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<div class="headertitle"><div class="title">quick_sort_iterative.cpp File Reference</div></div>
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<p>Quick Sort without recursion. This method uses the stack instead. Both recursive and iterative implementations have O(n log n) best case and O(n^2) worst case.
<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;stack&gt;</code><br />
<code>#include &lt;algorithm&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
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Include dependency graph for quick_sort_iterative.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html">sorting</a></td></tr>
<tr class="memdesc:d5/d91/namespacesorting"><td class="mdescLeft">&#160;</td><td class="mdescRight">for working with vectors <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:aac8f44b28b4aa96444383030b28f8b34" id="r_aac8f44b28b4aa96444383030b28f8b34"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html#aac8f44b28b4aa96444383030b28f8b34">sorting::partition</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt; &amp;arr, int start, int end)</td></tr>
<tr class="memdesc:aac8f44b28b4aa96444383030b28f8b34"><td class="mdescLeft">&#160;</td><td class="mdescRight">The partition function sorts the array from start to end and uses the last element as the pivot. <br /></td></tr>
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<tr class="memdesc:a263595fd9a0163b5b997b89fab3a0dc5"><td class="mdescLeft">&#160;</td><td class="mdescRight">The main sorting function. <br /></td></tr>
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<tr class="memdesc:a88ec9ad42717780d6caaff9d3d6977f9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
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<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Quick Sort without recursion. This method uses the stack instead. Both recursive and iterative implementations have O(n log n) best case and O(n^2) worst case. </p>
<p><a href="https://stackoverflow.com/questions/12553238/quicksort-iterative-or-recursive">https://stackoverflow.com/questions/12553238/quicksort-iterative-or-recursive</a> <a href="https://en.wikipedia.org/wiki/Quicksort">https://en.wikipedia.org/wiki/Quicksort</a> <a href="https://www.geeksforgeeks.org/iterative-quick-sort/">https://www.geeksforgeeks.org/iterative-quick-sort/</a> </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/sebe324" target="_blank">Sebe324</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 129</span>{</div>
<div class="line"><span class="lineno"> 130</span> <a class="code hl_function" href="#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>(); <span class="comment">// run self test implementation</span></div>
<div class="line"><span class="lineno"> 131</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 132</span>}</div>
<div class="ttc" id="aquick__sort__iterative_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> quick_sort_iterative.cpp:94</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a88ec9ad42717780d6caaff9d3d6977f9">&#9670;&#160;</a></span>tests()</h2>
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<td class="memname">void tests </td>
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<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 95</span>{</div>
<div class="line"><span class="lineno"> 96</span> <span class="comment">//TEST 1 - Positive numbers</span></div>
<div class="line"><span class="lineno"> 97</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> case1={100,534,1000000,553,10,61,2000,238,2756,9,12,56,30};</div>
<div class="line"><span class="lineno"> 98</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>&lt;&lt;<span class="stringliteral">&quot;TEST 1\n&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_ostream.html">std::cout</a>&lt;&lt;<span class="stringliteral">&quot;Before: \n&quot;</span>;</div>
<div class="line"><span class="lineno"> 100</span> <span class="keywordflow">for</span>(<span class="keyword">auto</span> x : case1) <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>&lt;&lt;x&lt;&lt;<span class="stringliteral">&quot;,&quot;</span>;</div>
<div class="line"><span class="lineno"> 101</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>&lt;&lt;<span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 102</span> <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a263595fd9a0163b5b997b89fab3a0dc5">sorting::iterativeQuickSort</a>(case1);</div>
<div class="line"><span class="lineno"> 103</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(case1),<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(case1)));</div>
<div class="line"><span class="lineno"> 104</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>&lt;&lt;<span class="stringliteral">&quot;Test 1 succesful!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 105</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>&lt;&lt;<span class="stringliteral">&quot;After: \n&quot;</span>;</div>
<div class="line"><span class="lineno"> 106</span> <span class="keywordflow">for</span>(<span class="keyword">auto</span> x : case1) <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>&lt;&lt;x&lt;&lt;<span class="stringliteral">&quot;,&quot;</span>;</div>
<div class="line"><span class="lineno"> 107</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>&lt;&lt;<span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 108</span> </div>
<div class="line"><span class="lineno"> 109</span> <span class="comment">//TEST 2 - Negative numbers</span></div>
<div class="line"><span class="lineno"> 110</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> case2={-10,-2,-5,-2,-3746,-785,-123, -452, -32456};</div>
