So far, we have implemented queues where one end is used for enqueuer, and is known as the rear, and the other end is used for dequeuer, and is known as the front. So, in general, each end should be used for a specific purpose. But what if we need to enqueuer and dequeuer from both ends? This is possible by using a concept called the double-ended queue or deque. In deque, both ends can be used for enqueue and dequeue operations. If we look at our queue implementation using linked list, we find that we can insert at last, insert at first, delete at last, and delete at first using our linked list implementation. If we implement a new deque class based on that, we can easily achieve our desired goals. The following figure depicts a double-ended queue:
Here is the implementation of a deque:
class DeQueue {
private $limit;
private $queue...
