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

Assuming you have some constraint on the start and end times, and on the resolution at which you do the scheduling, it seems like it would be fairly easy to turn each appointment into a bitmap of times it does/doesn't use, then do a counting sort (aka bucket sort) on the in-use slots. Since both of those are linear, the result should be linear (though if I'm thinking correctly, it should be linear on the number of time slots rather than the number of appointments).

At least if I asked this as an interview question, the main thing I'd be hoping for is the candidate to ask about those constraints (i.e., whether those constraints are allowed). Given the degree to which it's unrealistic to schedule appointments for 1000 years from now, or schedule to a precision of even a minute (not to mention something like a nanosecond), they strike me as reasonable constraints, but you should ask before assuming them.