Problem

Write methods to implement queues in a circular array with one unused entry in the array. That is, we consider that the array is full when the rear is two positions before the front; when the rear is one position before, it will always indicate an empty queue.

The word deque (pronounced either "deck" or "DQ") is a shortened form of double-ended queue and denotes a list in which entries can be added or removed from either the first or the last position of the list, but no changes can be made elsewhere in the list. Thus a deque is a generalization of both a stack and a queue. The fundamental operations on a deque are append_front, append_rear, serve_front, serve_rear, retrieve_front, and retrieve_rear.