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<TITLE>Implementing M-Way Search Trees</TITLE>
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<b>Data Structures and Algorithms 
with Object-Oriented Design Patterns in C++</b><br>
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<H2><A NAME="SECTION0011610000000000000000">Implementing <I>M</I>-Way Search Trees</A></H2>
<P>
<A NAME="secsrchtreemwayimpl">&#160;</A>
<P>
In order to illustrate the basic ideas,
this section describes an implementation
of <I>M</I>-way search trees in main memory.
According to Definition&nbsp;<A HREF="page301.html#defnmwaytree" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page301.html#defnmwaytree"><IMG  ALIGN=BOTTOM ALT="gif" SRC="cross_ref_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cross_ref_motif.gif"></A>,
each internal node of an <I>M</I>-way search tree has <I>n</I> subtrees,
where <I>n</I> is at least two and at most <I>M</I>.
Furthermore, if a node has <I>n</I> subtrees,
it must contain <I>n</I>-1 keys.
<P>
Figure&nbsp;<A HREF="page331.html#figmway" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page331.html#figmway"><IMG  ALIGN=BOTTOM ALT="gif" SRC="cross_ref_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cross_ref_motif.gif"></A> shows how we can implement
a single node of an <I>M</I>-way search tree.
The idea is that we use two arrays in each node--the first holds the keys
and the second contains pointers to the subtrees.
Since there are at most <I>M</I>-1 keys and <I>M</I> subtrees,
the first array is one element shorter than the second array.
<P>
<P><A NAME="21497">&#160;</A><A NAME="figmway">&#160;</A> <IMG WIDTH=575 HEIGHT=193 ALIGN=BOTTOM ALT="figure21140" SRC="img1355.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1355.gif"  ><BR>
<STRONG>Figure:</STRONG> Representing a Node of an <I>M</I>-Way Search Tree<BR>
<P><BR> <HR>
<UL> 
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