<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) {
        int n =nums.size();
      sort(nums.rbegin(), nums.rend());
      vector<int>idx(n,-1);
      vector<int>dp(n,1); 
        for(int i=n-1;i>=0;i--){
            for(int j=i+1;j<n;j++){
                if(nums[i]%nums[j]==0){
                    if(1+dp[j]>dp[i]){
                        idx[i]=j;
                        dp[i]=dp[j]+1;
                    }
                }
            }
        }
        
        vector<int>ans;
        int max_idx=-1;
        int max_num=0;
        for(int i=0;i<n;i++){
            if(dp[i]>max_num){
                max_num=dp[i];
                max_idx=i;
            }
        }

        while(max_idx!=-1){
            ans.push_back(nums[max_idx]);
            max_idx=idx[max_idx];
        }

        return ans;
    }
};
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