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<H1>red-black tree</H1>
<P>
(data structure)

<P>
<strong>Definition:</strong>
A nearly-balanced <a href="tree.html" tppabs="http://hissa.nist.gov/dads/HTML/tree.html"><em>tree</em></a> which uses an extra bit per  <a href="node.html" tppabs="http://hissa.nist.gov/dads/HTML/node.html"><em>node</em></a> to maintain balance.  No <a href="leaf.html" tppabs="http://hissa.nist.gov/dads/HTML/leaf.html"><em>leaf</em></a> is more than twice as far from the <a href="root.html" tppabs="http://hissa.nist.gov/dads/HTML/root.html"><em>root</em></a> as any other.
<P><strong>See also</strong>
<a href="leftrotation.html" tppabs="http://hissa.nist.gov/dads/HTML/leftrotation.html"><em>left rotation</em></a>, <a href="rightrotatn.html" tppabs="http://hissa.nist.gov/dads/HTML/rightrotatn.html"><em>right rotation</em></a>, <a href="avltree.html" tppabs="http://hissa.nist.gov/dads/HTML/avltree.html"><em>AVL tree</em></a>, <a href="balancedbitr.html" tppabs="http://hissa.nist.gov/dads/HTML/balancedbitr.html"><em>balanced binary tree</em></a>, <a href="btree.html" tppabs="http://hissa.nist.gov/dads/HTML/btree.html"><em>B-tree</em></a>.
<P><em>Note:
The extra bit "colors" the node red or black, hence the name. More formally, a red-black tree with n internal nodes has <a href="height.html" tppabs="http://hissa.nist.gov/dads/HTML/height.html"><em>height</em></a> at most 2 log<sub>2</sub>(n+1).  These were called "symmetric binary B-trees" when first invented.</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.ee.uwa.edu.au/%7Eplsd210/ds/red_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://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.ee.uwa.edu.au/%7Eplsd210/ds/red_black.html'" tppabs="http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.ee.uwa.edu.au/%7Eplsd210/ds/red_black.html">analysis, explanation, illustrations, and code (C)</A>

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Go to the
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If you have suggestions, corrections, or comments, please get in touch
with
<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>
&nbsp;(<a href="mailto:paul.black@nist.gov">paul.black@nist.gov</a>).

<p>
Entry modified Thu Jun 17 10:33:06 1999.<BR>
HTML page formatted Wed Dec 22 09:36:20 1999.

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