<div class="line"><span class="lineno"> 111</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>&lt;&lt;<span class="stringliteral">&quot;TEST 2\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 112</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>&lt;&lt;<span class="stringliteral">&quot;Before: \n&quot;</span>;</div>
<div class="line"><span class="lineno"> 113</span> <span class="keywordflow">for</span>(<span class="keyword">auto</span> x : case2) <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>&lt;&lt;x&lt;&lt;<span class="stringliteral">&quot;,&quot;</span>;</div>
<div class="line"><span class="lineno"> 114</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>&lt;&lt;<span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 115</span> <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a263595fd9a0163b5b997b89fab3a0dc5">sorting::iterativeQuickSort</a>(case2);</div>
<div class="line"><span class="lineno"> 116</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(case2),<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(case2)));</div>
<div class="line"><span class="lineno"> 117</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>&lt;&lt;<span class="stringliteral">&quot;Test 2 succesful!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 118</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>&lt;&lt;<span class="stringliteral">&quot;After: \n&quot;</span>;</div>
<div class="line"><span class="lineno"> 119</span> <span class="keywordflow">for</span>(<span class="keyword">auto</span> x : case2) <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>&lt;&lt;x&lt;&lt;<span class="stringliteral">&quot;,&quot;</span>;</div>
<div class="line"><span class="lineno"> 120</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>&lt;&lt;<span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 121</span>}</div>
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<div class="ttc" id="anamespacesorting_html_a263595fd9a0163b5b997b89fab3a0dc5"><div class="ttname"><a href="../../d5/d91/namespacesorting.html#a263595fd9a0163b5b997b89fab3a0dc5">sorting::iterativeQuickSort</a></div><div class="ttdeci">void iterativeQuickSort(std::vector&lt; int &gt; &amp;arr)</div><div class="ttdoc">The main sorting function.</div><div class="ttdef"><b>Definition</b> quick_sort_iterative.cpp:58</div></div>
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@@ -167,6 +167,12 @@ Functions</h2></td></tr>
<tr class="memitem:a6eb67c2f91c98cf4464f75b5882022de" id="r_a6eb67c2f91c98cf4464f75b5882022de"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a6eb67c2f91c98cf4464f75b5882022de"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a6eb67c2f91c98cf4464f75b5882022de">quicksort</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; arr, int32_t low, int32_t high)</td></tr>
<tr class="separator:a6eb67c2f91c98cf4464f75b5882022de"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aac8f44b28b4aa96444383030b28f8b34" id="r_aac8f44b28b4aa96444383030b28f8b34"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#aac8f44b28b4aa96444383030b28f8b34">partition</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt; &amp;arr, int start, int end)</td></tr>
<tr class="memdesc:aac8f44b28b4aa96444383030b28f8b34"><td class="mdescLeft">&#160;</td><td class="mdescRight">The partition function sorts the array from start to end and uses the last element as the pivot. <br /></td></tr>
<tr class="separator:aac8f44b28b4aa96444383030b28f8b34"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a263595fd9a0163b5b997b89fab3a0dc5" id="r_a263595fd9a0163b5b997b89fab3a0dc5"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a263595fd9a0163b5b997b89fab3a0dc5">iterativeQuickSort</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt; &amp;arr)</td></tr>
<tr class="memdesc:a263595fd9a0163b5b997b89fab3a0dc5"><td class="mdescLeft">&#160;</td><td class="mdescRight">The main sorting function. <br /></td></tr>
<tr class="separator:a263595fd9a0163b5b997b89fab3a0dc5"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae3a775d99dbbb94c130a973df0cfddcf" id="r_ae3a775d99dbbb94c130a973df0cfddcf"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ae3a775d99dbbb94c130a973df0cfddcf"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#ae3a775d99dbbb94c130a973df0cfddcf">recursive_bubble_sort</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; *nums, uint64_t n)</td></tr>
<tr class="memdesc:ae3a775d99dbbb94c130a973df0cfddcf"><td class="mdescLeft">&#160;</td><td class="mdescRight">This is an implementation of the recursive_bubble_sort. A vector is passed to the function which is then dereferenced, so that the changes are reflected in the original vector. It also accepts a second parameter of type <code>int</code> and name <code>n</code>, which is the size of the array. <br /></td></tr>
@@ -202,6 +208,7 @@ Functions</h2></td></tr>
<p>Sorting algorithms</p>
<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a> for std::assert for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a> for IO operations</p>
<p>Sorting algorithms</p>
<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/stack.html">std::stack</a> for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a> for assert</p>
<p>header files for collection of functions for a macro called assert which can be used to verify assumptions for io operations</p>
<p>Sorting algorithms</p>
<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted()</a>, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap()</a> for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a> for assert for initializing random number generator for IO operations</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a263595fd9a0163b5b997b89fab3a0dc5">&#9670;&#160;</a></span>iterativeQuickSort()</h2>
<div class="memitem">
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<td class="memname">void sorting::iterativeQuickSort </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>arr</em></span></td><td>)</td>
<td></td>
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<p>The main sorting function. </p>
