import re
import sys
def copy_board(board, sets):
"""Return a copy of board setting new squares from 'sets' dictionary."""
return [[sets.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(idx, size=3):
"""Return indexes to cover a box (3x3 sub-matrix of a board)."""
start = (idx // 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)]
nums = nums_in_box + nums_in_row + nums_in_column
return sorted(set(range(1, 9+1)) - set(nums))
def get_more_constrained_square(board):
"""Get the square in board with more constrains (less alternatives)."""
ranges = ((x, y) for x in range(9) for y in range(9))
constrains = [(len(get_alternatives_for_square(board, r, c)), (r, c))
for (r, c) in ranges if not board[r][c]]
if not constrains:
return
return min(constrains)[1]
def solve(board):
"""Return a solved Sudoku board (None if no solution was found)."""
pos = get_more_constrained_square(board)
if not pos:
return board # all squares are filled, so this board is the solution
nrow, ncolumn = pos
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 solved_board
def lines2board(lines):
"""Parse a text board stripping spaces and setting 0's for empty squares."""
spaces = re.compile("\s+")
return [[(int(c) if c in "123456789" else 0) for c in spaces.sub("", line)]
for line in lines if line.strip()]
def main(args):
"""Solve a Sudoku board read from a text 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:]))
Diff to Previous Revision
--- revision 8 2010-04-17 15:06:23
+++ revision 9 2010-04-22 18:04:35
@@ -1,13 +1,8 @@
-"""Simple brute-force Sudoku solver (FP style)."""
import re
import sys
-def first(it, default=None):
- """Return first element in iterator (default if exhausted)."""
- return next(it, default)
-
def copy_board(board, sets):
- """Return a copy of board setting new squares from 'values' dictionary."""
+ """Return a copy of board setting new squares from 'sets' dictionary."""
return [[sets.get((r, c), board[r][c]) for c in range(9)] for r in range(9)]
def get_alternatives_for_square(board, nrow, ncolumn):
@@ -21,22 +16,30 @@
nums_in_column = [board[r][ncolumn] for r in range(9)]
nums = nums_in_box + nums_in_row + nums_in_column
return sorted(set(range(1, 9+1)) - set(nums))
+
+def get_more_constrained_square(board):
+ """Get the square in board with more constrains (less alternatives)."""
+ ranges = ((x, y) for x in range(9) for y in range(9))
+ constrains = [(len(get_alternatives_for_square(board, r, c)), (r, c))
+ for (r, c) in ranges if not board[r][c]]
+ if not constrains:
+ return
+ return min(constrains)[1]
def solve(board):
"""Return a solved Sudoku board (None if no solution was found)."""
- pos = first((r, c) for r in range(9) for c in range(9) if not board[r][c])
+ pos = get_more_constrained_square(board)
if not pos:
- # all squares are filled, so this board is the solution
- return board
+ return board # all squares are filled, so this board is the solution
nrow, ncolumn = pos
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:
+ if solved_board:
return solved_board
def lines2board(lines):
- """Parse a text board setting 0's for empty squares."""
+ """Parse a text board stripping spaces and setting 0's for empty squares."""
spaces = re.compile("\s+")
return [[(int(c) if c in "123456789" else 0) for c in spaces.sub("", line)]
for line in lines if line.strip()]
