Execute the tests</span></div>
<div class="line"> <span class="keywordflow">return</span> 0; </div>
<div class="line">} </div>
</div><!-- fragment --> </div><!-- contents -->
</div><!-- doc-content -->
<div class="ttc" id="arat__maze_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../dc/d5a/rat__maze_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> rat_maze.cpp:84</div></div>
<div class="ttc" id="anamespacenumerical__methods_html"><div class="ttname"><a href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a></div><div class="ttdoc">for io operations</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 class="ttc" id="agraph__coloring_8cpp_html_gae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d3/d40/graph__coloring_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> graph_coloring.cpp:96</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="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="anamespacerunge__kutta_html"><div class="ttname"><a href="../../d2/de7/namespacerunge__kutta.html">runge_kutta</a></div><div class="ttdoc">Functions for Runge Kutta fourth order method.</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">asserting the test functions</div><div class="ttdef"><b>Definition:</b> rungekutta.cpp:31</div></div>
<div class="ttc" id="arungekutta_8cpp_html_a7b9f40c7b5e9749cc550f19be3dc8856"><div class="ttname"><a href="../../d1/da6/rungekutta_8cpp.html#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a></div><div class="ttdeci">double rungeKutta(double init_x, const double &amp;init_y, const double &amp;x, const double &amp;h)</div><div class="ttdoc">the Runge Kutta method finds the value of integration of a function in the given limits....</div><div class="ttdef"><b>Definition:</b> rungekutta.cpp:56</div></div>
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, <a class="el" href="de/d75/qr__eigen__values_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">qr_eigen_values.cpp</a>
, <a class="el" href="d3/d24/qr__decomposition_8cpp.html#a840291bc02cba5474a4cb46a9b9566fe">qr_decomposition.cpp</a>
, <a class="el" href="d3/d06/ode__semi__implicit__euler_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">ode_semi_implicit_euler.cpp</a>

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@@ -126,12 +126,12 @@ $(document).ready(function(){initNavTree('globals_func_s.html',''); initResizabl
<li>show_pascal()
: <a class="el" href="dc/d1a/pascal__triangle_8cpp.html#ad7a31d9cb2818d21b1ba12aead7f4c5c">pascal_triangle.cpp</a>
</li>
<li>sieve()
: <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#a60fa6579eab0db3c1c0ab1bf6d651be3">sieve_of_eratosthenes.cpp</a>
</li>
<li>Sieve()
: <a class="el" href="d4/d9c/primes__up__to__billion_8cpp.html#a031cada84819ed6426f58e4f7e81261c">primes_up_to_billion.cpp</a>
</li>
<li>sieve()
: <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#a60fa6579eab0db3c1c0ab1bf6d651be3">sieve_of_eratosthenes.cpp</a>
</li>
<li>SieveOfEratosthenes()
: <a class="el" href="db/d0d/prime__factorization_8cpp.html#affe577b9bce8f604f5e2f861c63c7099">prime_factorization.cpp</a>
</li>

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@@ -101,13 +101,14 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl
, <a class="el" href="d8/d76/morse__code_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">morse_code.cpp</a>
, <a class="el" href="db/d16/0__1__knapsack_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">0_1_knapsack.cpp</a>
, <a class="el" href="d2/d58/neural__network_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">neural_network.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="dc/dd9/strand__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">strand_sort.cpp</a>
, <a class="el" href="d4/d5d/math_2armstrong__number_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">armstrong_number.cpp</a>
, <a class="el" href="dc/dd9/strand__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">strand_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="d6/d10/cut__rod_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">cut_rod.cpp</a>
, <a class="el" href="d5/df6/check__amicable__pair_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">check_amicable_pair.cpp</a>
, <a class="el" href="d3/dfe/horspool_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">horspool.cpp</a>
, <a class="el" href="d7/d89/double__factorial_8cpp.html#abbbcebf3a2d0c67f4c3cfb5511a97981">double_factorial.cpp</a>
