368. Largest Divisible Subset

Difficulty: Medium
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:
nums: [1,2,3]
Result: [1,2] (of course, [1,3] will also be ok)

Example 2:
nums: [1,2,4,8]
Result: [1,2,4,8]

思路

本題是要找到陣列的最大可整除的子集。
首先對無序的陣列進行排序，依次遍歷陣列元素；
用排在當前元素前的每個數去整除該元素；
若可整除，則找到一個當前元素為最大倍數的可整除子集，該子集的元素個數為除數的最大子集個數加一，且該子集中排在當前元素前一位的數為除數，所有可整除子集中元素最多的子集為該元素的最大可整除子集；
所有元素的最大可整除子集中元素最多的即為最終結果。

程式碼

[C++]

class Solution {
public:
    vector<int>
 
 largestDivisibleSubset(vector<int>& nums) {
        vector<int> res;
        if (nums.size() == 0)
            return res;
        sort(nums.begin(), nums.end());
        vector<int> len(nums.size(), 1);
        vector<int> son(nums.size(), 0);
        int largest = 0;
        int
 
 largesti = 0;
        for (int i = 0; i < nums.size(); ++i) {
            for (int j = 0; j < i; ++j) {
                if (nums[i] % nums[j] == 0 && len[i] < len[j] + 1) {
                    len[i] = len[j] + 1;
                    son[i] = j;
                }
            }
            if (largest < len[i]) {
                largesti = i;
                largest = len[i];
            }
        }
        for (int i = 0; i < largest; ++i) {
            res.insert(res.begin(), nums[largesti]);
            largesti = son[largesti];
        }
        return res;
    }
};