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<H1>diminishing increment sort</H1>
<P>
(algorithm)

<P>
<strong>Definition:</strong>
A multipass, <a href="inplacesort.html" tppabs="http://hissa.nist.gov/dads/HTML/inplacesort.html"><em>in-place sort</em></a> algorithm which, on each pass, sorts <em>i</em> sets of <em>n/i</em> items, where <em>n</em> is the total number of items to sort.  Each set is every <em>i<sup>th</sup></em> item, e.g. set 1 is item 1, 1+i, 1+2i, etc., set 2 is item 2, 2+i, etc.  Typically each set is sorted with an  <a href="insertsrt.html" tppabs="http://hissa.nist.gov/dads/HTML/insertsrt.html"><em>insertion sort</em></a>.  On each succeeding pass, the increment, <em>i</em>, is reduced until it is 1 for the last pass.
<P><strong>See also</strong>
<a href="shellsort.html" tppabs="http://hissa.nist.gov/dads/HTML/shellsort.html"><em>shell sort</em></a>.
<P><em>Note:
Since items may move large distances at first, this method is quite efficient.  Donald E. Knuth extensively analyses this algorithm in [DEK, vol. 3, 5.2.1].  A good set of increments may be 2<sup>k</sup>+1, . . ., 9, 5, 3, 1 with the first increment no more than N/3. <P> Since one of the sets can be visualized as those items where the teeth of a comb touch, this is also known as a comb sort.  Using this analogy, the teeth get closer on each pass. <P> Invented by Donald Lewis Shell [Communications of the ACM, July, 1959, pages 30-32].</em>
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>
<H2>Implementation</H2>
<A HREF="javascript:if(confirm('http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.cs.ubc.ca/spider/harrison/Java/ShellSortAlgorithm.java  \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.cs.ubc.ca/spider/harrison/Java/ShellSortAlgorithm.java'" tppabs="http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.cs.ubc.ca/spider/harrison/Java/ShellSortAlgorithm.java">(Java)</A>.
<H2>More information</H2>
<A HREF="javascript:if(confirm('http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.cs.ubc.ca/spider/harrison/Java/sorting-demo.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.cs.ubc.ca/spider/harrison/Java/sorting-demo.html'" tppabs="http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.cs.ubc.ca/spider/harrison/Java/sorting-demo.html">demonstration</A>.

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Entry modified Tue Mar 30 10:35:45 1999.<BR>
HTML page formatted Wed Dec 22 09:35:09 1999.

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