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: 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`

1027. Longest Arithmetic Subsequence
``````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);
}
``````