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<b>Data Structures and Algorithms 
with Object-Oriented Design Patterns in C++</b><br>
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<H1><A NAME="SECTION0015200000000000000000">Backtracking Algorithms</A></H1>
<P>
In this section we consider
<em>backtracking algorithms</em><A NAME=32357>&#160;</A>.
As in the preceding section,
we view the problem to be solved as a sequence of decisions.
A backtracking algorithm systematically considers
all possible outcomes for each decision.
In this sense, backtracking algorithms are like the brute-force algorithms
discussed in the preceding section.
However, backtracking algorithms are distinguished by the way
in which the space of possible solutions is explored.
Sometimes a backtracking algorithm can detect that an exhaustive
search is unnecessary and, therefore,
it can perform much better.
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<LI> <A NAME="tex2html7433" HREF="page447.html#SECTION0015210000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page447.html#SECTION0015210000000000000000">Example-Balancing Scales</A>
<LI> <A NAME="tex2html7434" HREF="page448.html#SECTION0015220000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page448.html#SECTION0015220000000000000000">Representing the Solution Space</A>
<LI> <A NAME="tex2html7435" HREF="page449.html#SECTION0015230000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page449.html#SECTION0015230000000000000000">Abstract Backtracking Solvers</A>
<LI> <A NAME="tex2html7436" HREF="page452.html#SECTION0015240000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page452.html#SECTION0015240000000000000000">Branch-and-Bound Solvers</A>
<LI> <A NAME="tex2html7437" HREF="page454.html#SECTION0015250000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page454.html#SECTION0015250000000000000000">Example-0/1 Knapsack Problem Again</A>
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