Exact cover problem

The exact cover problem involves selecting a subset of options from a larger collection, such that every element in a set is covered exactly once—no overlaps or omissions. Imagine you have a set of items and various groups that each contain some of these items. The goal is to find a combination of these groups that together include all items exactly once. This problem appears in puzzles, scheduling, and resource allocation, where precise, non-overlapping coverage is needed. It requires strategic selection to ensure all elements are covered precisely, without duplication or gaps.