def naiive_backtrack(board_code):
"""Naiive backtracking algorithm used to find the solution to a board with missing clues.
Parameters
----------
board_code : string
Board code listed from top left to bottom right.
Returns
-------
string
Board code for solved board.
Raises
------
UnsolvableBoardException
If the board does not have a solution.
InvalidBoardException
If the board code is invalid.
"""
board = util.code_to_board(board_code)
if not util.board_is_valid(board):
raise util.InvalidBoardException
search_board = np.copy(board)
if util.board_is_solved(board):
return util.board_to_code(board)
position = 0
step = 0
while True:
step += 1
if position == 81:
if not util.board_is_solved(search_board):
raise util.InvalidBoardException # if we got here when solving there must have been an issue with the board code
print(f'Solved board in {step} steps')
return util.board_to_code(search_board)
x = util.to_x(position)
y = util.to_y(position)
if board[x][y] != 0:
position += 1
continue
while search_board[x][y] <= 9:
search_board[x][y] += 1
if util.position_is_valid(search_board, x, y):
position += 1
break
if search_board[x][y] == 10:
search_board[x][y] = 0
position -= 1
if position < 0:
raise util.UnsolvableBoardException
while board[util.to_x(position)][util.to_y(position)] != 0:
position -= 1
if position < 0:
raise util.UnsolvableBoardException
def naiive_backtrack_count(board_code):
"""Naiive backtracking algorithm used to count solutions to a board with missing clues.
Parameters
----------
board_code : string
Board code listed from top left to bottom right.
Returns
-------
int
The number of unique solutions the board has.
"""
board = util.code_to_board(board_code)
search_board = np.copy(board)
if util.board_is_solved(board):
return 1
position = 0
step = 0
solutions = 0
while True:
step += 1
if position == 81:
if not util.board_is_solved(search_board):
raise util.InvalidBoardException
solutions += 1
position -= 1
while board[util.to_x(position)][util.to_y(position)] != 0:
position -= 1
if position < 0:
print(f'found {solutions} solutions in {step} steps')
return solutions
x = util.to_x(position)
y = util.to_y(position)
if board[x][y] != 0:
position += 1
continue
while search_board[x][y] <= 9:
search_board[x][y] += 1
if util.position_is_valid(search_board, x, y):
position += 1
break
if search_board[x][y] == 10:
search_board[x][y] = 0
position -= 1
if position < 0:
print(f'found {solutions} solutions in {step} steps')
return solutions
while board[util.to_x(position)][util.to_y(position)] != 0:
position -= 1
if position < 0:
print(f'found {solutions} solutions in {step} steps')
return solutions
def test_position_is_valid():
board = util.code_to_board(boards['81'][0])
board[0][0] = -1
assert not util.position_is_valid(board, 0, 0)
board = util.code_to_board(boards['81'][0])
board[0][4] = board[0][0]
assert not util.position_is_valid(board, 0, 0)
assert not util.position_is_valid(board, 0, 4)
board = util.code_to_board(boards['81'][0])
board[4][0] = board[0][0]
assert not util.position_is_valid(board, 0, 0)
assert not util.position_is_valid(board, 4, 0)
board = util.code_to_board(boards['81'][0])
board[1][1] = board[0][0]
assert not util.position_is_valid(board, 0, 0)
assert not util.position_is_valid(board, 1, 1)
board = util.code_to_board(boards['81'][0])
for i in range(9 * 9):
x = util.to_x(i)
y = util.to_y(i)
assert util.position_is_valid(board, x, y)
def generate(filled_board):
positions = [(util.to_x(i), util.to_y(i)) for i in range(81)]
np.random.shuffle(positions)
board = np.copy(filled_board)
for x, y in tqdm(positions):
temp = board[x][y]
board[x][y] = 0
if dfs.test_unique(np.copy(board)):
continue
else:
board[x][y] = temp
return board
def test_code_to_board():
code = 3
with pytest.raises(util.InvalidBoardException) as err:
util.code_to_board(code)
assert f'Board code must be a string, got type {type(3)}' in str(err.value)
code = '33'
with pytest.raises(util.InvalidBoardException) as err:
util.code_to_board(code)
assert 'Board code must be 81 characters long' in str(err.value)
code = 'a' * 81
with pytest.raises(util.InvalidBoardException) as err:
util.code_to_board(code)
assert 'Board code must only contain numbers 0 - 9' in str(err.value)
code = '000304907830000000000600000050080000006250030000000806009000400000000001000023000'
board = util.code_to_board(code)
for i in range(9 * 9):
x = util.to_x(i)
y = util.to_y(i)
# remember we transpose the board
assert board[y][x] == int(code[i])
def test_coordinate_conversions():
for i in range(200):
assert util.to_x(i) == i % 9
assert util.to_y(i) == i // 9