def zero_up(puzzle, element_row, zero_x, zero_y,
size): # to move the zero upwards
zx = zero_x
for i in range(zx - 1, element_row - 1, -1):
puzzle[zero_x][zero_y], puzzle[i][zero_y] = swap(
puzzle, zero_x, zero_y, i, zero_y)
zero_x = i
pigame.display(size, puzzle, 0)
return (zero_x, zero_y)
def zero_left(puzzle, element_column, zero_x, zero_y,
size): # to move the zero leftwards
zy = zero_y
for i in range(zy - 1, element_column - 1, -1):
puzzle[zero_x][zero_y], puzzle[zero_x][i] = swap(
puzzle, zero_x, zero_y, zero_x, i)
zero_y = i
pigame.display(size, puzzle, 0)
return (zero_x, zero_y)
def first_row(puzzle, size, row, column, element_row,
element_column): # solves the topmost row in the given matrix.
cornercase = 0
shuffle = 0
starting_row = row
(zero_x, zero_y) = zero(puzzle, starting_row, size)
if column == size - 2: # when the element is to be placed in the
if element_row == row and element_column == size - 1: # second rightmost column,it places the element
cornercase = 1 # in the next row of the same column.
if element_row == row + 1 and element_column == size - 1 and zero_x == row and zero_y == size - 1:
puzzle[zero_x][zero_y], puzzle[zero_x + 1][zero_y] = swap(
puzzle, zero_x, zero_y, zero_x + 1, zero_y)
cornercase = 1
element_row = element_row - 1
zero_x = zero_x + 1
pigame.display(size, puzzle, 0)
row += 1
shuffle = 1
if column == size - 1: # when the element is to be placed in the rightmost column
column -= 1 # it places the element in the second rightmost column
# of the same row.
if zero_x <= row: # to move the zero when it is in the row smaller than
(zero_x, zero_y) = zero(
puzzle, starting_row,
size) # or equal to the concerned row as it might effect
puzzle[zero_x][zero_y], puzzle[zero_x + 1][zero_y] = swap(
puzzle, zero_x, zero_y, zero_x + 1, zero_y) # already solved
if zero_x + 1 == element_row and zero_y == element_column: #ones.
element_row = element_row - 1
zero_x = zero_x + 1
pigame.display(size, puzzle, 0)
# different moves based on the position of the element with respect to that of the position where it has
# to be brought
if element_column - column < 0:
(zero_x, zero_y,
flag) = shift_zero_tomove_ele_left(puzzle, zero_x, zero_y,
element_row, element_column,
column, size)
if flag == 1:
puzzle[zero_x][zero_y], puzzle[zero_x][zero_y - 1] = swap(
puzzle, zero_x, zero_y, zero_x, zero_y - 1)
zero_y = zero_y - 1
element_column = element_column + 1
pigame.display(size, puzzle, 0)
(zero_x, zero_y,
element_column) = shift_col_right(puzzle, zero_x, zero_y, element_row,
element_column, column, size)
if element_column - column > 0:
(zero_x, zero_y) = zero(puzzle, starting_row, size)
(zero_x, zero_y,
flag) = shift_zero_tomove_ele_right(puzzle, zero_x, zero_y,
element_row, element_column,
column, row, size)
if flag == 1:
puzzle[zero_x][zero_y], puzzle[zero_x][zero_y + 1] = swap(
puzzle, zero_x, zero_y, zero_x, zero_y + 1)
zero_y = zero_y + 1
element_column = element_column - 1
pigame.display(size, puzzle, 0)
(zero_x, zero_y,
element_column) = shift_col_left(puzzle, zero_x, zero_y, element_row,
element_column, column, size)
if element_row - row > 0:
(zero_x, zero_y) = zero(puzzle, starting_row, size)
(zero_x, zero_y,
flag) = shift_zero_tomove_ele_up(puzzle, zero_x, zero_y, element_row,
element_column, row, column, size)
if flag == 1:
puzzle[zero_x][zero_y], puzzle[zero_x + 1][zero_y] = swap(
puzzle, zero_x, zero_y, zero_x + 1, zero_y)
zero_x = zero_x + 1
element_row = element_row - 1
pigame.display(size, puzzle, 0)
(zero_x, zero_y, element_row) = shift_row_up(puzzle, zero_x, zero_y,
element_row,
element_column, row, size)
