#!/usr/bin/python
"""Simple brute-force Sudoku solver (FP style)."""
import re
import sys
def copy_board(board, values):
"""Return a copy of board setting new squares from values dictionary."""
return [[values.get((r, c), board[r][c]) for c in range(9)] for r in range(9)]
def get_alternatives_for_square(board, nrow, ncolumn):
"""Return sequence of valid digits for square (nrow, ncolumn) in board."""
def _box(pos, size=3):
start = (pos // size) * size
return range(start, start + size)
nums_in_box = [board[r][c] for r in _box(nrow) for c in _box(ncolumn)]
nums_in_row = [board[nrow][c] for c in range(9)]
nums_in_column = [board[r][ncolumn] for r in range(9)]
groups = [filter(bool, x) for x in [nums_in_box, nums_in_row, nums_in_column]]
return sorted(set(range(1, 10)) - reduce(set.union, map(set, groups)))
def solve(board):
"""Return a solved Sudoku board (None if it has no solution)."""
for nrow, ncolumn in ((r, c) for r in range(9) for c in range(9)):
if board[nrow][ncolumn]:
continue # digit set, move to the next square
for test_digit in get_alternatives_for_square(board, nrow, ncolumn):
test_board = copy_board(board, {(nrow, ncolumn): test_digit})
solved_board = solve(test_board)
if solved_board:
# return the solved board all the way up to break recursion
return solved_board
return
# all squares are filled so this must be the first solution.
return board
def lines2board(lines):
"""Parse a text board setting 0's for empty squares and ignoring all spaces."""
return [[(int(c) if c in "123456789" else 0) for c in re.sub("\s+", "", line)]
for line in lines if line.strip()]
def main(args):
"""Solve a Sudoku board read from a file."""
from pprint import pprint
path, = args
board = lines2board(open(path))
pprint(board)
pprint(solve(board))
if __name__ == '__main__':
sys.exit(main(sys.argv[1:]))