<p>The iterative quick sort uses the stack instead of recursion for saving and restoring the environment between calls. It does not need the end and start params, because it is not recursive. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">arr</td><td>array to be sorted </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 59</span>{</div>
<div class="line"><span class="lineno"> 60</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/stack.html">std::stack&lt;int&gt;</a> <a class="code hl_variable" href="../../dc/dc5/paranthesis__matching_8cpp.html#aa37d24a036d239b3b528f13b9de880c7">stack</a>;</div>
<div class="line"><span class="lineno"> 61</span> <span class="keywordtype">int</span> start = 0;</div>
<div class="line"><span class="lineno"> 62</span> <span class="keywordtype">int</span> end = arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()-1;</div>
<div class="line"><span class="lineno"> 63</span> <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a90df277532c23519aa7ac3c08ed90a1d">push</a>(start);</div>
<div class="line"><span class="lineno"> 64</span> <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a90df277532c23519aa7ac3c08ed90a1d">push</a>(end);</div>
<div class="line"><span class="lineno"> 65</span> </div>
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<div class="line"><span class="lineno"> 67</span> {</div>
<div class="line"><span class="lineno"> 68</span> end = <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#ae09630c4384903d187801921b2ddc709">top</a>();</div>
<div class="line"><span class="lineno"> 69</span> <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a3647fb4418890f19e0dc414b8092b8b0">pop</a>();</div>
<div class="line"><span class="lineno"> 70</span> start = <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#ae09630c4384903d187801921b2ddc709">top</a>();</div>
<div class="line"><span class="lineno"> 71</span> <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a3647fb4418890f19e0dc414b8092b8b0">pop</a>();</div>
<div class="line"><span class="lineno"> 72</span> </div>
<div class="line"><span class="lineno"> 73</span> <span class="keywordtype">int</span> pivotIndex = partition(arr,start,end);</div>
<div class="line"><span class="lineno"> 74</span> </div>
<div class="line"><span class="lineno"> 75</span> <span class="keywordflow">if</span>(pivotIndex -1 &gt; start)</div>
<div class="line"><span class="lineno"> 76</span> {</div>
<div class="line"><span class="lineno"> 77</span> <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a90df277532c23519aa7ac3c08ed90a1d">push</a>(start);</div>
<div class="line"><span class="lineno"> 78</span> <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a90df277532c23519aa7ac3c08ed90a1d">push</a>(pivotIndex-1);</div>
<div class="line"><span class="lineno"> 79</span> }</div>
<div class="line"><span class="lineno"> 80</span> </div>
<div class="line"><span class="lineno"> 81</span> <span class="keywordflow">if</span>(pivotIndex+1&lt;end)</div>
<div class="line"><span class="lineno"> 82</span> {</div>
<div class="line"><span class="lineno"> 83</span> <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a90df277532c23519aa7ac3c08ed90a1d">push</a>(pivotIndex+1);</div>
<div class="line"><span class="lineno"> 84</span> <a class="code hl_class" href="../../d1/dc2/classstack.html">stack</a>.<a class="code hl_function" href="../../d1/dc2/classstack.html#a90df277532c23519aa7ac3c08ed90a1d">push</a>(end);</div>
<div class="line"><span class="lineno"> 85</span> }</div>
<div class="line"><span class="lineno"> 86</span> }</div>
<div class="line"><span class="lineno"> 87</span>}</div>
<div class="ttc" id="aclassstack_html"><div class="ttname"><a href="../../d1/dc2/classstack.html">stack</a></div><div class="ttdoc">for std::invalid_argument</div><div class="ttdef"><b>Definition</b> stack.hpp:19</div></div>
<div class="ttc" id="aclassstack_html_a3647fb4418890f19e0dc414b8092b8b0"><div class="ttname"><a href="../../d1/dc2/classstack.html#a3647fb4418890f19e0dc414b8092b8b0">stack::pop</a></div><div class="ttdeci">void pop()</div><div class="ttdef"><b>Definition</b> stack.hpp:62</div></div>
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<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="astack_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/stack.html">std::stack</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aac8f44b28b4aa96444383030b28f8b34">&#9670;&#160;</a></span>partition()</h2>
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<td class="memname">int sorting::partition </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>arr</em></span>, </td>
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<p>The partition function sorts the array from start to end and uses the last element as the pivot. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">arr</td><td>the array to be sorted </td></tr>
<tr><td class="paramname">start</td><td>starting index </td></tr>
<tr><td class="paramname">end</td><td>ending index </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>int next index of the pivot </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 34</span>{</div>
<div class="line"><span class="lineno"> 35</span> <span class="keywordtype">int</span> pivot = arr[end];</div>
<div class="line"><span class="lineno"> 36</span> <span class="keywordtype">int</span> index = start - 1;</div>
<div class="line"><span class="lineno"> 37</span> </div>
<div class="line"><span class="lineno"> 38</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = start; j &lt; end; j++) {</div>
<div class="line"><span class="lineno"> 39</span> <span class="keywordflow">if</span> (arr[j] &lt;= pivot) {</div>
<div class="line"><span class="lineno"> 40</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[++index], arr[j]);</div>
<div class="line"><span class="lineno"> 41</span> }</div>