# in the case where the element has to be placed in the last and second last column
if shuffle == 1 and cornercase == 0:
if zero_y == size - 3:
puzzle[zero_x][zero_y], puzzle[zero_x + 1][zero_y] = swap(
puzzle, zero_x, zero_y, zero_x + 1, zero_y)
zero_x = zero_x + 1
pigame.display(size, puzzle, 0)
while zero_y < size - 1:
puzzle[zero_x][zero_y], puzzle[zero_x][zero_y + 1] = swap(
puzzle, zero_x, zero_y, zero_x, zero_y + 1)
zero_y = zero_y + 1
pigame.display(size, puzzle, 0)
while zero_x > starting_row:
puzzle[zero_x][zero_y], puzzle[zero_x - 1][zero_y] = swap(
puzzle, zero_x, zero_y, zero_x - 1, zero_y)
zero_x = zero_x - 1
pigame.display(size, puzzle, 0)
puzzle[zero_x][zero_y], puzzle[zero_x][zero_y - 1] = swap(
puzzle, zero_x, zero_y, zero_x, zero_y - 1)
zero_y = zero_y - 1
pigame.display(size, puzzle, 0)
puzzle[zero_x][zero_y], puzzle[zero_x + 1][zero_y] = swap(
puzzle, zero_x, zero_y, zero_x + 1, zero_y)
zero_x = zero_x + 1
pigame.display(size, puzzle, 0)
# a cornercase where a problem gets created when the element to be placed on the second most column
# is present in the last column of the same row.
if cornercase == 1:
for i in range(2):
(zero_x, zero_y) = zero_down(puzzle, element_row + 2 - i, zero_x,
zero_y, size)
(zero_x, zero_y) = zero_left(puzzle, element_column, zero_x,
zero_y, size)
(zero_x, zero_y) = zero_up(puzzle, element_row, zero_x, zero_y,
size)
element_row += 1
(zero_x, zero_y) = zero_right(puzzle, element_column + 1, zero_x,
zero_y, size)
(zero_x, zero_y) = zero_down(puzzle, element_row, zero_x, zero_y, size)
(zero_x, zero_y, abc) = shift_row_up(puzzle, zero_x, zero_y, row,
size - 1, row - 1, size)
(zero_x, zero_y) = zero_left(puzzle, element_column, zero_x, zero_y,
size)
(zero_x, zero_y) = zero_up(puzzle, row - 1, zero_x, zero_y, size)
(zero_x, zero_y) = zero_right(puzzle, element_column + 1, zero_x,
zero_y, size)
current = (row - 1) * size + size - 2
(i, j) = element(puzzle, row, size, current, final_puzzle)
first_row(puzzle, size, row - 1, size - 2, i, j)
def puzzle_solver(
puzzle, final_puzzle, start,
size): # function which gets recursively called to solve the problem.
if start == size - 2: # base case when the matrix becomes a 2X2 matrix.
flag = 0
count = 0
(zero_x, zero_y) = zero(puzzle, start, size)
if check(size, puzzle, final_puzzle):
flag = 1
pigame.exit(size, flag, puzzle)
while count < 12 and flag == 0: # it tries to solve the 2X2 matrix by rotating it anticlockwise.
# there are 12 such possibilities.
while zero_y < size - 1:
puzzle[zero_x][zero_y], puzzle[zero_x][zero_y + 1] = swap(
puzzle, zero_x, zero_y, zero_x, zero_y + 1)
zero_y = zero_y + 1
count += 1
pigame.display(size, puzzle, 0)
if check(size, puzzle, final_puzzle):
flag = 1
pigame.exit(size, flag, puzzle)
while zero_x < size - 1:
puzzle[zero_x][zero_y], puzzle[zero_x + 1][zero_y] = swap(
puzzle, zero_x, zero_y, zero_x + 1, zero_y)
zero_x = zero_x + 1
count += 1
pigame.display(size, puzzle, 0)
if check(size, puzzle, final_puzzle):
flag = 1
pigame.exit(size, flag, puzzle)
while zero_y > size - 2:
puzzle[zero_x][zero_y], puzzle[zero_x][zero_y - 1] = swap(
puzzle, zero_x, zero_y, zero_x, zero_y - 1)
zero_y = zero_y - 1
count += 1
pigame.display(size, puzzle, 0)
if check(size, puzzle, final_puzzle):
flag = 1
pigame.exit(size, flag, puzzle)
while zero_x > size - 2:
puzzle[zero_x][zero_y], puzzle[zero_x - 1][zero_y] = swap(
puzzle, zero_x, zero_y, zero_x - 1, zero_y)
zero_x = zero_x - 1
count += 1
pigame.display(size, puzzle, 0)
if check(size, puzzle, final_puzzle):
flag = 1
pigame.exit(size, flag, puzzle)
if flag == 0:
pigame.exit(size, flag, puzzle)
else:
