# LeetCode - 1027 - Longest Arithmetic Subsequence

## Problem

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

/**
* @param {number[]} A
* @return {number}
*/
var longestArithSeqLength = function(A) {
let maxSteps = 0;
for (let i=0;i<A.length;i++){
for (let j=i+1;j<A.length;j++){
let step = A[j] - A[i];
let nextStep = A[j] + step;
let curSteps = 2;
for (let k=j+1;k<A.length;k++){
if (A[k] == nextStep){
nextStep += step;
curSteps++;
}
}
if (curSteps > maxSteps) maxSteps = curSteps;
}
}
return maxSteps;

};


Details

Runtime: 1596 ms, faster than 52.53% of JavaScript online submissions for Longest Arithmetic Subsequence.

Memory Usage: 37.3 MB, less than 87.88% of JavaScript online submissions for Longest Arithmetic Subsequence.