An efficient solution to the exact cover problem can be useful in many situations. In this problem, you are welcome to use Knuth's Algorithm X (utilizing the Dancing Links technique), or any other solution.
The exact cover problem is specified here by a row vector, u, representing the universe, and a cell array, s, containing the sets (row vectors) with which to try to exactly cover the respective universe. Given u and s, return x, a cell array containing one or more sets from s that exactly cover u. If no solution exists, return an empty cell array.
For simplicity, you may assume that all universes consist of integers and that all sets in s are subsets of the respective universes. Solutions may not be unique.
Example:
u = 1:7;
s = {[1 4 7] [1 4] [4 5 7] [3 5 6] [2 3 6 7] [2 7]};
x = {[1 4] [3 5 6] [2 7]}
Solve

Solution Stats

17 Solutions

8 Solvers

Last Solution submitted on Aug 22, 2025

Last 200 Solutions

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers8

Tim Ramon Villamangca Stefan Abendroth Hongsheng Yu

Suggested Problems

More from this Author45

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!