Longest Arithmetic Subsequence of Given Difference

MediumDynamic Programming1d dp

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Problem

Given an integer array arr and an integer difference, find the longest subsequence of arr (elements kept in their original order, not necessarily adjacent) in which each element minus the one before it equals difference. Return the length of that subsequence. A single element always counts, so the answer is at least 1.

Examples

Input: arr = [1,2,3,4], difference = 1
Output: 4
The whole array `[1,2,3,4]` steps by 1.
Input: arr = [1,3,5,7], difference = 1
Output: 1
No two elements differ by exactly 1, so any single element is the best.
Input: arr = [1,5,7,8,5,3,4,2,1], difference = -2
Output: 4
The subsequence `[7,5,3,1]` steps by -2.

Constraints

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

What the interviewer grades

A correct solution is one of five scores. The report also grades problem understanding (did you clarify inputs and edge cases before coding), problem solving, communication while you work, code quality, and testing. See a sample report, or read up on the pattern in the lessons.

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