[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