Surely not BFS. That's something you can figure out from first principles and knowledge of some data structures like stacks and queues, but I'd expect knowledge of those data structures anyway.

Sure, I can, and I did, although I didn't come up with the super-hindsight-obvious solution I'm sure I learned three times over in college.

But it's the interview equivalent of your driving instructor making sure you adjust your side and rear view mirrors before you start the car.

I don’t care if candidates can figure out BFS under intense pressure in 30-60 minutes. That is nobody’s job anywhere ever. I want to know if someone can think creatively, if they’re a pain in the ass to work with, if they’re thoughtful and careful or if they shoot from the hip. Admittedly, these are hard to measure (which is one reason why I would support some kind of mild licensure, but that’s a different subject), but being able to derive BFS does not correlate with competence or ability. Maybe if you’re doing router hacking or something, I guess, but specific algorithms are so little of most developers’ careers.

Honestly, we all might as well read chicken entrails because that would be about as predictive as our current interview practices.

You’d be amazed at how little some otherwise competent people can figure out from first principles in an interview in front of a whiteboard.