# Share my C++ solution with some explanations

• Sort the set of distinct positive integers in descending order
if i < j < k, and nums[i] % nums[j] ==0, and nums[j] % nums[k] == 0, then there must be nums[i] % nums[k] == 0, that is why we need do sorting
dp[i] = max (dp[i], dp[j] + 1), 0 <= j < i && nums[j] % nums[i] == 0

``````class Solution {
public:
vector<int> largestDivisibleSubset(vector<int>& nums) {
vector<int> ret;
int n = nums.size();
if (n == 0)
return ret;

sort(nums.begin(), nums.end(), greater<int>());

vector<int> dp(n, 1);
vector<int> path(n, 0);
int max_len = 1;
int start = 0;

for (int i = 0; i < n; i++)
path[i] = i;

for (int i = 1; i < n; i++)
{
for (int j = 0; j < i; j++)
{
if (nums[j] % nums[i] == 0)
{
if (dp[i] < dp[j] + 1)
{
dp[i] = dp[j] + 1;
path[i] = j;

if (max_len < dp[i])
{
max_len = dp[i];
start = i;
}
}
}
}
}

while (path[start] != start)
{
ret.push_back(nums[start]);
start = path[start];
}
ret.push_back(nums[start]);

return ret;
}
};
``````

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