<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:
    unordered_set<int> cols; 
    unordered_set<int> rows; 
    unordered_set<int> diag1; 
    unordered_set<int> diag2;

    bool check(int x, int y){
        if (rows.count(x) || cols.count(y) || diag1.count(x - y) || diag2.count(x + y)) return false;

        return true; 
    }

    void helper(int x, int y, vector<string> &curr, vector<vector<string>> &ans){
        if (x == curr.size()){
            ans.push_back(curr);
            return;
        }
        if (y == curr.size()){
            return;
        }

        if (check(x, y)){
            curr[x][y] = 'Q';
            
            rows.insert(x);
            cols.insert(y);
            diag1.insert(x - y);
            diag2.insert(x + y);

            helper(x + 1, 0, curr, ans);
            
            diag2.erase(x + y);
            diag1.erase(x - y);
            cols.erase(y);
            rows.erase(x);
            
            curr[x][y] = '.';
        }

        helper(x, y + 1, curr, ans);
    }

    vector<vector<string>> solveNQueens(int n) {
        vector<string> curr; 
        vector<vector<string>> ans;

        string x; 

        for (int i = 0; i < n; i++) x.push_back('.');

        for (int i = 0; i < n; i++) curr.push_back(x);

        helper(0, 0, curr, ans);

        return ans;
    }
};
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