51. N 皇后

要求:不在横竖斜线
思路:回溯

class Solution {
public:
    vector<vector<string>> v;
    vector<vector<int>> q;
    bool inrow(int i,vector<string> &board){
        for(int k=0;k<board.size();++k)
            if(board[i][k]=='Q')return true;
        return false;
    }
    bool incol(int j,vector<string> &board){
        for(int k=0;k<board.size();++k)
            if(board[k][j]=='Q')return true;
        return false;
    }
    bool inlin(int i,int j,vector<string> &board){
        for(int k=0;k<q.size();++k)
            if(abs(i-q[k][0])==abs(j-q[k][1]))return true;
        return false;
    }
    void dfs(int n,vector<string> &board,int start){
        if(n==q.size()){
            v.push_back(board);
            return;
        }
        for(int i=start;i<n;++i){
            for(int j=0;j<n;++j){
                if(!inrow(i,board)&&!incol(j,board)&&!inlin(i,j,board)){
                    board[i][j]='Q';
                    q.push_back({i,j});
                    dfs(n,board,i+1);
                    q.pop_back();
                    board[i][j]='.';
                }
            }
        }
    }
    vector<vector<string>> solveNQueens(int n) {
        string row = string(n, '.');
        vector<string> board(n,row);
        dfs(n,board,0);
        return v;
    }
};
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