The score at point b is given by sb 2 21 sa2 weight

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Unformatted text preview: attan Is Not A Perfect Grid A3 A1 B What about diagonals? •  The score at point B is given by: sB = 2 21 sA2 + weight of the edge (A2, B) 22 S3,3 = 22 Traversing the Grid 3 different strategies: max sA3 + weight of the edge (A3, B) 0 0 12 sA1 + weight of the edge (A1, B) 20 5 0 4 12 4 12 0 1 3 8 18 3 2 2 3 2 5 7 5 Done! 1 5 1 5 3 8 17 3 5 3 4 13 5 A2 3 2 1 1 3 2 5 1 7 8 8 10 2 0 0 3 5 3 3 5 2 16 S2,2 = 16 0 5 3 2 1 3 3 8 2 1 1 17 S1,3 = 17 3 2 2 4 7 3 i 5 1 5 1 0 8 10 0 source 5 1 5 3 Dynamic Programming a) a)  Column by column b) Row by row c) Along diagonals c) b) •  solves problems by reusing solutions to overlapping subproblems •  Approaches: •  Bottom up, starting from the smaller problems. •  Top down, recursively, using result caching (memoization) •  Thus, dynamic programming is simply memoization of results of a recurrence, so that time is not spent recomputing solutions to subproblems. A memoized function "remembers" the results corresponding to some set of specific i...
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