<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());
        int n = nums.size();
        vector<int> subset_length(n,0);
        vector<int> previous_index(n,0);
        subset_length[0] = 1;
        previous_index[0] = -1;
        for(int i=1 ; i<n ; i++){
            subset_length[i] = 1;
            previous_index[i] = -1;

            for(int j = 0 ; j<i ; j++){
                if(nums[i] % nums[j] == 0){
                    if(subset_length[j] + 1 > subset_length[i]){
                        subset_length[i] = subset_length[j] + 1;
                        previous_index[i] = j ; 
                    }
                }
            }
        }
        int max_subset_length = 0;
        int max_subset_index = -1;
        for(int  i =0 ; i<n ; i++){
            if(subset_length[i] >= max_subset_length){
                max_subset_length = subset_length[i];
                max_subset_index = i;
            }
        }
        vector<int> result;
        while(max_subset_index != -1){
            result.push_back(nums[max_subset_index]);
            max_subset_index = previous_index[max_subset_index];
        }
        return result;
    }
};
*/

class Solution {
public:
    vector<int> largestDivisibleSubset(vector<int>& nums) {
        int n = nums.size();
        vector<int> dp(n,1) , hash(n);
        int maxi = 1;
        int lastIndex = 0;
        sort(nums.begin(),nums.end());
        for(int i = 0 ; i < n ; i++){
            hash[i] = i;
            for(int prev = 0 ; prev < i ; prev++){
                if(nums[i] % nums[prev] == 0 && 1 + dp[prev] > dp[i]){
                    dp[i]= 1 + dp[prev];
                    hash[i] = prev;
                }
            }
            if(dp[i] > maxi){
                maxi = dp[i];
                lastIndex = i;
            }
        }
        vector<int> temp;
        temp.push_back(nums[lastIndex]);
        while(hash[lastIndex] != lastIndex){
            lastIndex = hash[lastIndex];
            temp.push_back(nums[lastIndex]);
        }
        reverse(temp.begin(),temp.end());
        return temp;
    }
};
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