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
impl Solution {
    pub fn largest_divisible_subset(nums: Vec<i32>) -> Vec<i32> {
        let mut nums = nums;
        nums.sort();

        let n = nums.len();
        let mut f = vec![1; n];
        let mut k = 0;

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

        let mut m = f[k];
        let mut ans = Vec::new();

        for i in (0..=k).rev() {
            if nums[k] % nums[i] == 0 && f[i] == m {
                ans.push(nums[i]);
                k = i;
                m -= 1;
            }
        }

        ans
    }
}
