<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>

class Solution {
public:
    vector<int> largestDivisibleSubset(vector<int>& nums) {
        sort(nums.begin(), nums.end());

        pair<size_t, size_t> out;
        vector<vector<int>> dp(nums.size());
        for (size_t i = 0; i < nums.size(); i++) {
            size_t max_j = i;
            for (size_t j = 0; j < i; j++) {
                if (nums[i] % dp[j].back() != 0)
                    continue;
                if (max_j == i || dp[max_j].size() < dp[j].size())
                    max_j = j;
            }
            if (max_j != i) 
                dp[i] = dp[max_j];
            dp[i].push_back(nums[i]);

            if (out.first < dp[i].size())
                out = {dp[i].size(), i};
        }

        return dp[out.second];
    }
};
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