36. 有效的数独

请你判断一个 9x9 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 3x3 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 3x3 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 '.'

常规写法(行, 列, 小数独遍历判断是否重复)

from collections import defaultdict
class Solution:
    def isValidSudoku(self, board) -> bool:
        # 数独
        rows, cols = defaultdict(set), defaultdict(set) # 行, 列
        c = defaultdict(set) # 小数独

        # 计数大于1, 则返回false
        for i in range(9):
            for j in range(9):
                if board[i][j] == '.':
                    continue # 无需判断

                # 小数独
                c_index = i // 3 * 3 + j // 3 # 上面i占的小数独数量 + 下面j占的小数独数量 

                # rows[0], rows[1]... rows[8] 判断是否存在重复数字
                if (board[i][j] in rows[i]) or (board[i][j] in cols[j]) or (board[i][j] in c[c_index]):
                    return False

                rows[i].add(board[i][j])
                cols[j].add(board[i][j])
                c[c_index].add(board[i][j])
            
        return True