Of course it's doable. Like I said on my website, I need to get off my ass and start coding up linked lists, binary search trees and sorts "til I fucking throw up all over Manhattan". Yes, of course it's doable. I'm no dummy. I can stumble through it on the whiteboard as well -- I'm not deaf, dumb and clueless -- I don't just stand there at the whiteboard listlessly, with blank stares, if that's what you mean. If I practice enough, reciting from memory (and on the whiteboard), coding the stuff up perfectly will be trivial. But to me, that's gaming the interview.
Rather than memorizing stuff forever, you could develop your intuitions about data structure design trade-offs and what makes them behave the ways they do. After I learned OCaml, a lot of data structure design seemed obvious.
Also, read _Purely Functional Data Structures_ by Chris Okasaki. Unlike (say) CLRS (http://mitpress.mit.edu/algorithms/), it's even a pretty short book.
Exactly. The OP thinks that when I ask her to reverse a linked list, I expect her to whip out the perfect code from memory on the fly. I would be even more suspicious if you did that actually. I want you to structure the data. I want you to try out variants of reversing. It is ok if you can't give me the optimal solution in 5 minutes, as long as you demonstrate the capability to reason with data structures and pointers and tools at hand.
I'd actually recommend not reading Chris's book in isolation. There are a lot of things that are ugly to do in functional languages (w/ respect to data structures), but are easy with assignment (and of course vice-versa). I'd read Chris's book with Sedgewick (Sedgewick is a super applied algorithms text). This will help give a good balance.
I partially suggested it because it uses SML for the code. Even if one doesn't use OCaml / SML for actual programming, using the notation will probably help quite a bit with reasoning about data structures.
