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]

Tips:

DP，复杂度O(n^2)。

两个循环，第二个循环是for(int j = i; j>=0; j--),也就是对i之前的所有数求count的最大值，以便求出遍历到i是可得到的最大值。

除了count数组外，还需要用一个pre数组来存储当前节点的最大因数。

Code：

public class Solution {
    public List<Integer> largestDivisibleSubset(int[] nums) {
        int n = nums.length;
        int[] count = new int[n];
        int[] pre = new int[n];
        Arrays.sort(nums);
        int max = 0, index = 0;
        for (int i = 0; i < n; i++) {
            count[i] = 1;
            pre[i] = -1;
            for (int j = i; j >= 0; j--) {
                if (nums[i] % nums[j] == 0) {
                    if (count[i] < count[j] + 1) {
                        count[i] = count[j] + 1;
                        pre[i] = j;
                    }
                }
            }
            if (count[i] > max) {
                max = count[i];
                index = i;
            }
        }
        List<Integer> res = new ArrayList<>();
        for (int i = 1; i < max; i++) {
            res.add(nums[index]);
            index = pre[index];
        }
        return res;
    }
}