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<TITLE>Alternate Representations for Trees</TITLE>
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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="SECTION0010103000000000000000">Alternate Representations for Trees</A></H3>
<P>
Figure&nbsp;<A HREF="page254.html#figtree2" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page254.html#figtree2"><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 an alternate representation of
the tree  <IMG WIDTH=14 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline63428" SRC="img1096.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1096.gif"  > defined in Equation&nbsp;<A HREF="page251.html#eqntreestc" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page251.html#eqntreestc"><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>.
In this case,
the tree is represented as a set of nested regions in the plane.
In fact, what we have is a <em>Venn diagram</em><A NAME=15125>&#160;</A>
which corresponds to the view that a tree is a set of sets.
<P>
<P><A NAME="15287">&#160;</A><A NAME="figtree2">&#160;</A> <IMG WIDTH=575 HEIGHT=209 ALIGN=BOTTOM ALT="figure15126" SRC="img1111.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1111.gif"  ><BR>
<STRONG>Figure:</STRONG> An Alternate Graphical Representation for Trees<BR>
<P>
<P>
This hierarchical, set-within-a-set view of trees
is also evoked by considering the nested structure of computer programs.
E.g., consider the following fragment of C++ code:
<PRE>D: {
    E: {
        F: statement();
    }
    G: {
        H: {
            I: statement();
	}
        J: {
            K: statement();
            L: statement();
	}
        M: statement();
    }
}</PRE>
The nesting structure of this program
and the tree given in Equation&nbsp;<A HREF="page251.html#eqntreestc" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page251.html#eqntreestc"><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>
are <em>isomorphic</em><A NAME=15292>&#160;</A>.<A NAME="tex2html483" HREF="footnode.html#15293" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/footnode.html#15293"><IMG  ALIGN=BOTTOM ALT="gif" SRC="foot_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/foot_motif.gif"></A>
Therefore, it is not surprising that trees have an important
r&#244;le in the analysis and translation of computer programs.
<P>
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