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<HTML><HEAD><TITLE>Backtracking Algorithms</TITLE></HEAD><BODY bgcolor="#FFFFFF"> <a href="../index.html" target="_top"><img src="../icons/usins.gif" alt="Logo" align=right></a><b>Data Structures and Algorithms with Object-Oriented Design Patterns in Python</b><br><A NAME="tex2html6227" HREF="page440.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html6225" HREF="page433.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html6219" HREF="page438.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html6229" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <BR><HR><H1><A NAME="SECTION0014200000000000000000">Backtracking Algorithms</A></H1><P>In this section we consider<em>backtracking algorithms</em><A NAME=32181>&#160;</A>.As in the preceding section,we view the problem to be solved as a sequence of decisions.A backtracking algorithm systematically considersall possible outcomes for each decision.In this sense, backtracking algorithms are like the brute-force algorithmsdiscussed in the preceding section.However, backtracking algorithms are distinguished by the wayin which the space of possible solutions is explored.Sometimes a backtracking algorithm can detect that an exhaustivesearch is unnecessary and, therefore,it can perform much better.<P><BR> <HR><UL> <LI> <A NAME="tex2html6230" HREF="page440.html#SECTION0014210000000000000000">Example-Balancing Scales</A><LI> <A NAME="tex2html6231" HREF="page441.html#SECTION0014220000000000000000">Representing the Solution Space</A><LI> <A NAME="tex2html6232" HREF="page442.html#SECTION0014230000000000000000">Abstract Backtracking Solvers</A><LI> <A NAME="tex2html6233" HREF="page445.html#SECTION0014240000000000000000">Branch-and-Bound Solvers</A><LI> <A NAME="tex2html6234" HREF="page447.html#SECTION0014250000000000000000">Example-0/1 Knapsack Problem Again</A></UL><HR><A NAME="tex2html6227" HREF="page440.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html6225" HREF="page433.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html6219" HREF="page438.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html6229" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <P><ADDRESS><img src="../icons/bruno.gif" alt="Bruno" align=right><a href="../copyright.html">Copyright &#169; 2003</a> by <a href="../signature.html">Bruno R. Preiss, P.Eng.</a>  All rights reserved.</ADDRESS></BODY></HTML>

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