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
function solveNQueens(n: number): string[][] {
    const col: number[] = Array(n).fill(0);
    const dg: number[] = Array(n << 1).fill(0);
    const udg: number[] = Array(n << 1).fill(0);
    const ans: string[][] = [];
    const t: string[][] = Array.from({ length: n }, () => Array(n).fill('.'));
    const dfs = (i: number) => {
        if (i === n) {
            ans.push(t.map(x => x.join('')));
            return;
        }
        for (let j = 0; j < n; ++j) {
            if (col[j] + dg[i + j] + udg[n - i + j] === 0) {
                t[i][j] = 'Q';
                col[j] = dg[i + j] = udg[n - i + j] = 1;
                dfs(i + 1);
                col[j] = dg[i + j] = udg[n - i + j] = 0;
                t[i][j] = '.';
            }
        }
    };
    dfs(0);
    return ans;
}
