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<TITLE>Edge-Weighted and Vertex-Weighted Graphs</TITLE>
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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="SECTION0017250000000000000000">Edge-Weighted and Vertex-Weighted Graphs</A></H2>
<P>
An <em>edge-weighted graph</em><A NAME=49938> </A><A NAME=49939> </A>
is a graph in which
each edge has been assigned a <em>weight</em>.
Similarly, a <em>vertex-weighted graph</em><A NAME=49942> </A><A NAME=49943> </A>
is a graph in which
each vertex has been assigned a <em>weight</em>.
In such graphs,
the quantity represented by a weight depends on the application.
<P>
Since a graph is a container
that contains specifically vertices and edges,
it is not necessary to introduce new graph classes to represent
edge-weighted and vertex-weighted graphs.
Instead, we introduce two classes,
<tt>WeightedVertex</tt> and <tt>WeightedEdge</tt>.
By using instances of these new classes
together with the existing graph classes,
we can create arbitrary edge-weighted and vertex-weighted graphs.
Program <A HREF="page546.html#proggraph6h" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page546.html#proggraph6h"><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> contains the declarations
of the <tt>WeightedVertex</tt>
and <tt>WeightedEdge</tt> classes.
<P>
<P><A NAME="50116"> </A><A NAME="proggraph6h"> </A> <IMG WIDTH=575 HEIGHT=333 ALIGN=BOTTOM ALT="program49950" SRC="img2382.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img2382.gif" ><BR>
<STRONG>Program:</STRONG> <tt>WeightedVertex</tt> and <tt>WeightedEdge</tt> Class Definitions<BR>
<P>
<P>
Since the <tt>WeightedVertex</tt> class
is derived from the <tt>Vertex</tt> class,
instances of the former can be used wherever the latter is expected.
Therefore, we can create a vertex-weighted graph
simply by inserting weighted vertices into an instance
of one of the graph implementations discussed in the preceding section.
<P>
The <tt>WeightedVertex<T></tt> class
contains a single member variable called <tt>weight</tt>
which is a pointer to an <tt>Object</tt> instance.
Therefore, any object type can be used as the weight.
The constructor sets the weight to a given value,
and the member function <tt>Weight</tt> is used to access the weight.
<P>
The <tt>WeightedEdge<T></tt> class is implemented similarly.
I.e., weighted edge instances can be used wherever an edge is expected.
By inserting weighted edges into a graph,
we get an edge-weighted graph.
Clearly, if the application demands it,
it is possible to use both weighted vertices and weighted edges
in the same graph.
<P>
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