<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>> ans;

    void mark(int i, int j, vector<vector<int>>& vis, int n)
    {
        int rows, cols;
        //mark rows
        for(rows = 0; rows < n; rows++)
        {
            vis[rows][j] = 1;
        }

        //mark columns
        for(cols = 0; cols < n; cols++)
        {
            vis[i][cols] = 1;
        }

        //mark diagonals
        // +1, +1
        rows = i;
        cols = j;
        while(rows >= 0 && rows < n && cols >= 0 && cols < n)
        {
            vis[rows][cols] = 1;
            rows += 1;
            cols += 1;
        }

        // -1, -1
        rows = i;
        cols = j;
        while(rows >= 0 && rows < n && cols >= 0 && cols < n)
        {
            vis[rows][cols] = 1;
            rows += -1;
            cols += -1;
        }

        // -1, +1
        rows = i;
        cols = j;
        while(rows >= 0 && rows < n && cols >= 0 && cols < n)
        {
            vis[rows][cols] = 1;
            rows += -1;
            cols += 1;
        }

        // +1, -1
        rows = i;
        cols = j;
        while(rows >= 0 && rows < n && cols >= 0 && cols < n)
        {
            vis[rows][cols] = 1;
            rows += 1;
            cols += -1;
        }
    }

    void f(int i, int j, int n, vector<vector<int>>& vis, vector<string>& v)
    {
        if(i == n)
        {
            ans.push_back(v);
            return;
        }

        string s = "";
        for(int k = j; k < n; k++)
        {
            if(vis[i][k] == 1)
            {
                s = s + ".";
                continue;
            }

            s = s + "Q";
            for(int l = k+1; l < n; l++)
            {
                s = s + ".";
            }
            vector<vector<int>> t = vis;
            mark(i, k, t, n);
            v.push_back(s);
            f(i+1, 0, n, t, v);
            s.erase(k);
            v.pop_back();
            s = s + ".";
        }
    }

    vector<vector<string>> solveNQueens(int n) {
        vector<vector<int>> vis(n, vector<int>(n, 0));
        vector<string> v;
        f(0, 0, n, vis, v);
        return ans;
    }
};
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