368. Largest Divisible Subset

Posted 2021-02-09 ruruozhenhao

Given a set of distinct positive integers, find the largest subset such that every pair (Si, Sj) of elements in this subset satisfies:

Si % Sj = 0 or Sj % Si = 0.

If there are multiple solutions, return any subset is fine.

Example 1:

Input: [1,2,3]
Output: [1,2] (of course, [1,3] will also be ok)

Example 2:

Input: [1,2,4,8]
Output: [1,2,4,8]

 

Approach #1: DP. [C++]

class Solution {
public:
    vector<int> largestDivisibleSubset(vector<int>& nums) {
        int size = nums.size();
        
        sort(nums.begin(), nums.end());
        
        vector<int> dp(size, 1);
        vector<int> tmp(size, -1);
        vector<int> ans;
        
        if (size == 0) return ans;
        
        int idx = 0;
        for (int i = 0; i < size; ++i) {
            for (int j = 0; j < i; ++j) {
                if (nums[i] % nums[j] == 0 && dp[i] < dp[j] + 1) {
                    dp[i] = dp[j] + 1;
                    tmp[i] = j;
                }
                if (dp[i] > dp[idx]) idx = i;
            }
        }
        for (int i = idx; i != -1; i = tmp[i]) 
            ans.push_back(nums[i]);
        //reverse(ans.begin(), ans.end());
        
        return ans;
    }
};

　　

Analysis:

dp[i] : represent the number of elements in the subset which index from 0 to i.

tmp[i]: the previous factor‘s index of nums[i].