if i had to come up with a permutation algorithm as part of writing code, you'd better believe i'd look one up so that i'm sure i'm doing things optimally. i wouldn't trust myself to come up with the exactly right algorithm on the first try.
if i had to deal with some weird half-sorted array, i assume i'd be working in the same context as the problem and wouldn't have to make up a solution on the spot with limited details. why do you have a weird-ass data structure like that to begin with? that's the first question i'd ask.
personally i always ask a couple of simple questions (like FizzBuzz) and then talk experience. if you want to see a code sample, ask for one -- written on a computer, without someone hovering over the candidate's shoulder. coding solutions to weird questions on a whiteboard doesn't help anybody.