, <a class="el" href="dd/d12/vigenere__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">vigenere_cipher.cpp</a>
, <a class="el" href="d5/d90/palindrome__partitioning_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">palindrome_partitioning.cpp</a>
@@ -120,17 +121,17 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl
, <a class="el" href="d3/d4c/xor__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">xor_cipher.cpp</a>
, <a class="el" href="d3/d84/word__break_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">word_break.cpp</a>
, <a class="el" href="d4/d83/sum__of__digits_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">sum_of_digits.cpp</a>
, <a class="el" href="d0/d01/smallest__circle_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">smallest_circle.cpp</a>
, <a class="el" href="d1/da6/rungekutta_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">rungekutta.cpp</a>
, <a class="el" href="d4/d8d/jarvis__algorithm_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">jarvis_algorithm.cpp</a>
, <a class="el" href="d0/d01/smallest__circle_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">smallest_circle.cpp</a>
, <a class="el" href="d9/d69/median__search_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">median_search.cpp</a>
, <a class="el" href="d5/ddb/bogo__sort_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">bogo_sort.cpp</a>
, <a class="el" href="d7/d83/trie__tree_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">trie_tree.cpp</a>
, <a class="el" href="d6/dd8/is__graph__bipartite_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">is_graph_bipartite.cpp</a>
, <a class="el" href="d5/ddb/bogo__sort_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">bogo_sort.cpp</a>
, <a class="el" href="de/d07/cycle__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">cycle_sort.cpp</a>
, <a class="el" href="d2/d21/gnome__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">gnome_sort.cpp</a>
, <a class="el" href="df/d64/jumpgame_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">jumpgame.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>
</li>
<li>test1()
: <a class="el" href="d7/db9/hill__cipher_8cpp.html#a3147ad576f8a94a2a6b66948672b452b">hill_cipher.cpp</a>
@@ -147,28 +148,28 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl
, <a class="el" href="de/d75/qr__eigen__values_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">qr_eigen_values.cpp</a>
</li>
<li>test2()
: <a class="el" href="de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">qr_eigen_values.cpp</a>
: <a class="el" href="dd/d65/lu__decompose_8cpp.html#a0283886819c7c140a023582b7269e2d0">lu_decompose.cpp</a>
, <a class="el" href="d7/db9/hill__cipher_8cpp.html#a04391124480d2a49f2dec900237b0712">hill_cipher.cpp</a>
, <a class="el" href="dd/d0c/hamiltons__cycle_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">hamiltons_cycle.cpp</a>
, <a class="el" href="d5/db0/adaline__learning_8cpp.html#a379f7488a305f2571f2932b319931f82">adaline_learning.cpp</a>
, <a class="el" href="db/d01/brent__method__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">brent_method_extrema.cpp</a>
, <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a0283886819c7c140a023582b7269e2d0">kohonen_som_topology.cpp</a>
, <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a0283886819c7c140a023582b7269e2d0">kohonen_som_trace.cpp</a>
, <a class="el" href="d6/d9d/large__factorial_8cpp.html#a76aae4778fbe89a3d59fd61fbc050cfa">large_factorial.cpp</a>
, <a class="el" href="d4/d83/sum__of__digits_8cpp.html#a0283886819c7c140a023582b7269e2d0">sum_of_digits.cpp</a>
, <a class="el" href="db/d01/brent__method__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">brent_method_extrema.cpp</a>
, <a class="el" href="da/df2/durand__kerner__roots_8cpp.html#a0283886819c7c140a023582b7269e2d0">durand_kerner_roots.cpp</a>
, <a class="el" href="d6/d7a/golden__search__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">golden_search_extrema.cpp</a>
, <a class="el" href="dd/d65/lu__decompose_8cpp.html#a0283886819c7c140a023582b7269e2d0">lu_decompose.cpp</a>
, <a class="el" href="de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">qr_eigen_values.cpp</a>
, <a class="el" href="d0/d01/smallest__circle_8cpp.html#a0283886819c7c140a023582b7269e2d0">smallest_circle.cpp</a>
</li>
<li>test3()
