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Namespaces</h2></td></tr>
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Functions</h2></td></tr>
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<p>Given two strings in binary notation we want to multiply them and return the value. Simple approach is to multiply bits one by one which will give the time complexity of around O(n^2). To make it more efficient we will be using Karatsuba algorithm to find the product which will solve the problem O(nlogn) of time. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Swastyy" target="_blank">Swastika Gupta</a> </dd>
<dd>
<a href="https://github.com/poypoyan" target="_blank">Ameer Carlo Lubang</a> </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00037">37</a> of file <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html">karatsuba_algorithm_for_fast_multiplication.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 37</span> {</div>
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<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition</b> <a href="../../de/dc3/fibonacci__sum_8cpp_source.html#l00077">fibonacci_sum.cpp:77</a></div></div>
<div class="ttc" id="anamespacemachine__learning_html_a6f1c98c016ad34ff3d9f39372161bd35"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">machine_learning::sum</a></div><div class="ttdeci">T sum(const std::vector&lt; std::valarray&lt; T &gt; &gt; &amp;A)</div><div class="ttdef"><b>Definition</b> <a href="../../d8/d95/vector__ops_8hpp_source.html#l00232">vector_ops.hpp:232</a></div></div>
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<tr>
<td class="memname">int64_t divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></td> <td class="paramname"><span class="paramname"><em>str1</em></span>, </td>
<td class="paramtype">std::string</td> <td class="paramname"><span class="paramname"><em>str1</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></td> <td class="paramname"><span class="paramname"><em>str2</em></span>&#160;)</td>
<td class="paramtype">std::string</td> <td class="paramname"><span class="paramname"><em>str2</em></span>&#160;)</td>
</tr>
</table>
</div><div class="memdoc">
@@ -265,10 +279,12 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the product number value </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00112">112</a> of file <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html">karatsuba_algorithm_for_fast_multiplication.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 112</span> {</div>
<div class="line"><span class="lineno"> 113</span> int64_t len1 = str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 114</span> int64_t len2 = str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 115</span> int64_t n = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(len1, len2);</div>
<div class="line"><span class="lineno"> 113</span> int64_t len1 = str1.size();</div>
<div class="line"><span class="lineno"> 114</span> int64_t len2 = str2.size();</div>
<div class="line"><span class="lineno"> 115</span> int64_t n = std::max(len1, len2);</div>
<div class="line"><span class="lineno"> 116</span> </div>
<div class="line"><span class="lineno"> 117</span> <span class="keywordflow">if</span> (n == 0) {</div>
<div class="line"><span class="lineno"> 118</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 124</span> int64_t fh = n / 2; <span class="comment">// first half of string</span></div>
<div class="line"><span class="lineno"> 125</span> int64_t sh = n - fh; <span class="comment">// second half of string</span></div>
<div class="line"><span class="lineno"> 126</span> </div>
<div class="line"><span class="lineno"> 127</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Xl = <a class="code hl_function" href="#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str1, 0, fh, n); <span class="comment">// first half of first string</span></div>
<div class="line"><span class="lineno"> 128</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Xr = <a class="code hl_function" href="#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str1, fh, sh, n); <span class="comment">// second half of first string</span></div>
<div class="line"><span class="lineno"> 127</span> std::string Xl = <a class="code hl_function" href="#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str1, 0, fh, n); <span class="comment">// first half of first string</span></div>
<div class="line"><span class="lineno"> 128</span> std::string Xr = <a class="code hl_function" href="#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str1, fh, sh, n); <span class="comment">// second half of first string</span></div>
<div class="line"><span class="lineno"> 129</span> </div>
<div class="line"><span class="lineno"> 130</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Yl = <a class="code hl_function" href="#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str2, 0, fh, n); <span class="comment">// first half of second string</span></div>
<div class="line"><span class="lineno"> 131</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Yr = <a class="code hl_function" href="#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str2, fh, sh, n); <span class="comment">// second half of second string</span></div>
<div class="line"><span class="lineno"> 130</span> std::string Yl = <a class="code hl_function" href="#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str2, 0, fh, n); <span class="comment">// first half of second string</span></div>
<div class="line"><span class="lineno"> 131</span> std::string Yr = <a class="code hl_function" href="#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str2, fh, sh, n); <span class="comment">// second half of second string</span></div>
