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d2/d26/count__inversions_8cpp.html
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<p>two elements a[i] and a[j] form an inversion if <code>a[i]</code> &gt; <code>a[j]</code> and i &lt; j</p>
<p>Time Complexity --&gt; <code>O(n.log n)</code></p>
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<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160;<span class="comment">// parallelize on threads</span></div>
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<p>Functions for Vector Cross Product algorithms.
<a href="../../d4/d91/namespacevector__cross.html#details">More...</a></p>
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<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fibonacci.cpp">Fibonacci</a></li>
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<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/gcd_iterative_euclidean.cpp">Gcd Iterative Euclidean</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/gcd_of_n_numbers.cpp">Gcd Of N Numbers</a></li>
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<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/string_fibonacci.cpp">String Fibonacci</a></li>
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Numerical Methods</h1>

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<div class="textblock"><p>Implementation of <a href="https://en.wikipedia.org/wiki/Bogosort">Bogosort algorithm</a> </p>
<p>In computer science, bogosort (also known as permutation sort, stupid sort, slowsort, shotgun sort, random sort, monkey sort, bobosort or shuffle sort) is a highly inefficient sorting algorithm based on the generate and test paradigm. Two versions of this algorithm exist: a deterministic version that enumerates all permutations until it hits a sorted one, and a randomized version that randomly permutes its input.Randomized version is implemented here.</p>
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Algorithm</h3>
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<p>Calculates the <a href="https://en.wikipedia.org/wiki/Cross_product">Cross Product</a> and the magnitude of two mathematical 3D vectors.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;array&gt;</code><br />
<code>#include &lt;cmath&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
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<tr class="memdesc:dd/d47/namespacemath"><td class="mdescLeft">&#160;</td><td class="mdescRight">for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> <br /></td></tr>
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<tr class="memdesc:d4/d91/namespacevector__cross"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for Vector Cross Product algorithms. <br /></td></tr>
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<tr class="memdesc:abed307975124243d63fe2e118254defe"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to calculate the cross product of the passed arrays containing the direction ratios of the two mathematical vectors. <a href="../../df/d66/vector__cross__product_8cpp.html#abed307975124243d63fe2e118254defe">More...</a><br /></td></tr>
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<tr class="memitem:a4b2a9757a87c18e1642d72410ecfaba8"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8">math::vector_cross::mag</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; double, 3 &gt; &amp;vec)</td></tr>
<tr class="memdesc:a4b2a9757a87c18e1642d72410ecfaba8"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculates the magnitude of the mathematical vector from it's direction ratios. <a href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8">More...</a><br /></td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d66/vector__cross__product_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">namespace math <a href="../../df/d66/vector__cross__product_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="../../df/d66/vector__cross__product_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main Function. <a href="../../df/d66/vector__cross__product_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>Calculates the <a href="https://en.wikipedia.org/wiki/Cross_product">Cross Product</a> and the magnitude of two mathematical 3D vectors. </p>
<p>Cross Product of two vectors gives a vector. Direction Ratios of a vector are the numeric parts of the given vector. They are the tree parts of the vector which determine the magnitude (value) of the vector. The method of finding a cross product is the same as finding the determinant of an order 3 matrix consisting of the first row with unit vectors of magnitude 1, the second row with the direction ratios of the first vector and the third row with the direction ratios of the second vector. The magnitude of a vector is it's value expressed as a number. Let the direction ratios of the first vector, P be: a, b, c Let the direction ratios of the second vector, Q be: x, y, z Therefore the calculation for the cross product can be arranged as:</p>
<div class="fragment"><div class="line">P x Q:</div>
<div class="line"> 1 1 1</div>
<div class="line"> a b c</div>
<div class="line"> x y z</div>
</div><!-- fragment --><p>The direction ratios (DR) are calculated as follows: 1st DR, J: (b * z) - (c * y) 2nd DR, A: -((a * z) - (c * x)) 3rd DR, N: (a * y) - (b * x)</p>
<p>Therefore, the direction ratios of the cross product are: J, A, N The following C++ Program calculates the direction ratios of the cross products of two vector. The program uses a function, <a class="el" href="../../df/d66/vector__cross__product_8cpp.html#abed307975124243d63fe2e118254defe" title="Function to calculate the cross product of the passed arrays containing the direction ratios of the t...">cross()</a> for doing so. The direction ratios for the first and the second vector has to be passed one by one seperated by a space character.</p>