: <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">kohonen_som_trace.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="d0/d01/smallest__circle_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">smallest_circle.cpp</a>
, <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">kohonen_som_topology.cpp</a>
, <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="dd/d0c/hamiltons__cycle_8cpp.html#a0cc94918b6831f308d4fe4fa27f08299">hamiltons_cycle.cpp</a>
</li>
<li>test_1()
: <a class="el" href="d2/de9/heavy__light__decomposition_8cpp.html#a34b8683a2b429de5cce57e6d733ec817">heavy_light_decomposition.cpp</a>
@@ -182,8 +183,8 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl
: <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a6b5e744876fd980a3451cbb385d4e755">kohonen_som_topology.cpp</a>
</li>
<li>test_3()
: <a class="el" href="dd/da8/pigeonhole__sort_8cpp.html#af31ec5409537703d9c8a47350386b32a">pigeonhole_sort.cpp</a>
, <a class="el" href="d2/de9/heavy__light__decomposition_8cpp.html#af31ec5409537703d9c8a47350386b32a">heavy_light_decomposition.cpp</a>
: <a class="el" href="d2/de9/heavy__light__decomposition_8cpp.html#af31ec5409537703d9c8a47350386b32a">heavy_light_decomposition.cpp</a>
, <a class="el" href="dd/da8/pigeonhole__sort_8cpp.html#af31ec5409537703d9c8a47350386b32a">pigeonhole_sort.cpp</a>
</li>
<li>test_3d_classes()
: <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a9ab8c79ffb674a63f151f282faeb723b">kohonen_som_trace.cpp</a>
@@ -213,28 +214,28 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl
: <a class="el" href="d7/d75/postfix__evaluation_8cpp.html#a5b97d12e8b61484f756a8721992bfae1">postfix_evaluation.cpp</a>
</li>
<li>test_int()
: <a class="el" href="d3/d4c/quick__sort__3_8cpp.html#a07e5c62de28aeddea986890ce7ac1bda">quick_sort_3.cpp</a>
, <a class="el" href="d4/d7a/shell__sort2_8cpp.html#a895b313cb2671e8f712040460325573e">shell_sort2.cpp</a>
: <a class="el" href="d4/d7a/shell__sort2_8cpp.html#a895b313cb2671e8f712040460325573e">shell_sort2.cpp</a>
, <a class="el" href="d3/d4c/quick__sort__3_8cpp.html#a07e5c62de28aeddea986890ce7ac1bda">quick_sort_3.cpp</a>
</li>
<li>test_lamniscate()
: <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a412b7afa156306b1f8788643c91a1c60">kohonen_som_trace.cpp</a>
</li>
<li>tests()
: <a class="el" href="d9/d44/magic__number_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">magic_number.cpp</a>
, <a class="el" href="d7/d89/double__factorial_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">double_factorial.cpp</a>
, <a class="el" href="dd/d0d/insertion__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">insertion_sort.cpp</a>
, <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">sieve_of_eratosthenes.cpp</a>
, <a class="el" href="d1/d9a/hopcroft__karp_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">hopcroft_karp.cpp</a>
, <a class="el" href="d5/d67/complex__numbers_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">complex_numbers.cpp</a>
, <a class="el" href="d9/dfd/comb__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">comb_sort.cpp</a>
, <a class="el" href="df/ddd/connected__components_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">connected_components.cpp</a>
, <a class="el" href="d7/d1e/graph_2dijkstra_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">dijkstra.cpp</a>
, <a class="el" href="de/dde/lowest__common__ancestor_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">lowest_common_ancestor.cpp</a>
, <a class="el" href="d8/dd5/check__factorial_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">check_factorial.cpp</a>
, <a class="el" href="d6/d42/miller__rabin_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">miller_rabin.cpp</a>
, <a class="el" href="d0/da2/number__of__positive__divisors_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">number_of_positive_divisors.cpp</a>
, <a class="el" href="df/d82/breadth__first__search_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">breadth_first_search.cpp</a>
: <a class="el" href="d7/d89/double__factorial_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">double_factorial.cpp</a>
, <a class="el" href="d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">least_common_multiple.cpp</a>
, <a class="el" href="d8/dd5/check__factorial_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">check_factorial.cpp</a>
, <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">sieve_of_eratosthenes.cpp</a>
