# 1027. Longest Arithmetic Subsequence

[Link](https://leetcode.com/problems/longest-arithmetic-subsequence/)

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

**Example 2:**

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

**Example 3:**

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

**Constraints:**

* `2 <= A.length <= 1000`
* `0 <= A[i] <= 500`

#### Solution

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