AlgorithmX Problems and Solvers

Trying to efficiently write a program to provide me solutions to Dragonfjord's "A Puzzle a Day" has lead me down a slightly mind boggling path of learning what about Donald Knuth's AlgorithmX, as well as Exact Cover, and Dancing Link algorithms. I am definitely not an expert in this algorithm, but was able to get something working with the help of Ali Assaf's post and implementation of AlgorithmX.

The examples in this repository can solve Sudoku and Pentomino puzzles relativly quickly. While all these examples work in Python3, I highly recomend using pypy as it is much faster for these types of problems.

Example Pentomino Solver

from pentomino import Puzzle

BOARD = """
⬛⬛🟫🟫🟫⬛⬛
🟫🟫🟫🟫🟫🟫🟫
🟫🟫🟫🟫🟫🟫🟫
🟫🟫🟫⬛⬛⬛⬛
"""
PIECES = """
🟪🟪🟪 ⬛🟦⬛ ⬛🟥🟥 🟨🟨⬛ 🟩🟩🟩
⬛🟪⬛ 🟦🟦🟦 🟥🟥⬛ 🟨🟨⬛ ⬛⬛🟩
"""

solver = Puzzle(BOARD, PIECES, allow_reflections=True)
solutions = list(solver.find_solutions())
for board in solutions:
    print(board)

>>>
⬛⬛🟪🟩🟩⬛⬛
🟦🟪🟪🟪🟩🟨🟨
🟦🟦🟥🟥🟩🟨🟨
🟦🟥🟥⬛⬛⬛⬛

Example Dragonfjord Command Line Solver

Only show a single random solution is displayed when running from the command line as seeing all solutions was a bit unwieldy.

> python3 dragonfjord.py --month=5 --day=29
🟦🟦🟦🟦⬛🟧⬛
🟨🟦🟨🟧🟧🟧⬛
🟨🟨🟨🟧⬜⬜⬜
🟩🟩🟩⬜⬜🟫🟫
🟩🟪🟪🟥🟫🟫🟫
🟩🟪🟪🟥🟥🟥🟥
⬛🟪🟪⬛⬛⬛⬛

Found 66 solutions after 5.5s.

Example Sudoku Solver

This solver is not my code, but Ali Assaf's. Copied from his posted example, cleaned up Python 3 styles, and commented to help me understand. I included it in this repo to hopefully help other's learn this algorithm usage as well.

from sudoku import solve_sudoku

grid = [
    [0,1,0, 0,0,0, 0,3,0],
    [9,0,0, 0,2,0, 1,5,0],
    [0,0,0, 1,0,0, 0,6,4],
    [7,0,0, 0,0,0, 0,0,0],
    [8,0,0, 3,9,0, 5,0,6],
    [0,0,0, 0,0,0, 0,4,9],
    [5,0,0, 0,7,1, 0,0,0],
    [0,0,8, 0,0,0, 0,9,1],
    [0,4,0, 2,6,0, 0,0,5]]
for solution in solve_sudoku(grid):
    print(*solution, sep='\n')
    print()

>>>
[4, 1, 2, 7, 5, 6, 9, 3, 8]
[9, 8, 6, 4, 2, 3, 1, 5, 7]
[3, 5, 7, 1, 8, 9, 2, 6, 4]
[7, 9, 1, 6, 4, 5, 8, 2, 3]
[8, 2, 4, 3, 9, 7, 5, 1, 6]
[6, 3, 5, 8, 1, 2, 7, 4, 9]
[5, 6, 3, 9, 7, 1, 4, 8, 2]
[2, 7, 8, 5, 3, 4, 6, 9, 1]
[1, 4, 9, 2, 6, 8, 3, 7, 5]

Thanks To

Donald Knuth for coming up with AlgorithmX.
Ali Assaf for the short implementation of AlgorithX as well as a great write up and example.

License

GNU General Public License http://www.gnu.org/licenses/

pkkid / python-algorithmx