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].



1 class Solution {
 2     public int longestArithSeqLength(int[] A) {
 3         int res = 2, n = A.length;
 4         HashMap<Integer, Integer>[] dp = new HashMap[n];
 5         for (int j = 0; j < A.length; j++) {
 6             dp[j] = new HashMap<>();
 7             for (int i = 0; i < j; i++) {
 8                 int d = A[j] - A[i];
 9                 dp[j].put(d, dp[i].getOrDefault(d, 1) + 1);
10                 res = Math.max(res, dp[j].get(d));
11             }
12         }
13         return res;
14     }
15 }