Question: Problem 2 [50 points] Consider the following more general version of the Knapsack problem There are p groups of objects 0, 02. . . .

Problem 2 [50 points] Consider the following more general version of

Problem 2 [50 points] Consider the following more general version of the Knapsack problem There are p groups of objects 0, 02. . . . , op and a knapsack capacity W. Each object has a weight w and a value v. Our goal is to select a subset of objects such that: the total weights of selected objects is at most W at most one object is selected from any group, and the total value of the selected objects is maximized Suppose that n is the total number of objects in all the groups and V is the maximum value of any object, i.e., V-max v Give an O(nW) time algorithm for this general Knapsack problem. Explain why your algorithm is correct and analyze the running time of your algorithm Hint: Do a dynamic programming with increasing Knapsack capacity: z is an object NIOL

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