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 wx 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 any object, i.e., V = max x is an object vx. Give an O(nW) time algorithm for this general Knapsack problem. Explain the algorithm for this problem.

Hint: Do a dynamic programming with increasing Knapsack capacity