def main():
print("\n\n\nEnter the maze number that you want to solve.")
mazeNumber = int(input("[1]. maze1.txt \t 2. maze2.txt \t 3. maze3.txt\n"))
print("\n\nEnter algorithm number you would like to use.")
algoPref = int(
input(
"[1]. Djikstra's \n 2. Breadth First Searh \n 3. Depth First Search \n 4. Backtracking\n"
))
print("\n\nDo you want to get the output in color?")
color = input("[Y]es\t\tNo\n")
maze, start, end = mazes(mazeNumber)
if algoPref == 4:
path = backtracking(maze, start)
elif algoPref == 3:
path = dfs(maze, start)
elif algoPref == 2:
path = bfs(maze, start)
else:
path = djikstras(maze, start)
# Printing the maze with the solution for the respective path finding algorithm
currNode = end
while currNode != (0, 1):
nextNode = path[currNode]
connectTwoCells(maze, currNode, nextNode)
currNode = nextNode
if color == "Y" or color == "y" or color.capitalize() == "Yes":
printMazeInColor(maze)
else:
printMaze(maze)
def main():
"""
Shows how backtracking is applied
Renders the unsolved and solution of the given sudoku puzzle
"""
# Create a blank Sudoku board
board = create_empty_board()
# Sample Board config
board[0] = [0, 0, 0, 2, 6, 0, 7, 0, 1]
board[1] = [6, 8, 0, 0, 7, 0, 0, 9, 0]
board[2] = [1, 9, 0, 0, 0, 4, 5, 0, 0]
board[3] = [8, 2, 0, 1, 0, 0, 0, 4, 0]
board[4] = [0, 0, 4, 6, 0, 2, 9, 0, 0]
board[5] = [0, 5, 0, 0, 0, 3, 0, 2, 8]
board[6] = [0, 0, 9, 3, 0, 0, 0, 7, 4]
board[7] = [0, 4, 0, 0, 5, 0, 0, 3, 6]
board[8] = [7, 0, 3, 0, 1, 8, 0, 0, 0]
solved_board, steps = backtracking(deepcopy(board))
# Show unsolved puzzle
cv2.imshow("Unsolved", draw_puzzle(board))
cv2.waitKey(0)
if steps:
# Show solved puzzle
cv2.imshow(f"Solved in {steps} steps", draw_puzzle(solved_board))
cv2.waitKey(0)
else:
print("Invalid puzzle")
# Close all windows
cv2.destroyAllWindows()
def solve(self, d_i_list):
for d_i in d_i_list:
print 'DoF', d_i, self.hv_counts[d_i], self.dof[d_i]
dim = self.dim
candidates = self.candidates
cand_counts = [None, None]
prev_cand_counts = [None, None]
size = len([x for x in self.dof if x <= 500])
while True:
print 'Size =', size
for d_i in d_i_list[:size]:
self.d_i = d_i
this_dim = dim[d_i[0]]
that_dim = dim[1 - d_i[0]]
this_idx = d_i[1]
self.candidates[d_i] = []
for candidate in backtracking(range(this_dim), Choices, self.box_assignable):
if candidate not in self.candidates[d_i]:
self.candidates[d_i].append(candidate)
print 'D%d %2d %d/%d' % (d_i[0], d_i[1], len(self.candidates[d_i]), self.dof[d_i])
for d in (0, 1):
cand_counts[d] = [len(self.candidates[(d, idx)]) for idx in xrange(dim[1-d]) if (d, idx) in self.candidates]
print cand_counts[0]
print cand_counts[1]
if cand_counts[0] == prev_cand_counts[0] and cand_counts[1] == prev_cand_counts[1]:
print 'Candidate counts remain the same. Increasing size by', 4
size += 4
for d in (0, 1):
prev_cand_counts[d] = cand_counts[d]
if len(cand_counts[0]) == dim[0] and len(set(cand_counts[0])) == 1 and cand_counts[0][0] == 1:
print '** Found unique solution'
break
for y in xrange(dim[1]):
print ''.join([candidates[(0, y)][0][x] for x in xrange(dim[0])])
def test_findUnassignedLocation(self):
tempPuzzle = np.array([[7, 5, 6, 1, 3, 2, 8, 9, 4],[8, 9, 2, 6, 7, 4, 5, 3, 1],[4, 3, 1, 8, 5, 9, 6, 2, 7],[5, 4, 3, 9, 6, 8, 1, 7, 2],[2, 8, 9, 3, 0, 7, 4, 5, 6],[1, 6, 7, 4, 2, 5, 3, 8, 9],[3, 7, 4, 5, 9, 6, 2, 1, 8],[9, 1, 8, 2, 4, 3, 7, 6, 5],[6, 2, 5, 7, 8, 1, 9, 4, 3]])
position = [0,0]
b = backtracking.backtracking(tempPuzzle)
b.findUnassignedLocation(tempPuzzle, position)
self.assertEqual(position, [4,4], "Puzzle finds position wrong")
def test_not_fun_puzzles(not_fun_puzzles):
# Unpack
puzzles, solutions = not_fun_puzzles
for puzzle, solution in zip(puzzles, solutions):
solved, step = backtracking(puzzle)
assert (solved == solution).all()
assert step != 0
def test_difficult_puzzles(difficult_puzzles):
# Unpack
puzzles, solutions = difficult_puzzles
for puzzle, solution in zip(puzzles, solutions):
