I think the problem you would have with your boss would be that your boss asked you 'how long will this program run', and if you told them O(1), the question you are really answering is 'what is the time complexity of this algorithm, parameterised by the number of entries, as the number of entries tends towards infinity'.

If your boss really wanted O(), then they wouldn't care that hashing one key takes a day and another a second, because they're thinking in terms of a hash with infinite entries, so the difference between a day and a second to hash is irrelevant.

If you released software that was exponential, but your QA department only ever tested small inputs, I think it would be negligent to omit to your boss and|or clients the rate at which run-time could expand.

and I think it would be a horrible manager to not care about the difference between a day and a second.

Yeah I agree but my point is none of what you are talking about has anything to do with O(), which doesn't attempt or claim to do what you want to do.

It's like someone gave you a hammer and you're saying it's broken because it doesn't cut wood very well. It's not designed for that.

To implement the hash table you wouldn't have to hash the whole string... of course this will depend on the data that you are trying to store. Assuming that the data is random, 100 bytes vs. 100 terabytes, you only need to figure out what bucket the data is saved. You could still base it on this concept if sightly modified

Yes. A valid hash function certainly can be defined as a F(n): N x N -> n % 100

But that certainly cannot be considered a reasonable hash function. A string is basically an array of bytes (or code-points, in case of UTF-8).

To have any decent property (like, producing different outputs for miniscule changes in the input), you have to touch every element in the array.

For custom objects, yes, you don't have to hash every property, but for strings, yeah, the hash function will almost always depend on the length of the string.