<p>Magnitude of a vector is the square root of the sum of the squares of the direction ratios.</p>
<h3><a class="anchor" id="autotoc_md64"></a>
Example:</h3>
<p>An example of a running instance of the executable program: </p><pre class="fragment">Pass the first Vector: 1 2 3
</pre><p> Pass the second Vector: 4 5 6 The cross product is: -3 6 -3 Magnitude: 7.34847</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Shreyas-OwO">Shreyas Sable</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="abed307975124243d63fe2e118254defe"></a>
<h2 class="memtitle"><span class="permalink"><a href="#abed307975124243d63fe2e118254defe">&#9670;&nbsp;</a></span>cross()</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt;double, 3&gt; math::vector_cross::cross </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; double, 3 &gt; &amp;&#160;</td>
<td class="paramname"><em>A</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; double, 3 &gt; &amp;&#160;</td>
<td class="paramname"><em>B</em>&#160;</td>
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<p>Function to calculate the cross product of the passed arrays containing the direction ratios of the two mathematical vectors. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">A</td><td>contains the direction ratios of the first mathematical vector. </td></tr>
<tr><td class="paramname">B</td><td>contains the direction ration of the second mathematical vector. </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the direction ratios of the cross product. </dd></dl>
<p>Performs the cross product as shown in @algorithm.</p>
<div class="fragment"><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; {</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/array.html">std::array&lt;double, 3&gt;</a> product;<span class="comment"></span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160;<span class="comment"> /// Performs the cross product as shown in @algorithm.</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160;<span class="comment"></span> product[0] = (A[1] * B[2]) - (A[2] * B[1]);</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; product[1] = -((A[0] * B[2]) - (A[2] * B[0]));</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; product[2] = (A[0] * B[1]) - (A[1] * B[0]);</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <span class="keywordflow">return</span> product;</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; }</div>
<div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a4b2a9757a87c18e1642d72410ecfaba8">&#9670;&nbsp;</a></span>mag()</h2>
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<td class="memname">double math::vector_cross::mag </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; double, 3 &gt; &amp;&#160;</td>
<td class="paramname"><em>vec</em></td><td>)</td>
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<p>Calculates the magnitude of the mathematical vector from it's direction ratios. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">vec</td><td>an array containing the direction ratios of a mathematical vector. </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>type: double description: the magnitude of the mathematical vector from the given direction ratios. </dd></dl>
<div class="fragment"><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; {</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <span class="keywordtype">double</span> magnitude = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">sqrt</a>((vec[0] * vec[0]) + (vec[1] * vec[1]) + (vec[2] * vec[2]));</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; <span class="keywordflow">return</span> magnitude;</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; }</div>
<div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
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<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>
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<p>Main Function. </p>
<p>Asks the user to enter the direction ratios for each of the two mathematical vectors using <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> </p><dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p>Tests the functions with sample input before asking for user input.</p>
<p>Gets the values for the first vector.</p>
<p>Gets the values for the second vector.</p>
<p>Displays the output out.</p>
<p>Displays the magnitude of the cross product.</p>
<div class="fragment"><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; {</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160;<span class="comment"> /// Tests the functions with sample input before asking for user input.</span></div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160;<span class="comment"></span> <a class="code" href="../../df/d66/vector__cross__product_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</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/container/array.html">std::array&lt;double, 3&gt;</a> vec1;</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a> vec2;</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160;<span class="comment"> /// Gets the values for the first vector.</span></div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160;<span class="comment"></span> <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;\nPass the first Vector: &quot;</span>;</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_istream.html">std::cin</a> &gt;&gt; vec1[0] &gt;&gt; vec1[1] &gt;&gt; vec1[2];</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160;<span class="comment"> /// Gets the values for the second vector.