, <a class="el" href="d9/dfd/comb__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">comb_sort.cpp</a>
, <a class="el" href="d5/d67/complex__numbers_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">complex_numbers.cpp</a>
, <a class="el" href="d0/da2/number__of__positive__divisors_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">number_of_positive_divisors.cpp</a>
, <a class="el" href="d7/d1e/graph_2dijkstra_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">dijkstra.cpp</a>
, <a class="el" href="d6/d42/miller__rabin_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">miller_rabin.cpp</a>
, <a class="el" href="d1/d9a/hopcroft__karp_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">hopcroft_karp.cpp</a>
, <a class="el" href="df/d82/breadth__first__search_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">breadth_first_search.cpp</a>
, <a class="el" href="df/ddd/connected__components_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">connected_components.cpp</a>
, <a class="el" href="d9/d44/magic__number_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">magic_number.cpp</a>
, <a class="el" href="dd/d0d/insertion__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">insertion_sort.cpp</a>
, <a class="el" href="de/dde/lowest__common__ancestor_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">lowest_common_ancestor.cpp</a>
</li>
<li>TH()
: <a class="el" href="db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">tower_of_hanoi.cpp</a>

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@@ -123,14 +123,14 @@ $(document).ready(function(){initNavTree('globals_i.html',''); initResizable();
<li>is_square()
: <a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html#a4921874435266592b222e3f2eda0e01f">ordinary_least_squares_regressor.cpp</a>
</li>
<li>IsPrime()
: <a class="el" href="da/d7b/primality__test_8cpp.html#a2bfa6adead2bdcbf1dac94cbe08d7eaf">primality_test.cpp</a>
<li>isPrime()
: <a class="el" href="d8/d53/modular__inverse__fermat__little__theorem_8cpp.html#a09660096b134753128952246f4f4e4bd">modular_inverse_fermat_little_theorem.cpp</a>
</li>
<li>isprime
: <a class="el" href="db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">prime_factorization.cpp</a>
</li>
<li>isPrime()
: <a class="el" href="d8/d53/modular__inverse__fermat__little__theorem_8cpp.html#a09660096b134753128952246f4f4e4bd">modular_inverse_fermat_little_theorem.cpp</a>
<li>IsPrime()
: <a class="el" href="da/d7b/primality__test_8cpp.html#a2bfa6adead2bdcbf1dac94cbe08d7eaf">primality_test.cpp</a>
</li>
<li>it_ternary_search()
: <a class="el" href="dc/dfe/ternary__search_8cpp.html#ae30dfe2894191bfeffe5b3b1854b95b0">ternary_search.cpp</a>

View File

@@ -101,35 +101,36 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable();
, <a class="el" href="da/dc3/linked__list_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">linked_list.cpp</a>
, <a class="el" href="da/d8d/depth__first__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">depth_first_search.cpp</a>
, <a class="el" href="d4/d45/gcd__recursive__euclidean_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">gcd_recursive_euclidean.cpp</a>
, <a class="el" href="dc/dfe/ternary__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">ternary_search.cpp</a>
, <a class="el" href="dc/db5/text__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">text_search.cpp</a>
, <a class="el" href="d5/ddb/bogo__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">bogo_sort.cpp</a>
, <a class="el" href="d6/d9d/large__factorial_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">large_factorial.cpp</a>
, <a class="el" href="d5/ddb/bogo__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">bogo_sort.cpp</a>
, <a class="el" href="d9/dfd/comb__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">comb_sort.cpp</a>
, <a class="el" href="de/d07/cycle__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">cycle_sort.cpp</a>
, <a class="el" href="d7/d1e/graph_2dijkstra_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">dijkstra.cpp</a>
, <a class="el" href="d5/d83/lcm__sum_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">lcm_sum.cpp</a>
, <a class="el" href="de/d07/cycle__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">cycle_sort.cpp</a>
, <a class="el" href="d2/d21/gnome__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">gnome_sort.cpp</a>
, <a class="el" href="d2/d52/heap__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">heap_sort.cpp</a>
