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<b><font face="Arial, Helvetica, sans-serif" size="4" color="#000000">〖<font color="#0033CC">Lemma5.2</font>〗Relation between number of leaf nodes and nodes
of degree 2:
For any noempty binary tree, T, if n0 is the number of leaf nodes
and n2 the number of nodes of degree 2, then<i><font color="#FF0000">
n0 = n2 + 1</font></i></font></b></pre>
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<pre><b><font face="Arial, Helvetica, sans-serif" size="4" color="#000000"><font color="#FF0000">Proof:</font> <i> n = n0 + n1 + n2</i>
<i> B = n1 + 2 n2 </i> <i><font size="3" color="#CC0099"> </font></i>
<i>n = 1 + n1 + 2 n2</i>
<i>-----> n0 = n2 + 1</i>
<i><font size="3" color="#CC0099">( B is the number of branches, n = B + 1)</font></i></font></b></pre>
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<pre><img src="IMAGE/tree5-2.gif" width="298" height="197"></pre>
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<pre align="left"><b><font face="Arial, Helvetica, sans-serif" size="4" color="#000000">【<font color="#0033CC">definition</font>】A full binary tree of depth k is a binary tree of depth
having <img src="IMAGE/2k-10.gif" width="66" height="29"> nodes , k >= 0
<img src="IMAGE/tree0.gif" width="300" height="177">
【<font color="#0033CC">definition</font>】A binary tree with n nodes and depth k is complete
iff its nodes correspond to the nodes numbered from 1 to n in
the full binary tree of depth k.
</font></b></pre>
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