solved, step = backtracking(puzzle)
assert (solved == solution).all()
assert step != 0
def test_intermediate_puzzles(intermediate_puzzles):
# Unpack
puzzles, solutions = intermediate_puzzles
for puzzle, solution in zip(puzzles, solutions):
solved, step = backtracking(puzzle)
assert (solved == solution).all()
assert step != 0
def run():
path = input(
"Which method do you want to use? \nBrute force (1), Dynamic (2), Best First Branch Bound (3), or Backtracking (4)?\nOr press q to quit : "
)
if path == '1':
time1 = datetime.datetime.now()
print(bruteforce.bruteforce(W, items[2], items[1], len(items[0])))
time2 = datetime.datetime.now()
tdelta = time2 - time1
print("Brute force: Time taken: %s ms" %
int(tdelta.total_seconds() * 1000))
print("\n")
run()
elif path == '2':
time1 = datetime.datetime.now()
print(dynamic.dynamic(W, items[2], items[1], len(items[0])))
time2 = datetime.datetime.now()
tdelta = time2 - time1
print("Dynamic: Time taken: %s ms" %
int(tdelta.total_seconds() * 1000))
print("\n")
run()
elif path == '3':
time1 = datetime.datetime.now()
print(
firstBranchBound.firstBranchBound(W, items[2], items[1],
len(items[0])))
time2 = datetime.datetime.now()
tdelta = time2 - time1
print("Best First Branch Bound: Time taken: %s ms" %
int(tdelta.total_seconds() * 1000))
print("\n")
run()
elif path == '4':
time1 = datetime.datetime.now()
print(backtracking.backtracking(W, items[2], items[1], len(items[0])))
time2 = datetime.datetime.now()
tdelta = time2 - time1
print("Backtracking: Time taken: %s ms" %
int(tdelta.total_seconds() * 1000))
print("\n")
run()
elif path == 'q':
sys.exit("See ya!")
else:
print("Error: no valid option chosen. Please try again.")
print("\n")
run()
def GradientDescent(f, d_f, x0, epson=0.0001):
from backtracking import backtracking
x = [x0]
while True:
# determine d_x
d_x = -d_f(x[-1])
if d_x**2 <= epson:
break
t = backtracking(f, d_f, x[-1], d_x)
x.append(x[-1] + t * d_x)
# print "%3.3f,%.3f,%.3f" % (d_x,t,x[-1])
# print "Final x: ",x[-1]
return x
def NewtonMethod(f, d_f, dd_f, x0, epson=0.0001):
from backtracking import backtracking
x = [x0]
while True:
df = d_f(x[-1])
ddf = dd_f(x[-1])
if (df**2 / ddf) / 2 <= epson:
break
d_x = -df / ddf
t = backtracking(f, d_f, x[-1], d_x)
x.append(x[-1] + t * d_x)
# print "%3.3f,%.3f,%.3f" % (d_x,t,x[-1])
# print "Final x: %.3f" % (x[-1])
return x
def gradientdescent(f, df, x0, e, alpha, beta):
x_vals = []
x = x0
k = 0 #number of iteration
while 1:
#print k, x, f(x)
# store each x, f(x) into separate list
x_vals.append(x)
dx = -df(x)
t = backtracking(f, df, x, dx, alpha, beta)
x = x + t * dx
if (abs(df(x)) <= e):
return x_vals, k
k = k + 1
def run():
path = input("Which method do you want to use? \nBrute force (1), Dynamic (2), Best First Branch Bound (3), or Backtracking (4)?\nOr press q to quit : ")
if path == '1':
time1 = datetime.datetime.now()
print( bruteforce.bruteforce(W, items[2], items[1], len(items[0])) )
time2 = datetime.datetime.now()
tdelta = time2 - time1
print("Brute force: Time taken: %s ms" % int(tdelta.total_seconds()*1000) )
print("\n")
run()
elif path == '2':
time1 = datetime.datetime.now()
print( dynamic.dynamic(W, items[2], items[1], len(items[0])) )
time2 = datetime.datetime.now()
tdelta = time2 - time1
print("Dynamic: Time taken: %s ms" % int(tdelta.total_seconds()*1000) )
print("\n")
run()
elif path == '3':
time1 = datetime.datetime.now()
print( firstBranchBound.firstBranchBound(W, items[2], items[1], len(items[0])) )
time2 = datetime.datetime.now()
tdelta = time2 - time1
print("Best First Branch Bound: Time taken: %s ms" % int(tdelta.total_seconds()*1000) )
print("\n")
run()
elif path == '4':
time1 = datetime.datetime.now()
print( backtracking.backtracking(W, items[2], items[1], len(items[0])) )
time2 = datetime.datetime.now()
tdelta = time2 - time1
print("Backtracking: Time taken: %s ms" % int(tdelta.total_seconds()*1000) )
print("\n")
run()
elif path == 'q':
sys.exit("See ya!")