, <a class="el" href="d4/d21/least__common__multiple_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">least_common_multiple.cpp</a>
, <a class="el" href="d2/d52/heap__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">heap_sort.cpp</a>
, <a class="el" href="dd/d0d/insertion__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">insertion_sort.cpp</a>
, <a class="el" href="de/d7b/merge__insertion__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">merge_insertion_sort.cpp</a>
, <a class="el" href="d3/dce/linkedlist__implentation__usingarray_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">linkedlist_implentation_usingarray.cpp</a>
, <a class="el" href="dd/d0c/hamiltons__cycle_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">hamiltons_cycle.cpp</a>
, <a class="el" href="d9/d44/magic__number_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">magic_number.cpp</a>
, <a class="el" href="de/d7b/merge__insertion__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">merge_insertion_sort.cpp</a>
, <a class="el" href="d5/d4c/group__sorting.html#gae66f6b31b5ad750f1fe042a706a4e3d4">merge_sort.cpp</a>
, <a class="el" href="d3/d92/pancake__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">pancake_sort.cpp</a>
, <a class="el" href="d6/d42/miller__rabin_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">miller_rabin.cpp</a>
, <a class="el" href="d6/dce/rabin__karp_8cpp.html#a840291bc02cba5474a4cb46a9b9566fe">rabin_karp.cpp</a>
, <a class="el" href="de/d6a/knuth__morris__pratt_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">knuth_morris_pratt.cpp</a>
, <a class="el" href="d3/dfe/horspool_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">horspool.cpp</a>
, <a class="el" href="d3/d7d/brute__force__string__searching_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">brute_force_string_searching.cpp</a>
, <a class="el" href="dc/dd9/strand__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">strand_sort.cpp</a>
, <a class="el" href="d4/d7a/shell__sort2_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">shell_sort2.cpp</a>
, <a class="el" href="d3/d92/pancake__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">pancake_sort.cpp</a>
, <a class="el" href="dd/da8/pigeonhole__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">pigeonhole_sort.cpp</a>
, <a class="el" href="d1/d21/quick__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">quick_sort.cpp</a>
, <a class="el" href="d1/d9a/hopcroft__karp_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">hopcroft_karp.cpp</a>
, <a class="el" href="d0/d6d/modular__exponentiation_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">modular_exponentiation.cpp</a>
, <a class="el" href="d1/d21/quick__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">quick_sort.cpp</a>
, <a class="el" href="d3/d4c/quick__sort__3_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">quick_sort_3.cpp</a>
, <a class="el" href="d4/d7a/shell__sort2_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">shell_sort2.cpp</a>
, <a class="el" href="d8/d53/modular__inverse__fermat__little__theorem_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">modular_inverse_fermat_little_theorem.cpp</a>
, <a class="el" href="d6/d2c/caesar__cipher_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">caesar_cipher.cpp</a>
, <a class="el" href="df/dd0/queue__using__two__stacks_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">queue_using_two_stacks.cpp</a>
@@ -138,7 +139,6 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable();
, <a class="el" href="df/def/power__for__huge__numbers_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">power_for_huge_numbers.cpp</a>
, <a class="el" href="de/dde/lowest__common__ancestor_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">lowest_common_ancestor.cpp</a>
, <a class="el" href="db/d0d/prime__factorization_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">prime_factorization.cpp</a>
, <a class="el" href="dc/dfe/ternary__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">ternary_search.cpp</a>
, <a class="el" href="d9/d69/median__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">median_search.cpp</a>
, <a class="el" href="d9/d02/linear__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">linear_search.cpp</a>
, <a class="el" href="df/d39/interpolation__search2_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">interpolation_search2.cpp</a>
