'''
Brute-force, backtracking Sudoku solver in about fifteen lines.
Works on Python 2.6 and Python 3.
'''
def solve(s):
'''
Solve a Sudoku:
- Accepts s, a sequence of 81 integers from 0 to 9 in row of
column order, zeros indicating the cells to fill.
- Returns the first found solution as a sequence of 81 integers in
the 1 to 9 interval (same row or column order than input), or None
if no solution exists.
'''
try:
i = s.index(0)
except ValueError:
# No empty cell left: solution found
return s
c = [s[j] for j in range(81)
if not ((i-j)%9 * (i//9^j//9) * (i//27^j//27 | (i%9//3^j%9//3)))]
for v in range(1, 10):
if v not in c:
r = solve(s[:i]+[v]+s[i+1:])
if r is not None:
return r
#-------------------------------------------------------------------------------
# Let's test it!
#
if __name__ == '__main__':
class Sudoku(list):
'''Sudokus with nicer IO'''
def __init__(self, content):
list.__init__(self, [int(i) for i in content.split()]
if isinstance(content, str) else content)
def __str__(self):
return '\n'.join(
' '.join([(str(j) if j != 0 else '-')
for j in self[i*9:(i+1)*9]]) for i in range(9))
problem = Sudoku('''
5 3 0 0 7 0 0 0 0
6 0 0 1 9 5 0 0 0
0 9 8 0 0 0 0 6 0
8 0 0 0 6 0 0 0 3
4 0 0 8 0 3 0 0 1
7 0 0 0 2 0 0 0 6
0 6 0 0 0 0 2 8 0
0 0 0 4 1 9 0 0 5
0 0 0 0 8 0 0 7 9
''')
solution = Sudoku('''
5 3 4 6 7 8 9 1 2
6 7 2 1 9 5 3 4 8
1 9 8 3 4 2 5 6 7
8 5 9 7 6 1 4 2 3
4 2 6 8 5 3 7 9 1
7 1 3 9 2 4 8 5 6
9 6 1 5 3 7 2 8 4
2 8 7 4 1 9 6 3 5
3 4 5 2 8 6 1 7 9
''')
result = Sudoku(solve(problem))
print('==== Problem ====\n{0}\n\n=== Solution ====\n{1}'.format(
problem, result))
assert(result == solution)
