<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> solve(vector<int>& nums ,int index,vector<vector<int>> &dp){
    if(index==nums.size()) return {};
    if(!dp[index].empty()) return dp[index];
    vector<int> ans{nums[index]};
    vector<int> temp;
    for(int j=index+1;j<nums.size();j++){
        if (nums[j] % nums[index] == 0) {
                temp = solve(nums, j, dp);
                if (temp.size() + 1 > ans.size()) {
                    ans = temp;
                    ans.push_back(nums[index]);
                }
            }
    }
    
    // if(temp.size()>=ans.size()) return temp;
    return dp[index]=ans;

    


}
    vector<int> largestDivisibleSubset(vector<int>& nums) {

        sort(nums.begin(),nums.end());
        int n=nums.size();
        vector<vector<int>> dp(n);
        vector<int> res;
        for(int index=n-1;index>=0;index--){
            
                // vector<int> ans{nums[index]};
                dp[index].push_back(nums[index]);
                // vector<int> temp;
                for(int j=index+1;j<nums.size();j++){
                    if (nums[j] % nums[index] == 0 ) {
                            
                            if (dp[j].size() + 1 > dp[index].size()) {
                                dp[index]=dp[j];
                                dp[index].push_back(nums[index]);
                            }
                        }
                }

                            //  for(auto it:ans){
                            //     cout<<it<<" ";
                            //  }
                            //  cout<<endl;


if (dp[index].size() > res.size()) {
                res = dp[index];
            }            //  else dp[index]=ans;
             

        }
        return res;
    }
};
13100