Largest Divisible Subset
<p>Given a set of <strong>distinct</strong> positive integers <code>nums</code>, return the largest subset <code>answer</code> such that every pair <code>(answer[i], answer[j])</code> of elements in this subset satisfies:</p>

<ul>
	<li><code>answer[i] % answer[j] == 0</code>, or</li>
	<li><code>answer[j] % answer[i] == 0</code></li>
</ul>

<p>If there are multiple solutions, return any of them.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3]
<strong>Output:</strong> [1,2]
<strong>Explanation:</strong> [1,3] is also accepted.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,4,8]
<strong>Output:</strong> [1,2,4,8]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 2 * 10<sup>9</sup></code></li>
	<li>All the integers in <code>nums</code> are <strong>unique</strong>.</li>
</ul>
Array; Math; Dynamic Programming; Sorting
function largestDivisibleSubset(nums: number[]): number[] {
    nums.sort((a, b) => a - b);
    const n = nums.length;
    const f: number[] = Array(n).fill(1);
    let k = 0;

    for (let i = 0; i < n; ++i) {
        for (let j = 0; j < i; ++j) {
            if (nums[i] % nums[j] === 0) {
                f[i] = Math.max(f[i], f[j] + 1);
            }
        }
        if (f[k] < f[i]) {
            k = i;
        }
    }

    let m = f[k];
    const ans: number[] = [];
    for (let i = k; m > 0; --i) {
        if (nums[k] % nums[i] === 0 && f[i] === m) {
            ans.push(nums[i]);
            k = i;
            --m;
        }
    }

    return ans;
}
