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<HTML><HEAD><TITLE>More Terminology</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="tex2html4129" HREF="page255.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html4127" HREF="page252.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html4121" HREF="page253.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A> <A NAME="tex2html4131" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <BR><HR><H3><A NAME="SECTION009102000000000000000">More Terminology</A></H3><P>Consider a tree <I>T</I> containing the set of nodes <I>R</I>as given by Definition <A HREF="page252.html#defntree"><IMG ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A>.<UL><LI> The <em>level</em><A NAME=14476> </A> or <em>depth</em><A NAME=14478> </A> of a node <IMG WIDTH=44 HEIGHT=22 ALIGN=MIDDLE ALT="tex2html_wrap_inline62855" SRC="img1056.gif" > in a tree <I>T</I> is the length of the unique path in <I>T</I> from its root <I>r</I> to the node <IMG WIDTH=11 HEIGHT=14 ALIGN=MIDDLE ALT="tex2html_wrap_inline62821" SRC="img1050.gif" >. For example, the root of <I>T</I> is at level zero and the roots of the subtrees are of <I>T</I> are at level one.<LI> The <em>height of a node</em><A NAME=14480> </A> <IMG WIDTH=44 HEIGHT=22 ALIGN=MIDDLE ALT="tex2html_wrap_inline62855" SRC="img1056.gif" > in a tree <I>T</I> is the length of the longest path from node <IMG WIDTH=11 HEIGHT=14 ALIGN=MIDDLE ALT="tex2html_wrap_inline62821" SRC="img1050.gif" > to a leaf. Therefore, the leaves are all at height zero.<LI> The <em>height of a tree</em><A NAME=14482> </A><A NAME=14483> </A> <I>T</I> is the height of its root node <I>r</I>.<LI> Consider two nodes <IMG WIDTH=11 HEIGHT=14 ALIGN=MIDDLE ALT="tex2html_wrap_inline62821" SRC="img1050.gif" > and <IMG WIDTH=13 HEIGHT=15 ALIGN=MIDDLE ALT="tex2html_wrap_inline62841" SRC="img1053.gif" > in a tree <I>T</I>. The node <IMG WIDTH=11 HEIGHT=14 ALIGN=MIDDLE ALT="tex2html_wrap_inline62821" SRC="img1050.gif" > is an <em>ancestor</em><A NAME=14485> </A> of the node <IMG WIDTH=13 HEIGHT=15 ALIGN=MIDDLE ALT="tex2html_wrap_inline62841" SRC="img1053.gif" > if there exists a path in <I>T</I> from <IMG WIDTH=11 HEIGHT=14 ALIGN=MIDDLE ALT="tex2html_wrap_inline62821" SRC="img1050.gif" > to <IMG WIDTH=13 HEIGHT=15 ALIGN=MIDDLE ALT="tex2html_wrap_inline62841" SRC="img1053.gif" >. Notice that <IMG WIDTH=11 HEIGHT=14 ALIGN=MIDDLE ALT="tex2html_wrap_inline62821" SRC="img1050.gif" > and <IMG WIDTH=13 HEIGHT=15 ALIGN=MIDDLE ALT="tex2html_wrap_inline62841" SRC="img1053.gif" > may be the same node. That is, a node is its own ancestor. However, the node <IMG WIDTH=11 HEIGHT=14 ALIGN=MIDDLE ALT="tex2html_wrap_inline62821" SRC="img1050.gif" > is a <em>proper ancestor</em><A NAME=14487> </A> if there exists a path <I>p</I> in <I>T</I> from <IMG WIDTH=11 HEIGHT=14 ALIGN=MIDDLE ALT="tex2html_wrap_inline62821" SRC="img1050.gif" > to <IMG WIDTH=13 HEIGHT=15 ALIGN=MIDDLE ALT="tex2html_wrap_inline62841" SRC="img1053.gif" > such that the length of the path <I>p</I> is non-zero.<LI> Similarly, node <IMG WIDTH=13 HEIGHT=15 ALIGN=MIDDLE ALT="tex2html_wrap_inline62841" SRC="img1053.gif" > is a <em>descendant</em><A NAME=14489> </A> of the node <IMG WIDTH=11 HEIGHT=14 ALIGN=MIDDLE ALT="tex2html_wrap_inline62821" SRC="img1050.gif" > if there exists a path in <I>T</I> from <IMG WIDTH=11 HEIGHT=14 ALIGN=MIDDLE ALT="tex2html_wrap_inline62821" SRC="img1050.gif" > to <IMG WIDTH=13 HEIGHT=15 ALIGN=MIDDLE ALT="tex2html_wrap_inline62841" SRC="img1053.gif" >. And since <IMG WIDTH=11 HEIGHT=14 ALIGN=MIDDLE ALT="tex2html_wrap_inline62821" SRC="img1050.gif" > and <IMG WIDTH=13 HEIGHT=15 ALIGN=MIDDLE ALT="tex2html_wrap_inline62841" SRC="img1053.gif" > may be the same node, a node is its own descendant. The node <IMG WIDTH=13 HEIGHT=15 ALIGN=MIDDLE ALT="tex2html_wrap_inline62841" SRC="img1053.gif" > is a <em>proper descendant</em><A NAME=14491> </A> if there exists a path <I>p</I> in <I>T</I> from <IMG WIDTH=11 HEIGHT=14 ALIGN=MIDDLE ALT="tex2html_wrap_inline62821" SRC="img1050.gif" > to <IMG WIDTH=13 HEIGHT=15 ALIGN=MIDDLE ALT="tex2html_wrap_inline62841" SRC="img1053.gif" > such that the length of the path <I>p</I> is non-zero.</UL><HR><A NAME="tex2html4129" HREF="page255.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html4127" HREF="page252.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html4121" HREF="page253.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A> <A NAME="tex2html4131" 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 © 2003</a> by <a href="../signature.html">Bruno R. 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