[gamegoblin]

Most in-place algorithms. E.g. quicksort

You can do merge sort in Haskell asymptotically as well as C, but not quicksort (because you can't mutate things in place).

I am of course omitting things like ST which do give you this sort of ability in Haskell, but I doubt that's what the OP meant by "purely functional".

[whateveracct]

ST is exactly the same sort of thing junke was talking about, except it also uses the type system to ensure the imperative core doesn't leak into the outside world.