Queue From Two Stacks

A queue serves items in the order they arrived, while a stack serves the newest item first. Build a class StackQueue that behaves like a queue but keeps its items in two Python lists used only as stacks: add with append, remove with pop() from the end, look at the last item and check the length.

• enqueue(x) adds x at the back of the queue.
• dequeue() removes the item at the front and returns it.
• peek() returns the item at the front without removing it.
• size() returns how many items are waiting.
• is_empty() returns True when the queue holds nothing.

Over a long run of calls, each call should take constant time on average.

Examples

q = StackQueue()
q.enqueue("a")
q.enqueue("b")
q.enqueue("c")
q.dequeue()   # returns 'a'
q.peek()      # returns 'b'
q.enqueue("d")
q.size()      # returns 3
q.is_empty()  # returns False

Constraints

• Up to 100,000 calls in total.
• dequeue and peek are only called when the queue is not empty.