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<H1>balance</H1>
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(definition)

<P>
<strong>Definition:</strong>
The (weight) balance of a tree is the number of <a href="leaf.html" tppabs="http://hissa.nist.gov/dads/HTML/leaf.html"><em>leaves</em></a> of the <a href="leftsubtree.html" tppabs="http://hissa.nist.gov/dads/HTML/leftsubtree.html"><em>left subtree</em></a> of a tree, denoted |T<sub>l</sub>|, divided by the total number of leaves of the tree.  Formally,  <img src="rho2-1.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/rho2.gif"   border=0 height=14 width=6  alt="rho" align=middle>(T) = |T<sub>l</sub>|/|T|.
<P><strong>See also</strong>
<a href="weightbaltre.html" tppabs="http://hissa.nist.gov/dads/HTML/weightbaltre.html"><em>weight-balanced tree</em></a>, <a href="heightbaltre.html" tppabs="http://hissa.nist.gov/dads/HTML/heightbaltre.html"><em>height-balanced tree</em></a>.
<P><em>Note:
The balance of a node is the balance of the (sub)tree rooted at that node. After <strong>Johann Blieberger</strong> &lt;blieb@auto.tuwien.ac.at&gt;, <em>Discrete Loops and Worst Case Performance</em>, page 22.</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 Jun  8 11:19:12 1999.<BR>
HTML page formatted Wed Dec 22 09:34:45 1999.

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