← All Solvers
🧩 Exact Cover
Band 10 — The Uranus transformer. Cover each element exactly once.
7
Ready
Sets available (each must be used at most once, each element covered exactly once)
Algorithm: Knuth's Algorithm X (Dancing Links)
Depth-first search that chooses an uncovered element, tries each set covering it, and recursively covers remaining elements. Dancing Links implements the matrix as circular doubly-linked lists for O(1) row/column removal.
Why This Matters
The Exact Cover transformer (Uranus) is the Omnitranslator — it finds the unique covering that explains all data. Sudoku, tiling, and the 72-band translation all reduce to exact cover.