</span></div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160;<span class="comment"></span> <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;\nPass the second Vector: &quot;</span>;</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; vec2[0] &gt;&gt; vec2[1] &gt;&gt; vec2[2];</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160;<span class="comment"> /// Displays the output out.</span></div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160;<span class="comment"></span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a> product = <a class="code" href="../../df/d66/vector__cross__product_8cpp.html#abed307975124243d63fe2e118254defe">math::vector_cross::cross</a>(vec1, vec2);</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</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;\nThe cross product is: &quot;</span> &lt;&lt; product[0] &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; product[1] &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; product[2] &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160;<span class="comment"> /// Displays the magnitude of the cross product.</span></div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160;<span class="comment"></span> <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;Magnitude: &quot;</span> &lt;&lt; <a class="code" href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8">math::vector_cross::mag</a>(product) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<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; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160;}</div>
<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
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<div class="ttc" id="avector__cross__product_8cpp_html_a4b2a9757a87c18e1642d72410ecfaba8"><div class="ttname"><a href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8">math::vector_cross::mag</a></div><div class="ttdeci">double mag(const std::array&lt; double, 3 &gt; &amp;vec)</div><div class="ttdoc">Calculates the magnitude of the mathematical vector from it's direction ratios.</div><div class="ttdef"><b>Definition:</b> vector_cross_product.cpp:83</div></div>
<div class="ttc" id="avector__cross__product_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../df/d66/vector__cross__product_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">namespace math</div><div class="ttdef"><b>Definition:</b> vector_cross_product.cpp:94</div></div>
<div class="ttc" id="avector__cross__product_8cpp_html_abed307975124243d63fe2e118254defe"><div class="ttname"><a href="../../df/d66/vector__cross__product_8cpp.html#abed307975124243d63fe2e118254defe">math::vector_cross::cross</a></div><div class="ttdeci">std::array&lt; double, 3 &gt; cross(const std::array&lt; double, 3 &gt; &amp;A, const std::array&lt; double, 3 &gt; &amp;B)</div><div class="ttdoc">Function to calculate the cross product of the passed arrays containing the direction ratios of the t...</div><div class="ttdef"><b>Definition:</b> vector_cross_product.cpp:69</div></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>namespace math </p>
<p>test function.</p>
<p>test the <a class="el" href="../../df/d66/vector__cross__product_8cpp.html#abed307975124243d63fe2e118254defe" title="Function to calculate the cross product of the passed arrays containing the direction ratios of the t...">cross()</a> and the <a class="el" href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8" title="Calculates the magnitude of the mathematical vector from it&#39;s direction ratios.">mag()</a> functions. </p>
<p>Tests the <a class="el" href="../../df/d66/vector__cross__product_8cpp.html#abed307975124243d63fe2e118254defe" title="Function to calculate the cross product of the passed arrays containing the direction ratios of the t...">cross()</a> function.</p>
<p>Tests the <a class="el" href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8" title="Calculates the magnitude of the mathematical vector from it&#39;s direction ratios.">mag()</a> function.</p>
<div class="fragment"><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; {<span class="comment"></span></div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160;<span class="comment"> /// Tests the cross() function.</span></div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160;<span class="comment"></span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;double, 3&gt;</a> t_vec = <a class="code" href="../../df/d66/vector__cross__product_8cpp.html#abed307975124243d63fe2e118254defe">math::vector_cross::cross</a>({1, 2, 3}, {4, 5, 6});</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; assert(t_vec[0] == -3 &amp;&amp; t_vec[1] == 6 &amp;&amp; t_vec[2] == -3);</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160;<span class="comment"> /// Tests the mag() function.</span></div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160;<span class="comment"></span> <span class="keywordtype">double</span> t_mag = <a class="code" href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8">math::vector_cross::mag</a>({6, 8, 0});</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; assert(t_mag == 10);</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160;}</div>
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<li>sieve()
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</li>
<li>Sieve()
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<li>sieve()
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<li>SieveOfEratosthenes()
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</li>
