input: def solve_sudoku(board): 
      """
      This function is designed to solve a Sudoku puzzle by finding all vacant cells and
      placing numbers in them that do not already exist in the same row, column, or 3x3 box.
      The function uses backtracking to explore possible solutions and returns the solved board.
  
      >>> 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)
      True
      """
    
      def find_vacant_cell(board, l): 
          for row in range(9): 
              for col in range(9): 
                  if board[row][col] == 0: 
                      l[0] = row 
                      l[1] = col 
                      return True
          return False
    
      def is_safe(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): 
          l = [0, 0] 
          if (not find_vacant_cell(board,l)): 
              return True
          row = l[0] 
          col = l[1] 
          for num in range(1, 10): 
              if (is_safe(board, row, col, num)): 
                  board[row][col] = num 
                  if (solve(board)): 
                      return True
                  board[row][col] = 0
          return False
    
      if (solve(board)): 
          return True
      else: 
          return False
output:     return solve_sudoku(board)