Count number of 1's in binary representation

Question

Efficient way to count number of 1s in the binary representation of a number in O(1) if you have enough memory to play with. This is an interview question I found on an onli

Answer 1

That will be the shortest answer in my SO life: lookup table.

Apparently, I need to explain a bit: "if you have enough memory to play with" means, we've got all the memory we need (nevermind technical possibility). Now, you don't need to store lookup table for more than a byte or two. While it'll technically be Ω(log(n)) rather than O(1), just reading a number you need is Ω(log(n)), so if that's a problem, then the answer is, impossible—which is even shorter.

Which of two answers they expect from you on an interview, no one knows.

There's yet another trick: while engineers can take a number and talk about Ω(log(n)), where n is the number, computer scientists will say that actually we're to measure running time as a function of a length of an input, so what engineers call Ω(log(n)) is actually Ω(k), where k is the number of bytes. Still, as I said before, just reading a number is Ω(k), so there's no way we can do better than that.