The Skyline Problem

Sweep x-coordinates from left to right. Sort buildings by their left edge and use a max-heap containing active (height, rightEdge) pairs. At each next event x, add every building starting there, and remove heap entries whose right edge is at or before x. The current skyline height is the heap's maximum height, or zero when no building is active. Emit [x, height] only when this height differs from the previously emitted height. Process all starts and ends at the same x together before emitting, otherwise duplicate x-coordinates or temporary incorrect heights appear. A common implementation chooses the next x from either the next building start or the nearest active end. Time is O(n log n) for sorting and heap operations, with O(n) space. Equivalent event formulations encode starts and ends explicitly but need careful tie ordering.