_368.java

package com.fishercoder.solutions;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

/**
 * 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:

 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]
 */
public class _368 {

    public static class Solution1 {
        /** Credit: https://discuss.leetcode.com/topic/49652/classic-dp-solution-similar-to-lis-o-n-2 */
        public List<Integer> largestDivisibleSubset(int[] nums) {
            int len = nums.length;
            int[] count = new int[len];
            int[] pre = new int[len];
            Arrays.sort(nums);
            int max = 0;
            int index = -1;
            for (int i = 0; i < len; i++) {
                count[i] = 1;
                pre[i] = -1;
                for (int j = i - 1; j >= 0; j--) {
                    if (nums[i] % nums[j] == 0) {
                        if (1 + count[j] > count[i]) {
                            count[i] = count[j] + 1;
                            pre[i] = j;
                        }
                    }
                }
                if (count[i] > max) {
                    max = count[i];
                    index = i;
                }
            }
            List<Integer> res = new ArrayList<>();
            while (index != -1) {
                res.add(nums[index]);
                index = pre[index];
            }
            return res;
        }
    }

}