Puzzle Solver

About

Solve logic puzzles by simply describing the puzzle's rules as constraints. This is suitable for solving puzzles with integer variables such as Sudoku, Killer Sudoku, Kakuro, and Zebra puzzles.

The puzzle solver maintains a list of candidates for each puzzle variable. It solves puzzles by eliminating candidates that would lead to a contradiction and taking any forced moves that were exposed in the process. This is repeated until it gets stuck, whereupon it will perform a backtracking search -- it will assign a single variable and continue with the candidate elimination step again.

Examples

A few example programs are provided in the tests/ directory:

• Hidato - https://en.wikipedia.org/wiki/Hidato
• Kakuro - https://en.wikipedia.org/wiki/Kakuro
• Killer Sudoku - https://en.wikipedia.org/wiki/Killer_sudoku
• Magic Square - https://en.wikipedia.org/wiki/Magic_square
• N-queens problem - https://en.wikipedia.org/wiki/Eight_queens_puzzle
• Send More Money - https://en.wikipedia.org/wiki/Verbal_arithmetic
• Sudoku - https://en.wikipedia.org/wiki/Sudoku
• Sujiko - https://en.wikipedia.org/wiki/Sujiko
• Zebra puzzle (Einstein's riddle) - https://en.wikipedia.org/wiki/Zebra_Puzzle

To clone this repository, run:

git clone https://github.com/wangds/puzzle-solver.git

Then build the library and run the test programs using Cargo.

cargo test --test sudoku -- --nocapture

Basic Usage

We will demonstrate how to solve the equation "SEND + MORE = MONEY". Add Puzzle Solver as a dependency to your project's Cargo.toml:

[dependencies]
puzzle-solver = "0.2"

Import the library in your project, e.g.:

extern crate puzzle_solver;

use puzzle_solver::Puzzle;

First, we create a puzzle object and the 8 puzzle variables (S,E,N,D,M,O,R,Y).

let mut puzzle = Puzzle::new();
let vars = puzzle.new_vars_with_candidates_1d(8, &[0,1,2,3,4,5,6,7,8,9]);
let (s, e, n, d) = (vars[0], vars[1], vars[2], vars[3]);
let (m, o, r, y) = (vars[4], vars[5], vars[6], vars[7]);

All eight puzzle variables have been initialised to be any number between 0 and 9. However, we know that the numbers are not allowed to begin with zero, so we remove the choices of S = 0 and M = 0.

puzzle.remove_candidates(s, &[0]);
puzzle.remove_candidates(m, &[0]);

We add the constraint that the variables should be all different:

puzzle.all_different(&vars);

We write the equation as another puzzle constraint:

puzzle.equals(
    (1000 * s + 100 * e + 10 * n + d) + (1000 * m + 100 * o + 10 * r + e),
    10000 * m + 1000 * o + 100 * n + 10 * e + y);

And we solve!

let solution = puzzle.solve_any().expect("solution");
assert_eq!(solution[o], 0);
assert_eq!(solution[m], 1);
assert_eq!(solution[y], 2);
assert_eq!(solution[e], 5);
assert_eq!(solution[n], 6);
assert_eq!(solution[d], 7);
assert_eq!(solution[r], 8);
assert_eq!(solution[s], 9);

Documentation

• Documentation.

Author

David Wang