@@ -171,6 +171,7 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable();
, <a class="el" href="da/de7/decimal__to__hexadecimal_8cpp.html#a840291bc02cba5474a4cb46a9b9566fe">decimal_to_hexadecimal.cpp</a>
, <a class="el" href="d1/d76/buzz__number_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">buzz_number.cpp</a>
, <a class="el" href="df/dc8/successive__approximation_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">successive_approximation.cpp</a>
, <a class="el" href="d1/da6/rungekutta_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">rungekutta.cpp</a>
, <a class="el" href="de/d75/qr__eigen__values_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">qr_eigen_values.cpp</a>
, <a class="el" href="d3/d24/qr__decomposition_8cpp.html#a840291bc02cba5474a4cb46a9b9566fe">qr_decomposition.cpp</a>
, <a class="el" href="d3/d06/ode__semi__implicit__euler_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">ode_semi_implicit_euler.cpp</a>

View File

@@ -126,12 +126,12 @@ $(document).ready(function(){initNavTree('globals_s.html',''); initResizable();
<li>show_pascal()
: <a class="el" href="dc/d1a/pascal__triangle_8cpp.html#ad7a31d9cb2818d21b1ba12aead7f4c5c">pascal_triangle.cpp</a>
</li>
<li>Sieve()
: <a class="el" href="d4/d9c/primes__up__to__billion_8cpp.html#a031cada84819ed6426f58e4f7e81261c">primes_up_to_billion.cpp</a>
</li>
<li>sieve()
: <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#a60fa6579eab0db3c1c0ab1bf6d651be3">sieve_of_eratosthenes.cpp</a>
</li>
<li>Sieve()
: <a class="el" href="d4/d9c/primes__up__to__billion_8cpp.html#a031cada84819ed6426f58e4f7e81261c">primes_up_to_billion.cpp</a>
</li>
<li>SieveOfEratosthenes()
: <a class="el" href="db/d0d/prime__factorization_8cpp.html#affe577b9bce8f604f5e2f861c63c7099">prime_factorization.cpp</a>
</li>

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@@ -101,13 +101,14 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
, <a class="el" href="d8/d76/morse__code_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">morse_code.cpp</a>
, <a class="el" href="db/d16/0__1__knapsack_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">0_1_knapsack.cpp</a>
, <a class="el" href="d2/d58/neural__network_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">neural_network.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="dc/dd9/strand__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">strand_sort.cpp</a>
, <a class="el" href="d4/d5d/math_2armstrong__number_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">armstrong_number.cpp</a>
, <a class="el" href="dc/dd9/strand__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">strand_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="d6/d10/cut__rod_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">cut_rod.cpp</a>
, <a class="el" href="d5/df6/check__amicable__pair_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">check_amicable_pair.cpp</a>
, <a class="el" href="d3/dfe/horspool_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">horspool.cpp</a>
, <a class="el" href="d7/d89/double__factorial_8cpp.html#abbbcebf3a2d0c67f4c3cfb5511a97981">double_factorial.cpp</a>
, <a class="el" href="dd/d12/vigenere__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">vigenere_cipher.cpp</a>
, <a class="el" href="d5/d90/palindrome__partitioning_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">palindrome_partitioning.cpp</a>
@@ -120,17 +121,17 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
, <a class="el" href="d3/d4c/xor__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">xor_cipher.cpp</a>
, <a class="el" href="d3/d84/word__break_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">word_break.cpp</a>
, <a class="el" href="d4/d83/sum__of__digits_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">sum_of_digits.cpp</a>
, <a class="el" href="d0/d01/smallest__circle_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">smallest_circle.cpp</a>
, <a class="el" href="d1/da6/rungekutta_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">rungekutta.cpp</a>
, <a class="el" href="d4/d8d/jarvis__algorithm_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">jarvis_algorithm.cpp</a>
, <a class="el" href="d0/d01/smallest__circle_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">smallest_circle.cpp</a>
, <a class="el" href="d9/d69/median__search_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">median_search.cpp</a>
