<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:
    string pattern(int c, int n) {
        string s(n, '.');
        s[c] = 'Q';
        return s;
    }

    void helper(int n, int r, vector<int> col_track, vector<int> main_dia,
                vector<int> anti_dia, vector<string> temp,
                vector<vector<string>>& ans) {
        // Part of answer
        if (r == n) {
            ans.push_back(temp);
            return;
        }

        for (int i = 0; i < n; i++) {
            int sum = r+i;
            int sub = r-i;
            if(col_track[i] == 1 || main_dia[sub+n-1] == 1 || anti_dia[sum] == 1)
                continue;

            col_track[i] = 1;
            main_dia[sub+n-1] = 1;
            anti_dia[sum] = 1;
            string s = pattern(i, n);
            temp.push_back(s);
            helper(n, r + 1, col_track, main_dia, anti_dia, temp, ans);
            col_track[i] = 0;
            main_dia[sub+n-1] = 0;
            anti_dia[sum] = 0;
            temp.pop_back();
        }
        return;
    }

    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> ans;
        vector<int> col_track(n,0);
        vector<int> main_dia(2*n-1,0);
        vector<int> anti_dia(2*n,0);
        helper(n, 0, col_track, main_dia, anti_dia, {}, ans);
        return ans;
    }
};
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