The PARTITION problem is: Given a set S of n integers, can it be split into...
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The PARTITION problem¹ 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 Σa€ Aa= ΣbEB 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? The PARTITION problem¹ 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 Σa€ Aa= ΣbEB 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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a One approach to solve the PARTITION problem with a time complexity of OnM is by using dynamic prog... View the full answer
Related Book For
Algorithm Design And Applications
ISBN: 9781118335918
1st Edition
Authors: Michael T. Goodrich, Roberto Tamassia
Posted Date:
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