else:
print("Error: no valid option chosen. Please try again.")
print("\n")
run()
def test_usedInBox(self):
b = backtracking.backtracking(puzzle)
self.assertTrue(b.usedInBox(puzzle, 3, 3, 7), "not finding box duplicates")
def test_invalid_puzzles(invalid_puzzles):
for puzzle in invalid_puzzles:
solved, step = backtracking(puzzle)
assert (solved == puzzle).all()
assert step == 0
def test_usedInRow(self):
b = backtracking.backtracking(puzzle)
self.assertTrue(b.usedInRow(puzzle, 6, 3), "not finding row duplicates")
def test_usedInCol(self):
b = backtracking.backtracking(puzzle)
self.assertTrue(b.usedInCol(puzzle, 2, 1), "not finding column duplicates")
def main(img_path):
sudoku_solver('0000.png')
board = digit_recognizer()
backtracking(board)
from classes import Board
from backtracking import backtracking
#https://dlbeer.co.nz/articles/sudoku.html
def board_loader(board):
with open(board) as f:
board = csv.reader(f)
board = [i for i in board]
return board
if __name__ == "__main__":
board = sys.argv[1]
board = board_loader(board)
board = Board(board)
sol = backtracking(board, 0)
if sol:
total = sol[0]
moves = sol[1:]
for i in moves:
board.board[i[0]][i[1]] = i[2]
print("success")
else:
print("fail")
def minimize_f(x0, f, grad_f, bounds = None, method = 'projected_gradient'):
"""Solution of convex optimization problem, possibly with constraints.
Inputs:
x0: Starting point
f: Objective function
grad_f: Gradient of f
bounds: Upper and lower bounds of the optimization problem. If
specified, it must be of the form [(lower_b, upper_b)] and its
length must be the same as the dimension of the problem
method: Method used for solving the optimization problem
Outputs:
x: Solution of the optimization problem
f_x: Value of the function at x
grad_x: Gradient at x
it: Number of iterations needed
"""
x = x0.copy()
fun_obj = lambda x: (f(x), grad_f(x))
f_x, grad_x = fun_obj(x)
c1 = 1e-1
ls_interp = 1
ls_multi = 1
convergence = False
precision = 1e-5
it = 0
it_max = 5000
if bounds == None:
l_bounds = -np.inf * np.ones(x.shape)
u_bounds = np.inf * np.ones(x.shape)
else:
l_bounds = np.array([l for (l,u) in bounds])
u_bounds = np.array([u for (l,u) in bounds])
while not convergence:
it += 1
d = -grad_x.copy()
gtd = np.inner(d, grad_x)
t = 1
t, x_new, f_new, g_new, _ = backtracking(x, t, d, f_x, grad_x, f_x, \
gtd, c1, ls_interp = ls_interp, ls_multi = ls_multi, \
fun_obj = fun_obj)
x = x_new.copy()
x = np.maximum(x, l_bounds)
x = np.minimum(x, u_bounds)
if (x != x_new).any():
f_new = f(x)
g_new = grad_f(x)
convergence = np.inner(f_new - f_x, f_new - f_x) < precision ** 2 \
and it < it_max
f_x = f_new.copy()
grad_x = g_new.copy()
return (x, f_x, grad_x, it)
for i in range(0, len(inputArray)):
for j in range(0, len(inputArray[i])):
if (type(inputArray[i][j]) == int):
if (inputArray[i][j] > n):
raise error_incorrect_input
else:
if (inputArray[i][j] != '_'):
raise error_incorrect_input
checkInput(inputArray, nmkArray)
print("Which would you like to implement: ")
print("\t1. Backtracking + MRV heuristic")
print("\t2. Backtracking + MRV + Forward Checking")
print("\t3. Backtracking + MRV + Constraint Propagation")
num = input("")
temp = "None"
if (num == "2"):
temp = "FC"
elif (num == "3"):
temp = "CP"
backtracking.backtracking(inputArray, nmkArray, temp)
except error_incorrect_input:
print("\nIncorrect input, please try again!\n")
except FileNotFoundError:
print("\nThis file does not exist, please try again!\n")
# testInput2.txt
# testInput.txt
def main():
"""
Loops through all unsolved sudoku puzzle images, and perform all operations from grid extraction, cell extraction,
digit classification to backtracking to find the solution of the puzzle
