Professor Bin is attempting to load bags into the trunk of her car and seeks to load as many bags as possible. The bags are of various sizes (and are infinitely flexible, while maintaining the same volume). She plans to use a greedy algorithm to solve this problem. (a) State the greedy algorithm for this problem (b) Does this problem have the greedy-choice property? Why or why not? (c) Does this problem have the optimal substructure property? Why or why not? (d) Would there be a greedy solution if instead of optimizing the number of boxes, she instead seeks to fill the largest possible fraction of the space in the trunk? Why or why not?

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A:

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