<p>The <strong>n-queens</strong> puzzle is the problem of placing <code>n</code> queens on an <code>n x n</code> chessboard such that no two queens attack each other.</p>

<p>Given an integer <code>n</code>, return <em>all distinct solutions to the <strong>n-queens puzzle</strong></em>. You may return the answer in <strong>any order</strong>.</p>

<p>Each solution contains a distinct board configuration of the n-queens&#39; placement, where <code>&#39;Q&#39;</code> and <code>&#39;.&#39;</code> both indicate a queen and an empty space, respectively.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/13/queens.jpg" style="width: 600px; height: 268px;" />
<pre>
<strong>Input:</strong> n = 4
<strong>Output:</strong> [[&quot;.Q..&quot;,&quot;...Q&quot;,&quot;Q...&quot;,&quot;..Q.&quot;],[&quot;..Q.&quot;,&quot;Q...&quot;,&quot;...Q&quot;,&quot;.Q..&quot;]]
<strong>Explanation:</strong> There exist two distinct solutions to the 4-queens puzzle as shown above
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> [[&quot;Q&quot;]]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 9</code></li>
</ul>

class Solution {
public:
    vector<vector<string>> solveNQueens(int n) {

        vector<vector<int>> ans;
        vector<vector<string>> Ans;
        vector<int>state(n,-1);
        solve(ans,state,0);
        string s,s1;
        while(n--){
            s+=".";
        }
        vector<string>cur; 
        for(auto it:ans){
            cur.clear();
            for(auto it1:it){
                s1 = s;
                s1[it1] = 'Q';
                cur.push_back(s1);
            }
            Ans.push_back(cur);
        }
        return Ans;
    }
    void solve(vector<vector<int>>&ans,vector<int>state,int m){

        if(check(state,m)){
            if(m==state.size()){
                ans.push_back(state);
                return;}
            else {
                for(int i = 0;i<state.size();i++){
                    state[m]=i;
                    solve(ans,state,m+1);
                }
            }
        }
        return ;
    }

    bool check(vector<int>state,int m){
        if(m==0) return true;
        return (check_v(state,m)&&check_d(state,m));
    }
    bool check_v(vector<int>state,int m){
        for(int i = 0;i<m;i++){
            for(int j = i+1;j<m;j++){
                if(state[i]==state[j]) return false;
            }
        }
        return true;
    }
    bool check_d(vector<int>state,int m){
        for(int i = 0;i<m;i++){
            for(int j = i+1;j<m;j++){
                if(abs(state[i]-state[j])==j-i) return false;
            }
        }
        return true;
    }
};

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