Question

The post office sells stamps of a variety of different denominations (values), and different sizes. Consider a set of n stamps, where each stamp i has a specific denomination di and a size si . All denominations are distinct. All input numbers are positive integers. We can use stamp denominations multiple times. When buying stamps that total to a given postage amount P, we want to minimize the total size of the stamps (to leave the most addressing space on the envelope).

(a) Design and write, in pseudocode, a dynamic programming algorithm that will, given the information about n stamps (denominations {di} and sizes {si}) and a postage amount P, find the minimum total size of stamps that will add to exactly P (if such a set exists).

(b) Adapt your algorithm from (a) to find the set of stamps that produces the minimum.

(c) Analyze the running time (in terms of input size) of your algorithm from (a).

Answer 1

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