A simple brute-force Sudoku solver written in functional-programming style. This code is not aimed for speed, the goal is to write a clear, compact and (hopefully) pedagogical functional solution.

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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 constrains:
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:]))
``` |

To test the code create a text file containing the grid. Example (mysudoku.txt):

```
6 - - - - - - 8 3
- - 7 1 - - - - 4
- - 9 - - 2 7 - -
- - - 5 - 9 - - -
1 - - 3 4 8 - - 9
- - - 7 - 1 - - -
- - 5 9 - - 3 - -
3 - - - - 6 1 - -
7 6 - - - - - - 8
```

And then run:

```
$ python sudoku.py mysudoku.txt
```

Using a list to represent a Sudoku board is the most obvious option, but we could also have represented it as a dictionary of pairs (position, digit). Check here a possible solution using a dictionary as board.

Functional programming (FP) is an extremely powerful paradigm. Although Python is not a functional language (Haskell, OCaml, Scheme or Erlang are -more or less- pure FP languages), we can take advantage of some of its features (first-class functions, list comprehensions, the itertools module) to write nice functional constructions.

Here are some links on how to use Functional Programming with Python: