Expand description
dlx_rs is a Rust library for solving exact cover/constraint problems problems using Knuth’s Dancing Links (DLX) algorithm.
It also provides specific interfaces for some common exact cover problems, specifically:
- arbitrary Sudokus
- N queens problem
- Pentomino tilings (TODO)
- graph colouring (TODO)
Setting up a general constraint problem
A constraint problem may be expressed in terms of a number of items [i1,…,i_N] and options [o1,…,o_M]. Each of the options “covers” some of the items, e.g. picking option o1 might involve selecting items i1, i5, and i7. The constraint problem is to find a collection of options which cover all of the items exactly once.
We can do this in code as
use dlx_rs::Solver;
let mut s = Solver::new(7);
s.add_option("o1",&[3,5]);
s.add_option("o2",&[1,5,7]);
s.add_option("o3",&[2,3,6]);
s.add_option("o4",&[1,4,6]);
s.add_option("o5",&[2,7]);
s.add_option("o6",&[4,5,7]);
let sol = s.next().unwrap();
assert_eq!(sol,["o4","o5","o1"]);
Solving a Sudoku
use dlx_rs::Sudoku;
// Define sudoku grid, 0 is unknown number
let sudoku = vec![
5, 3, 0, 0, 7, 0, 0, 0, 0,
6, 0, 0, 1, 9, 5, 0, 0, 0,
0, 9, 8, 0, 0, 0, 0, 6, 0,
8, 0, 0, 0, 6, 0, 0, 0, 3,
4, 0, 0, 8, 0, 3, 0, 0, 1,
7, 0, 0, 0, 2, 0, 0, 0, 6,
0, 6, 0, 0, 0, 0, 2, 8, 0,
0, 0, 0, 4, 1, 9, 0, 0, 5,
0, 0, 0, 0, 8, 0, 0, 7, 9,
];
// Create new sudoku from this grid
let mut s = Sudoku::new_from_input(&sudoku);
let true_solution = vec![
5, 3, 4, 6, 7, 8, 9, 1, 2,
6, 7, 2, 1, 9, 5, 3, 4, 8,
1, 9, 8, 3, 4, 2, 5, 6, 7,
8, 5, 9, 7, 6, 1, 4, 2, 3,
4, 2, 6, 8, 5, 3, 7, 9, 1,
7, 1, 3, 9, 2, 4, 8, 5, 6,
9, 6, 1, 5, 3, 7, 2, 8, 4,
2, 8, 7, 4, 1, 9, 6, 3, 5,
3, 4, 5, 2, 8, 6, 1, 7, 9,
];
// Checks only solution is true solution
let solution = s.next().unwrap();
assert_eq!(solution, true_solution);
assert_eq!(s.next(), None);