Once a solution is found, renders the answers on the unsolved sudoku image
"""
# Load trained model
model = tf.keras.models.load_model('digits_classifier/models/model.h5')
image_directory = "images/unsolved"
for file_name in os.listdir(image_directory):
# Load image
image = cv2.imread(filename=os.path.join(image_directory, file_name),
flags=cv2.IMREAD_COLOR)
# Check if image is too big
# If so, Standardise image size to avoid error in cell image manipulation
# Cells must fit in 28x28 for the model, big images will exceed this threshold with aspect ratio resize
if image.shape[1] > 700:
image = imutils.resize(image, width=700)
# Extract grid
grid_coordinates = get_grid_dimensions(image)
# Check if grid is found
if grid_coordinates is not None:
# Crop grid with transformation
grid = transform_grid(image, grid_coordinates)
# Image preprocessing, reduce noise such as numbers/dots, cover all numbers
thresh = reduce_noise(grid)
# Contour detection again, this time we are extracting the grid
cnts, hierarchy = cv2.findContours(thresh, cv2.RETR_TREE,
cv2.CHAIN_APPROX_SIMPLE)
# Filter out non square contours
cnts = filter_non_square_contours(cnts)
# Convert contours into data to work with
# Do a check if grid is fully extracted, no missing, no duplicates etc
if len(cnts) == 81:
# Sort grid into nested list format same as sudoku
grid_contours = sort_grid_contours(cnts)
# Create a blank Sudoku board
board = create_empty_board()
# Run digit classifier
for row_index, row in enumerate(grid_contours):
for box_index, box in enumerate(row):
# Extract cell ROI from contour
x, y, width, height = cv2.boundingRect(box)
roi = grid[y:y + height, x:x + width]
# Convert to greyscale
roi = cv2.cvtColor(roi, cv2.COLOR_BGR2GRAY)
# Image thresholding & invert image
digit_inv = cv2.adaptiveThreshold(
roi, 255, cv2.ADAPTIVE_THRESH_GAUSSIAN_C,
cv2.THRESH_BINARY_INV, 27, 11)
# Remove surrounding noise
digit = sudoku_cells_reduce_noise(digit_inv)
# Digit present
if digit is not None:
# Reshape to fit model input
digit = digit.reshape((1, 28, 28, 1))
# Make prediction
board[row_index][box_index] = np.argmax(
model.predict(digit), axis=-1)[0] + 1
# Perform backtracking to solve detected puzzle
solved_board, steps = backtracking(copy.deepcopy(board))
# Check if puzzle is valid
if steps:
# Solved
# Draw answers on the sudoku image
for row_index, row in enumerate(board):
for box_index, box in enumerate(row):
# Filter for BLANK_STATES
if box == BLANK_STATE:
x, y, width, height = cv2.boundingRect(
grid_contours[row_index][box_index])
# Calculate font size
for num in np.arange(1.0, 10.0, 0.1):
text_size = cv2.getTextSize(
str(solved_board[row_index]
[box_index]),
fontFace=cv2.FONT_HERSHEY_DUPLEX,
fontScale=num,
thickness=2)
font_size = num
if text_size[0][
0] > width // 2 or text_size[0][
1] > height // 2:
break
# Fill in answers in sudoku image
cv2.putText(
image,
str(solved_board[row_index][box_index]),
(x + grid_coordinates[0][0] +
(width * 1 // 4),
y + grid_coordinates[0][1] +
(height * 3 // 4)),
cv2.FONT_HERSHEY_SIMPLEX, font_size,
(0, 255, 0), 2)
# Fill in information at bottom left
cv2.putText(image, f"Solved in {steps} steps",
(0, image.shape[0]), cv2.FONT_HERSHEY_SIMPLEX,
font_size, (0, 255, 0), 2)
# Save answers in solved directory
cv2.imwrite(
f"images/solved/{os.path.splitext(file_name)[0]}.png",
image)
print(f"File: {file_name}, Solved in {steps} steps")
else:
# Cannot be solved (Wrong/invalid puzzle)
# Reasons can be invalid puzzle or grid/digits detected wrongly
print(
f"File: {file_name}, Invalid puzzle or digit detection error"
)
else:
# Unable to tally 81 boxes
print(f"File: {file_name}: Unable to detect 81 cells in grid")
else:
# Fail to detect grid
print(f"File: {file_name}, Unable to detect grid")
