Created
February 19, 2016 17:41
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Simple sudoku solver with froward checking and look ahead
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5 1 7 | 6 9 8 | 2 3 4 | |
2 8 9 | 1 3 4 | 7 5 6 | |
3 4 6 | 2 7 5 | 8 9 1 | |
- - - + - - - + - - - | |
6 7 2 | 8 4 9 | 3 1 5 | |
1 3 8 | 5 2 6 | 9 4 7 | |
9 5 4 | 7 1 3 | 6 8 2 | |
- - - + - - - + - - - | |
4 9 5 | 3 6 2 | 1 7 8 | |
7 2 3 | 4 8 1 | 5 6 9 | |
8 6 1 | 9 5 7 | 4 2 3 |
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import sys | |
from copy import deepcopy | |
def output(a): | |
sys.stdout.write(str(a)) | |
N = 9 | |
field = [[5,1,7,6,0,0,0,3,4], | |
[2,8,9,0,0,4,0,0,0], | |
[3,4,6,2,0,5,0,9,0], | |
[6,0,2,0,0,0,0,1,0], | |
[0,3,8,0,0,6,0,4,7], | |
[0,0,0,0,0,0,0,0,0], | |
[0,9,0,0,0,0,0,7,8], | |
[7,0,3,4,0,0,5,6,0], | |
[0,0,0,0,0,0,0,0,0]] | |
def print_field(field): | |
for i in range(N): | |
for j in range(N): | |
cell = field[i][j] | |
if cell == 0 or isinstance(cell, set): | |
output('.') | |
else: | |
output(cell) | |
if (j + 1) % 3 == 0 and j < 8: | |
output(' |') | |
if j != 8: | |
output(' ') | |
output('\n') | |
if (i + 1) % 3 == 0 and i < 8: | |
output("- - - + - - - + - - -\n") | |
def read(field): | |
""" Read field into state (replace 0 with set of possible values) """ | |
state = deepcopy(field) | |
for i in range(N): | |
for j in range(N): | |
cell = state[i][j] | |
if cell == 0: | |
state[i][j] = set(range(1,10)) | |
return state | |
state = read(field) | |
def done(state): | |
""" Are we done? """ | |
for row in state: | |
for cell in row: | |
if isinstance(cell, set): | |
return False | |
return True | |
def propagate_step(state): | |
""" Propagate one step """ | |
new_units = False | |
for i in range(N): | |
row = state[i] | |
values = set([x for x in row if not isinstance(x, set)]) | |
for j in range(N): | |
if isinstance(state[i][j], set): | |
state[i][j] -= values | |
if len(state[i][j]) == 1: | |
state[i][j] = state[i][j].pop() | |
new_units = True | |
elif len(state[i][j]) == 0: | |
return False, None | |
for j in range(N): | |
column = [state[x][j] for x in range(N)] | |
values = set([x for x in column if not isinstance(x, set)]) | |
for i in range(N): | |
if isinstance(state[i][j], set): | |
state[i][j] -= values | |
if len(state[i][j]) == 1: | |
state[i][j] = state[i][j].pop() | |
new_units = True | |
elif len(state[i][j]) == 0: | |
return False, None | |
for x in range(3): | |
for y in range(3): | |
values = set() | |
for i in range(3*x, 3*x+3): | |
for j in range(3*y, 3*y+3): | |
cell = state[i][j] | |
if not isinstance(cell, set): | |
values.add(cell) | |
for i in range(3*x, 3*x+3): | |
for j in range(3*y, 3*y+3): | |
if isinstance(state[i][j], set): | |
state[i][j] -= values | |
if len(state[i][j]) == 1: | |
state[i][j] = state[i][j].pop() | |
new_units = True | |
elif len(state[i][j]) == 0: | |
return False, None | |
return True, new_units | |
def propagate(state): | |
""" Propagate until we reach a fixpoint """ | |
while True: | |
solvable, new_unit = propagate_step(state) | |
if not solvable: | |
return False | |
if not new_unit: | |
return True | |
def solve(state): | |
""" Solve sudoku """ | |
solvable = propagate(state) | |
if not solvable: | |
return None | |
if done(state): | |
return state | |
for i in range(N): | |
for j in range(N): | |
cell = state[i][j] | |
if isinstance(cell, set): | |
for value in cell: | |
new_state = deepcopy(state) | |
new_state[i][j] = value | |
solved = solve(new_state) | |
if solved is not None: | |
return solved | |
return None | |
print_field(solve(state)) |
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