<div class="line"><span class="lineno"> 132</span> </div>
<div class="line"><span class="lineno"> 133</span> <span class="comment">// calculating the three products of inputs of size n/2 recursively</span></div>
<div class="line"><span class="lineno"> 134</span> int64_t product1 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xl, Yl);</div>
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<div class="line"><span class="lineno"> 141</span> (product3 - product1 - product2) * (1 &lt;&lt; sh) +</div>
<div class="line"><span class="lineno"> 142</span> product2; <span class="comment">// combining the three products to get the final result.</span></div>
<div class="line"><span class="lineno"> 143</span>}</div>
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_aad9e3edfe156b59fc06a5585403fe0d6"><div class="ttname"><a href="#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a></div><div class="ttdeci">std::string safe_substr(const std::string &amp;str, int64_t x1, int64_t x2, int64_t n)</div><div class="ttdoc">Wrapper function for substr that considers leading zeros.</div><div class="ttdef"><b>Definition</b> karatsuba_algorithm_for_fast_multiplication.cpp:86</div></div>
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_aad9e3edfe156b59fc06a5585403fe0d6"><div class="ttname"><a href="#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a></div><div class="ttdeci">std::string safe_substr(const std::string &amp;str, int64_t x1, int64_t x2, int64_t n)</div><div class="ttdoc">Wrapper function for substr that considers leading zeros.</div><div class="ttdef"><b>Definition</b> <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00086">karatsuba_algorithm_for_fast_multiplication.cpp:86</a></div></div>
<div class="ttc" id="anamespacekaratsuba__algorithm_html"><div class="ttname"><a href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a></div><div class="ttdoc">Functions for the Karatsuba algorithm for fast multiplication implementation.</div></div>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00181">181</a> of file <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html">karatsuba_algorithm_for_fast_multiplication.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 181</span> {</div>
<div class="line"><span class="lineno"> 182</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 183</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 184</span>}</div>
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> karatsuba_algorithm_for_fast_multiplication.cpp:151</div></div>
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<div class="memproto">
<table class="memname">
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> divide_and_conquer::karatsuba_algorithm::safe_substr </td>
<td class="memname">std::string divide_and_conquer::karatsuba_algorithm::safe_substr </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;</td> <td class="paramname"><span class="paramname"><em>str</em></span>, </td>
<td class="paramtype">const std::string &amp;</td> <td class="paramname"><span class="paramname"><em>str</em></span>, </td>
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<td class="paramkey"></td>
@@ -379,11 +387,13 @@ Here is the call graph for this function:</div>
<dl class="section return"><dt>Returns</dt><dd>the "safe" substring for the algorithm <em>without</em> leading zeros </dd>
<dd>
"0" if substring spans to leading zeros only </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00086">86</a> of file <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html">karatsuba_algorithm_for_fast_multiplication.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 86</span> {</div>
<div class="line"><span class="lineno"> 87</span> int64_t len = str.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 87</span> int64_t len = str.size();</div>
<div class="line"><span class="lineno"> 88</span> </div>
<div class="line"><span class="lineno"> 89</span> <span class="keywordflow">if</span> (len &gt;= n) {</div>
<div class="line"><span class="lineno"> 90</span> <span class="keywordflow">return</span> str.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(x1, x2);</div>
<div class="line"><span class="lineno"> 90</span> <span class="keywordflow">return</span> str.substr(x1, x2);</div>
<div class="line"><span class="lineno"> 91</span> }</div>
<div class="line"><span class="lineno"> 92</span> </div>
<div class="line"><span class="lineno"> 93</span> int64_t y1 = x1 - (n - len); <span class="comment">// index in str of first char of substring of &quot;whole&quot; string</span></div>
@@ -392,18 +402,12 @@ Here is the call graph for this function:</div>
<div class="line"><span class="lineno"> 96</span> <span class="keywordflow">if</span> (y2 &lt; 0) {</div>
<div class="line"><span class="lineno"> 97</span> <span class="keywordflow">return</span> <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><span class="lineno"> 98</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (y1 &lt; 0) {</div>
<div class="line"><span class="lineno"> 99</span> <span class="keywordflow">return</span> str.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(0, y2 + 1);</div>
<div class="line"><span class="lineno"> 99</span> <span class="keywordflow">return</span> str.substr(0, y2 + 1);</div>
<div class="line"><span class="lineno"> 100</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 101</span> <span class="keywordflow">return</span> str.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(y1, x2);</div>
<div class="line"><span class="lineno"> 101</span> <span class="keywordflow">return</span> str.substr(y1, x2);</div>
