## dlx-rs

Implementation of dancing links in Rust

### 5 releases(1 stable)

 1.0.0 Mar 18, 2023 Jul 30, 2022 Jul 12, 2022 Jul 9, 2022 Jun 23, 2022

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# dlx_rs

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
• Aztec diamond
• 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 [i_1,...,i_N] and options [o_1,...,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.

This can be expressed in terms of a matrix, where each option covers the items for which the corresponding entry is 1, and doesn't if it is 0

``````     i1  i2  i3  i4  i5  i6  i7
o1   0   0   1   0   1   0   0
o2   1   0   0   1   0   0   0
o3   0   1   1   0   0   0   0
o4   1   0   0   1   0   1   0
o5   0   1   0   0   0   0   1
o6   0   0   0   1   1   0   1
``````

The exact cover problem is that of finding a collection of options such that a 1 appears exactly once in each column.

This is achieved in the case above by selecting options [o_1,o_4,o_5].

The code to solve this is

``````use dlx_rs::Solver;
let mut s = Solver::new(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);
``````