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<HTML><HEAD><TITLE>Heap-Ordered Binomial Trees</TITLE></HEAD><BODY bgcolor="#FFFFFF"> <a href="../index.html" target="_top"><img src="../icons/usins.gif" alt="Logo" align=right></a><b>Data Structures and Algorithms with Object-Oriented Design Patterns in Python</b><br><A NAME="tex2html5480" HREF="page373.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html5478" HREF="page371.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html5472" HREF="page371.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html5482" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <BR><HR><H3><A NAME="SECTION0011431000000000000000">Heap-Ordered Binomial Trees</A></H3><P>Since binomial trees are simply general trees with a special shape,we can make use of the <tt>GeneralTree</tt> classpresented in Section&nbsp;<A HREF="page276.html#sectreesgeneral"><IMG  ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A>to implement the <tt>BinomialTree</tt> class.(See Figure&nbsp;<A HREF="page356.html#figclasses7"><IMG  ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A>).<P>Program&nbsp;<A HREF="page372.html#progbinomialQueueh"><IMG  ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A> introduces the <tt>BinomialQueue</tt> classand the nested class <tt>BinomialTree</tt>.The <tt>BinomialQueue</tt> class extendsthe abstract <tt>MergeablePriorityQueue</tt> classdefined in Program&nbsp;<A HREF="page352.html#progmergeablePriorityQueuea"><IMG  ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A>.The <tt>BinomialTree</tt> class extends the <tt>GeneralTree</tt> classintroduced in Program&nbsp;<A HREF="page276.html#proggeneralTreea"><IMG  ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A>.<P>No new instance attributes a declared in the <tt>BinomialTree</tt> class.Remember that the implementation of the <tt>GeneralTree</tt> classuses a linked list to contain the pointers to the subtrees,since the degree of a node in a general tree may be arbitrarily large. Also, the <tt>GeneralTree</tt> class already keeps track of thedegree of a node in its <tt>_degree</tt> instance attribute.Since the degree of the root node of a binomial tree of order <I>k</I> is <I>k</I>,it is not necessary to keep track of the order explicitly.The <tt>_degree</tt> variable serves this purpose nicely.<P><P><A NAME="26710">&#160;</A><A NAME="progbinomialQueueh">&#160;</A> <IMG WIDTH=575 HEIGHT=199 ALIGN=BOTTOM ALT="program26647" SRC="img1502.gif"  ><BR><STRONG>Program:</STRONG> <tt>BinomialQueue.BinomialTree</tt> class <tt>__init__</tt> method.<BR><P><HR><A NAME="tex2html5480" HREF="page373.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html5478" HREF="page371.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html5472" HREF="page371.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html5482" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <P><ADDRESS><img src="../icons/bruno.gif" alt="Bruno" align=right><a href="../copyright.html">Copyright &#169; 2003</a> by <a href="../signature.html">Bruno R. Preiss, P.Eng.</a>  All rights reserved.</ADDRESS></BODY></HTML>

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