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36. 有效的数独

题目

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。

  1. 数字 1-9 在每一行只能出现一次。
  2. 数字 1-9 在每一列只能出现一次。
  3. 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：

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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：

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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 ‘.’

注意事项

这道题显然用hash表来做很直接，此时需要注意3*3的块状区域如何计算。

代码实现

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class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        // 3*9个hash表，分别存每一行、每一列以及每一块的情况
        vector<vector<int>> rows(9,vector<int>(10,0));
        vector<vector<int>> cols(9,vector<int>(10,0));
        vector<vector<int>> blocks(9,vector<int>(10,0));

        for(int i=0;i<board.size();i++){
            for(int j=0;j<board[0].size();j++){
                if(board[i][j]=='.')
                    continue;
                int k = board[i][j]-'0'-1;

                rows[i][k]++;
                cols[j][k]++;
                blocks[i/3*3+j/3][k]++;
                // 如果大于1说明该行/块/列出现过
                if(rows[i][k]>1 || cols[j][k]>1 || blocks[i/3*3+j/3][k]>1){
                    return false;
                }
            }
        }
        return true;
    }
};