Largest Divisible Subset

Description

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]

Solution

在一个集合中找到一个满足任两个数之间能整除的最长子集，对顺序没有要求，我们可以先排序

若从小到大排序，则从小到大取数加入子集的过程中满足：新加入的数能被所有已在集合中的数整除，进一步应该满足前一个数是后一个数的因子。

这样我们可以用动态规划得到全局最优解：
设 dp[n] 表示最大数为nums[n]的最长子集，转移方程为：
dp[n] = max{ dp[i] + 1} [前提条件 nums[n] % nums[i] == 0]

Code

class Solution {public:    vector<int> largestDivisibleSubset(vector<int>& nums) {        sort(nums.begin(), nums.end());        vector<int> dp(nums.size(), 1);        vector<int> parent(nums.size(), 0);        for (int i=0; i<nums.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;                    parent[i] = j;                }            }        }        int m = 0, mi = 0;        for (int i=0; i<dp.size(); i++) {            if (dp[i] > m) {                m = dp[i];                mi = i;            }        }        vector<int> ret;        while (m--) {            ret.push_back(nums[mi]);            mi = parent[mi];        }        return ret;    }};

LeetCode 368. Largest Divisible Subset
LeetCode C++ Solution with Explanations