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Please help with exercise 11.11. Exercise 11.11. Consider the 0/1 Knapsack problem with two knapsacks having capacities mi and m2 respectively We haven items x,...
Please help with exercise 11.11.
Exercise 11.11. Consider the 0/1 Knapsack problem with two knapsacks having capacities mi and m2 respectively We haven items x,... ,"n. Item ai has an associated weightw and profitpi. The goal is to fill as many items as possible in the two knapsacks so that we maximize the total profit. An item can be chosen to be put in either of the two knapsacks (if possible) or not chosen at all. Assume that weights, profits, mi, and m2 are all positive ntegers (i) Show that the optimal substructure property holds for the problem. (ii) Let f (i, 2) be the optimal solution for the subproblem restricted to the first i items.x1,..., a, such that the two knapsacks have capacities y and y2 respectively. Give a recursive formulation for computing f (,2) (iii) Give the pseudo-code of the resulting algorithm. You can give either a DP algorithm or a memoized algorithm. Analyze the running time of your algorithm. (iv) Describe how to change the algorithm so that it also generates the optimum solution (i.e., which items are chosen and in which knapsack)Step by Step Solution
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