<div class="line"><span class="lineno"> 102</span> }</div>
<div class="line"><span class="lineno"> 103</span>}</div>
<div class="ttc" id="asubstr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">std::string::substr</a></div><div class="ttdeci">T substr(T... args)</div></div>
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<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00151">151</a> of file <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html">karatsuba_algorithm_for_fast_multiplication.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 151</span> {</div>
<div class="line"><span class="lineno"> 152</span> <span class="comment">// 1st test</span></div>
<div class="line"><span class="lineno"> 153</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s11 = <span class="stringliteral">&quot;1&quot;</span>; <span class="comment">// 1</span></div>
<div class="line"><span class="lineno"> 154</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s12 = <span class="stringliteral">&quot;1010&quot;</span>; <span class="comment">// 10</span></div>
<div class="line"><span class="lineno"> 155</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test... &quot;</span>;</div>
<div class="line"><span class="lineno"> 153</span> std::string s11 = <span class="stringliteral">&quot;1&quot;</span>; <span class="comment">// 1</span></div>
<div class="line"><span class="lineno"> 154</span> std::string s12 = <span class="stringliteral">&quot;1010&quot;</span>; <span class="comment">// 10</span></div>
<div class="line"><span class="lineno"> 155</span> std::cout &lt;&lt; <span class="stringliteral">&quot;1st test... &quot;</span>;</div>
<div class="line"><span class="lineno"> 156</span> assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
<div class="line"><span class="lineno"> 157</span> s11, s12) == 10);</div>
<div class="line"><span class="lineno"> 158</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 158</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 159</span> </div>
<div class="line"><span class="lineno"> 160</span> <span class="comment">// 2nd test</span></div>
<div class="line"><span class="lineno"> 161</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s21 = <span class="stringliteral">&quot;11&quot;</span>; <span class="comment">// 3</span></div>
<div class="line"><span class="lineno"> 162</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s22 = <span class="stringliteral">&quot;1010&quot;</span>; <span class="comment">// 10</span></div>
<div class="line"><span class="lineno"> 163</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test... &quot;</span>;</div>
<div class="line"><span class="lineno"> 161</span> std::string s21 = <span class="stringliteral">&quot;11&quot;</span>; <span class="comment">// 3</span></div>
<div class="line"><span class="lineno"> 162</span> std::string s22 = <span class="stringliteral">&quot;1010&quot;</span>; <span class="comment">// 10</span></div>
<div class="line"><span class="lineno"> 163</span> std::cout &lt;&lt; <span class="stringliteral">&quot;2nd test... &quot;</span>;</div>
<div class="line"><span class="lineno"> 164</span> assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
<div class="line"><span class="lineno"> 165</span> s21, s22) == 30);</div>
<div class="line"><span class="lineno"> 166</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 166</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 167</span> </div>
<div class="line"><span class="lineno"> 168</span> <span class="comment">// 3rd test</span></div>
<div class="line"><span class="lineno"> 169</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s31 = <span class="stringliteral">&quot;110&quot;</span>; <span class="comment">// 6</span></div>
<div class="line"><span class="lineno"> 170</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s32 = <span class="stringliteral">&quot;1010&quot;</span>; <span class="comment">// 10</span></div>
<div class="line"><span class="lineno"> 171</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3rd test... &quot;</span>;</div>
<div class="line"><span class="lineno"> 169</span> std::string s31 = <span class="stringliteral">&quot;110&quot;</span>; <span class="comment">// 6</span></div>
<div class="line"><span class="lineno"> 170</span> std::string s32 = <span class="stringliteral">&quot;1010&quot;</span>; <span class="comment">// 10</span></div>
<div class="line"><span class="lineno"> 171</span> std::cout &lt;&lt; <span class="stringliteral">&quot;3rd test... &quot;</span>;</div>
<div class="line"><span class="lineno"> 172</span> assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
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<div class="line"><span class="lineno"> 174</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 174</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 175</span>}</div>
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<div class="headertitle"><div class="title">karatsuba_algorithm_for_fast_multiplication.cpp</div></div>
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<a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span> </div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#include &lt;cassert&gt;</span> </div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include &lt;cstring&gt;</span> </div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include &lt;iostream&gt;</span> </div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include &lt;vector&gt;</span> </div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../dd/dba/namespacedivide__and__conquer.html">divide_and_conquer</a> {</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a> {</div>
