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Given n positive integers, partition them into two disjoint subsets with the same sum of their elements. (Note that the problem does not always have a solution.) Design an exhaustive search algorithm for this problem. Try to minimize the number of subsets the algorithm needs to generate.

Given n positive integers, partition them into two disjoint subsets with the same sum of their elements. (Note that the problem does not always have a solution.) Design an exhaustive search algorithm for this problem. Try to minimize the number of subsets the algorithm needs to generate.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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**Partition Problem and Algorithm Design** **Problem Statement:** Given \( n \) positive integers, partition them into two disjoint subsets such that the sum of the elements in each subset is equal. Note that the problem does not always have a solution. **Algorithm Design Task:** Design an exhaustive search algorithm to solve this problem. The goal is to minimize the number of subsets the algorithm needs to generate. **Considerations:** - The algorithm should systematically explore possible subset combinations. - Since finding such partitions can be computationally expensive due to the nature of exhaustive search, optimizing the search process to reduce the number of subsets generated is critical. - Ensure the algorithm can handle cases where no solution exists by checking all possibilities or implementing early stopping conditions when infeasibility is determined.
Transcribed Image Text:**Partition Problem and Algorithm Design** **Problem Statement:** Given \( n \) positive integers, partition them into two disjoint subsets such that the sum of the elements in each subset is equal. Note that the problem does not always have a solution. **Algorithm Design Task:** Design an exhaustive search algorithm to solve this problem. The goal is to minimize the number of subsets the algorithm needs to generate. **Considerations:** - The algorithm should systematically explore possible subset combinations. - Since finding such partitions can be computationally expensive due to the nature of exhaustive search, optimizing the search process to reduce the number of subsets generated is critical. - Ensure the algorithm can handle cases where no solution exists by checking all possibilities or implementing early stopping conditions when infeasibility is determined.
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