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 '.'

以下程序实现了这一功能：

#include <bits/stdc++.h>
using namespace std;
class Solution
{
public:bool isValidSudoku(vector<vector<char>> &board){for (int i = 0; i < board.size(); i++){vector<bool> mark(10);for (int j = 0; j < board.size(); j++){if (!valid(board, mark, i, j)){return false;}}}for (int j = 0; j < board.size(); j++){vector<bool> mark(10);for (int i = 0; i < board.size(); i++){if (!valid(board, mark, i, j)){return false;}}}for (int k = 0; k < board.size(); k++){int sr = k / 3 * 3;int sc = (k % 3) * 3;vector<bool> mark(10);for (int i = sr; i < sr + 3; i++){for (int j = sc; j < sc + 3; j++){if (!valid(board, mark, i, j)){return false;}}}}return true;}
private:bool valid(vector<vector<char>> &board, vector<bool> &mark, int i, int j){if (board[i][j] != '.'){int index = board[i][j] - '0';if (mark[index]){return false;}else{mark[index] = 1;}}return true;}
};

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