<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:
    void mark(int row,int col,vector<vector<bool>> &pos){
        int nx,ny;
        int n = pos.size();
        for(int i=0;i<n;i++){
            pos[row][i] = true;
            pos[i][col] = true;
            nx = row+i;
            ny = col+i;
            if(nx>=0 && nx<n && ny>=0 && ny<n){
                pos[nx][ny] = true;
            }
            nx = row-i;
            ny = col+i;
            if(nx>=0 && nx<n && ny>=0 && ny<n){
                pos[nx][ny] = true;
            }
            nx = row+i;
            ny = col-i;
            if(nx>=0 && nx<n && ny>=0 && ny<n){
                pos[nx][ny] = true;
            }
            nx = row-i;
            ny = col-i;
            if(nx>=0 && nx<n && ny>=0 && ny<n){
                pos[nx][ny] = true;
            }
        }
    }

    void util(int ind,vector<vector<bool>> pos,vector<int> temp,vector<vector<int>>& ans){
        int n = pos.size();
        if(ind==n){
            ans.push_back(temp);
            return;
        }
        vector<vector<bool>> pos2;
        for(int i=0;i<n;i++){
            if(!pos[ind][i]){
                pos2 = pos;
                mark(ind,i,pos2);
                temp.push_back(i);
                util(ind+1,pos2,temp,ans);
                temp.pop_back();
            }
        }
    }
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<bool>> pos(n,vector<bool> (n,false));
        vector<vector<int>> ans;
        util(0,pos,{},ans);
        vector<vector<string>> pla;
        string s(n, '.');
        for(int i=0;i<ans.size();i++){
            vector<string> temp;
            for(int j=0;j<n;j++){
                s[ans[i][j]] = 'Q';
                temp.push_back(s);
                s[ans[i][j]] = '.';
            }
            pla.push_back(temp);
        }
        return pla;
    }
};
31628