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<H1>Dutch National Flag</H1>
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(algorithm)

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<strong>Definition:</strong>
Rearrange elements in an <a href="array.html" tppabs="http://hissa.nist.gov/dads/HTML/array.html"><em>array</em></a> into three groups: bottom, middle, and top.  During execution, the top group grows down from the top of the array, the bottom grows up from the bottom, and the middle is kept just above the bottom.  Indices keep the locations just below the top, just above the bottom, and just above the middle in three indices.  At each step, examine the element just above the middle. If it belongs to the top group, swap it with the element just below the top.  If it belongs in the bottom, swap it with the element just above the bottom.  If it is in the middle, leave it.  Update whichever index is appropriate. Complexity is <a href="bigOnotation.html" tppabs="http://hissa.nist.gov/dads/HTML/bigOnotation.html"><em>O(n)</em></a> moves and examinations.
<P><em>Note:
Using this in <a href="quicksort.html" tppabs="http://hissa.nist.gov/dads/HTML/quicksort.html"><em>quicksort</em></a> to <a href="partition.html" tppabs="http://hissa.nist.gov/dads/HTML/partition.html"><em>partition</em></a> elements, with the pivot being the middle, lets quicksort avoid "resorting" elements which equal the pivot.</em>
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>

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Entry modified Tue Dec 21 14:38:07 1999.<BR>
HTML page formatted Wed Dec 22 09:35:13 1999.

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