Use a sweep line algorithm with a max-heap to process building start and end events in sorted order, tracking the current maximum height. At each event, update the heap and record a key point if the maximum height changes.
Pro tip: Clarify edge cases upfront, such as adjacent buildings with the same height or zero-width buildings, and mention that the output should exclude redundant points where height doesn't change.
Confirm that the skyline is a list of (x, height) points where the height changes, and that buildings are axis-aligned rectangles. Discuss input format and constraints.
Select a sweep line approach: create events for each building's left and right edges, sort them by x-coordinate, and use a max-heap to track active heights.
Iterate through sorted events. For a left edge, push the height onto the heap; for a right edge, mark it as removed (lazy deletion). After each event, clean the heap top and compare the current max height to the previous one.
When the max height changes, append a key point (x, new height). Handle cases like multiple events at the same x, zero-height buildings, and ensure no duplicate points.
State time complexity O(n log n) due to sorting and heap operations, and space O(n). Walk through a small example to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.