<div class="line"><span class="lineno"> 42</span> }</div>
<div class="line"><span class="lineno"> 43</span> </div>
<div class="line"><span class="lineno"> 44</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[index + 1], arr[end]);</div>
<div class="line"><span class="lineno"> 45</span> <span class="keywordflow">return</span> index + 1;</div>
<div class="line"><span class="lineno"> 46</span>}</div>
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<tr id="row_22_15_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d1/d21/quick__sort_8cpp.html" target="_self">quick_sort.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Quicksort" target="_blank">Quick sort implementation</a> in C++ </td></tr>
<tr id="row_22_16_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d3/d4c/quick__sort__3_8cpp.html" target="_self">quick_sort_3.cpp</a></td><td class="desc">Implementation Details </td></tr>
<tr id="row_22_17_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d8/d61/radix__sort2_8cpp.html" target="_self">radix_sort2.cpp</a></td><td class="desc">Algorithm of <a href="https://en.wikipedia.org/wiki/Radix_sort" target="_blank">Radix sort</a> </td></tr>
<tr id="row_22_18_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d1/daa/random__pivot__quick__sort_8cpp.html" target="_self">random_pivot_quick_sort.cpp</a></td><td class="desc">Implementation of the <a href="https://www.sanfoundry.com/cpp-program-implement-quick-sort-using-randomisation" target="_blank">Random Pivot Quick Sort</a> algorithm </td></tr>
<tr id="row_22_19_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d3/df9/recursive__bubble__sort_8cpp.html" target="_self">recursive_bubble_sort.cpp</a></td><td class="desc">This is an implementation of a recursive version of the <a href="https://www.geeksforgeeks.org/recursive-bubble-sort/" target="_blank">Bubble sort algorithm</a> </td></tr>
<tr id="row_22_20_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d9f/selection__sort__recursive_8cpp.html" target="_self">selection_sort_recursive.cpp</a></td><td class="desc">Implementation of the <a href="https://en.wikipedia.org/wiki/Selection_sort" target="_blank">Selection sort</a> implementation using recursion </td></tr>
<tr id="row_22_21_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d7a/shell__sort2_8cpp.html" target="_self">shell_sort2.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Shell_sort" target="_blank">Shell sort</a> algorithm </td></tr>
<tr id="row_22_22_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d4f/stooge__sort_8cpp.html" target="_self">stooge_sort.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Stooge_sort" target="_blank">Stooge sort implementation</a> in C++ </td></tr>
<tr id="row_22_23_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="dc/dd9/strand__sort_8cpp.html" target="_self">strand_sort.cpp</a></td><td class="desc">Implementation of <a href="https://en.wikipedia.org/wiki/Strand_sort" target="_blank">Strand Sort</a> algorithm </td></tr>
<tr id="row_22_24_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="db/d3f/wave__sort_8cpp.html" target="_self">wave_sort.cpp</a></td><td class="desc">Implementation of the <a href="https://www.geeksforgeeks.org/sort-array-wave-form-2/" target="_blank">Wave sort</a> algorithm </td></tr>
<tr id="row_22_25_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d1/dcc/wiggle__sort_8cpp.html" target="_self">wiggle_sort.cpp</a></td><td class="desc">[Wiggle Sort Algorithm] (<a href="https://leetcode.com/problems/wiggle-sort-ii/">https://leetcode.com/problems/wiggle-sort-ii/</a>) Implementation </td></tr>
<tr id="row_22_17_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d3/d22/quick__sort__iterative_8cpp.html" target="_self">quick_sort_iterative.cpp</a></td><td class="desc">Quick Sort without recursion. This method uses the stack instead. Both recursive and iterative implementations have O(n log n) best case and O(n^2) worst case </td></tr>
<tr id="row_22_18_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d8/d61/radix__sort2_8cpp.html" target="_self">radix_sort2.cpp</a></td><td class="desc">Algorithm of <a href="https://en.wikipedia.org/wiki/Radix_sort" target="_blank">Radix sort</a> </td></tr>
<tr id="row_22_19_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d1/daa/random__pivot__quick__sort_8cpp.html" target="_self">random_pivot_quick_sort.cpp</a></td><td class="desc">Implementation of the <a href="https://www.sanfoundry.com/cpp-program-implement-quick-sort-using-randomisation" target="_blank">Random Pivot Quick Sort</a> algorithm </td></tr>
<tr id="row_22_20_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d3/df9/recursive__bubble__sort_8cpp.html" target="_self">recursive_bubble_sort.cpp</a></td><td class="desc">This is an implementation of a recursive version of the <a href="https://www.geeksforgeeks.org/recursive-bubble-sort/" target="_blank">Bubble sort algorithm</a> </td></tr>
<tr id="row_22_21_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d9f/selection__sort__recursive_8cpp.html" target="_self">selection_sort_recursive.cpp</a></td><td class="desc">Implementation of the <a href="https://en.wikipedia.org/wiki/Selection_sort" target="_blank">Selection sort</a> implementation using recursion </td></tr>
<tr id="row_22_22_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d7a/shell__sort2_8cpp.html" target="_self">shell_sort2.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Shell_sort" target="_blank">Shell sort</a> algorithm </td></tr>
<tr id="row_22_23_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d4f/stooge__sort_8cpp.html" target="_self">stooge_sort.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Stooge_sort" target="_blank">Stooge sort implementation</a> in C++ </td></tr>
<tr id="row_22_24_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="dc/dd9/strand__sort_8cpp.html" target="_self">strand_sort.cpp</a></td><td class="desc">Implementation of <a href="https://en.wikipedia.org/wiki/Strand_sort" target="_blank">Strand Sort</a> algorithm </td></tr>
