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<H1>select and partition</H1>
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(classic problem)

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<strong>Definition:</strong>
Given an <a href="array.html" tppabs="http://hissa.nist.gov/dads/HTML/array.html"><em>array</em></a> A of <em>n</em> elements and a positive integer k  <img src="leq.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/leq.gif" border=0 height=7  width=14 alt="less than or equal to"> n, find the <em>k<sup>th</sup></em> smallest element of A and <a href="partition.html" tppabs="http://hissa.nist.gov/dads/HTML/partition.html"><em>partition</em></a> the array such that A[1],  ..., A[k-1]  <img src="leq.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/leq.gif" border=0 height=7  width=14 alt="less than or equal to"> A[k]  <img src="leq.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/leq.gif" border=0 height=7  width=14 alt="less than or equal to"> A[k+1],  ..., A[n].
<P><strong>See also</strong>
<a href="modifind.html" tppabs="http://hissa.nist.gov/dads/HTML/modifind.html"><em>MODIFIND</em></a>, <a href="find.html" tppabs="http://hissa.nist.gov/dads/HTML/find.html"><em>Find</em></a>, <a href="selectkth.html" tppabs="http://hissa.nist.gov/dads/HTML/selectkth.html"><em>select k<sup>th</sup> element</em></a>.
<P><em>Note:
Algorithms to solve this problem are often used in <a href="sort.html" tppabs="http://hissa.nist.gov/dads/HTML/sort.html"><em>sort</em></a> algorithms.  Implementations have been published by C. A. R. Hoare (Algorithm 65, <a href="find.html" tppabs="http://hissa.nist.gov/dads/HTML/find.html"><em>Find</em></a>, CACM, Vol. 4, No. 7, July 1961, page 321), R. W. Floyd and R. L. Rivest (CACM, Vol. 18, No. 3, March 1975, page 173), and Vladimir Zabrodsky (<a href="modifind.html" tppabs="http://hissa.nist.gov/dads/HTML/modifind.html"><em>MODIFIND</em></a>, Elektronika, No. 6, 1992, pages 33-34). These can be easily changed to find the k<sup>th</sup> largest element.</em>
<P>Author: <a href="terms.html#authorVZ" tppabs="http://hissa.nist.gov/dads/terms.html#authorVZ">VZ</a>
<H2>Implementation</H2>
<A HREF="javascript:if(confirm('http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.geocities.com/SiliconValley/Garage/3323/3alg.html  \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address.  \n\nDo you want to open it from the server?'))window.location='http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.geocities.com/SiliconValley/Garage/3323/3alg.html'" tppabs="http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.geocities.com/SiliconValley/Garage/3323/3alg.html">analysis and comparison (Rexx)</A>

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<a href="javascript:if(confirm('http://hissa.nist.gov/~black/black.html  \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address.  \n\nDo you want to open it from the server?'))window.location='http://hissa.nist.gov/~black/black.html'" tppabs="http://hissa.nist.gov/~black/black.html">Paul E. Black</a>
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<p>
Entry modified Tue Jun  8 12:06:17 1999.<BR>
HTML page formatted Wed Dec 22 09:36:25 1999.

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