Dancing Links

Dancing Links is a clever algorithm used for efficiently solving exact cover problems, where the goal is to select subsets that cover all elements exactly once. Imagine a group of people (elements) needing to be paired with activities (subsets) without overlaps. The algorithm utilizes a linked data structure, allowing it to quickly add and remove these associations while exploring possible solutions. As it searches for a solution, it "dances" between choices, backtracking smartly when a path doesn’t work. This method is particularly useful in puzzles like Sudoku, where it rapidly explores options and finds valid arrangements.