<tr id="row_22_25_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="db/d3f/wave__sort_8cpp.html" target="_self">wave_sort.cpp</a></td><td class="desc">Implementation of the <a href="https://www.geeksforgeeks.org/sort-array-wave-form-2/" target="_blank">Wave sort</a> algorithm </td></tr>
<tr id="row_22_26_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d1/dcc/wiggle__sort_8cpp.html" target="_self">wiggle_sort.cpp</a></td><td class="desc">[Wiggle Sort Algorithm] (<a href="https://leetcode.com/problems/wiggle-sort-ii/">https://leetcode.com/problems/wiggle-sort-ii/</a>) Implementation </td></tr>
<tr id="row_23_" class="odd"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_23_" class="arrow" onclick="dynsection.toggleFolder('23_')">&#9658;</span><span id="img_23_" class="iconfclosed" onclick="dynsection.toggleFolder('23_')">&#160;</span><a class="el" href="dir_73a3cc5065b223eb41b02873c0e19f0e.html" target="_self">strings</a></td><td class="desc"></td></tr>
<tr id="row_23_0_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d3/db2/boyer__moore_8cpp.html" target="_self">boyer_moore.cpp</a></td><td class="desc">The <a href="https://en.wikipedia.org/wiki/Boyer%E2%80%93Moore_string-search_algorithm" target="_blank">BoyerMoore</a> algorithm searches for occurrences of pattern P in text T by performing explicit character comparisons at different alignments. Instead of a brute-force search of all alignments (of which there are n - m + 1), BoyerMoore uses information gained by preprocessing P to skip as many alignments as possible </td></tr>
<tr id="row_23_1_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d3/d7d/brute__force__string__searching_8cpp.html" target="_self">brute_force_string_searching.cpp</a></td><td class="desc">String pattern search - brute force </td></tr>

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<li>test_longest_common_string_length_for_reversed_inputs()&#160;:&#160;<a class="el" href="da/d0d/longest__common__string_8cpp.html#a23ab67b0d9600697695fc8679462d8fe">longest_common_string.cpp</a></li>
<li>test_longest_common_string_length_is_symmetric()&#160;:&#160;<a class="el" href="da/d0d/longest__common__string_8cpp.html#ad1e613c1b85cc04ed931b6c745fec155">longest_common_string.cpp</a></li>
<li>test_remove()&#160;:&#160;<a class="el" href="df/d42/binary__search__tree2_8cpp.html#ab1333c3ea06dcad896ee204bbd407c4e">binary_search_tree2.cpp</a></li>
<li>tests()&#160;:&#160;<a class="el" href="d1/db7/dynamic__programming_2armstrong__number_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">armstrong_number.cpp</a>, <a class="el" href="da/d0d/longest__common__string_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">longest_common_string.cpp</a>, <a class="el" href="d7/d07/bidirectional__dijkstra_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">bidirectional_dijkstra.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="da/d4b/depth__first__search__with__stack_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">depth_first_search_with_stack.cpp</a>, <a class="el" href="d7/d1e/graph_2dijkstra_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">dijkstra.cpp</a>, <a class="el" href="d1/d9a/hopcroft__karp_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">hopcroft_karp.cpp</a>, <a class="el" href="de/dde/lowest__common__ancestor_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">lowest_common_ancestor.cpp</a>, <a class="el" href="de/d88/travelling__salesman__problem_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">travelling_salesman_problem.cpp</a>, <a class="el" href="d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">boruvkas_minimum_spanning_tree.cpp</a>, <a class="el" href="df/dcb/greedy__algorithms_2dijkstra_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">dijkstra.cpp</a>, <a class="el" href="d0/d51/approximate__pi_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">approximate_pi.cpp</a>, <a class="el" href="d8/db1/binomial__calculate_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">binomial_calculate.cpp</a>, <a class="el" href="d5/df6/check__amicable__pair_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">check_amicable_pair.cpp</a>, <a class="el" href="d8/dd5/check__factorial_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">check_factorial.cpp</a>, <a class="el" href="db/d93/check__prime_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">check_prime.cpp</a>, <a class="el" href="d5/d67/complex__numbers_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">complex_numbers.cpp</a>, <a class="el" href="d7/d89/double__factorial_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">double_factorial.cpp</a>, <a class="el" href="d9/d00/factorial_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">factorial.cpp</a>, <a class="el" href="d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">least_common_multiple.cpp</a>, <a class="el" href="d9/d44/magic__number_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">magic_number.cpp</a>, <a class="el" href="d6/d42/miller__rabin_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">miller_rabin.cpp</a>, <a class="el" href="de/dab/ncr__modulo__p_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">ncr_modulo_p.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="d8/ddf/sieve__of__eratosthenes_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">sieve_of_eratosthenes.cpp</a>, <a class="el" href="db/d6b/kelvin__to__celsius_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">kelvin_to_celsius.cpp</a>, <a class="el" href="dc/de1/recursive__tree__traversal_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">recursive_tree_traversal.cpp</a>, <a class="el" href="d6/d2e/fenwick__tree_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">fenwick_tree.cpp</a>, <a class="el" href="d9/d02/linear__search_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">linear_search.cpp</a>, <a class="el" href="d9/dfd/comb__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">comb_sort.cpp</a>, <a class="el" href="dd/d0d/insertion__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">insertion_sort.cpp</a>, <a class="el" href="d1/d21/quick__sort_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">quick_sort.cpp</a>, <a class="el" href="d8/d61/radix__sort2_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">radix_sort2.cpp</a>, <a class="el" href="d3/db2/boyer__moore_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">boyer_moore.cpp</a>, <a class="el" href="de/d6a/knuth__morris__pratt_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">knuth_morris_pratt.cpp</a></li>
