The Skyline Problem
Given the locations and heights of all buildings, output the skyline formed by these buildings. This is a sweep-line algorithm problem, typically solved with a Priority Queue.
Why Interviewers Ask This
Stripe evaluates candidates on their ability to handle complex geometric problems with edge cases. This question tests mastery of sweep-line algorithms and priority queues, requiring precise handling of overlapping intervals and simultaneous events. It specifically assesses logical rigor in managing state transitions when building heights change at identical x-coordinates.
How to Answer This Question
1. Clarify the input format and output requirements, noting that the skyline is a list of key points where height changes. 2. Propose a sweep-line approach: collect all building start and end coordinates as events, sorting them by x-coordinate. 3. Handle ties carefully: process left edges before right edges if x-coordinates match, or prioritize higher buildings first depending on specific logic needs. 4. Use a max-heap (priority queue) to track active building heights efficiently. 5. Iterate through sorted events: add heights for starts, remove heights for ends, and record a new key point only when the current maximum height differs from the previous one. 6. Discuss time complexity O(N log N) due to sorting and heap operations, emphasizing why this beats brute force methods.
Key Points to Cover
- Explicitly defining the tie-breaking logic for simultaneous x-coordinates
- Using a max-heap to efficiently track the current maximum height
- Implementing a lazy removal strategy for the priority queue
- Correctly identifying key points only when the maximum height changes
- Demonstrating O(N log N) time complexity analysis
Sample Answer
To solve the Skyline Problem efficiently, I would treat each building's left and right edges as discrete events. First, I'd create a list of these events, storing the x-coordinate, type (start or end), and height. For st…
Common Mistakes to Avoid
- Failing to handle multiple events at the same x-coordinate correctly, leading to incorrect peaks
- Attempting to remove elements from the heap immediately upon seeing an end event, causing inefficiency
- Ignoring the case where a building ends exactly where another begins, potentially missing a height drop
- Not verifying that the result contains only distinct consecutive points with different heights
Sound confident on this question in 5 minutes
Answer once and get a 30-second AI critique of your structure, content, and delivery. First attempt is free — no signup needed.