# [Solved] Given an array nums of integers, return the length of the longest arithmetic subsequence in nums.

## Question

Given an array `nums` of integers, return the length of the longest arithmetic subsequence in `nums`.

Recall that a subsequence of an array `nums` is a list `nums[i1], nums[i2], ..., nums[ik]` with `0 <= i1 < i2 < ... < ik <= nums.length - 1`, and that a sequence `seq` is arithmetic if `seq[i+1] - seq[i]` are all the same value (for `0 <= i < seq.length - 1`).

Example 1:

```Input: nums = [3,6,9,12]
Output: 4
Explanation:
The whole array is an arithmetic sequence with steps of length = 3.
```

Example 2:

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

Example 3:

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

Constraints:

• `2 <= nums.length <= 1000`
• `0 <= nums[i] <= 500`

## Python Solution

```class Solution:
def longestArithSeqLength(self, A: List[int]) -> int:
d = {}
n = len(A)

for i in range(n):
for j in range(i+1,n):
if (i,A[j]-A[i]) not in d:
d[(j,A[j]-A[i])] = 1
else:
d[(j,A[j]-A[i])] = 1 + d[(i,A[j]-A[i])]

# print(d)
m = 0
for i in d:
m = max(m,d[i])

return m+1``` ##### Abhishek Sharma

Started my Data Science journey in my 2nd year of college and since then continuously into it because of the magical powers of ML and continuously doing projects in almost every domain of AI like ML, DL, CV, NLP.

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