Question: Problem 2 [50 points] Consider the following more general version of the Knapsack problem There are p groups of objects O1, O2,.. , Op and

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 O1, O2,.. , Op and a knapsack capacity W. Each object x has a weight w and a value vx. 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 vg. Give an O(nW) time algorithm for this general Knapsack any object, ie., V-max problem. Explain why your algorithm is correct and analyze the running time of your algorithm. Hint: Do a dynamic programming with increasing Knapsack capacity x is an object

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