Question: We discussed the fractional Knapsack problem in class as a problem solvable by a greedy algorithm. However, the 0-1 Knapsack problem was not solvable by

We discussed the fractional Knapsack problem in class as a problem solvable by a greedy algorithm. However, the 0-1 Knapsack problem was not solvable by a Greedy algorithm but it is solvable through dynamic programming.

(a)To apply dynamic programing the problem needs to have sub optimality. Proof that the 0-1 Knapsack problem has sub-optimality.

(b) Develop a recursive strategy to solve the 0-1 Knapsack problem leveraging the sub optimality property shown in (a).

(c)Develop a bottom up dynamic programing method to solve the 0-1 Knapsack problem.

(d)Compare the computational complexity between the recursive and the dynamic programing solution.

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