Minimize Array Amplitude After Removing a Contiguous Block
Company: Hudson River Trading
Role: Software Engineer
Category: Software Engineering Fundamentals
Difficulty: medium
Interview Round: Technical Screen
Given an array of integers and an integer `K`, remove exactly `K` contiguous elements so that the amplitude of the remaining array, defined as `max(remaining) - min(remaining)`, is minimized. Return the minimum possible amplitude.
### Constraints & Assumptions
- The remaining array is non-empty.
- K is between 0 and n-1 unless clarified.
- The removed elements must be contiguous.
- Aim for O(n) after preprocessing or direct linear scans.
### Clarifying Questions to Ask
- Can K be zero?
- Can numbers be negative?
- If multiple removals tie, do we need the indices?
- What should happen if K equals n?
- How large is n?
### What a Strong Answer Covers
```premium-lock What a Strong Answer Covers
```
### Follow-up Questions
- How would you return the removed interval?
- How would this change for removing up to K elements?
- Can you do it with less memory?
- How would updates to the array affect the design?
Quick Answer: This Hudson River Trading software engineering question evaluates array reasoning for minimizing amplitude after removing a contiguous block. It prepares candidates to think about range effects, prefix and suffix information, and edge cases around removal length.