> On the other hand, I genuinely do feel theory is really important. While not knowing the minutia of a tim-sort doesn't indicate that you'll be a bad engineer, not knowing the runtime efficiency of a sort can lead to some really awful code. Not knowing when to use a hash table instead of a nested-for loop can be a sign that you don't really know what you're doing, and not knowing some rough theory on concurrency indicates that I might be stuck debugging your race conditions or deadlock.

Theory is important but what's more important is how someone applies the theory to actual problem solving.

Reversing a binary tree isn't testing your knowledge of theory as much as it's really just testing memorization of a very very specific application. Knowing how to reverse a binary tree or how a hash map works is pointless if the person can't identify when to use them when solving an actual higher level problem. No one is ever given a binary tree and told to reverse it in the real world, they are given a business problem that you identify can be solved efficiently by modelling it as a binary tree and reversing it.

I'd bet most of the good people who fail the "reverse a binary tree" type of questions would succeed if you give them a realistic problem to solve without forcing a very specific solution onto them. Either they will come up to the realization that the solution is to think of the problem in terms of binary tree or they won't.

And neither is a terribly bad answer either. If they recognize you gave them a problem that can be represented as a binary tree and efficiently solved by reversing it then there you go, not only did you prove they knew the "theory" but they knew how to apply it as well. If they don't recognize it you gain valuable insight into their line of thinking and they might find novel ways to represent the problem and apply other theoretical concepts that solve it efficiently (maybe more maybe less).