for column in range(
start,
size - 2): # to look at different columns in the topmost row
# till the third last column.
current = start * size + column
(i, j) = element(puzzle, start, size, current, final_puzzle)
first_row(puzzle, size, start, column, i, j)
current = start * size + size - 1 # after that it sends the last column of that row to be placed in its position.
(i, j) = element(puzzle, start, size, current, final_puzzle)
first_row(puzzle, size, start, size - 1, i, j)
current = start * size + size - 2 # after that it sends the second last column of that row to be placed in its position.
(i, j) = element(puzzle, start, size, current, final_puzzle)
first_row(puzzle, size, start, size - 2, i, j)
for row in range(
start + 1, size -
2): # to look at different row in the leftmostmost column
# till the third last row.
current = row * size + start
(i, j) = element(puzzle, start, size, current, final_puzzle)
first_column(puzzle, size, row, start, i, j)
current = (
size - 1
) * size + start # after that it sends the last row of the column to be placed in its position.
(i, j) = element(puzzle, start, size, current, final_puzzle)
first_column(puzzle, size, size - 1, start, i, j)
current = (
size - 2
) * size + start # after that it sends the secondlast row of the column to be placed in its position.
(i, j) = element(puzzle, start, size, current, final_puzzle)
first_column(puzzle, size, size - 2, start, i, j)
puzzle_solver(puzzle, final_puzzle, start + 1, size)
def first_column(puzzle, size, row, column, element_row,
element_column): #solves the leftmost column in the matrix.
shuffle = 0
starting_column = column
cornercase = 0
(zero_x, zero_y) = zero(puzzle, starting_column, size)
if row == size - 2: # when the element is to be placed in the
if element_column == column and element_row == size - 1: # second last row, it places the element
cornercase = 1 # in the next column of the same row.
if element_column == column + 1 and element_row == size - 1 and zero_y == column and zero_x == size - 1:
cornercase = 1
puzzle[zero_x][zero_y], puzzle[zero_x][zero_y + 1] = swap(
puzzle, zero_x, zero_y, zero_x, zero_y + 1)
element_column = element_column - 1
zero_y = zero_y + 1
pigame.display(size, puzzle, 0)
column += 1
shuffle = 1
if row == size - 1: # when the element is to be placed in the last row, it places the
row -= 1 # element in the second last row of the same column.
# different moves based on the position of the element with respect to that of the position where it has
# to be brought
if zero_y <= column:
(zero_x, zero_y) = zero(puzzle, starting_column, size)
puzzle[zero_x][zero_y], puzzle[zero_x][zero_y + 1] = swap(
puzzle, zero_x, zero_y, zero_x, zero_y + 1)
if zero_x == element_row and zero_y + 1 == element_column:
element_column = element_column - 1
zero_y = zero_y + 1
pigame.display(size, puzzle, 0)
if element_row - row < 0:
(zero_x, zero_y,
flag) = shift_zero_tomove_ele_down(puzzle, zero_x, zero_y,
element_row, element_column, row,
size)
if flag == 1:
puzzle[zero_x][zero_y], puzzle[zero_x - 1][zero_y] = swap(
puzzle, zero_x, zero_y, zero_x - 1, zero_y)
zero_x = zero_x - 1
element_row = element_row + 1
pigame.display(size, puzzle, 0)
(zero_x, zero_y,
element_row) = shift_row_down(puzzle, zero_x, zero_y, element_row,
element_column, row, size)
if element_row - row > 0:
