Leetcode 368. Largest Divisible Subset

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]

Analysis:
The idea is the same as LIS.



Code (Java):

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class Solution {     public List<Integer> largestDivisibleSubset(int[] nums) {         List<Integer> ans = new ArrayList<>();         if (nums == null || nums.length == 0) {             return ans;         }                   Arrays.sort(nums);                   int[] dp = new int[nums.length];         int max = 1;         for (int i = 0; i < nums.length; i++) {             dp[i] = 1;             for (int j = 0; j < i; j++) {                 if (nums[i] % nums[j] == 0) {                     dp[i] = Math.max(dp[i], dp[j] + 1);                     max = Math.max(max, dp[i]);                 }             }         }                   // print the largest set         //         int i = nums.length - 1;         while (i >= 0 && dp[i] != max) {             i--;         }                   ans.add(nums[i]);         i--;         max--;                   while (i >= 0) {             if ((ans.get(ans.size() - 1) % nums[i]) == 0 && dp[i] == max) {                 ans.add(nums[i]);                 max--;             }             i--;         }                             return ans;     } }