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<p>Implementation of <a href="https://en.wikipedia.org/wiki/Median_of_medians" target="_blank">Median search</a> algorithm. @cases from <a href="https://brilliant.org/wiki/median-finding-algorithm/" target="_blank">here</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;algorithm&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
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Include dependency graph for median_search.cpp:</div>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/dca/namespacesearch.html">search</a></td></tr>
<tr class="memdesc:d9/dca/namespacesearch"><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="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/dd4/namespacemedian__search.html">median_search</a></td></tr>
<tr class="memdesc:da/dd4/namespacemedian__search"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for <a href="https://en.wikipedia.org/wiki/Median_search" target="_blank">Median search</a> algorithm. <br /></td></tr>
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<tr class="memitem:a868847218f694e78bf433a0ff7648bae" id="r_a868847218f694e78bf433a0ff7648bae"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a868847218f694e78bf433a0ff7648bae">search::median_search::median_of_medians</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt; &amp;A, const int &amp;idx)</td></tr>
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<tr class="memitem:ae1a3968e7947464bee7714f6d43b7002" id="r_ae1a3968e7947464bee7714f6d43b7002"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ae1a3968e7947464bee7714f6d43b7002">test</a> ()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implementation of <a href="https://en.wikipedia.org/wiki/Median_of_medians" target="_blank">Median search</a> algorithm. @cases from <a href="https://brilliant.org/wiki/median-finding-algorithm/" target="_blank">here</a> </p>
<p>Given an array A[1,...,n] of n numbers and an index i, where 1 ≤ i ≤ n, find the i-th smallest element of A. median_of_medians(A, i): #divide A into sublists of len 5 sublists = [A[j:j+5] for j in range(0, len(A), 5)] medians = [sorted(sublist)[len(sublist)/2] for sublist in sublists] if len(medians) &lt;= 5: pivot = sorted(medians)[len(medians)/2] else: #the pivot is the median of the medians pivot = median_of_medians(medians, len(medians)/2) #partitioning step low = [j for j in A if j &lt; pivot] high = [j for j in A if j &gt; pivot] k = len(low) if i &lt; k: return median_of_medians(low,i) elif i &gt; k: return median_of_medians(high,i-k-1) else: #pivot = k return pivot</p>
<dl class="section note"><dt>Note</dt><dd>this algorithm implements median search for only arrays which have distinct elements</dd></dl>
<p>Here are some example lists you can use to see how the algorithm works A = [1,2,3,4,5,1000,8,9,99] (Contain Unique Elements) B = [1,2,3,4,5,6] (Contains Unique Elements) print median_of_medians(A, 0) #should be 1 print median_of_medians(A,7) #should be 99 print median_of_medians(B,4) #should be 5</p>
<dl class="section author"><dt>Author</dt><dd>Unknown author </dd>
<dd>
<a href="https://github.com/Rp-sushil" target="_blank">Sushil Kumar</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>
<td>(</td>
<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<p>Main function </p>
<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="#ae1a3968e7947464bee7714f6d43b7002">test</a>();</div>
<div class="line"><span class="lineno"> 131</span> <span class="keywordtype">int</span> n = 0;</div>
<div class="line"><span class="lineno"> 132</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter Size of Array: &quot;</span>;</div>
<div class="line"><span class="lineno"> 133</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
<div class="line"><span class="lineno"> 134</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> a(n);</div>
<div class="line"><span class="lineno"> 135</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter Array: &quot;</span>;</div>
<div class="line"><span class="lineno"> 136</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i &lt; n; i++){</div>
<div class="line"><span class="lineno"> 137</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; a[i];</div>
<div class="line"><span class="lineno"> 138</span> }</div>
<div class="line"><span class="lineno"> 139</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Median: &quot;</span>; <span class="comment">// Median defination: https://en.wikipedia.org/wiki/Median</span></div>
<div class="line"><span class="lineno"> 140</span> <span class="keywordtype">int</span> x = <a class="code hl_function" href="#a868847218f694e78bf433a0ff7648bae">search::median_search::median_of_medians</a>(a, (n - 1) / 2);</div>
<div class="line"><span class="lineno"> 141</span> <span class="keywordflow">if</span>(n % 2 == 0){</div>
<div class="line"><span class="lineno"> 142</span> <span class="keywordtype">int</span> y = <a class="code hl_function" href="#a868847218f694e78bf433a0ff7648bae">search::median_search::median_of_medians</a>(a, n / 2);</div>
<div class="line"><span class="lineno"> 143</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; (float(x) + float(y))/2.0;</div>
<div class="line"><span class="lineno"> 144</span> }</div>
