What's Up with O(1)?

Question

I have been noticing some very strange usage of O(1) in discussion of algorithms involving hashing and types of search, often in the context of using a dictionary type provi

Answer 1

In general, I think people use them comparatively without regard to exactness. For example, hash-based data structures are O(1) (average) look up if designed well and you have a good hash. If everything hashes to a single bucket, then it's O(n). Generally, though one uses a good algorithm and the keys are reasonably distributed so it's convenient to talk about it as O(1) without all the qualifications. Likewise with lists, trees, etc. We have in mind certain implementations and it's simply more convenient to talk about them, when discussing generalities, without the qualifications. If, on the other hand, we're discussing specific implementations, then it probably pays to be more precise.