(zero_x, zero_y) = zero(puzzle, starting_column, size)
(zero_x, zero_y,
flag) = shift_zero_tomove_ele_up(puzzle, zero_x, zero_y, element_row,
element_column, row, column, size)
if flag == 1:
puzzle[zero_x][zero_y], puzzle[zero_x + 1][zero_y] = swap(
puzzle, zero_x, zero_y, zero_x + 1, zero_y)
zero_x = zero_x + 1
element_row = element_row - 1
pigame.display(size, puzzle, 0)
(zero_x, zero_y, element_row) = shift_row_up(puzzle, zero_x, zero_y,
element_row,
element_column, row, size)
if element_column - column > 0:
(zero_x, zero_y) = zero(puzzle, starting_column, size)
(zero_x, zero_y,
flag) = shift_zero_tomove_ele_right(puzzle, zero_x, zero_y,
element_row, element_column,
column, row, size)
if flag == 1:
puzzle[zero_x][zero_y], puzzle[zero_x][zero_y + 1] = swap(
puzzle, zero_x, zero_y, zero_x, zero_y + 1)
zero_y = zero_y + 1
element_column = element_column - 1
pigame.display(size, puzzle, 0)
(zero_x, zero_y,
element_column) = shift_col_left(puzzle, zero_x, zero_y, element_row,
element_column, column, size)
# in the case where the element has to be placed in the last and second last column
if shuffle == 1 and cornercase == 0:
if zero_x == size - 3:
puzzle[zero_x][zero_y], puzzle[zero_x][zero_y + 1] = swap(
puzzle, zero_x, zero_y, zero_x, zero_y + 1)
zero_y = zero_y + 1
pigame.display(size, puzzle, 0)
while zero_x < size - 1:
puzzle[zero_x][zero_y], puzzle[zero_x + 1][zero_y] = swap(
puzzle, zero_x, zero_y, zero_x + 1, zero_y)
zero_x = zero_x + 1
pigame.display(size, puzzle, 0)
while zero_y > starting_column:
puzzle[zero_x][zero_y], puzzle[zero_x][zero_y - 1] = swap(
puzzle, zero_x, zero_y, zero_x, zero_y - 1)
zero_y = zero_y - 1
pigame.display(size, puzzle, 0)
puzzle[zero_x][zero_y], puzzle[zero_x - 1][zero_y] = swap(
puzzle, zero_x, zero_y, zero_x - 1, zero_y)
zero_x = zero_x - 1
pigame.display(size, puzzle, 0)
puzzle[zero_x][zero_y], puzzle[zero_x][zero_y + 1] = swap(
puzzle, zero_x, zero_y, zero_x, zero_y + 1)
zero_y = zero_y + 1
pigame.display(size, puzzle, 0)
# a cornercase where a problem gets created when the element to be placed on the second most row
# is present in the last row of the same column.
if cornercase == 1:
for i in range(2):
(zero_x, zero_y) = zero_right(puzzle, element_column + 2, zero_x,
zero_y, size)
(zero_x, zero_y) = zero_up(puzzle, element_row, zero_x, zero_y,
size)
(zero_x, zero_y) = zero_left(puzzle, element_column, zero_x,
zero_y, size)
(zero_x, zero_y) = zero_down(puzzle, element_row + 1, zero_x,
zero_y, size)
(zero_x, zero_y) = zero_right(puzzle, element_column + 2, zero_x,
zero_y, size)
(zero_x, zero_y, abc) = shift_col_left(puzzle, zero_x, zero_y,
size - 1, element_column + 1,
element_column, size)
(zero_x, zero_y) = zero_up(puzzle, row, zero_x, zero_y, size)
(zero_x, zero_y) = zero_left(puzzle, element_column, zero_x, zero_y,
size)
(zero_x, zero_y) = zero_down(puzzle, size - 1, zero_x, zero_y, size)
current = (size - 2) * size + column - 1
(i, j) = element(puzzle, column, size, current, final_puzzle)
first_column(puzzle, size, size - 1, column - 1, i, j)
) * size + start # after that it sends the last row of the column to be placed in its position.
(i, j) = element(puzzle, start, size, current, final_puzzle)
first_column(puzzle, size, size - 1, start, i, j)
current = (
size - 2
) * size + start # after that it sends the secondlast row of the column to be placed in its position.
