N-Queens
<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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0000-0099/0051.N-Queens/images/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>
Array; Backtracking
public class Solution {
    private int n;
    private int[] col;
    private int[] dg;
    private int[] udg;
    private IList<IList<string>> ans = new List<IList<string>>();
    private IList<string> t = new List<string>();

    public IList<IList<string>> SolveNQueens(int n) {
        this.n = n;
        col = new int[n];
        dg = new int[n << 1];
        udg = new int[n << 1];
        dfs(0);
        return ans;
    }

    private void dfs(int i) {
        if (i == n) {
            ans.Add(new List<string>(t));
            return;
        }
        for (int j = 0; j < n; ++j) {
            if (col[j] + dg[i + j] + udg[n - i + j] == 0) {
                char[] row = new char[n];
                Array.Fill(row, '.');
                row[j] = 'Q';
                t.Add(new string(row));
                col[j] = dg[i + j] = udg[n - i + j] = 1;
                dfs(i + 1);
                col[j] = dg[i + j] = udg[n - i + j] = 0;
                t.RemoveAt(t.Count - 1);
            }
        }
    }
}
