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)
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Author:James Kurose, Keith Ross
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Chapter1: Computer Networks And The Internet
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Transcribed Image Text:**Partitioning Positive Integers into Equal Sum Subsets**
Given \( n \) positive integers, the task is to partition them into two disjoint subsets such that the sum of the elements in each subset is equal. It is important to note that a solution may not always exist for every set of integers. The challenge is to design an exhaustive search algorithm to solve this problem while minimizing the number of subsets generated by the algorithm.
**Understanding the Problem:**
- The problem involves dividing a set of integers into two parts with equal sums.
- Not all sets have a valid partition satisfying the conditions.
**Algorithm Design:**
- An exhaustive search approach is proposed.
- The objective is to explore possible subsets systematically.
- The focus is on minimizing the generation of unnecessary subsets, optimizing the process.
This is a classic problem in computer science that deals with decision-making and optimization, specifically focusing on partition problems under subset constraints.
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