Leetcode #1218: Longest Arithmetic Subsequence of Given Difference
In this guide, we solve Leetcode #1218 Longest Arithmetic Subsequence of Given Difference in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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. A subsequence is a sequence that can be derived from arr by deleting some or no elements without changing the order of the remaining elements.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Hash Table, Dynamic Programming
Intuition
Fast membership checks and value lookups are the heart of this problem, which makes a hash map the natural choice.
By storing what we have already seen (or counts/indexes), we can answer the question in one pass without backtracking.
Approach
Scan the input once, using the map to detect when the condition is satisfied and to update state as you go.
This keeps the solution linear while remaining easy to explain in an interview setting.
Steps:
- Initialize a hash map for seen items or counts.
- Iterate through the input, querying/updating the map.
- Return the first valid result or the final computed value.
Example
Input: arr = [1,2,3,4], difference = 1
Output: 4
Explanation: The longest arithmetic subsequence is [1,2,3,4].
Python Solution
class Solution:
def longestSubsequence(self, arr: List[int], difference: int) -> int:
f = defaultdict(int)
for x in arr:
f[x] = f[x - difference] + 1
return max(f.values())
Complexity
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.