<div class="foldopen" id="foldopen00037" data-start="{" data-end="}">
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"><a class="line" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ad76f5cac3ef8dc034f6abb99b64c2b20"> 37</a></span>std::string <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ad76f5cac3ef8dc034f6abb99b64c2b20">add_strings</a>(std::string first, std::string second) {</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> std::string result; <span class="comment">// to store the resulting sum bits</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// make the string lengths equal</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> int64_t len1 = first.size();</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> int64_t len2 = second.size();</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> std::string zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordflow">if</span> (len1 &lt; len2) {</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len2 - len1; i++) {</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> zero += first;</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> first = zero;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> zero = <span class="stringliteral">&quot;0&quot;</span>; <span class="comment">// Prevents CI from failing</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> }</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len1 &gt; len2) {</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len1 - len2; i++) {</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> zero += second;</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> second = zero;</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> zero = <span class="stringliteral">&quot;0&quot;</span>; <span class="comment">// Prevents CI from failing</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> }</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> }</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> </div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> int64_t length = std::max(len1, len2);</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> int64_t carry = 0;</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">for</span> (int64_t i = length - 1; i &gt;= 0; i--) {</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> int64_t firstBit = first.at(i) - <span class="charliteral">&#39;0&#39;</span>;</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> int64_t secondBit = second.at(i) - <span class="charliteral">&#39;0&#39;</span>;</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> </div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> int64_t sum = (char(firstBit ^ secondBit ^ carry)) + <span class="charliteral">&#39;0&#39;</span>; <span class="comment">// sum of 3 bits</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> result.insert(result.begin(), sum);</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> </div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> carry = char((firstBit &amp; secondBit) | (secondBit &amp; carry) |</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> (firstBit &amp; carry)); <span class="comment">// sum of 3 bits</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> }</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> </div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordflow">if</span> (carry) {</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> result.insert(result.begin(), <span class="charliteral">&#39;1&#39;</span>); <span class="comment">// adding 1 incase of overflow</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> }</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keywordflow">return</span> result;</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span>}</div>
</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="foldopen" id="foldopen00086" data-start="{" data-end="}">
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"><a class="line" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aad9e3edfe156b59fc06a5585403fe0d6"> 86</a></span>std::string <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aad9e3edfe156b59fc06a5585403fe0d6">safe_substr</a>(<span class="keyword">const</span> std::string &amp;str, int64_t x1, int64_t x2, int64_t n) {</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> int64_t len = str.size();</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> </div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keywordflow">if</span> (len &gt;= n) {</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keywordflow">return</span> str.substr(x1, x2);</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> }</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> </div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> int64_t y1 = x1 - (n - len); <span class="comment">// index in str of first char of substring of &quot;whole&quot; string</span></div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> int64_t y2 = (x1 + x2 - 1) - (n - len); <span class="comment">// index in str of last char of substring of &quot;whole&quot; string</span></div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> </div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="keywordflow">if</span> (y2 &lt; 0) {</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordflow">return</span> <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (y1 &lt; 0) {</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="keywordflow">return</span> str.substr(0, y2 + 1);</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keywordflow">return</span> str.substr(y1, x2);</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> }</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span>}</div>
