input: def solve_sudoku(board):
      """Solve a Sudoku puzzle using backtracking algorithm.
  
      >>> board = [
      ...     [7, 8, 0, 4, 0, 0, 1, 2, 0],
      ...     [6, 0, 0, 0, 7, 5, 0, 0, 9],
      ...     [0, 0, 0, 6, 0, 1, 0, 7, 8],
      ...     [0, 0, 7, 0, 4, 0, 2, 6, 0],
      ...     [0, 0, 1, 0, 5, 0, 9, 3, 0],
      ...     [9, 0, 4, 0, 6, 0, 0, 0, 5],
      ...     [0, 7, 0, 3, 0, 0, 0, 1, 2],
      ...     [1, 2, 0, 0, 0, 7, 4, 0, 0],
      ...     [0, 4, 9, 2, 0, 6, 0, 0, 7]
      ... ]
      >>> solve_sudoku(board)
      [7, 8, 5, 4, 3, 9, 1, 2, 6]
      [6, 1, 2, 8, 7, 5, 3, 4, 9]
      [4, 9, 3, 6, 2, 1, 5, 7, 8]
      [8, 5, 7, 9, 4, 3, 2, 6, 1]
      [2, 6, 1, 7, 5, 8, 9, 3, 4]
      [9, 3, 4, 1, 6, 2, 7, 8, 5]
      [5, 7, 8, 3, 9, 4, 6, 1, 2]
      [1, 2, 6, 5, 8, 7, 4, 9, 3]
      [3, 4, 9, 2, 1, 6, 8, 5, 7]
      """
output:     def is_valid(board, row, col, num):
          for i in range(9):
              if board[row][i] == num or board[i][col] == num:
                  return False
          start_row, start_col = 3 * (row // 3), 3 * (col // 3)
          for i in range(3):
              for j in range(3):
                  if board[start_row + i][start_col + j] == num:
                      return False
          return True
  
      def solve(board):
          for row in range(9):
              for col in range(9):
                  if board[row][col] == 0:
                      for num in range(1, 10):
                          if is_valid(board, row, col, num):
                              board[row][col] = num
                              if solve(board):
                                  return True
                              board[row][col] = 0
                      return False
          return True
  
      solve(board)
      return board