<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:
    std::vector<int> largestDivisibleSubset(std::vector<int>& nums) {
        std::sort(nums.begin(), nums.end());
        std::vector<std::vector<int> > dp(nums.size());

        dp[0].push_back(1);
        dp[0].push_back(0);

        int maxSetSize = 1;
        int maxSetIndex = 0;
        for(int i =1; i < nums.size(); i++){
            int curr = nums[i];

            dp[i].push_back(1);
            dp[i].push_back(i);

            for(int j = i-1; j >=0; j--){
                if (! (curr % nums[j]) ){
                    if (dp[i][0] <= dp[j][0]){
                        dp[i][0] = dp[j][0] + 1;
                        dp[i][1] = j;
                    }
                }

            }

            if (dp[i][0] > maxSetSize){
                maxSetSize = dp[i][0];
                maxSetIndex = i;

            }
        }

        // now we have the size of it as maxSetSize;

        std::vector<int> result;
        result.push_back(nums[maxSetIndex]);

        while(dp[maxSetIndex][1] != maxSetIndex){
            maxSetIndex = dp[maxSetIndex][1];
            result.push_back(nums[maxSetIndex]);

        }

        std::reverse(result.begin(), result.end());

        return result;


    }
};
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