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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="SECTION0017230000000000000000">Abstract Graphs and Digraphs</A></H2>
<P>
Directed graphs and undirected graphs have many common characteristics.
Therefore, it seems reasonable to make use of inheritance
in the implementation of graph classes.
However, there are several possible ways in which to organize the
class hierarchy:
<DL ><DT><STRONG>Option A</STRONG>
<DD>
We could use a common abstract base class <tt>Graph</tt> to encapsulate
the common attributes of all graphs
and then derive two different classes <tt>UndirectedGraph</tt>
and <tt>DirectedGraph</tt> from the common base class.
<DT><STRONG>Option B</STRONG>
<DD>
Use <tt>DirectedGraph</tt> as the base class
and derive the class <tt>UndirectedGraph</tt> from it.
In this scenario we view an undirected graph as a directed graph
that has its arrows removed.
<DT><STRONG>Option C</STRONG>
<DD>
Use <tt>UndirectedGraph</tt> as the base class
and derive the class <tt>DirectedGraph</tt> from it.
In this scenario we view a directed graph as an undirected graph
with arrows added.
<P>
</DL>
<P>
As shown in Figure <A HREF="page536.html#figclasses9" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page536.html#figclasses9"><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>,
we have chosen to use option C.
We have chosen this approach because many algorithms
for undirected graphs can also be used with directed graphs.
On the other hand, it is often the case that algorithms
for directed graphs cannot be used with undirected graphs.
<P>
Program <A HREF="page539.html#proggraph3h" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page539.html#proggraph3h"><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 two abstract classes,
<tt>Graph</tt> and <tt>Digraph</tt>.
The <tt>Graph</tt> class is the base class
from which concrete classes that represent <em>undirected</em> graphs are derived.
The <tt>Digraph</tt> abstract class extends the <tt>Graph</tt> class.
The <tt>Digraph</tt> class is the base class
from which concrete classes that represent <em>directed</em> graphs are derived.
<P>
<P><A NAME="50083"> </A><A NAME="proggraph3h"> </A> <IMG WIDTH=575 HEIGHT=849 ALIGN=BOTTOM ALT="program49769" SRC="img2378.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img2378.gif" ><BR>
<STRONG>Program:</STRONG> <tt>Graph</tt> and <tt>Digraph</tt> Class Definitions<BR>
<P>
<P>
The <tt>Graph</tt> class is an abstract base class
since it contains pure virtual member functions.
The graph class adds two member variables to those inherited
from the base classes--<tt>numberOfEdges</tt> and <tt>numberOfVertices</tt>.
A default constructor for the <tt>Graph</tt> class is also declared.
The effect of this constructor is to initialize both
member variables with the value zero.
Therefore, a graph is initially empty--it contains neither vertices nor edges.
<P>
A number of <tt>Graph</tt> class member
functions are declared in Program <A HREF="page539.html#proggraph3h" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page539.html#proggraph3h"><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>.
There are essentially three groups of member functions:
accessors and mutators, iterators, and traversals.
The operations performed by the member functions
are explained in the following sections.
<P>
<BR> <HR>
<UL>
<LI> <A NAME="tex2html8582" HREF="page540.html#SECTION0017231000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page540.html#SECTION0017231000000000000000">Accessors and Mutators</A>
<LI> <A NAME="tex2html8583" HREF="page541.html#SECTION0017232000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page541.html#SECTION0017232000000000000000">Iterators</A>
<LI> <A NAME="tex2html8584" HREF="page542.html#SECTION0017233000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page542.html#SECTION0017233000000000000000">Graph Traversals</A>
</UL>
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