36. 有效的数独

请你判断一个 9×9 的数独是否有效。只需要 根据以下规则 ，验证已经填入的数字是否有效即可。

数字 1-9 在每一行只能出现一次。
数字 1-9 在每一列只能出现一次。
数字 1-9 在每一个以粗实线分隔的 3×3 宫内只能出现一次。（请参考示例图）
数独部分空格内已填入了数字，空白格用 ‘.’ 表示。

注意：
一个有效的数独（部分已被填充）不一定是可解的。
只需要根据以上规则，验证已经填入的数字是否有效即可。

示例 1：

输入：board =
[["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"]]
输出：true

示例 2：

输入：board =
[["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"]]
输出：false
解释：除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例1 相同。 但由于位于左上角的 3×3 宫内有两个 8 存在, 因此这个数独是无效的。

提示：

• board.length == 9
• board[i].length == 9
• board[i][j] 是一位数字或者 ‘.’

Python 解答：

class Solution:
    def isValidSudoku(self, board: List[List[str]]) -> bool:
        aset = set()
        bset = set()
        for i in range(9):
            for j in range(9):
                if board[i][j] != '.':
                    if board[i][j] not in aset:
                        aset.add(board[i][j])
                    else:
                        return False
                if board[j][i] != '.':
                    if board[j][i] not in bset:
                        bset.add(board[j][i])
                    else:
                        return False
            aset.clear()
            bset.clear()
        cset = set()
        for i in range(3):
            for j in range(3):
                for m in range(3):
                    for n in range(3):
                        if board[3*i+m][3*j+n] != '.':
                            if board[3*i+m][3*j+n] not in cset:
                                cset.add(board[3*i+m][3*j+n])
                            else:
                                return False
                cset.clear()
        return True