# GE330_lect18 - Lecture 18 Dynamic Programming Problems...

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Lecture 18 Dynamic Programming Problems April 13, 2009

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Dynamic Programming The material is in Chapter 10 1
Dynamic Programming Decompose a problem into several stages; Each stage comprise a much simpler problem, sometime called a subproblem; Require a recursive equation linking diﬀerent stages; No general rule for the design a dynamic programming algo- rithm, it is very application-dependent; Takes a reasonable amount of practice before one is fully comfortable with it. 2

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Dynamic Programming: Shortest Path In the follow network, we want to ﬁnd the shortest route from node 1 to node 7. We know algorithms for solving this problem, but now we want to use dynamic programming. We decompose the problem into stages as delineated by the vertical dashed lines in the ﬁgure on the next slide. 3
Dynamic Programming: Shortest Path The idea here is to compute the shortest distance from the start- ing node to all the terminal nodes of a stage and then use these distance as input data to the immediately succeeding stage. 4

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Dynamic Programming: Shortest Path Stage 1 Starting from node 1, stage 1 includes three end nodes (2, 3, and 4). It is easy to calculate: Shortest distance from node 1 to node 2 = 7(from node 1); Shortest distance from node 1 to node 3 = 8(from node 1); Shortest distance from node 1 to node 4 = 5(from node 1) . Stage 2
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GE330_lect18 - Lecture 18 Dynamic Programming Problems...

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