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Sudoku_CSP.py
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Sudoku_CSP.py
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import numpy as np
import time
import copy
start_time = time.time()
end_time = 0
backtracks = 0
recursion_count = 0
peer_dict = {}
row_list = []
col_list = []
square_list = []
unit_list = []
# #easy
# sudoku = [['7', '9', '0', '4', '0', '2', '3', '8', '1'],
# ['5', '0', '3', '0', '0', '0', '9', '0', '0'],
# ['0', '0', '0', '0', '3', '0', '0', '7', '0'],
# ['0', '0', '0', '0', '0', '5', '0', '0', '2'],
# ['9', '2', '0', '8', '1', '0', '7', '0', '0'],
# ['4', '6', '0', '0', '0', '0', '5', '1', '9'],
# ['0', '1', '0', '0', '0', '0', '2', '3', '8'],
# ['8', '0', '0', '0', '4', '1', '0', '0', '0'],
# ['0', '0', '9', '0', '8', '0', '1', '0', '4']]
#hard
# sudoku = [['8', '0', '0', '0', '0', '0', '0', '0', '0'],
# ['0', '0', '3', '6', '0', '0', '0', '0', '0'],
# ['0', '7', '0', '0', '9', '0', '2', '0', '0'],
# ['0', '5', '0', '0', '0', '7', '0', '0', '0'],
# ['0', '0', '0', '0', '4', '5', '7', '0', '0'],
# ['0', '0', '0', '1', '0', '0', '0', '3', '0'],
# ['0', '0', '1', '0', '0', '0', '0', '6', '8'],
# ['0', '0', '8', '5', '0', '0', '0', '1', '0'],
# ['0', '9', '0', '0', '0', '0', '4', '0', '0']]
#super hard
sudoku = [['0', '6', '1', '0', '0', '7', '0', '0', '3'],
['0', '9', '2', '0', '0', '3', '0', '0', '0'],
['0', '0', '0', '0', '0', '0', '0', '0', '0'],
['0', '0', '8', '5', '3', '0', '0', '0', '0'],
['0', '0', '0', '0', '0', '0', '5', '0', '4'],
['5', '0', '0', '0', '0', '8', '0', '0', '0'],
['0', '4', '0', '0', '0', '0', '0', '0', '1'],
['0', '0', '0', '1', '6', '0', '8', '0', '0'],
['6', '0', '0', '0', '0', '0', '0', '0', '0']]
print(np.matrix(sudoku))
def get_unit_list():
global unit_list
global row_list
global col_list
global square_list
for y in range(0, 9):
row_list_tmp = []
col_list_tmp = []
for x in range(0, 9):
rowpos = [y, x]
colpos = [x, y]
row_list_tmp.append(tuple(rowpos))
col_list_tmp.append(tuple(colpos))
row_list.append(row_list_tmp)
col_list.append(col_list_tmp)
for x in range(0, 9, 3):
for y in range(0, 9, 3):
square_list_tmp = []
x0 = (x // 3) * 3 # top left position in box
y0 = (y // 3) * 3
for i in range(3):
for j in range(3):
grid = [y0 + i, x0 + j]
square_list_tmp.append(tuple(grid))
square_list.append(square_list_tmp)
unit_list = row_list + col_list + square_list
# sudoku[linha][coluna]
def fill_matrix():
for i in range(0, 9):
for j in range(0, 9):
if sudoku[i][j] == '0':
sudoku[i][j] = '123456789'
def find_peers():
global peer_dict
for y in range(0, 9):
for x in range(0, 9):
pos = [y, x]
peer_list = []
for peer_pos in range(0, 9):
row = [peer_pos, x]
col = [y, peer_pos]
if row != pos:
peer_list.append(row)
if col != pos:
peer_list.append(col)
x0 = (x // 3) * 3 # top left position in box
y0 = (y // 3) * 3
for i in range(3):
for j in range(3):
grid = [y0 + i, x0 + j]
if grid != pos:
peer_list.append(grid)
i = 0
peer_set = set(tuple(i) for i in peer_list)
peer_list = list(peer_set)
peer_dict[tuple(pos)] = peer_list
print("Finished Peer List")
def eliminate(matrix_sudoku):
solved_list = []
# iterate through solved values and keep position in a list
for position_key in peer_dict:
y = position_key[0]
x = position_key[1]
if len(matrix_sudoku[y][x]) == 1:
position = [y, x]
solved_list.append(position)
for solved_pos in solved_list:
