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# Longest Arithmetic Sequence

## Longest Arithmetic Sequence

## 题目地址

<https://leetcode.com/problems/longest-arithmetic-sequence/>

## 题目描述

```
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].

Note:
2 <= A.length <= 2000
0 <= A[i] <= 10000
```

## 代码

### Approach #1 DP

`dp[diff][index]` equals to the length of arithmetic sequence at `index` with difference `diff`.

```java
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;
  }
}
```