module SlowQueue exposing
  (Queue, empty, isEmpty, enqueue, dequeue, peek)

type Queue a =
  Q (List a)

empty : Queue a
empty =
  Q []

isEmpty : Queue a -> Bool
isEmpty q =
  q == empty

enqueue : a -> Queue a -> Queue a      -- Theta(n)
enqueue x (Q xs) =
  Q (xs ++ [x])

dequeue : Queue a -> Maybe (Queue a)   -- O(1)
dequeue (Q xs) =
  case xs of
    _::xs_ -> Just (Q xs_)
    []     -> Nothing

peek : Queue a -> Maybe a              -- O(1)
peek (Q xs) =
  case xs of
    x::_   -> Just x
    []     -> Nothing