CayleyR Package Solves TopSpin Puzzle Using Cycle Intersection

Solving complex permutation puzzles, such as the TopSpin(n,k), can be approached using graph theory. The CayleyR R package offers a novel method to tackle these challenges by identifying cycle intersections within Cayley graphs. This package is built upon an iterative bidirectional search algorithm. The core of the algorithm involves generating random operation sequences from both the starting and desired permutation states, which in turn create cycles within the Cayley graph of the symmetric group Sn. If these cycles intersect, a direct solution path is found. If not, a distance-guided bridge selection strategy is used to narrow the gap, and the process is repeated. The CayleyR implementation combines a C++ hash-indexed state store with optional Vulkan GPU acceleration, making it an efficient tool for combinatorial problem-solving.