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In class, we studied the fractional [0, 1]-knapsack problem using a greedy approach. In this assignment, we work on the {0, 1}-knapsack problem using dynamic programming. You are given n objects which cannot be broken into smaller pieces. Moreover, you have eractly one copy of each object. Each object i (where 1 0 and value vi 0. You have a knapsack that can carry a total weight not exceeding W. Your goal is to fill the knapsack in a way that maximizes the total value of the included objects, while respecting the capacity constraint. For each object i (where 1 S i