input: def solve_sudoku(board):
      """ This function solves any Sudoku puzzle by attempting to fill vacant cells 
      with numbers in the range of 1 to 9, ensuring each number is valid in its row, 
      column, and 3x3 subgrid.
      >>> solve_sudoku([
          [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]
      ])
      [
          [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 or board[row//3*3 + i//3][col//3*3 + i%3] == 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