<div class="line"><span class="lineno"> 145</span> <span class="keywordflow">else</span>{</div>
<div class="line"><span class="lineno"> 146</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; x;</div>
<div class="line"><span class="lineno"> 147</span> }</div>
<div class="line"><span class="lineno"> 148</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nTo find i-th smallest element &quot;</span>;</div>
<div class="line"><span class="lineno"> 149</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEnter i: &quot;</span>;</div>
<div class="line"><span class="lineno"> 150</span> <span class="keywordtype">int</span> idx = 0;</div>
<div class="line"><span class="lineno"> 151</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; idx;</div>
<div class="line"><span class="lineno"> 152</span> idx--;</div>
<div class="line"><span class="lineno"> 153</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; idx + 1&lt;&lt; <span class="stringliteral">&quot;-th smallest element: &quot;</span> &lt;&lt; <a class="code hl_function" href="#a868847218f694e78bf433a0ff7648bae">search::median_search::median_of_medians</a>(a, idx) &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;</div>
<div class="line"><span class="lineno"> 154</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 155</span>}</div>
<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<div class="ttc" id="amedian__search_8cpp_html_a868847218f694e78bf433a0ff7648bae"><div class="ttname"><a href="#a868847218f694e78bf433a0ff7648bae">search::median_search::median_of_medians</a></div><div class="ttdeci">int median_of_medians(const std::vector&lt; int &gt; &amp;A, const int &amp;idx)</div><div class="ttdef"><b>Definition</b> median_search.cpp:62</div></div>
<div class="ttc" id="amedian__search_8cpp_html_ae1a3968e7947464bee7714f6d43b7002"><div class="ttname"><a href="#ae1a3968e7947464bee7714f6d43b7002">test</a></div><div class="ttdeci">void test()</div><div class="ttdef"><b>Definition</b> median_search.cpp:107</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a868847218f694e78bf433a0ff7648bae">&#9670;&#160;</a></span>median_of_medians()</h2>
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<td class="memname">int search::median_search::median_of_medians </td>
<td>(</td>
<td class="paramtype">const <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>A</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int &amp;</td> <td class="paramname"><span class="paramname"><em>idx</em></span>&#160;)</td>
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<p>This function search the element in an array for the given index. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">A</td><td>array where numbers are saved </td></tr>
<tr><td class="paramname">idx</td><td>current index in array </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>corresponding element which we want to search. </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 62</span> {</div>
<div class="line"><span class="lineno"> 63</span> <span class="keywordtype">int</span> pivot = 0; <span class="comment">// initialized with zero</span></div>
<div class="line"><span class="lineno"> 64</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> a(A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>());</div>
<div class="line"><span class="lineno"> 65</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> m;</div>
<div class="line"><span class="lineno"> 66</span> <span class="keywordtype">int</span> r = a.size();</div>
<div class="line"><span class="lineno"> 67</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i &lt; r; i += 5){</div>
<div class="line"><span class="lineno"> 68</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/sort.html">std::sort</a>(a.begin() + i, a.begin() + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(r, i + 5));</div>
<div class="line"><span class="lineno"> 69</span> <span class="keywordtype">int</span> mid = (i + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(r, i + 5)) / 2;</div>
<div class="line"><span class="lineno"> 70</span> m.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(a[mid]);</div>
<div class="line"><span class="lineno"> 71</span> }</div>
<div class="line"><span class="lineno"> 72</span> <span class="keywordtype">int</span> sz = int(m.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());</div>
<div class="line"><span class="lineno"> 73</span> <span class="keywordflow">if</span>(sz &lt;= 5){</div>
<div class="line"><span class="lineno"> 74</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/sort.html">std::sort</a>(m.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), m.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>());</div>
<div class="line"><span class="lineno"> 75</span> pivot = m[(sz- 1) / 2];</div>
<div class="line"><span class="lineno"> 76</span> }</div>
<div class="line"><span class="lineno"> 77</span> <span class="keywordflow">else</span>{</div>
<div class="line"><span class="lineno"> 78</span> pivot = <a class="code hl_function" href="#a868847218f694e78bf433a0ff7648bae">median_of_medians</a>(m, idx);</div>
<div class="line"><span class="lineno"> 79</span> }</div>
<div class="line"><span class="lineno"> 80</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> low;</div>
