leetcode 36：有效的数独

题目传送门
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。
上图是一个部分填充的有效的数独。
数独部分空格内已填入了数字，空白格用 ‘.’ 表示。
示例 1:
输入:
[
[“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:
[
[“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。
说明:
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。
给定数独序列只包含数字 1-9 和字符 ‘.’ 。
给定数独永远是 9x9 形式的。

思路：按照题目要求，一行不能有同样的数字，一列不能有同样的数字，3*3小方格也不能有相同的数字。所以我们可以用一个二维布尔变量数组a[i][j],表示当前行或者列中j有没有出现过，结果为true时说明不符合数独规则，输出false，如果为false时说明j第一次在本行或者列出现，将a[i][j]设为true，继续判断。

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        if(board.size()==0)  return false;
        else
        {
         vector<vector<bool>> row(9,vector<bool>(9,false));
         vector<vector<bool>> col(9,vector<bool>(9,false));
         vector<vector<bool>> cell(9,vector<bool>(9,false));
         for(int i=0;i<9;i++)
            for(int j=0;j<9;j++)
            {
               if(board[i][j]>='0'&&board[i][j]<='9')
               {
                   int num=board[i][j]-'1';
                   if(row[i][num]||col[num][j]||cell[3*(i/3)+j/3][num])//小的3*3模块依次从左到右从上到下编号
                      return false;
                    row[i][num]=true;
                    col[num][j]=true;
                   cell[3*(i/3)+j/3][num]=true;
               }
            }
            return true;
        }
    }
};