Counting Candy Crush configurations.
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| Title: | Counting Candy Crush configurations. |
|---|---|
| Authors: | Hamilton, Adam1 (AUTHOR) adam.h.hamilton@adelaide.edu.au, Nguyen, Giang T.1 (AUTHOR) giang.nguyen@adelaide.edu.au, Roughan, Matthew1 (AUTHOR) matthew.roughan@adelaide.edu.au |
| Source: | Discrete Applied Mathematics. May2021, Vol. 295, p47-56. 10p. |
| Subjects: | Candy, Polynomial approximation, Polynomial time algorithms, Counting, Hypergraphs |
| Abstract: | A k -stable c -coloured Candy Crush grid is a weak proper c -colouring of a particular type of k -uniform hypergraph. In this paper we introduce a fully polynomial randomised approximation scheme (FPRAS) which counts the number of k -stable c -coloured Candy Crush grids of a given size (m , n) for certain values of c and k. We implemented this algorithm on Matlab, and found that in a Candy Crush grid with 7 available colours there are approximately 4. 3 × 1 0 61 3-stable colourings. (Note that, typical Candy Crush games are played with 6 colours and our FPRAS is not guaranteed to work in expected polynomial time with k = 3 and c = 6.) We also discuss the applicability of this FPRAS to the problem of counting the number of weak c -colourings of other, more general hypergraphs. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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