【Leetcode】Largest Divisible Subset

タイトルリンク:https://leetcode.com/problems/largest-divisible-subset/
タイトル: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]
考え方:dp dp配列は、0~iからi番目の要素を含む最大divisible subset size pre配列から状態遷移中の方向をマークし、最大値を遡及する際の解集を表す.dp[i]=max{dp[i],dp[j]+1}
アルゴリズム:

    public List<Integer> largestDivisibleSubset(int[] nums) {
        LinkedList<Integer> res = new LinkedList<Integer>();
        if (nums.length == 0) {
            return res;
        }
        Arrays.sort(nums);

        int dp[] = new int[nums.length]; //   0~i  nums[i]   subset size
        int pre[] = new int[nums.length];//         size        
        int maxIdx = -1, max = -1;

        for (int i = 0; i < nums.length; i++) { //   
            dp[i] = 1;
            pre[i] = -1;
        }

        for (int i = 1; i < nums.length; i++) {
            for (int j = 0; j < i; j++) {
                if (nums[i] % nums[j] == 0 && dp[i] < dp[j] + 1) {
                    dp[i] = dp[j] + 1;
                    pre[i] = j;// 
                }
            }
        }

        for (int i = 0; i < nums.length; i++) {//       size          
            if (dp[i] > max) {
                max = dp[i];
                maxIdx = i;
            }
        }

        for (int i = maxIdx; i >= 0;) { //    
            res.addFirst(nums[i]);
            i = pre[i];
        }
        return res;
    }