leetcode#36. Valid Sudoku

判断一个 9×9 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 3×3 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

class Solution {
public:
    //这个题只需要检查有效数度，不要求解，所以我们只在这里做一部分。因为leetcode上还有一道解数独的题，所以我在这里先把函数写好了，但最后有没有用上，我不太记得了。
    bool isValidSudoku(vector<vector<char>>& board) 
    {
        if (board.empty() || board[0].empty()) return false;
        int m = board.size(), n = board[0].size();
        //这个标识非常有用，因为之后我们还要用它来解数独
        vector<vector<bool> > rowFlag(m, vector<bool>(n, false));//ffffffff以8个bit代表每个数字在m行有没有出现，默认是没有
        vector<vector<bool> > colFlag(m, vector<bool>(n, false));//ffffffff
        vector<vector<bool> > cellFlag(m, vector<bool>(n, false));//
        for (int i = 0; i < m; ++i) 
        {
            for (int j = 0; j < n; ++j)
            {
                if (board[i][j] >= '1' && board[i][j] <= '9') 
                {
                    int c = board[i][j] - '1';
                    if (rowFlag[i][c] || colFlag[j][c] || cellFlag[3 * (i / 3) + j / 3][c]) return false;//如果已行/列/小格出现，无效
                    rowFlag[i][c] = true;
                    colFlag[j][c] = true;
                    cellFlag[3 * (i / 3) + j / 3][c] = true;
                }
            }
        }
        return true;

    }
//得到下一个空格
    pair<int,int> getNextblank(vector<vector<char>>& board,pair<int,int> pos,char c)
    {

        for(int i=pos.first;i!=board.size();++i)
            for(int j=0;j!=board[0].size();++j)
            {
                if(board[i][j]==c&&(i*board[0].size()+j>pos.first*board[0].size()+pos.second))
                    return {i,j};
            }
        return {};

    }
    //返回可插入的字符列表
    vector<bool> getValidChar(vector<vector<char>>& board,pair<int,int> pos,vector<vector<bool> > rowFlag,vector<vector<bool> > colFlag,
                             vector<vector<bool> > cellFlag)
    {
        int m = board.size(), n = board[0].size();
        int row=pos.first; int col=pos.second;
        auto chars1=rowFlag[row];
        auto chars2=colFlag[col];
        auto chars3=cellFlag[3 * (row/ 3) + col / 3];
        vector<bool> result(chars1.size(),false);
        for(int i=0;i!=chars1.size();++i)
        {
            if(!chars1[i]&&!chars2[i]&&!chars3[i])
                result[i]=true;  
            else
                result[i]=false;
        }
        return result;        
    }

};