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

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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