<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) {
        unordered_set<int> col;
        unordered_set<int> posDiag;
        unordered_set<int> negDiag;

        vector<vector<char>> grid(n, vector<char>(n, '.'));
        vector<vector<string>> res;

        dfs(0, col, posDiag, negDiag, grid, res);
        return res;
    }

    void dfs(int r, unordered_set<int>& col, unordered_set<int>& posDiag,
             unordered_set<int>& negDiag, vector<vector<char>>& grid,
             vector<vector<string>>& res) {
        
        if (r == grid.size()) {
            vector<string> result;
            for (const auto& row : grid) {
                result.emplace_back(row.begin(), row.end());
            }
            res.push_back(result);
            return;
        }

        for (int c = 0; c < grid.size(); ++c) {
            if (col.find(c) == col.end() && posDiag.find(r+c) == posDiag.end()
                && negDiag.find(r-c) == negDiag.end()) {

                col.insert(c);
                posDiag.insert(r+c);
                negDiag.insert(r-c);
                grid[r][c] = 'Q';

                dfs(r+1, col, posDiag, negDiag, grid, res);

                col.erase(c);
                posDiag.erase(r+c);
                negDiag.erase(r-c);
                grid[r][c] = '.';
            }
        }        
    }
};
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