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<TITLE>Implementation</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="SECTION0017413000000000000000">Implementation</A></H3>
<P>
A version of Dijkstra's algorithm is shown in Program <A HREF="page568.html#proggraphalgs2c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page568.html#proggraphalgs2c"><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>.
The <tt>DijkstrasAlgorithm</tt> function takes two arguments.
The first is a <tt>const</tt> reference to a directed graph instance.
It is assumed that the directed graph is an edge-weighted graph
in which the weights are instances of the
<tt>Int</tt> class defined in Program <A HREF="page116.html#progwrapper2h" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page116.html#progwrapper2h"><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>.
The second argument is a <tt>const</tt> reference to the start node.
<P>
<P><A NAME="52081"> </A><A NAME="proggraphalgs2c"> </A> <IMG WIDTH=575 HEIGHT=907 ALIGN=BOTTOM ALT="program52078" SRC="img2479.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img2479.gif" ><BR>
<STRONG>Program:</STRONG> Dijkstra's Algorithm<BR>
<P>
<P>
The <tt>DijkstrasAlgorithm</tt> routine returns its result
in the form of a shortest-path graph.
Therefore, the return value is a reference to a <tt>Digraph</tt> instance.
The function allocates the storage, constructs the shortest-path graph
and returns a reference to that graph.
<P>
The main data structures used are called
<tt>table</tt> and <tt>queue</tt> (lines 4-5).
The former is an array of <IMG WIDTH=48 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline72635" SRC="img2480.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img2480.gif" > <tt>TableEntry</tt> elements.
The latter is a reference to a priority queue.
In this case,
a <tt>BinaryHeap</tt> of length <IMG WIDTH=16 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline71793" SRC="img2367.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img2367.gif" > is used.
(See Section <A HREF="page354.html#secpqueuesbinheaps" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page354.html#secpqueuesbinheaps"><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>).
<P>
The algorithm begins by setting the tentative distance for the start
vertex to zero and inserting the start vertex into the priority
queue with priority zero (lines 7-8).
<P>
The main loop of the routine comprises lines 8-35.
In each iteration of this loop the vertex with the smallest distance
is dequeued (lines 10-12).
The vertex is processed only if its table entry
indicates that the shortest path is not already known (line 13).
<P>
When a vertex <tt>v0</tt> is processed,
its shortest path is deemed to be <em>known</em> (line 15).
Then each vertex <tt>v1</tt> adjacent to vertex is considered (lines 16-19).
The distance to <tt>v1</tt> along the path that passes through <tt>v0</tt>
is computed (lines 20-23).
If this distance is less than the tentative distance
associated with <tt>v1</tt>,
entries in the table for <tt>v1</tt> are updated,
and the <tt>v1</tt> is given a new priority
and inserted into the priority queue (lines 24-29).
<P>
The main loop terminates when all the shortest paths have been found.
The shortest-path graph is then
constructed using the information in the table (lines 38-45).
<P>
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