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<b><font face="Arial, Helvetica, sans-serif" size="4" color="#FF0000">Extended binary tree</font><font face="Arial, Helvetica, sans-serif" size="4" color="#000000">
n nodes --> n+1 null links --> n+1 external nodes (failure node )
<i><font color="#FF0000">extended binary tree</font></i> -- a binary tree with external nodes added
<img src="image/text10-j.gif" width="466" height="149">
<i><font color="#0033CC">internal path length </font></i><font color="#0033CC"><i>( I )</i></font> --- the sum over all internal nodes the
lengths of the paths from the root to those nodes.
I = 0+1+1+2+3 = 7
<i><font color="#0033CC">external path length ( E ) </font></i>--- the sum over all external nodes the
lengths of the paths from the root to those nodes.
E = 2+2+4+4+3+2 = 17
<font color="#FF0000">E = I + 2n</font></font></b></pre>
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<pre><b><font face="Arial, Helvetica, sans-serif" size="4" color="#000000"><font color="#FF0000">the worst case</font>: I = <img src="image/si.gif" width="33" height="51" align="middle"> = n(n-1) / 2
<font color="#FF0000">the best case: </font> I = <img src="image/slogn.gif" width="98" height="48" align="middle"> = O( n log n )</font></b></pre>
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<pre align="left"><b><font face="Arial, Helvetica, sans-serif" size="4" color="#000000"> complete binary tree (min internal path length)
</font></b></pre>
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