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<H1>binomial heap</H1>
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(data structure)

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<strong>Definition:</strong>
A <a href="priorityque.html" tppabs="http://hissa.nist.gov/dads/HTML/priorityque.html"><em>priority queue</em></a> made of a <a href="forest.html" tppabs="http://hissa.nist.gov/dads/HTML/forest.html"><em>forest</em></a> of <a href="binomialtree.html" tppabs="http://hissa.nist.gov/dads/HTML/binomialtree.html"><em>binomial trees</em></a> with the <a href="heapproperty.html" tppabs="http://hissa.nist.gov/dads/HTML/heapproperty.html"><em>heap property</em></a> numbered k=0, 1, 2,  ..., n, each containing either 0 or 2<sup>k</sup> <a href="node.html" tppabs="http://hissa.nist.gov/dads/HTML/node.html"><em>nodes</em></a>. Each tree is formed by linking two of its predecessors, by joining one at the <a href="root.html" tppabs="http://hissa.nist.gov/dads/HTML/root.html"><em>root</em></a> of the other.  The operations of insert a value, decrease a value, delete a value, and merge or join (<a href="meld.html" tppabs="http://hissa.nist.gov/dads/HTML/meld.html"><em>meld</em></a>) two queues take <a href="bigOnotation.html" tppabs="http://hissa.nist.gov/dads/HTML/bigOnotation.html"><em>O( log n)</em></a> time.  The find minimum operation is a constant <a href="theta.html" tppabs="http://hissa.nist.gov/dads/HTML/theta.html"><em> <img src="Theta-1.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/Theta.gif"  border=0 height=10 width=8  alt="Capital Theta">(1)</em></a>.
<P><strong>See also</strong>
<a href="fibonacheap.html" tppabs="http://hissa.nist.gov/dads/HTML/fibonacheap.html"><em>Fibonnaci heap</em></a>.
<P><em>Note:
Binomial heaps are so called because the number of nodes at each level of each subtree is a binomial coefficient.  Sometimes called a binomial queue. After LK.</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 Fri Jul 16 09:12:49 1999.<BR>
HTML page formatted Wed Dec 22 09:34:48 1999.

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