</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> </div>
<div class="foldopen" id="foldopen00112" data-start="{" data-end="}">
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"><a class="line" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86"> 112</a></span>int64_t <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(std::string str1, std::string str2) {</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> int64_t len1 = str1.size();</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> int64_t len2 = str2.size();</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> int64_t n = std::max(len1, len2);</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> </div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keywordflow">if</span> (n == 0) {</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> }</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="keywordflow">return</span> (str1[0] - <span class="charliteral">&#39;0&#39;</span>) * (str2[0] - <span class="charliteral">&#39;0&#39;</span>);</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> }</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> </div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> int64_t fh = n / 2; <span class="comment">// first half of string</span></div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> int64_t sh = n - fh; <span class="comment">// second half of string</span></div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> </div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> std::string Xl = <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str1, 0, fh, n); <span class="comment">// first half of first string</span></div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> std::string Xr = <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str1, fh, sh, n); <span class="comment">// second half of first string</span></div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> </div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> std::string Yl = <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str2, 0, fh, n); <span class="comment">// first half of second string</span></div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> std::string Yr = <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str2, fh, sh, n); <span class="comment">// second half of second string</span></div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> </div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="comment">// calculating the three products of inputs of size n/2 recursively</span></div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> int64_t product1 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xl, Yl);</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> int64_t product2 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xr, Yr);</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> int64_t product3 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ad76f5cac3ef8dc034f6abb99b64c2b20">divide_and_conquer::karatsuba_algorithm::add_strings</a>(Xl, Xr),</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ad76f5cac3ef8dc034f6abb99b64c2b20">divide_and_conquer::karatsuba_algorithm::add_strings</a>(Yl, Yr));</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> </div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="keywordflow">return</span> product1 * (1 &lt;&lt; (2 * sh)) +</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> (product3 - product1 - product2) * (1 &lt;&lt; sh) +</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> product2; <span class="comment">// combining the three products to get the final result.</span></div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span>}</div>
</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span>} <span class="comment">// namespace karatsuba_algorithm</span></div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span>} <span class="comment">// namespace divide_and_conquer</span></div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> </div>
<div class="foldopen" id="foldopen00151" data-start="{" data-end="}">
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"><a class="line" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d"> 151</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>() {</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="comment">// 1st test</span></div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> std::string s11 = <span class="stringliteral">&quot;1&quot;</span>; <span class="comment">// 1</span></div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> std::string s12 = <span class="stringliteral">&quot;1010&quot;</span>; <span class="comment">// 10</span></div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> std::cout &lt;&lt; <span class="stringliteral">&quot;1st test... &quot;</span>;</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> s11, s12) == 10);</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> </div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="comment">// 2nd test</span></div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> std::string s21 = <span class="stringliteral">&quot;11&quot;</span>; <span class="comment">// 3</span></div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> std::string s22 = <span class="stringliteral">&quot;1010&quot;</span>; <span class="comment">// 10</span></div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> std::cout &lt;&lt; <span class="stringliteral">&quot;2nd test... &quot;</span>;</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> s21, s22) == 30);</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> </div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="comment">// 3rd test</span></div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> std::string s31 = <span class="stringliteral">&quot;110&quot;</span>; <span class="comment">// 6</span></div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> std::string s32 = <span class="stringliteral">&quot;1010&quot;</span>; <span class="comment">// 10</span></div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> std::cout &lt;&lt; <span class="stringliteral">&quot;3rd test... &quot;</span>;</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> s31, s32) == 60);</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span>}</div>
