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 4.3×1061 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.
Submitted Version (
Free)
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call