(i, j) = element(puzzle, start, size, current, final_puzzle)
first_column(puzzle, size, size - 2, start, i, j)
puzzle_solver(puzzle, final_puzzle, start + 1, size)
if __name__ == "__main__":
size = input(
"enter the size of the square matrix: ") # size of the sliding puzzle
print
print "Give 0 to represent the blank space to represent the blank space in the initial and final state"
print "You can only slide a block if it is adjacent to the blank space."
print
print "enter the initial state of puzzle : "
puzzle = [raw_input().strip().split()[:size]
for i in range(size)] # take the initial state of the puzzle.
print "enter the final state of the solver:"
final_puzzle = []
for x in range(size):
final_puzzle.extend(
raw_input().strip().split()[:size]) # final state of the puzzle.
pigame.display(size, puzzle, 0)
puzzle_solver(puzzle, final_puzzle, 0, size)
def shift_row_down(puzzle, zero_x, zero_y, element_row, element_column, row,
size): # to move the column of the element
while element_row < row: # downwards
flag = 0
if element_column == size - 1:
puzzle[zero_x][zero_y], puzzle[zero_x][zero_y - 1] = swap(
puzzle, zero_x, zero_y, zero_x, zero_y - 1)
zero_y = zero_y - 1
pigame.display(size, puzzle, 0)
flag = 1
else:
puzzle[zero_x][zero_y], puzzle[zero_x][zero_y + 1] = swap(
puzzle, zero_x, zero_y, zero_x, zero_y + 1)
zero_y = zero_y + 1
pigame.display(size, puzzle, 0)
for x in range(2):
puzzle[zero_x][zero_y], puzzle[zero_x + 1][zero_y] = swap(
puzzle, zero_x, zero_y, zero_x + 1, zero_y)
zero_x = zero_x + 1
pigame.display(size, puzzle, 0)
if flag == 1:
puzzle[zero_x][zero_y], puzzle[zero_x][zero_y + 1] = swap(
puzzle, zero_x, zero_y, zero_x, zero_y + 1)
zero_y = zero_y + 1
pigame.display(size, puzzle, 0)
else:
puzzle[zero_x][zero_y], puzzle[zero_x][zero_y - 1] = swap(
puzzle, zero_x, zero_y, zero_x, zero_y - 1)
zero_y = zero_y - 1
pigame.display(size, puzzle, 0)
puzzle[zero_x][zero_y], puzzle[zero_x - 1][zero_y] = swap(
puzzle, zero_x, zero_y, zero_x - 1, zero_y)
zero_x = zero_x - 1
element_row = element_row + 1
pigame.display(size, puzzle, 0)
return (zero_x, zero_y, element_row)
def shift_col_left(puzzle, zero_x, zero_y, element_row, element_column, column,
size): # to move the column of the element
while element_column > column: # towards left
flag = 0
if element_row == size - 1:
puzzle[zero_x][zero_y], puzzle[zero_x - 1][zero_y] = swap(
puzzle, zero_x, zero_y, zero_x - 1, zero_y)
zero_x = zero_x - 1
pigame.display(size, puzzle, 0)
flag = 1
else:
puzzle[zero_x][zero_y], puzzle[zero_x + 1][zero_y] = swap(
puzzle, zero_x, zero_y, zero_x + 1, zero_y)
zero_x = zero_x + 1
pigame.display(size, puzzle, 0)
for x in range(2):
puzzle[zero_x][zero_y], puzzle[zero_x][zero_y - 1] = swap(
puzzle, zero_x, zero_y, zero_x, zero_y - 1)
zero_y = zero_y - 1
pigame.display(size, puzzle, 0)
if flag == 1:
puzzle[zero_x][zero_y], puzzle[zero_x + 1][zero_y] = swap(
puzzle, zero_x, zero_y, zero_x + 1, zero_y)
zero_x = zero_x + 1
pigame.display(size, puzzle, 0)
else:
puzzle[zero_x][zero_y], puzzle[zero_x - 1][zero_y] = swap(
puzzle, zero_x, zero_y, zero_x - 1, zero_y)
zero_x = zero_x - 1
pigame.display(size, puzzle, 0)
puzzle[zero_x][zero_y], puzzle[zero_x][zero_y + 1] = swap(
puzzle, zero_x, zero_y, zero_x, zero_y + 1)
zero_y = zero_y + 1
element_column = element_column - 1
pigame.display(size, puzzle, 0)
return (zero_x, zero_y, element_column)