DLX (Dancing Links X)

Dancing Links (DLX) is a technique used to efficiently solve combinatorial problems like exact cover, where you select subsets that cover all elements without overlaps. It employs a specialized data structure—doubly linked lists—to represent the problem's options. When searching for a solution, DLX rapidly adds or removes options by updating pointers, allowing backtracking without rebuilding the entire structure. The "dancing" refers to the way links are dynamically reconfigured during problem-solving. This approach significantly speeds up processes like solving Sudoku, polyomino tilings, and other constraint-based puzzles.