<li>tests()&#160;:&#160;<a class="el" href="d1/db7/dynamic__programming_2armstrong__number_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">armstrong_number.cpp</a>, <a class="el" href="da/d0d/longest__common__string_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">longest_common_string.cpp</a>, <a class="el" href="d7/d07/bidirectional__dijkstra_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">bidirectional_dijkstra.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="da/d4b/depth__first__search__with__stack_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">depth_first_search_with_stack.cpp</a>, <a class="el" href="d7/d1e/graph_2dijkstra_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">dijkstra.cpp</a>, <a class="el" href="d1/d9a/hopcroft__karp_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">hopcroft_karp.cpp</a>, <a class="el" href="de/dde/lowest__common__ancestor_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">lowest_common_ancestor.cpp</a>, <a class="el" href="de/d88/travelling__salesman__problem_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">travelling_salesman_problem.cpp</a>, <a class="el" href="d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">boruvkas_minimum_spanning_tree.cpp</a>, <a class="el" href="df/dcb/greedy__algorithms_2dijkstra_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">dijkstra.cpp</a>, <a class="el" href="d0/d51/approximate__pi_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">approximate_pi.cpp</a>, <a class="el" href="d8/db1/binomial__calculate_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">binomial_calculate.cpp</a>, <a class="el" href="d5/df6/check__amicable__pair_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">check_amicable_pair.cpp</a>, <a class="el" href="d8/dd5/check__factorial_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">check_factorial.cpp</a>, <a class="el" href="db/d93/check__prime_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">check_prime.cpp</a>, <a class="el" href="d5/d67/complex__numbers_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">complex_numbers.cpp</a>, <a class="el" href="d7/d89/double__factorial_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">double_factorial.cpp</a>, <a class="el" href="d9/d00/factorial_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">factorial.cpp</a>, <a class="el" href="d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">least_common_multiple.cpp</a>, <a class="el" href="d9/d44/magic__number_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">magic_number.cpp</a>, <a class="el" href="d6/d42/miller__rabin_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">miller_rabin.cpp</a>, <a class="el" href="de/dab/ncr__modulo__p_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">ncr_modulo_p.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="d8/ddf/sieve__of__eratosthenes_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">sieve_of_eratosthenes.cpp</a>, <a class="el" href="db/d6b/kelvin__to__celsius_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">kelvin_to_celsius.cpp</a>, <a class="el" href="dc/de1/recursive__tree__traversal_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">recursive_tree_traversal.cpp</a>, <a class="el" href="d6/d2e/fenwick__tree_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">fenwick_tree.cpp</a>, <a class="el" href="d9/d02/linear__search_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">linear_search.cpp</a>, <a class="el" href="d9/dfd/comb__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">comb_sort.cpp</a>, <a class="el" href="dd/d0d/insertion__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">insertion_sort.cpp</a>, <a class="el" href="d1/d21/quick__sort_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">quick_sort.cpp</a>, <a class="el" href="d3/d22/quick__sort__iterative_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">quick_sort_iterative.cpp</a>, <a class="el" href="d8/d61/radix__sort2_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">radix_sort2.cpp</a>, <a class="el" href="d3/db2/boyer__moore_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">boyer_moore.cpp</a>, <a class="el" href="de/d6a/knuth__morris__pratt_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">knuth_morris_pratt.cpp</a></li>
<li>TH()&#160;:&#160;<a class="el" href="db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">tower_of_hanoi.cpp</a></li>
<li>tolowerRoman()&#160;:&#160;<a class="el" href="de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">decimal_to_roman_numeral.cpp</a></li>
<li>toupperRoman()&#160;:&#160;<a class="el" href="de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">decimal_to_roman_numeral.cpp</a></li>

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@@ -146,7 +146,7 @@ $(function(){initNavTree('globals_t.html',''); initResizable(true); });
<li>test_longest_common_string_length_is_symmetric()&#160;:&#160;<a class="el" href="da/d0d/longest__common__string_8cpp.html#ad1e613c1b85cc04ed931b6c745fec155">longest_common_string.cpp</a></li>
