<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>

// void sort(vector<int>& nums) {
//     for(int i = 0; i < nums.size() - 1; ++i) {
//         for(int j = i + 1; j < nums.size(); ++j) {
//             if(nums[j] < nums[i]) {
//                 int temp = nums[j];
//                 nums[j] = nums[i];
//                 nums[i] = temp;
//             }
//         }        
//     }
// }

// class Solution {
// public:
//     vector<int> largestDivisibleSubset(vector<int>& nums) {
//         sort(nums);

//         set<int> numSet;
//         for(const auto & num: nums) {
//             numSet.insert(num);
//         }

//         vector<int> resultSet;
//         for (auto it = nums.rbegin(); it != nums.rend(); ++it) {
//             int currentNum = *it;
//             vector<int> currentSet = {currentNum};
//             for(int i = 1; i < currentNum; ++i) {
//                 if(currentNum % i == 0 && numSet.contains(i)) {
//                     currentSet.push_back(i);
//                 }
//             }
//             auto subResult = largestDivisibleSubset(currentSet);
//             while(subResult.size() != currentSet.size()) {
//                 subResult = largestDivisibleSubset(currentSet);
//             }
//             currentSet = subResult;
//             if(currentSet.size() > resultSet.size()) {
//                 resultSet = currentSet;
//             }
//         }


//         return resultSet;
//     }
// };

class Solution {
public:
    vector<int> largestDivisibleSubset(vector<int>& nums) {
        int size = nums.size();
        sort(nums.begin(), nums.end(), [](const int val1, const int val2)->bool{
            return val1 > val2;
        });
        vector<vector<int>> multChain(size);
        int maxChainSize = 0;
        for(int currIndx = 0; currIndx < size; currIndx++){
            vector<int> currChain = {nums[currIndx]};
            int maxPrevChainSize = 0;
            int maxPrevChainIndx = -1;
            for(int prevIndx = currIndx - 1; prevIndx > -1; prevIndx--){
                int currChainSize = multChain[prevIndx].size();
                if(maxPrevChainSize <  currChainSize && nums[prevIndx] % nums[currIndx] == 0){
                      maxPrevChainSize  = currChainSize;
                      maxPrevChainIndx = prevIndx;
                }
            }
            if(maxPrevChainIndx != -1){
                for(auto mult : multChain[maxPrevChainIndx]){
                    currChain.push_back(mult);
                }
            }
            multChain[currIndx] = currChain;
            maxChainSize = max(maxChainSize, (int)currChain.size());
        }
        for(auto &currChain : multChain){
            if(maxChainSize == currChain.size())return currChain;
        }
        return {};
    }    
};
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