def impossible_test(self):
# impossible
puzzles = [
# From https://norvig.com/sudoku.html -> column 4, no 1 possible because of triple 5-6 doubles and triple 1s
'.....5.8....6.1.43..........1.5........1.6...3.......553.....61........4.........',
# obvious doubles
'12.......34...............5...........5..........................................',
'11.......34...............5......................................................',
]
for puzzle in puzzles:
puzzle = str2grid(puzzle)
s = Sudoku(puzzle)
s.flush_candidates()
self.assertFalse(s.check_possible()[0])
# possible
puzzles = [
'280070309600104007745080006064830100102009800000201930006050701508090020070402050',
'000010030009005008804006025000000600008004000120087000300900200065008000900000000',
'1.....................................5..........................................',
]
for puzzle in [puzzles[1]]:
puzzle = str2grid(puzzle)
s = Sudoku(puzzle)
s.flush_candidates()
self.assertTrue(s.check_possible()[0])
def test_impossible(self):
# impossible
puzzles = [
'.....5.8....6.1.43..........1.5........1.6...3.......553.....61........4.........',
'12.......34...............5...........5..........................................',
'11.......34...............5...........5..........................................',
]
for puzzle in puzzles:
puzzle = SudokuGrid(puzzle)
s = Sudoku(puzzle)
s.flush_candidates()
self.assertFalse(s.check_possible()[0])
# possible
puzzles = [
'280070309600104007745080006064830100102009800000201930006050701508090020070402050',
'000010030009005008804006025000000600008004000120087000300900200065008000900000000',
'1.....................................5..........................................',
]
for puzzle in [puzzles[1]]:
puzzle = SudokuGrid(puzzle)
s = Sudoku(puzzle)
s.flush_candidates()
self.assertTrue(s.check_possible()[0])
def solveSudoku(grid, num_boxes=SIZE, verbose=True, all_solutions=False):
"""
idea based on https://dev.to/aspittel/how-i-finally-wrote-a-sudoku-solver-177g
Try each step until failure, and repeat:
1) write numbers with only have 1 option
2) write candidates with only 1 option/ 2 pairs
3) with multiple options, take a guess and branch (backtrack)
"""
def solve(game, depth=0, progress_factor=1):
nonlocal calls, depth_max, progress, progress_update, update_increment
calls += 1
depth_max = max(depth, depth_max)
solved = False
while not solved:
solved = True # assume solved
edited = False # if no edits, either done or stuck
for i in range(game.n):
for j in range(game.n):
if game.grid[i][j] == 0:
solved = False
options = game.candidates[i][j]
if len(options) == 0:
progress += progress_factor
return False # this call is going nowhere
elif len(options) == 1: # Step 1
game.place_and_erase(i, j,
list(options)[0]) # Step 2
# game.flush_candidates() # full grid cleaning
edited = True
if not edited: # changed nothing in this round -> either done or stuck
if solved:
progress += progress_factor
solution_set.append(grid2str(game.grid.copy()))
return True
else:
# Find the box with the least number of options and take a guess
# The place_and_erase() call changes this dynamically
min_guesses = (game.n + 1, -1)
for i in range(game.n):
for j in range(game.n):
options = game.candidates[i][j]
if len(options) < min_guesses[0] and len(
options) > 1:
min_guesses = (len(options), (i, j))
i, j = min_guesses[1]
options = game.candidates[i][j]
# backtracking check point:
progress_factor *= (1 / len(options))
for y in options:
game_next = deepcopy(game)
game_next.place_and_erase(i, j, y)
# game_next.flush_candidates() # full grid cleaning
solved = solve(game_next,
depth=depth + 1,
progress_factor=progress_factor)
if solved and not all_solutions:
break # return 1 solution
if verbose and progress > progress_update:
print("%.1f" % (progress * 100), end='...')
progress_update = ((progress // update_increment) +
1) * update_increment
return solved
return solved
calls, depth_max = 0, 0
progress, update_increment, progress_update = 0.0, 0.01, 0.01
solution_set = []
game = Sudoku(grid)
game.flush_candidates() # check for obvious candidates
possible, message = game.check_possible()
if not possible:
print('Error on board. %s' % message)
info = {
'calls': calls,
'max depth': depth_max,
'nsolutions': len(solution_set),
}
return solution_set, False, info
if verbose:
print("solving: ", end='')
solve(game, depth=0)
if verbose:
print("100.0")
solved = (len(solution_set) >= 1)
info = {
'calls': calls,
'max depth': depth_max,
'nsolutions': len(solution_set),
}
return solution_set, solved, info
