Question: Problem 2 [50 points] Consider the following more general version of the Knapsack problem. There are p groups of objects Oi,O2. . . . .

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 Oi,O2. . . . . Op and a knapsack capacity W. Each objectr 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 (nWime 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. r is an object

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