51.N-Queens

N-Queens Total Accepted: 27650 Total Submissions: 104979  Question   Solution

The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other.

Given an integer n, return all distinct solutions to the n-queens puzzle.

Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space respectively.

For example,
There exist two distinct solutions to the 4-queens puzzle: [ [".Q..",  // Solution 1 "...Q", "Q...", "..Q."], ["..Q.",  // Solution 2 "Q...", "...Q", ".Q.."] ]

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思路：回溯法=枚举+约束函数&限界函数，不属于排列树，不属于子集树。

class Solution { public:
    void _backtrack(vector<vector<string>> &res,vector<int> &tem_one_res,int n,int t){
        if(t>=n){
            vector<string> one_res;
            for(auto i:tem_one_res){
                string s(n,'.');
                s[i]='Q';
                one_res.push_back(s);
            }
            res.push_back(one_res);
            return;
        } else{
            for(int j=0;j<n;++j){
                bool attack_flag=false;
                for(int i=0;i<t;++i){
                    if(tem_one_res[i]==j || abs(tem_one_res[i]-j)==(t-i)){
                        attack_flag=true;
                        break;
                    }
                }
                if(!attack_flag){
                    tem_one_res.push_back(j);
                    _backtrack(res,tem_one_res,n,t+1);
                    tem_one_res.pop_back();
                }
            }
        }
    }
    vector<vector<string> > solveNQueens(int n) {
        vector<vector<string>> res;
        if(n<1) return res;
        vector<int> tem_one_res;
        _backtrack(res,tem_one_res,n,0);
        return res;
    }
};