FInd overlapping appointments in O(n) time?

Question

I was recently asked this question in an interview. Even though I was able to come up the O(n²) solution, the interviewer was obsessed with an O(<

Answer 1

A naive approach might be to build two parallel trees, one ordered by the beginning point, and one ordered by the ending point of each interval. This allows discarding half of each tree in O(log n) time, but the results must be merged, requiring O(n) time. This gives us queries in O(n + log n) = O(n).