Problem 4. Assume that you were given N cents (N is an integer) and you were asked to break up the N cents into coins consisting of 1 cent, 2 cents and 5 cents. Prove that a greedy algorithm always gives the optimal solution.

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Q: Does a greedy algorithm finds the optimal solution to the integer knapsack problem

A:

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A: For 14: NoFor 6: NoFor 10: NoFor 100: Yes

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Introduction to Greedy Algorithm

A greedy algorithm is a problem-solving method that makes the locally optimal selection at every stage to reach a globally optimal solution. It solves a problem in two stages: Scanning the list of items and Optimization. However, in most problems, the greedy algorithm fails to provide a globally optimal solution.