36. Valid Sudoku

Determine if a 9x9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:

1. Each row must contain the digits 1-9 without repetition.
2. Each column must contain the digits 1-9 without repetition.
3. Each of the 9 3x3 sub-boxes of the grid must contain the digits 1-9 without repetition.

A partially filled sudoku which is valid.

The Sudoku board could be partially filled, where empty cells are filled with the character '.'.

Example 1:

Input:
[
  ["5","3",".",".","7",".",".",".","."],
  ["6",".",".","1","9","5",".",".","."],
  [".","9","8",".",".",".",".","6","."],
  ["8",".",".",".","6",".",".",".","3"],
  ["4",".",".","8",".","3",".",".","1"],
  ["7",".",".",".","2",".",".",".","6"],
  [".","6",".",".",".",".","2","8","."],
  [".",".",".","4","1","9",".",".","5"],
  [".",".",".",".","8",".",".","7","9"]
]
Output: true

Example 2:

Input:
[
  ["8","3",".",".","7",".",".",".","."],
  ["6",".",".","1","9","5",".",".","."],
  [".","9","8",".",".",".",".","6","."],
  ["8",".",".",".","6",".",".",".","3"],
  ["4",".",".","8",".","3",".",".","1"],
  ["7",".",".",".","2",".",".",".","6"],
  [".","6",".",".",".",".","2","8","."],
  [".",".",".","4","1","9",".",".","5"],
  [".",".",".",".","8",".",".","7","9"]
]
Output: false
Explanation: Same as Example 1, except with the 5 in the top left corner being 
    modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid.

Note:

• A Sudoku board (partially filled) could be valid but is not necessarily solvable.
• Only the filled cells need to be validated according to the mentioned rules.
• The given board contain only digits 1-9 and the character '.'.
• The given board size is always 9x9.

一个比较简洁的写法，最内层循环用三个tuple来记录行、列和小方格

class Solution(object):
    def isValidSudoku(self, board):
        """
        :type board: List[List[str]]
        :rtype: bool
        """
        seen=set()
        for i in range(9):
            for j in range(9):
                num=board[i][j]
                if num!='.':
                    for tup in ((num,i),(j,num),(i/3,j/3,num)):
                        if tup in seen:
                            return False
                        seen.add(tup)
        return True

比较麻烦的写法：

class Solution:
    def isValidSudoku(self, board: List[List[str]]) -> bool:
        for i in board:
            tmp=[]
            for j in i:
                if j=='.':
                    continue
                if j in tmp:
                    return False
                else:
                    tmp.append(j)
            
        tmp=[[] for i in range(9)]

        for i in range(len(board)):
            for j in range(len(board[i])):
                if board[i][j]=='.':
                    continue
                if board[i][j] in tmp[j]:
                    return False
                else:
                    tmp[j].append(board[i][j])

        tmp=[[] for i in range(9)]
        for i in range(len(board)):
            for j in range(len(board[i])):
                row_index=i//3
                col_index=j//3
                index=row_index*3+col_index
                if board[i][j]=='.':
                    continue
                if board[i][j] in tmp[index]:
                    return False
                else:
                    tmp[index].append(board[i][j])
        return True