, <a class="el" href="d5/ddb/bogo__sort_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">bogo_sort.cpp</a>
, <a class="el" href="d7/d83/trie__tree_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">trie_tree.cpp</a>
, <a class="el" href="d6/dd8/is__graph__bipartite_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">is_graph_bipartite.cpp</a>
, <a class="el" href="d5/ddb/bogo__sort_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">bogo_sort.cpp</a>
, <a class="el" href="de/d07/cycle__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">cycle_sort.cpp</a>
, <a class="el" href="d2/d21/gnome__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">gnome_sort.cpp</a>
, <a class="el" href="df/d64/jumpgame_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">jumpgame.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>
</li>
<li>test1()
: <a class="el" href="d7/db9/hill__cipher_8cpp.html#a3147ad576f8a94a2a6b66948672b452b">hill_cipher.cpp</a>
@@ -148,7 +149,7 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
</li>
<li>test2()
: <a class="el" href="d7/db9/hill__cipher_8cpp.html#a04391124480d2a49f2dec900237b0712">hill_cipher.cpp</a>
, <a class="el" href="de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">qr_eigen_values.cpp</a>
, <a class="el" href="dd/d65/lu__decompose_8cpp.html#a0283886819c7c140a023582b7269e2d0">lu_decompose.cpp</a>
, <a class="el" href="dd/d0c/hamiltons__cycle_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">hamiltons_cycle.cpp</a>
, <a class="el" href="d5/db0/adaline__learning_8cpp.html#a379f7488a305f2571f2932b319931f82">adaline_learning.cpp</a>
, <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a0283886819c7c140a023582b7269e2d0">kohonen_som_topology.cpp</a>
@@ -158,25 +159,25 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
, <a class="el" href="db/d01/brent__method__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">brent_method_extrema.cpp</a>
, <a class="el" href="da/df2/durand__kerner__roots_8cpp.html#a0283886819c7c140a023582b7269e2d0">durand_kerner_roots.cpp</a>
, <a class="el" href="d6/d7a/golden__search__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">golden_search_extrema.cpp</a>
, <a class="el" href="dd/d65/lu__decompose_8cpp.html#a0283886819c7c140a023582b7269e2d0">lu_decompose.cpp</a>
, <a class="el" href="de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">qr_eigen_values.cpp</a>
, <a class="el" href="d0/d01/smallest__circle_8cpp.html#a0283886819c7c140a023582b7269e2d0">smallest_circle.cpp</a>
</li>
<li>test3()
: <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">kohonen_som_trace.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="d0/d01/smallest__circle_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">smallest_circle.cpp</a>
, <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">kohonen_som_topology.cpp</a>
, <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="dd/d0c/hamiltons__cycle_8cpp.html#a0cc94918b6831f308d4fe4fa27f08299">hamiltons_cycle.cpp</a>
</li>
<li>test_1()
: <a class="el" href="d2/de9/heavy__light__decomposition_8cpp.html#a34b8683a2b429de5cce57e6d733ec817">heavy_light_decomposition.cpp</a>
, <a class="el" href="dd/da8/pigeonhole__sort_8cpp.html#a34b8683a2b429de5cce57e6d733ec817">pigeonhole_sort.cpp</a>
</li>
<li>test_2()
: <a class="el" href="d2/de9/heavy__light__decomposition_8cpp.html#a458410412185a5f09199deaff7157a8d">heavy_light_decomposition.cpp</a>
, <a class="el" href="dd/da8/pigeonhole__sort_8cpp.html#a458410412185a5f09199deaff7157a8d">pigeonhole_sort.cpp</a>
: <a class="el" href="dd/da8/pigeonhole__sort_8cpp.html#a458410412185a5f09199deaff7157a8d">pigeonhole_sort.cpp</a>
, <a class="el" href="d2/de9/heavy__light__decomposition_8cpp.html#a458410412185a5f09199deaff7157a8d">heavy_light_decomposition.cpp</a>
</li>
<li>test_2d_classes()
: <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a6b5e744876fd980a3451cbb385d4e755">kohonen_som_topology.cpp</a>
@@ -223,21 +224,21 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
: <a class="el" href="d3/d7d/brute__force__string__searching_8cpp.html#ae2abaa9caa13fff35e45edca00bee123">brute_force_string_searching.cpp</a>
</li>
<li>tests()
: <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">sieve_of_eratosthenes.cpp</a>
, <a class="el" href="d7/d1e/graph_2dijkstra_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">dijkstra.cpp</a>
