# Longest Arithmetic Subsequence of Given Difference

Given an integer array arr and an integer difference, return the length of the longest subsequence in arr which is an arithmetic sequence such that the difference between adjacent elements in the subsequence equals difference.

Example 1:

Input: arr = [1,2,3,4], difference = 1
Output: 4
Explanation: The longest arithmetic subsequence is [1,2,3,4].


Example 2:

Input: arr = [1,3,5,7], difference = 1
Output: 1
Explanation: The longest arithmetic subsequence is any single element.


Example 3:

Input: arr = [1,5,7,8,5,3,4,2,1], difference = -2
Output: 4
Explanation: The longest arithmetic subsequence is [7,5,3,1].


Constraints:

• 1 <= arr.length <= 10^5
• -10^4 <= arr[i], difference <= 10^4

Solution:

Count the length of valid array that ends at position i: then cnt[num[i]] = cnt[num[i]-d]+1

class Solution {
public:
int longestSubsequence(vector<int>& arr, int diff) {
unordered_map<int,int> pos;

int ans = 1;

for(int i : arr){
pos[i] = max(pos[i],pos[i-diff]+1);
ans = max(ans, pos[i]);
}

return ans;
}
};