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<b>Data Structures and Algorithms 
with Object-Oriented Design Patterns in C++</b><br>
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<H3><A NAME="SECTION0010634000000000000000"><tt>Key</tt> and <tt>Subtree</tt> Member Functions</A></H3>
<P>
Program&nbsp;<A HREF="page280.html#proggentree2c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page280.html#proggentree2c"><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> defines the various <tt>GeneralTree</tt> class
member functions for manipulating general trees.
The <tt>Key</tt> member function is a member variable accessor
that simply returns a reference
to the object contained by the root node of the tree.
Clearly, its running time is <I>O</I>(1).
<P>
<P><A NAME="16769">&#160;</A><A NAME="proggentree2c">&#160;</A> <IMG WIDTH=575 HEIGHT=639 ALIGN=BOTTOM ALT="program16693" SRC="img1173.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1173.gif"  ><BR>
<STRONG>Program:</STRONG> <tt>GeneralTree</tt> Class <tt>Key</tt>, 	<tt>Subtree</tt>, <tt>AttachSubtree</tt>and <tt>DetachSubtree</tt> Member Function Definitions<BR>
<P>
<P>
The <tt>Subtree</tt> member function takes as its lone argument
an <tt>unsigned int</tt>, <tt>i</tt>,
which must be between 0 and  <IMG WIDTH=76 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline63946" SRC="img1174.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1174.gif"  >,
where <tt>degree</tt> is the degree of the root node of the tree.
It returns a reference to the  <IMG WIDTH=20 HEIGHT=13 ALIGN=BOTTOM ALT="tex2html_wrap_inline63948" SRC="img1175.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1175.gif"  > subtree of the given tree.
The <tt>Subtree</tt> routine simply takes <tt>i</tt> steps down the linked list
and returns a reference to the appropriate subtree.
Assuming that <tt>i</tt> is valid,
the worst case running time for <tt>Subtree</tt> is <I>O</I>(<I>d</I>),
where  <IMG WIDTH=80 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline63952" SRC="img1176.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1176.gif"  > is the degree of the root node of the tree.
<P>
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