<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();
        int maxi=1;
        int LastIndex=0;
        vector<int> dp(n,1), hash(n);
        sort(nums.begin(),nums.end());
        for(int i=0;i<n;i++)
        {
            hash[i]=i;
            for(int prev=0;prev<=i-1;prev++)
            {
                if((nums[i]%nums[prev]==0) && dp[i]<1+dp[prev]) 
                {
                    dp[i]=dp[prev]+1;
                    hash[i]=prev;
                }
            }
            if(dp[i]>maxi)
            {
                maxi=dp[i];
                LastIndex=i;
            }
        }
        vector<int> ans;
        ans.push_back(nums[LastIndex]);
        while(hash[LastIndex]!=LastIndex)
        {
            LastIndex=hash[LastIndex];
            ans.push_back(nums[LastIndex]);
        }
        return ans;
    }
};
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