11/21/2022 0 Comments Games like minesweeper![]() However, there is an argument that, if the minesweeper board is already known to be consistent, solving it is only guaranteed to be co-NP-complete, and might be (or not be) NP-complete.Īnd here is the raining defending Minesweeper world rekord holder Kamil Muranski performs his skillful play. This transforms into the fact that, in its general formulation, the minesweeper is indeed algorithmically NP-complete. This is true even for binary integer programming where variables can only be 0 or 1 rather than arbitrary integers. Unlike simple linear programming, integer programming problems are typically NP-hard. Algorithmic solutions to these problems are typically sought with the use of integer linear programming. In fact, the minesweeper is one of the classical board puzzles based on algebras of binary variables. What does all of this beautiful mathematics says to a passionate gamer? Namely, what would be a good algorithm for solving the puzzle, and is the solution computationally hard? Teytaud “Combining Myopic Optimization and Tree Search: Application to MineSweeper”.Īs for games like minesweeper in general, some of them were found to be connected with percolation theory (which is one of the most fashionable branches of probability at the moment), as well as with Markov decision processes, and computational complexity studies.Ī good example of research in this direction is a paper “The Minesweeper game: Percolation and Complexity” written by Elchanan Mossel from Microsoft Research. Some advanced studies exploring different algorithms and their relation to probabilistic models of the Minesweeper can be seen in the paper “Optimistic Heuristics for MineSweeper” by O. The object of each puzzle is to use logic to deduce the locations of the 10 battleships hidden in the 10-by-10 ocean grid. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |