Prove that the greedy approach to the fractional knapsack, Computer Engineering

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Prove that the greedy approach to the fractional knapsack

Problem

1. Prove that the greedy approach to the Fractional Knapsack problem yields an optimal solution.

2. Show that the worst-case number of entries computed by the refined dynamic programming algorithm for the 0-1 Knapsack problem is in ?(2 n). Do this by considering the instance in which W = 2n -2 and wi = 2i-1 for 1 ≤ i ≤ n.

3. Show that in the refined dynamic programming algorithm for the 0-1 Knapsack problem, the total number of entries computed is about (W + 1) × (n + 1) /2, when n = W + 1 and wi = 1 for all i.

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Computer Engineering: Prove that the greedy approach to the fractional knapsack

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