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<li>predict_OLS_regressor()
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<div class="contents">
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<p><a href="https://gitpod.io/#https://github.com/TheAlgorithms/C-Plus-Plus"><img src="https://img.shields.io/badge/Gitpod-Ready--to--Code-blue?logo=gitpod" alt="Gitpod Ready-to-Code" class="inline"/></a> <a href="https://lgtm.com/projects/g/TheAlgorithms/C-Plus-Plus/context:cpp"><img src="https://img.shields.io/lgtm/grade/cpp/g/TheAlgorithms/C-Plus-Plus.svg?logo=lgtm&amp;logoWidth=18" alt="Language grade: C/C++" style="pointer-events: none;" class="inline"/></a> <a href="https://gitter.im/TheAlgorithms"><img src="https://img.shields.io/badge/Chat-Gitter-ff69b4.svg?label=Chat&amp;logo=gitter&amp;style=flat-square" alt="Gitter chat" style="pointer-events: none;" class="inline"/></a> <a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/CONTRIBUTING.md"><img src="https://img.shields.io/static/v1.svg?label=Contributions&amp;message=Welcome&amp;color=0059b3&amp;style=flat-square" alt="contributions welcome" style="pointer-events: none;" class="inline"/></a> <img src="https://img.shields.io/github/repo-size/TheAlgorithms/C-Plus-Plus?color=red&amp;style=flat-square" alt="GitHub repo size" class="inline"/> <a href="https://TheAlgorithms.github.io/C-Plus-Plus"><img src="https://github.com/TheAlgorithms/C-Plus-Plus/workflows/Doxygen%20CI/badge.svg" alt="Doxygen CI" style="pointer-events: none;" class="inline"/></a> <a href="https://github.com/TheAlgorithms/C-Plus-Plus/actions?query=workflow%3A%22Awesome+CI+Workflow%22"><img src="https://github.com/TheAlgorithms/C-Plus-Plus/workflows/Awesome%20CI%20Workflow/badge.svg" alt="Awesome CI" style="pointer-events: none;" class="inline"/></a></p>
<h1><a class="anchor" id="autotoc_md64"></a>
<h1><a class="anchor" id="autotoc_md65"></a>
Overview</h1>
<p>The repository is a collection of open-source implementation of a variety of algorithms implemented in C++ and licensed under <a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/LICENSE">MIT License</a>. The algorithms span a variety of topics from computer science, mathematics and statistics, data science, machine learning, engineering, etc.. The implementations and the associated documentation are meant to provide a learning resource for educators and students. Hence, one may find more than one implementation for the same objective but using a different algorithm strategies and optimizations.</p>
<h1><a class="anchor" id="autotoc_md65"></a>
<h1><a class="anchor" id="autotoc_md66"></a>
Features</h1>
<ul>
<li>The repository provides implementations of various algorithms in one of the most fundamental general purpose languages - <a href="https://en.wikipedia.org/wiki/C%2B%2B">C++</a>.</li>
@@ -110,12 +110,12 @@ Features</h1>
<li>Self-checks within programs ensure correct implementations with confidence.</li>
<li>Modular implementations and OpenSource licensing enable the functions to be utilized conveniently in other applications.</li>
</ul>
<h1><a class="anchor" id="autotoc_md66"></a>
<h1><a class="anchor" id="autotoc_md67"></a>
Documentation</h1>
<p><a href="https://TheAlgorithms.github.io/C-Plus-Plus">Online Documentation</a> is generated from the repository source codes directly. The documentation contains all resources including source code snippets, details on execution of the programs, diagrammatic representation of program flow, and links to external resources where necessary. The documentation also introduces interactive source code with links to documentation for C++ STL library functions used. Click on <a href="https://TheAlgorithms.github.io/C-Plus-Plus/files.html">Files menu</a> to see the list of all the files documented with the code.</p>
<p><a href="https://thealgorithms.github.io/C-Plus-Plus">Documentation of Algorithms in C++</a> by <a href="https://github.com/TheAlgorithms/C-Plus-Plus/graphs/contributors">The Algorithms Contributors</a> is licensed under <a href="https://creativecommons.org/licenses/by-sa/4.0/?ref=chooser-v1">CC BY-SA 4.0</a><br />
<a href="https://creativecommons.org/licenses/by-sa/4.0"><img src="https://mirrors.creativecommons.org/presskit/icons/cc.svg" alt="Creative Commons License" style="pointer-events: none; height:22px!important;margin-left: 3px;vertical-align:text-bottom;" class="inline"/><img src="https://mirrors.creativecommons.org/presskit/icons/by.svg" alt="Credit must be given to the creator" style="pointer-events: none; height:22px!important;margin-left: 3px;vertical-align:text-bottom;" class="inline"/><img src="https://mirrors.creativecommons.org/presskit/icons/sa.svg" alt="Adaptations must be shared under the same terms" style="pointer-events: none; height:22px!important;margin-left: 3px;vertical-align:text-bottom;" class="inline"/></a></p>
<h1><a class="anchor" id="autotoc_md67"></a>
<h1><a class="anchor" id="autotoc_md68"></a>
Contributions</h1>
<p>As a community developed and maintained repository, we welcome new un-plagiarized quality contributions. Please read our <a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/CONTRIBUTING.md">Contribution Guidelines</a>. </p>
</div></div><!-- PageDoc -->

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<tr id="row_63_"><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>
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<tr id="row_65_"><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_66_" 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_67_"><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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</div><!-- directory -->
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