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题目描述

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。

作者：LeetCode-Solution
链接：https://leetcode-cn.com/problems/valid-sudoku/solution/you-xiao-de-shu-du-by-leetcode-solution-50m6/
来源：力扣（LeetCode）
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算法思路

一次遍历：
利用哈希表记录每一行，每一列，每一个小九宫格的数字出现的个数。
只需要一次遍历，有重复的数字就返回false，没有则返回true。

代码实现

class Solution {public:bool isValidSudoku(vector<vector<char>>& board){int a[9][9] = { 0 };int b[9][9] = { 0 };int box[3][3][9] = { 0 };for (int i = 0; i < 9; i++){for (int j = 0; j < 9; j++){int c = board[i][j];if (c != '.'){int index = c - '0' - 1;a[i][index]++;b[j][index]++;box[i / 3][j / 3][index]++;if (a[i][index] > 1 || b[j][index] > 1 || box[i / 3][j / 3][index] > 1){return false;}}}}return true;}
};

复杂度分析

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。