, <a class="el" href="dd/d0d/insertion__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">insertion_sort.cpp</a>
: <a class="el" href="d1/d9a/hopcroft__karp_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">hopcroft_karp.cpp</a>
, <a class="el" href="d9/dfd/comb__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">comb_sort.cpp</a>
, <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">sieve_of_eratosthenes.cpp</a>
, <a class="el" href="df/ddd/connected__components_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">connected_components.cpp</a>
, <a class="el" href="d0/da2/number__of__positive__divisors_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">number_of_positive_divisors.cpp</a>
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, <a class="el" href="d7/d1e/graph_2dijkstra_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">dijkstra.cpp</a>
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<li>TH()
: <a class="el" href="db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">tower_of_hanoi.cpp</a>

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<tr id="row_38_" 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/d60/namespacerat__maze.html" target="_self">rat_maze</a></td><td class="desc">Functions for <a href="https://www.codesdope.com/blog/article/backtracking-to-
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<tr id="row_39_"><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/dca/namespacesearch.html" target="_self">search</a></td><td class="desc">Search algorithms </td></tr>
<tr id="row_40_" 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_41_"><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">Sorting algorithms </td></tr>
<tr id="row_42_" 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">Range queries using sparse-tables </td></tr>
<tr id="row_43_"><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_44_" 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="d2/dcf/namespacestatistics.html" target="_self">statistics</a></td><td class="desc">Statistical algorithms </td></tr>
<tr id="row_45_"><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/dcc/namespacestd.html" target="_self">std</a></td><td class="desc">STL namespace </td></tr>
<tr id="row_46_" 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">Strand Sort</a> algorithm </td></tr>
<tr id="row_47_"><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_48_" 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_49_"><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_50_" 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">vigenère cipher</a> algorithm </td></tr>
<tr id="row_51_"><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/">Wiggle Sort</a> algorithm </td></tr>
<tr id="row_52_" 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/d53/namespaceword__break.html" target="_self">word_break</a></td><td class="desc">Functions for <a href="https://leetcode.com/problems/word-break/">Word Break</a> problem </td></tr>
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<tr id="row_40_" 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/dca/namespacesearch.html" target="_self">search</a></td><td class="desc">Search algorithms </td></tr>
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<tr id="row_42_" 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">Sorting algorithms </td></tr>
<tr id="row_43_"><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">Range queries using sparse-tables </td></tr>
<tr id="row_44_" 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_45_"><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/dcf/namespacestatistics.html" target="_self">statistics</a></td><td class="desc">Statistical algorithms </td></tr>
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<tr id="row_48_" 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_49_"><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_50_" 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_51_"><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">vigenère cipher</a> algorithm </td></tr>
<tr id="row_52_" 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/">Wiggle Sort</a> algorithm </td></tr>
<tr id="row_53_"><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/">Word Break</a> problem </td></tr>
<tr id="row_54_" 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">XOR cipher</a> algorithm </td></tr>
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