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<div class="headertitle"><div class="title">median_search.cpp File Reference</div></div>
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<p><a href="../../d9/d69/median__search_8cpp_source.html">Go to the source code of this file.</a></p>
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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="../../d9/dca/namespacesearch.html">search</a></td></tr>
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<tr class="memdesc:d9/dca/namespacesearch"><td class="mdescLeft">&#160;</td><td class="mdescRight">for std::assert <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="memitem:median_5Fsearch" id="r_median_5Fsearch"><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 std::vector&lt; int &gt; &amp;A, const int &amp;idx)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<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>
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<a href="https://github.com/Rp-sushil" target="_blank">Sushil Kumar</a> </dd></dl>
<p class="definition">Definition in file <a class="el" href="../../d9/d69/median__search_8cpp_source.html">median_search.cpp</a>.</p>
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