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Dynamic programming algorithm for problem

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Reference no: EM132274476

Assume that you attend a boring science convention that takes place in a conference center that is arranged as a n by m grid with a mini-exhibition at each node. To attract customers, each exhibition offers a certain number of free pizza slices to passing customers. You want to move from north-west corner to the south-east corner of the conference center. Since you do not want to spend too much time there, in each step you may either move south or east. Your goal is to maximize the total number of free pizza slices you can get.

More formally, if you pass by the exhibition located at node (i,j) where 0 ≤ i ≤ n and 0 ≤ j ≤ m, you get p[i,j] slices of pizza. You are told all of the p[x,y] a priori. Your goal is to design a path from (0, 0) to (n, m) allowing you to consume as much of pizza as you can!

Give an efficient (i.e., polynomial in n and m) dynamic programming algorithm for this problem, and analyze its running time.

Reference no: EM132274476

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