1027. Longest Arithmetic Sequence

Given an array A of integers, return the length of the longest arithmetic subsequence in A.

Recall that a subsequence of A is a list A[i_1], A[i_2], ..., A[i_k] with 0 <= i_1 < i_2 < ... < i_k <= A.length - 1, and that a sequence B is arithmetic if B[i+1] - B[i] are all the same value (for 0 <= i < B.length - 1).

Example 1:

Input: [3,6,9,12]
Output: 4
Explanation: 
The whole array is an arithmetic sequence with steps of length = 3.

Example 2:

Input: [9,4,7,2,10]
Output: 3
Explanation: 
The longest arithmetic subsequence is [4,7,10].

Example 3:

Input: [20,1,15,3,10,5,8]
Output: 4
Explanation: 
The longest arithmetic subsequence is [20,15,10,5].

分析：
对于每个数字A[i]，我们需要知道这个数字A[i]到它之前每个数字A[j] (0 < j < i)的差diff，以及这个差值diff在A[j]那里已经存在了多少次了，并且用那个次数作为A[i]对于A[j].

class Solution {
    public int longestArithSeqLength(int[] A) {
        int res = 2, n = A.length;
        HashMap<Integer, Integer>[] dp = new HashMap[n];
        for (int j = 0; j < A.length; j++) {
            dp[j] = new HashMap<>();
            for (int i = 0; i < j; i++) {
                int d = A[j] - A[i];
                dp[j].put(d, dp[i].getOrDefault(d, 1) + 1);
                res = Math.max(res, dp[j].get(d));
            }
        }
        return res;
    }
}