y = solved_pos[0]
x = solved_pos[1]
digit = matrix_sudoku[y][x]
for peer in peer_dict[tuple(solved_pos)]:
y = peer[0]
x = peer[1]
matrix_sudoku[y][x] = matrix_sudoku[y][x].replace(digit, '')
return matrix_sudoku
def hidden_single(matrix_sudoku):
for unit in unit_list:
for digit in '123456789':
boxes_with_digit = []
for box in unit:
y = box[0]
x = box[1]
if digit in matrix_sudoku[y][x]:
position = [y, x]
boxes_with_digit.append(tuple(position))
if len(boxes_with_digit) == 1:
y, x = boxes_with_digit[0]
matrix_sudoku[y][x] = digit
return matrix_sudoku
def reduce_sudoku(matrix_sudoku):
global peer_dict
global backtracks
stalled = False
while not stalled:
# need to count how many values are already solved
solved_values_before = 0
for position_key in peer_dict:
y = position_key[0]
x = position_key[1]
if len(matrix_sudoku[y][x]) == 1:
solved_values_before = solved_values_before + 1
# use eliminate strategy
matrix_sudoku = eliminate(matrix_sudoku)
# use hidden single strategy
matrix_sudoku = hidden_single(matrix_sudoku)
# count how many boxes have been solved after trying the two strategies
solved_values_after = 0
for position_key in peer_dict:
y = position_key[0]
x = position_key[1]
if len(matrix_sudoku[y][x]) == 1:
solved_values_after = solved_values_after + 1
stalled = solved_values_before == solved_values_after
# check if there are any boxes with zero possibilities (sanity check)
# if there is an error backtracking is applied
for position_key in peer_dict:
y = position_key[0]
x = position_key[1]
if len(matrix_sudoku[y][x]) == 0:
backtracks = backtracks + 1
return False
return matrix_sudoku
def search(matrix_sudoku): # bruteforce search
global recursion_count
global backtracks
global peer_dict
matrix_sudoku = reduce_sudoku(matrix_sudoku)
if matrix_sudoku is False:
return False # Failed earlier
list_of_lenghts = []
for position_key in peer_dict:
y = position_key[0]
x = position_key[1]
list_of_lenghts.append(len(sudoku[y][x]))
if all(list_of_lenghts[i] == 1 for i in range(len(list_of_lenghts))):
print(np.matrix(matrix_sudoku))
return matrix_sudoku ## Solved
##find unfilled squares with the fewest possibilities
unfilled_squares = {}
for position_key in peer_dict:
y = position_key[0]
x = position_key[1]
if len(matrix_sudoku[y][x]) > 1:
position = [y, x]
unfilled_squares[tuple(position)] = len(matrix_sudoku[y][x])
min = 99
for key, value in unfilled_squares.items():
if value < min:
min = value
pos_min = key
# y = pos_min[0]
# x = pos_min[1]
print(np.matrix(matrix_sudoku))
print("Backtracks {}".format(backtracks))
print("Recursions {}".format(recursion_count))
end_time = time.time()
print("Solve time:{} ms ".format((end_time - start_time) * 1000))
# recursion to solve sudoku when the other strategies dont find any new boxes
y = pos_min[0]
x = pos_min[1]
for possibility in matrix_sudoku[y][x]:
new_matrix = copy.deepcopy(matrix_sudoku)
new_matrix[y][x] = possibility
recursion_count = recursion_count + 1
attempt = search(new_matrix)
if attempt:
return attempt
def start_solving(sudoku):
global end_time
global start_time
global backtracks
global recursion_count
get_unit_list()
find_peers()
fill_matrix()
solved_sudoku = search(sudoku)
print(np.matrix(solved_sudoku))
print("Backtracks {}".format(backtracks))
print("Recursions {}".format(recursion_count))
end_time = time.time()
print("Solve time:{} ms ".format((end_time - start_time) * 1000))
start_solving(sudoku)