Leetcode 36： 有效的数独

题目描述：
请你判断一个 9 x 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 3x3 宫内只能出现一次。（请参考示例图）
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。
空白格用 ‘.’ 表示。
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
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。
思路：
按照数独的要求，利用哈希表（set）检查所给是否是满足要求的即可。

class Solution(object):
    def isValidSudoku(self, board):
        """
        :type board: List[List[str]]
        :rtype: bool
        """
        # 首先判断行是否满足
        for i in range(9):
            set_h = set()
            for j in range(9):
                if board[i][j] != '.':
                    if board[i][j] not in set_h:
                        set_h.add(board[i][j])
                    elif board[i][j] in set_h:
                        return False
        # 判断列是都满足
        for p in range(9):  # 列数
            set_l = set()
            for q in range(9):  # 行数
                if board[q][p] != '.':
                    if board[q][p] not in set_l:
                        set_l.add(board[q][p])
                    elif board[q][p] in set_l:
                        return False
        # 判断每个3*3格子是否满足
        for g_h in range(3):
            for g_l in range(3):
                set_g = set()
                for i_g in range(3):
                    for i_l in range(3):
                        if board[i_g+g_h*3][i_l+g_l*3] != '.':
                            if board[i_g+g_h*3][i_l+g_l*3] not in set_g:
                                set_g.add(board[i_g+g_h*3][i_l+g_l*3])
                            else:
                                return False
        return True

时间复杂度：O(1)。数独共有 81 个单元格，只需要对每个单元格遍历一次即可。
空间复杂度：O(1)。由于数独的大小固定，因此哈希表的空间也是固定的。