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<TITLE>Implementing 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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<H1><A NAME="SECTION0011400000000000000000">Implementing Search Trees</A></H1>
<P>
Since search trees are designed to support efficient searching,
it is only appropriate that they be implemented as
classes derived from the <tt>SearchableContainer</tt> abstract base class.
Recall from Section&nbsp;<A HREF="page127.html#secadtssrchcont" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page127.html#secadtssrchcont"><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> that the searchable container
interface includes the member functions <tt>Find</tt>, <tt>IsMember</tt>,
<tt>Insert</tt>, and <tt>Withdraw</tt>.
<P>
<P><A NAME="19294">&#160;</A><A NAME="figclasses6">&#160;</A> <IMG WIDTH=575 HEIGHT=108 ALIGN=BOTTOM ALT="figure19290" SRC="img1287.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1287.gif"  ><BR>
<STRONG>Figure:</STRONG> Object Class Hierarchy<BR>
<P>
<P>
Program&nbsp;<A HREF="page311.html#progtree3h" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page311.html#progtree3h"><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> declares the <tt>SearchTree</tt> abstract base class.
The <tt>SearchTree</tt> is derived from the classes <tt>Tree</tt>
and <tt>SearchableContainer</tt>.
The <tt>Tree</tt> class encapsulates those interface elements
which are common to trees and search trees.
The common member functions include
<tt>Key</tt>, <tt>Subtree</tt>, <tt>IsEmpty</tt>,
<tt>IsLeaf</tt>, <tt>Height</tt>, and <tt>Degree</tt>,
as well as all of the various traversal routines
(see Section&nbsp;<A HREF="page266.html#sectreesimpltree" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page266.html#sectreesimpltree"><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>).
<P>
<P><A NAME="19503">&#160;</A><A NAME="progtree3h">&#160;</A> <IMG WIDTH=575 HEIGHT=143 ALIGN=BOTTOM ALT="program19310" SRC="img1288.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1288.gif"  ><BR>
<STRONG>Program:</STRONG> <tt>SearchTree</tt> Class Definition<BR>
<P>
<P>
In addition, two more member functions are defined--<tt>FindMin</tt> and <tt>FindMax</tt>.
These functions are accessors.
The function <tt>FindMin</tt> returns a reference to the object contained
in the search tree having the smallest key.
Similarly, the function <tt>FindMax</tt> returns a reference to the contained
object having the largest key.
<P>
<BR> <HR>
<UL> 
<LI> <A NAME="tex2html5775" HREF="page312.html#SECTION0011410000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page312.html#SECTION0011410000000000000000">Binary Search Trees</A>
<LI> <A NAME="tex2html5776" HREF="page316.html#SECTION0011420000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page316.html#SECTION0011420000000000000000">Inserting Items in a Binary Search Tree</A>
<LI> <A NAME="tex2html5777" HREF="page318.html#SECTION0011430000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page318.html#SECTION0011430000000000000000">Removing Items from a Binary Search Tree</A>
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