## 1027. 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:4Explanation:The whole array is an arithmetic sequence with steps of length = 3.

**Example 2:**

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

**Example 3:**

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

**Constraints:**

`2 <= A.length <= 1000`

`0 <= A[i] <= 500`

## Rust Solution

```
struct Solution;
use std::collections::HashMap;
impl Solution {
fn longest_arith_seq_length(a: Vec<i32>) -> i32 {
let mut res = 0;
let n = a.len();
let mut dp: Vec<HashMap<i32, i32>> = vec![HashMap::new(); n];
for i in 0..n {
for j in 0..i {
let diff = a[i] - a[j];
let len_j = *dp[j].entry(diff).or_default();
let len_i = dp[i].entry(diff).or_default();
*len_i = len_j + 1;
res = res.max(*len_i);
}
}
res + 1
}
}
#[test]
fn test() {
let a = vec![3, 6, 9, 12];
let res = 4;
assert_eq!(Solution::longest_arith_seq_length(a), res);
let a = vec![9, 4, 7, 2, 10];
let res = 3;
assert_eq!(Solution::longest_arith_seq_length(a), res);
let a = vec![20, 1, 15, 3, 10, 5, 8];
let res = 4;
assert_eq!(Solution::longest_arith_seq_length(a), res);
}
```

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