> response to the question of whether sequence A is a sub-
> sequence of sequence B.
If you can't solve this really fast it means you haven't practiced enough for the interviews.
> of course calculating the permutations of a list is n-
> squared
If I understand you correctly, it is actually n!, because there are n! permutations of n objects.
Basically, your problem seems to be lack of preparation. You study a lot but you haven't studied things that are asked in the interviews well enough.
I would recommend "Cracking the Coding Interview" book. Of course you need to actually solve problems from it. There is lots of valuable advice there. Courses on algorithms on Coursera are also pretty good.