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<HTML><HEAD><TITLE>Bottom-Up Algorithms: Dynamic Programming</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="tex2html6443" HREF="page459.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html6441" HREF="page433.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html6435" HREF="page457.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A> <A NAME="tex2html6445" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <BR><HR><H1><A NAME="SECTION0014400000000000000000">Bottom-Up Algorithms: Dynamic<BR> Programming</A></H1><P>In this section we consider a bottom-up algorithmic paradigmcalled <em>dynamic programming</em><A NAME=33092> </A>.In order to solve a given problem,a series of subproblems is solved.The series of subproblems is devised carefully in such a waythat each subsequent solution is obtained by combining the solutions to one or more of the subproblems that have already been solved.All intermediate solutions are kept in a tablein order to prevent unnecessary duplication of effort.<P><BR> <HR><UL> <LI> <A NAME="tex2html6446" HREF="page459.html#SECTION0014410000000000000000">Example-Generalized Fibonacci Numbers</A><LI> <A NAME="tex2html6447" HREF="page460.html#SECTION0014420000000000000000">Example-Computing Binomial Coefficients</A><LI> <A NAME="tex2html6448" HREF="page461.html#SECTION0014430000000000000000">Application: Typesetting Problem</A></UL><HR><A NAME="tex2html6443" HREF="page459.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html6441" HREF="page433.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html6435" HREF="page457.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A> <A NAME="tex2html6445" 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 © 2003</a> by <a href="../signature.html">Bruno R. Preiss, P.Eng.</a> All rights reserved.</ADDRESS></BODY></HTML>⌨️ 快捷键说明
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