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sudoku_naive.py
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sudoku_naive.py
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# Using NuSMV to solve a Sudoku problem.
N = 9
NS = 3
opt = False
def load_problem(file_name: str) -> [[int]]:
with open(file_name, 'r') as f:
rows = [(line.replace('\n', '').split(' '))[:N] for line in f.readlines()][:N]
f.close()
board = [[int(elem) for elem in col] for col in rows]
return board
def get_conflicts(idx) -> [int]:
row, col = divmod(idx, N)
row_conflicts = set(range(row * N, (row + 1) * N))
col_conflicts = set(range(col, N * N, N))
box_row, _ = divmod(row, NS)
box_col, _ = divmod(col, NS)
start = box_row * NS * N + box_col * NS
box_conflicts = []
for dx in range(NS):
for dy in range(NS):
box_conflicts.append(start + dx * N + dy)
box_conflicts = set(box_conflicts)
conflicts = list((row_conflicts.union(col_conflicts)).union(box_conflicts))
conflicts.remove(idx)
return conflicts
def gen_candidates(board: [[int]]) -> [[int]]:
candidates = [set() for _ in range(N * N)]
repeat = False
for i in range(N):
for j in range(N):
idx = i * N + j
if board[i][j] == 0:
if opt:
conflicts = set([board[to_row(con)][to_col(con)] for con in get_conflicts(idx)])
numbers = set(range(1, N + 1))
c = numbers - conflicts
if len(c) == 1:
board[i][j] = (list(c))[0]
repeat = True
candidates[idx] = c
else:
candidates[idx] = range(1, N + 1)
else:
candidates[idx] = [board[i][j]]
if opt and repeat:
return gen_candidates(board)
return candidates
def to_row(idx: int) -> int:
ret, _ = divmod(idx, N)
return ret
def to_col(idx: int) -> int:
_, ret = divmod(idx, N)
return ret
def gen_spec(board: [[int]]) -> str:
all_specs = []
for idx in range(N * N):
row, col = divmod(idx, N)
all_specs.extend(['board[%i] != board[%i]' % (idx, other)
for other in get_conflicts(idx) if other > idx])
return ' & '.join(all_specs)
def print_board(board: [[int or str]]):
for i in range(N):
print(' '.join(map(str, board[i])))
code = """-- auto generated model
MODULE main
VAR
board: array 0..80 of 1..9;
ASSIGN
%s
LTLSPEC
!G (%s);
"""
def gen_code(candidates: [[int]], spec: str) -> str:
assigns = ['board[%i] := {%s};' % (idx, ', '.join(map(str, candidates[idx]))) for idx in range(N * N)]
return code % ('\n'.join(assigns), spec)
if __name__ == '__main__':
import sys
if len(sys.argv) >= 2:
if len(sys.argv) >= 3:
opt = True if sys.argv[2] == '-on' else False
input_file = sys.argv[1]
else:
print('Usage: python %s <input_file> [-on | -off]')
sys.exit(1)
prob = load_problem(input_file)
# show problem
print('-> problem <-')
print_board(prob)
# construct model
src = gen_code(gen_candidates(prob), gen_spec(prob))
with open('tmp.smv', 'w') as f:
f.write(src)
f.close()
# call NuSMV
import os
print('running NuSMV...')
os.system('NuSMV -bmc tmp.smv > tmp.out')
print('done')
# read output
with open('tmp.out', 'r') as f:
content = f.read()
f.close()
# parse output
import re
pat = re.compile(r'board\[(?P<index>\d+)\] = (?P<val>[1-9])')
answer = [[0 for _ in range(N)] for _ in range(N)]
for match in pat.finditer(content):
idx = int(match.group('index'))
answer[to_row(idx)][to_col(idx)] = match.group('val')
# display answer
print('-> answer <-')
print_board(answer)