<li>test_remove()&#160;:&#160;<a class="el" href="df/d42/binary__search__tree2_8cpp.html#ab1333c3ea06dcad896ee204bbd407c4e">binary_search_tree2.cpp</a></li>
<li>test_set&#160;:&#160;<a class="el" href="d3/d7d/brute__force__string__searching_8cpp.html#ae2abaa9caa13fff35e45edca00bee123">brute_force_string_searching.cpp</a></li>
<li>tests()&#160;:&#160;<a class="el" href="d1/db7/dynamic__programming_2armstrong__number_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">armstrong_number.cpp</a>, <a class="el" href="da/d0d/longest__common__string_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">longest_common_string.cpp</a>, <a class="el" href="d7/d07/bidirectional__dijkstra_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">bidirectional_dijkstra.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="da/d4b/depth__first__search__with__stack_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">depth_first_search_with_stack.cpp</a>, <a class="el" href="d7/d1e/graph_2dijkstra_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">dijkstra.cpp</a>, <a class="el" href="d1/d9a/hopcroft__karp_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">hopcroft_karp.cpp</a>, <a class="el" href="de/dde/lowest__common__ancestor_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">lowest_common_ancestor.cpp</a>, <a class="el" href="de/d88/travelling__salesman__problem_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">travelling_salesman_problem.cpp</a>, <a class="el" href="d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">boruvkas_minimum_spanning_tree.cpp</a>, <a class="el" href="df/dcb/greedy__algorithms_2dijkstra_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">dijkstra.cpp</a>, <a class="el" href="d0/d51/approximate__pi_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">approximate_pi.cpp</a>, <a class="el" href="d8/db1/binomial__calculate_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">binomial_calculate.cpp</a>, <a class="el" href="d5/df6/check__amicable__pair_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">check_amicable_pair.cpp</a>, <a class="el" href="d8/dd5/check__factorial_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">check_factorial.cpp</a>, <a class="el" href="db/d93/check__prime_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">check_prime.cpp</a>, <a class="el" href="d5/d67/complex__numbers_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">complex_numbers.cpp</a>, <a class="el" href="d7/d89/double__factorial_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">double_factorial.cpp</a>, <a class="el" href="d9/d00/factorial_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">factorial.cpp</a>, <a class="el" href="d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">least_common_multiple.cpp</a>, <a class="el" href="d9/d44/magic__number_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">magic_number.cpp</a>, <a class="el" href="d6/d42/miller__rabin_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">miller_rabin.cpp</a>, <a class="el" href="de/dab/ncr__modulo__p_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">ncr_modulo_p.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="d8/ddf/sieve__of__eratosthenes_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">sieve_of_eratosthenes.cpp</a>, <a class="el" href="db/d6b/kelvin__to__celsius_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">kelvin_to_celsius.cpp</a>, <a class="el" href="dc/de1/recursive__tree__traversal_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">recursive_tree_traversal.cpp</a>, <a class="el" href="d6/d2e/fenwick__tree_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">fenwick_tree.cpp</a>, <a class="el" href="d9/d02/linear__search_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">linear_search.cpp</a>, <a class="el" href="d9/dfd/comb__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">comb_sort.cpp</a>, <a class="el" href="dd/d0d/insertion__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">insertion_sort.cpp</a>, <a class="el" href="d1/d21/quick__sort_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">quick_sort.cpp</a>, <a class="el" href="d8/d61/radix__sort2_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">radix_sort2.cpp</a>, <a class="el" href="d3/db2/boyer__moore_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">boyer_moore.cpp</a>, <a class="el" href="de/d6a/knuth__morris__pratt_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">knuth_morris_pratt.cpp</a></li>
<li>tests()&#160;:&#160;<a class="el" href="d1/db7/dynamic__programming_2armstrong__number_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">armstrong_number.cpp</a>, <a class="el" href="da/d0d/longest__common__string_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">longest_common_string.cpp</a>, <a class="el" href="d7/d07/bidirectional__dijkstra_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">bidirectional_dijkstra.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="da/d4b/depth__first__search__with__stack_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">depth_first_search_with_stack.cpp</a>, <a class="el" href="d7/d1e/graph_2dijkstra_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">dijkstra.cpp</a>, <a class="el" href="d1/d9a/hopcroft__karp_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">hopcroft_karp.cpp</a>, <a class="el" href="de/dde/lowest__common__ancestor_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">lowest_common_ancestor.cpp</a>, <a class="el" href="de/d88/travelling__salesman__problem_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">travelling_salesman_problem.cpp</a>, <a class="el" href="d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">boruvkas_minimum_spanning_tree.cpp</a>, <a