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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="SECTION0015232000000000000000">Breadth-First Solver</A></H3>
<P>
If we can find the optimal solution
by doing a depth-first traversal of the solution space,
then we can find the solution with a breadth-first traversal too.
As defined in Section <A HREF="page257.html#sectreestraversals" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page257.html#sectreestraversals"><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>,
a breadth-first traversal of a tree visits the nodes
in the order of their depth in the tree.
I.e., first the root is visited,
then the children of the root are visited,
then the grandchildren are visited, and so on.
<P>
As shown in Program <A HREF="page451.html#progsolution4h" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page451.html#progsolution4h"><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>BreadthFirstSolver</tt> class simply provides
an implementation for the <tt>DoSolve</tt> member function.
<P>
<P><A NAME="33617"> </A><A NAME="progsolution4h"> </A> <IMG WIDTH=575 HEIGHT=85 ALIGN=BOTTOM ALT="program32749" SRC="img1841.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1841.gif" ><BR>
<STRONG>Program:</STRONG> <tt>BreadthFirstSolver</tt> Class Definition<BR>
<P>
<P>
The body of the <tt>DoSolve</tt> routine is given in Program <A HREF="page451.html#progsolution3c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page451.html#progsolution3c"><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>.
This non-recursive, breadth-first traversal algorithm
uses a queue to keep track of nodes to be visited.
The initial solution is enqueued first.
Then the following steps are repeated until the queue is empty:
<OL><LI>
Dequeue the first solution in the queue.<LI>
If the solution is complete,
call the <tt>UpdateBest</tt> routine to keep track
of the solution which minimizes the objective function.<LI>
Otherwise the solution is not complete.
Enqueue all its successors.
</OL>
Clearly, this algorithm does a complete traversal
of the solution space.<A NAME="tex2html864" HREF="footnode.html#33620" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/footnode.html#33620"><IMG ALIGN=BOTTOM ALT="gif" SRC="foot_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/foot_motif.gif"></A>
<P>
<P><A NAME="33621"> </A><A NAME="progsolution3c"> </A> <IMG WIDTH=575 HEIGHT=468 ALIGN=BOTTOM ALT="program32766" SRC="img1842.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1842.gif" ><BR>
<STRONG>Program:</STRONG> <tt>BreadthFirstSolver</tt> Class <tt>DoSolve</tt> Member Function Definition<BR>
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