Alternative Approach to Achieve a Solution of Derangement Problems by Dynamic Programming
Derangement is one well-known problem in the filed of probability theory. An instance of a derangement problem contains a finite collection C of n paired objects, C = {(x1, y1), …, (xn, yn)}. The derangement problem asks how many ways to generate a new collection C′ ≠ C such that for each (xi, yj )...
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| Format: | Conference or Workshop Item |
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2023
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| Online Access: | https://repository.li.mahidol.ac.th/handle/123456789/82651 |
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| Institution: | Mahidol University |
| Summary: | Derangement is one well-known problem in the filed of probability theory. An instance of a derangement problem contains a finite collection C of n paired objects, C = {(x1, y1), …, (xn, yn)}. The derangement problem asks how many ways to generate a new collection C′ ≠ C such that for each (xi, yj ) ∈ C′, i ≠ j. We propose an efficient dynamic programming algorithm that divides an instance of the derangement problem into several subproblems. During a recursive process of unrolling a subproblem, there exists a repeated procedure that allows us to make a use of a subsolution that has already been computed. We present the methodology to formulate a concept of this subproblem as well as parts of designing and analyzing an efficiency of the proposed algorithm. |
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