[AnimalMuppet]

First of all, what's your downside? You didn't seek the interviews, so I suspect you're already employed? Then your downside is that you may waste a vacation day or two on interviews that don't result in a new job. That's not the worst thing in the world.

They aren't necessarily testing your ability to solve the exact problem. The thing is, at Google or FB scale, the difference between o(log n) and o(1) can be huge. It can be millions of dollars in hardware cost. So they really care about the ability of people to find a way to do it in as optimal a way as possible. But, again, they aren't necessarily expecting you to solve it in 30 minutes. They want to watch your thinking process as you tackle the problem.

And, if they do ask something that you know cold, your reward will probably that they very quickly ask something else. They (I presume) aren't trying to see if you know all the algorithms. (We've got this company called Google that does a pretty good job of helping you look up an algorithm if you need it.) They want to see how you work on one you don't.

If I'm reading their intent correctly, then you cannot study well enough for this, because they will move away from what you know. So don't worry that your studying wasn't good enough. Nobody's is. If, from your studying, you kind of got how to attack problems like these, then that's about as good a preparation as is possible.

And if you completely fail... you didn't lose much.