class="el" href="df/dcb/greedy__algorithms_2dijkstra_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">dijkstra.cpp</a>, <a class="el" href="d0/d51/approximate__pi_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">approximate_pi.cpp</a>, <a class="el" href="d8/db1/binomial__calculate_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">binomial_calculate.cpp</a>, <a class="el" href="d5/df6/check__amicable__pair_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">check_amicable_pair.cpp</a>, <a class="el" href="d8/dd5/check__factorial_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">check_factorial.cpp</a>, <a class="el" href="db/d93/check__prime_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">check_prime.cpp</a>, <a class="el" href="d5/d67/complex__numbers_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">complex_numbers.cpp</a>, <a class="el" href="d7/d89/double__factorial_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">double_factorial.cpp</a>, <a class="el" href="d9/d00/factorial_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">factorial.cpp</a>, <a class="el" href="d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">least_common_multiple.cpp</a>, <a class="el" href="d9/d44/magic__number_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">magic_number.cpp</a>, <a class="el" href="d6/d42/miller__rabin_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">miller_rabin.cpp</a>, <a class="el" href="de/dab/ncr__modulo__p_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">ncr_modulo_p.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="d8/ddf/sieve__of__eratosthenes_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">sieve_of_eratosthenes.cpp</a>, <a class="el" href="db/d6b/kelvin__to__celsius_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">kelvin_to_celsius.cpp</a>, <a class="el" href="dc/de1/recursive__tree__traversal_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">recursive_tree_traversal.cpp</a>, <a class="el" href="d6/d2e/fenwick__tree_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">fenwick_tree.cpp</a>, <a class="el" href="d9/d02/linear__search_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">linear_search.cpp</a>, <a class="el" href="d9/dfd/comb__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">comb_sort.cpp</a>, <a class="el" href="dd/d0d/insertion__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">insertion_sort.cpp</a>, <a class="el" href="d1/d21/quick__sort_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">quick_sort.cpp</a>, <a class="el" href="d3/d22/quick__sort__iterative_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">quick_sort_iterative.cpp</a>, <a class="el" href="d8/d61/radix__sort2_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">radix_sort2.cpp</a>, <a class="el" href="d3/db2/boyer__moore_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">boyer_moore.cpp</a>, <a class="el" href="de/d6a/knuth__morris__pratt_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">knuth_morris_pratt.cpp</a></li>
<li>TH()&#160;:&#160;<a class="el" href="db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">tower_of_hanoi.cpp</a></li>
<li>tolowerRoman()&#160;:&#160;<a class="el" href="de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">decimal_to_roman_numeral.cpp</a></li>
<li>toupperRoman()&#160;:&#160;<a class="el" href="de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">decimal_to_roman_numeral.cpp</a></li>

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@@ -209,6 +209,7 @@ $(function(){initNavTree('namespacemembers_func.html',''); initResizable(true);
<li>isBipartite()&#160;:&#160;<a class="el" href="df/dce/namespacegraph.html#a84b0551489c613a681cc83b34450da4b">graph</a></li>
<li>isPowerOfTwo()&#160;:&#160;<a class="el" href="d7/d81/namespacebit__manipulation.html#a5032470c9974bbd6ec254bf296530a5f">bit_manipulation</a></li>
<li>iterativeFactorial()&#160;:&#160;<a class="el" href="dd/d47/namespacemath.html#a2565c745aac2f9561cc6fd9e56d9b77a">math</a></li>
<li>iterativeQuickSort()&#160;:&#160;<a class="el" href="d5/d91/namespacesorting.html#a263595fd9a0163b5b997b89fab3a0dc5">sorting</a></li>
</ul>
@@ -262,6 +263,7 @@ $(function(){initNavTree('namespacemembers_func.html',''); initResizable(true);
<h3><a id="index_p" name="index_p"></a>- p -</h3><ul>
<li>parallelogram_area()&#160;:&#160;<a class="el" href="dd/d47/namespacemath.html#a5de184925e68658f15415dd53954df4f">math</a></li>
<li>parallelogram_perimeter()&#160;:&#160;<a class="el" href="dd/d47/namespacemath.html#a0efb235330ff48e14fd31faaccbcebb3">math</a></li>
<li>partition()&#160;:&#160;<a class="el" href="d5/d91/namespacesorting.html#aac8f44b28b4aa96444383030b28f8b34">sorting</a></li>
<li>phiFunction()&#160;:&#160;<a class="el" href="dd/d47/namespacemath.html#ac37d3ba52eb296597d7a024ba8c4a5a5">math</a></li>
<li>pigeonSort()&#160;:&#160;<a class="el" href="d5/d91/namespacesorting.html#a0e9e1b21a1684585e9e50f9afe4d53a3">sorting</a></li>
<li>pop_back()&#160;:&#160;<a class="el" href="d8/d77/namespacemachine__learning.html#ae10178b082f0205c326550877d998e5d">machine_learning</a></li>

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@@ -124,6 +124,7 @@ $(function(){initNavTree('namespacemembers_i.html',''); initResizable(true); });
<li>isBipartite()&#160;:&#160;<a class="el" href="df/dce/namespacegraph.html#a84b0551489c613a681cc83b34450da4b">graph</a></li>
<li>isPowerOfTwo()&#160;:&#160;<a class="el" href="d7/d81/namespacebit__manipulation.html#a5032470c9974bbd6ec254bf296530a5f">bit_manipulation</a></li>
<li>iterativeFactorial()&#160;:&#160;<a class="el" href="dd/d47/namespacemath.html#a2565c745aac2f9561cc6fd9e56d9b77a">math</a></li>
<li>iterativeQuickSort()&#160;:&#160;<a class="el" href="d5/d91/namespacesorting.html#a263595fd9a0163b5b997b89fab3a0dc5">sorting</a></li>
</ul>
</div><!-- contents -->
</div><!-- doc-content -->

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