</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> </div>
<div class="foldopen" id="foldopen00181" data-start="{" data-end="}">
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"><a class="line" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 181</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span>}</div>
</div>
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="#l00151">karatsuba_algorithm_for_fast_multiplication.cpp:151</a></div></div>
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_aad9e3edfe156b59fc06a5585403fe0d6"><div class="ttname"><a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a></div><div class="ttdeci">std::string safe_substr(const std::string &amp;str, int64_t x1, int64_t x2, int64_t n)</div><div class="ttdoc">Wrapper function for substr that considers leading zeros.</div><div class="ttdef"><b>Definition</b> <a href="#l00086">karatsuba_algorithm_for_fast_multiplication.cpp:86</a></div></div>
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_ad76f5cac3ef8dc034f6abb99b64c2b20"><div class="ttname"><a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ad76f5cac3ef8dc034f6abb99b64c2b20">divide_and_conquer::karatsuba_algorithm::add_strings</a></div><div class="ttdeci">std::string add_strings(std::string first, std::string second)</div><div class="ttdoc">Binary addition.</div><div class="ttdef"><b>Definition</b> <a href="#l00037">karatsuba_algorithm_for_fast_multiplication.cpp:37</a></div></div>
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="#l00181">karatsuba_algorithm_for_fast_multiplication.cpp:181</a></div></div>
<div class="ttc" id="anamespacedivide__and__conquer_html"><div class="ttname"><a href="../../dd/dba/namespacedivide__and__conquer.html">divide_and_conquer</a></div><div class="ttdoc">for std::vector</div></div>
<div class="ttc" id="anamespacekaratsuba__algorithm_html"><div class="ttname"><a href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a></div><div class="ttdoc">Functions for the Karatsuba algorithm for fast multiplication implementation.</div></div>
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<li class="navelem"><a class="el" href="../../dir_93bc990c5cceb745f78af6949e9ef947.html">divide_and_conquer</a></li><li class="navelem"><a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html">karatsuba_algorithm_for_fast_multiplication.cpp</a></li>
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<div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
<div id="projectname">TheAlgorithms/C++<span id="projectnumber">&#160;1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
<div id="projectbrief">All the algorithms implemented in C++</div>
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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:aeca22dbe4563358960e907a40cd3e1ac" id="r_aeca22dbe4563358960e907a40cd3e1ac"><td class="memTemplParams" colspan="2">template&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> N&gt; </td></tr>
<tr class="memitem:aeca22dbe4563358960e907a40cd3e1ac"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#aeca22dbe4563358960e907a40cd3e1ac">spirograph</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt; double, double &gt;, N &gt; *points, double l, double k, double rot)</td></tr>
<tr class="memitem:aeca22dbe4563358960e907a40cd3e1ac" id="r_aeca22dbe4563358960e907a40cd3e1ac"><td class="memTemplParams" colspan="2">template&lt;std::size_t N&gt; </td></tr>
<tr class="memitem:aeca22dbe4563358960e907a40cd3e1ac"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#aeca22dbe4563358960e907a40cd3e1ac">spirograph</a> (std::array&lt; std::pair&lt; double, double &gt;, N &gt; *points, double l, double k, double rot)</td></tr>
<tr class="separator:aeca22dbe4563358960e907a40cd3e1ac"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="memdesc:a8e83a64e8443fff1e5ffdc1c299c1e99"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test function to save resulting points to a CSV file. <br /></td></tr>
@@ -128,12 +145,12 @@ Functions</h2></td></tr>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> N&gt; </div>
template&lt;std::size_t N&gt; </div>
<table class="memname">
<tr>
<td class="memname">void spirograph::spirograph </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt; double, double &gt;, N &gt; *</td> <td class="paramname"><span class="paramname"><em>points</em></span>, </td>
<td class="paramtype">std::array&lt; std::pair&lt; double, double &gt;, N &gt; *</td> <td class="paramname"><span class="paramname"><em>points</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
@@ -177,13 +194,15 @@ y &amp;=&amp; R\left[ (1-k) \sin (t) - l\cdot k\cdot\sin \left(\frac{1-k}{k}t\ri
</dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[out]</td><td class="paramname">points</td><td>Array of 2D points represented as <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a> </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">points</td><td>Array of 2D points represented as std::pair </td></tr>
