Give a pseudopolynomial algorithm for Knapsack. Strive for running time of O(nB), but make sure running time is polynomial in n and B. The Knapsack problem is defined as follows. An instance consists of n items 1, 2, . . . , n where item i has size si and profit pi , and a knapsack size B with B = si for all i = 1, 2, . . . , n. All the numbers are integers. A feasible solution consists of a subset Q of {1, 2, . . . , n} such that P i?Q si = B. The objective is to maximize the total profit of Q – that is P i?Q pi . Present the pseudocode, discuss correctness, and analyze the running time.
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