<div class="line"><span class="lineno"> 81</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> high;</div>
<div class="line"><span class="lineno"> 82</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i &lt; r; i++){</div>
<div class="line"><span class="lineno"> 83</span> <span class="keywordflow">if</span>(a[i] &lt; pivot){</div>
<div class="line"><span class="lineno"> 84</span> low.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(a[i]);</div>
<div class="line"><span class="lineno"> 85</span> }</div>
<div class="line"><span class="lineno"> 86</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span>(a[i] &gt; pivot){</div>
<div class="line"><span class="lineno"> 87</span> high.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(a[i]);</div>
<div class="line"><span class="lineno"> 88</span> }</div>
<div class="line"><span class="lineno"> 89</span> }</div>
<div class="line"><span class="lineno"> 90</span> <span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> = int(low.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());</div>
<div class="line"><span class="lineno"> 91</span> <span class="keywordflow">if</span>(idx &lt; k){</div>
<div class="line"><span class="lineno"> 92</span> <span class="keywordflow">return</span> <a class="code hl_function" href="#a868847218f694e78bf433a0ff7648bae">median_of_medians</a>(low, idx);</div>
<div class="line"><span class="lineno"> 93</span> }</div>
<div class="line"><span class="lineno"> 94</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span>(idx &gt; k){</div>
<div class="line"><span class="lineno"> 95</span> <span class="keywordflow">return</span> <a class="code hl_function" href="#a868847218f694e78bf433a0ff7648bae">median_of_medians</a>(high, idx-k-1);</div>
<div class="line"><span class="lineno"> 96</span> }</div>
<div class="line"><span class="lineno"> 97</span> <span class="keywordflow">else</span>{</div>
<div class="line"><span class="lineno"> 98</span> <span class="keywordflow">return</span> pivot;</div>
<div class="line"><span class="lineno"> 99</span> }</div>
<div class="line"><span class="lineno"> 100</span>}</div>
<div class="ttc" id="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/begin.html">std::vector::begin</a></div><div class="ttdeci">T begin(T... args)</div></div>
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition</b> composite_simpson_rule.cpp:117</div></div>
<div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/end.html">std::vector::end</a></div><div class="ttdeci">T end(T... args)</div></div>
<div class="ttc" id="amin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a></div><div class="ttdeci">T min(T... args)</div></div>
<div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
<div class="ttc" id="asort_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/sort.html">std::sort</a></div><div class="ttdeci">T sort(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae1a3968e7947464bee7714f6d43b7002">&#9670;&#160;</a></span>test()</h2>
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<td class="memname">void test </td>
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<p>Function to test above algorithm </p>
<div class="fragment"><div class="line"><span class="lineno"> 107</span> {</div>
<div class="line"><span class="lineno"> 108</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> A{25,21,98,100,76,22,43,60,89,87};</div>
<div class="line"><span class="lineno"> 109</span> <span class="keywordtype">int</span> i = 3;</div>
<div class="line"><span class="lineno"> 110</span> assert(A[6] == search::median_search::median_of_medians(A, i)); <span class="comment">// A[6] = 43, is the fourth smallest element.</span></div>
<div class="line"><span class="lineno"> 111</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;test case:1 passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 112</span> </div>
<div class="line"><span class="lineno"> 113</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> B{1,2,3,4,5,6};</div>
<div class="line"><span class="lineno"> 114</span> <span class="keywordtype">int</span> j = 4;</div>
<div class="line"><span class="lineno"> 115</span> assert(B[4] == search::median_search::median_of_medians(B, j)); <span class="comment">// B[4] = 5, is the fifth smallest element.</span></div>
<div class="line"><span class="lineno"> 116</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;test case:2 passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 117</span> </div>
<div class="line"><span class="lineno"> 118</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> C{1,2,3,4,5,1000,8,9,99};</div>
<div class="line"><span class="lineno"> 119</span> <span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> = 3;</div>
<div class="line"><span class="lineno"> 120</span> assert(C[3] == search::median_search::median_of_medians(C, k)); <span class="comment">// C[3] = 4, is the fourth smallest element.</span></div>
<div class="line"><span class="lineno"> 121</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;test case:3 passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 122</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;--All tests passed--\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 123</span>}</div>
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