<tr><td class="paramdir"></td><td class="paramname">l</td><td>the relative distance of marker from the centre of inner circle and \(0\le l\le1\) </td></tr>
<tr><td class="paramdir"></td><td class="paramname">k</td><td>the ratio of radius of inner circle to outer circle and \(0&lt;k&lt;1\) </td></tr>
<tr><td class="paramdir"></td><td class="paramname">rot</td><td>the number of rotations to perform (can be fractional value) </td></tr>
</table>
</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="../../da/d77/spirograph_8cpp_source.html#l00070">70</a> of file <a class="el" href="../../da/d77/spirograph_8cpp_source.html">spirograph.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 71</span> {</div>
<div class="line"><span class="lineno"> 72</span> <span class="keywordtype">double</span> dt = rot * 2.f * M_PI / N;</div>
<div class="line"><span class="lineno"> 73</span> <span class="keywordtype">double</span> R = 1.f;</div>
@@ -195,20 +214,13 @@ y &amp;=&amp; R\left[ (1-k) \sin (t) - l\cdot k\cdot\sin \left(\frac{1-k}{k}t\ri
<div class="line"><span class="lineno"> 79</span><span class="preprocessor">#endif</span></div>
<div class="line"><span class="lineno"> 80</span> <span class="keywordflow">for</span> (step = 0; step &lt; N; step++) {</div>
<div class="line"><span class="lineno"> 81</span> <span class="keywordtype">double</span> t = dt * step;</div>
<div class="line"><span class="lineno"> 82</span> <span class="keywordtype">double</span> first = R * (k1 * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a>(t) + l * k * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a>(k1 * t / k));</div>
<div class="line"><span class="lineno"> 83</span> <span class="keywordtype">double</span> second = R * (k1 * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a>(t) - l * k * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a>(k1 * t / k));</div>
<div class="line"><span class="lineno"> 82</span> <span class="keywordtype">double</span> first = R * (k1 * std::cos(t) + l * k * std::cos(k1 * t / k));</div>
<div class="line"><span class="lineno"> 83</span> <span class="keywordtype">double</span> second = R * (k1 * std::sin(t) - l * k * std::sin(k1 * t / k));</div>
<div class="line"><span class="lineno"> 84</span> points[0][step].first = first;</div>
<div class="line"><span class="lineno"> 85</span> points[0][step].second = second;</div>
<div class="line"><span class="lineno"> 86</span> }</div>
<div class="line"><span class="lineno"> 87</span>}</div>
<div class="ttc" id="acos_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a></div><div class="ttdeci">T cos(T... args)</div></div>
<div class="ttc" id="asin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a></div><div class="ttdeci">T sin(T... args)</div></div>
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<p>Test function to save resulting points to a CSV file. </p>
<p class="definition">Definition at line <a class="el" href="../../da/d77/spirograph_8cpp_source.html#l00093">93</a> of file <a class="el" href="../../da/d77/spirograph_8cpp_source.html">spirograph.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 93</span> {</div>
<div class="line"><span class="lineno"> 94</span> <span class="keyword">const</span> <span class="keywordtype">size_t</span> N = 500;</div>
<div class="line"><span class="lineno"> 95</span> <span class="keywordtype">double</span> l = 0.3, k = 0.75, rot = 10.;</div>
<div class="line"><span class="lineno"> 96</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_stringstream.html">std::stringstream</a> fname;</div>
<div class="line"><span class="lineno"> 97</span> fname &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(3) &lt;&lt; <span class="stringliteral">&quot;spirograph_&quot;</span> &lt;&lt; l &lt;&lt; <span class="stringliteral">&quot;_&quot;</span> &lt;&lt; k &lt;&lt; <span class="stringliteral">&quot;_&quot;</span> &lt;&lt; rot</div>
<div class="line"><span class="lineno"> 96</span> std::stringstream fname;</div>
<div class="line"><span class="lineno"> 97</span> fname &lt;&lt; std::setw(3) &lt;&lt; <span class="stringliteral">&quot;spirograph_&quot;</span> &lt;&lt; l &lt;&lt; <span class="stringliteral">&quot;_&quot;</span> &lt;&lt; k &lt;&lt; <span class="stringliteral">&quot;_&quot;</span> &lt;&lt; rot</div>
<div class="line"><span class="lineno"> 98</span> &lt;&lt; <span class="stringliteral">&quot;.csv&quot;</span>;</div>
<div class="line"><span class="lineno"> 99</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp(fname.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_stringstream/str.html">str</a>());</div>
<div class="line"><span class="lineno"> 99</span> std::ofstream fp(fname.str());</div>
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<div class="line"><span class="lineno"> 101</span> perror(fname.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_stringstream/str.html">str</a>().c_str());</div>
<div class="line"><span class="lineno"> 101</span> perror(fname.str().c_str());</div>
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<div class="line"><span class="lineno"> 104</span> </div>
<div class="line"><span class="lineno"> 105</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::pair&lt;double, double&gt;</a>, N&gt; points;</div>
<div class="line"><span class="lineno"> 105</span> std::array&lt;std::pair&lt;double, double&gt;, N&gt; points;</div>
<div class="line"><span class="lineno"> 106</span> </div>
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<div class="line"><span class="lineno"> 108</span> </div>
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