'''
Write a program to solve a Sudoku puzzle by filling the empty cells. A sudoku solution must satisfy all of the following rules: Each of the digits 1-9 must occur exactly once in each row.
generate working python code that implements the Storyboard class and Scene class
'''
# Define the Sudoku grid as a 9x9 list of lists, where 0 represents an empty cell
grid = [
[5, 3, 0, 0, 7, 0, 0, 0, 0],
[6, 0, 0, 1, 9, 5, 0, 0, 0],
[0, 9, 8, 0, 0, 0, 0, 6, 0],
[8, 0, 0, 0, 6, 0, 0, 0, 3],
[4, 0, 0, 8, 0, 3, 0, 0, 1],
[7, 0, 0, 0, 2, 0, 0, 0, 6],
[0, 6, 0, 0, 0, 0, 2, 8, 0],
[0, 0, 0, 4, 1, 9, 0, 0, 5],
[0, 0, 0, 0, 8, 0, 0, 7, 9]
]
def solve_sudoku(grid):
"""
Solves a Sudoku puzzle using a recursive backtracking algorithm.
"""
# Find the next empty cell in the grid
for row in range(9):
for col in range(9):
if grid[row][col] == 0:
# Try each digit from 1 to 9 in the empty cell
for digit in range(1, 10):
if is_valid(grid, row, col, digit):
# If the digit is valid, place it in the cell and recurse
grid[row][col] = digit
if solve_sudoku(grid):
return True
# If the recursion doesn't lead to a solution, backtrack
grid[row][col] = 0
# If none of the digits work, the puzzle is unsolvable
return False
# If there are no empty cells, the puzzle is solved
return True
def is_valid(grid, row, col, digit):
"""
Checks if a given digit is valid in a given cell of the Sudoku grid.
"""
# Check if the digit is already in the same row or column
for i in range(9):
if grid[row][i] == digit or grid[i][col] == digit:
return False
# Check if the digit is already in the same 3x3 subgrid
subgrid_row = (row // 3) * 3
subgrid_col = (col // 3) * 3
for i in range(subgrid_row, subgrid_row + 3):
for j in range(subgrid_col, subgrid_col + 3):
if grid[i][j] == digit:
return False
# If the digit passes all tests, it is valid
return True
# Solve the Sudoku puzzle
solve_sudoku(grid)
# Print the solved grid
for row in grid:
print(row)