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The PARTITION problem is: Given a set S of n integers, can it be split into two subsets with equal sums? That is, are

The PARTITION problem is: Given a set S of n integers, can it be split into two subsets with equal sums? That

The PARTITION problem is: Given a set S of n integers, can it be split into two subsets with equal sums? That is, are there subsets A and B such that AUB= S, AnB = 0, and a Aa= bEB b? For example, for S {1,2,3}, then the answer is YES, because A = {1, 2} and B = {3} give a partition. However, if S = {1, 2, 3, 100}, the answer is NO. = (a) Describe and analyze an algorithm to solve PARTITION in time O(nM), where n is the size of the input set and M is the sum of the absolute values of its elements. Hint: Use an algorithm design strategy we've learned earlier this class. (b) Why doesn't this algorithm imply that P = NP?

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