<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:
    bool isSafe(int line, int col, int n, vector<string> &temp,
        vector<bool> hor, vector<bool> ver, vector<bool> diag1, vector<bool> diag2) {

        if(hor[line] || ver[col] || diag1[n-(col-line)] || diag2[line+col])
            return false;
        return true;
    }
    void nQueens_rec(int line, int n, vector<string> &temp, vector<vector<string>> &res, 
        vector<bool> hor, vector<bool> ver, vector<bool> diag1, vector<bool> diag2) {

        if(line >= n) {
            res.push_back(temp);
            return;
        }

        for(int col=0; col<n; col++) {
            if(isSafe(line, col, n, temp, hor, ver, diag1, diag2)) {
                temp[line][col] = 'Q';
                hor[line] = true;
                ver[col] = true;
                diag2[line+col] = true;
                diag1[n-(col-line)] = true;
                nQueens_rec(line+1, n, temp, res, hor, ver, diag1, diag2);
                temp[line][col] = '.';
                hor[line] = false;
                ver[col] = false;
                diag2[line+col] = false;
                diag1[n-(col-line)] = false;
            }
        }

    }
    vector<vector<string>> solveNQueens(int n) {
        string temp = "";
        for(int i=0; i<n; i++) 
            temp += '.';
        
        vector<string> tempRes;
        for(int i=0; i<n; i++)
            tempRes.push_back(temp);
        
        // hashing
        vector<bool> hor(n, false);
        vector<bool> ver(n, false);
        vector<bool> diag1(2*n, false);
        vector<bool> diag2(2*n - 1, false);
        
        vector<vector<string>> res;
        nQueens_rec(0, n, tempRes, res, hor, ver, diag1, diag2);
        return res;
    }
};
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