Technical Interview Question: Design a circular queue using a doubly linked list in a programming language of your choice. The circular queue should support operations such as enqueuing, dequeuing, checking if the queue is full or empty, and displaying the elements of the queue.

Answer:

# Node class for the doubly linked list
class Node:
    def __init__(self, data):
        self.data = data
        self.next = None
        self.prev = None


# CircularQueue class to implement the circular queue using the doubly linked list
class CircularQueue:
    def __init__(self, k):
        self.capacity = k
        self.size = 0
        self.head = None
        self.tail = None
    
    # Method to enqueue an element into the circular queue
    def enQueue(self, value):
        if self.isFull():
            return False
        new_node = Node(value)
        if self.isEmpty():
            self.head = new_node
            self.tail = new_node
        else:
            self.tail.next = new_node
            new_node.prev = self.tail
            self.head.prev = new_node
            new_node.next = self.head
            self.tail = new_node
        self.size += 1
        return True
    
    # Method to dequeue an element from the circular queue
    def deQueue(self):
        if self.isEmpty():
            return False
        if self.size == 1:
            self.head = None
            self.tail = None
        else:
            self.head = self.head.next
            self.head.prev = self.tail
            self.tail.next = self.head
        self.size -= 1
        return True
     
    # Method to check if the circular queue is empty
    def isEmpty(self):
        return self.size == 0
    
    # Method to check if the circular queue is full
    def isFull(self):
        return self.size == self.capacity
    
    # Method to display the elements of the circular queue
    def display(self):
        if self.isEmpty():
            print("Queue is empty")
        else:
            current = self.head
            while True:
                print(current.data, end=" ")
                current = current.next
                if current == self.head:
                    break
            print()


# Example usage
cq = CircularQueue(5)
cq.enQueue(1)
cq.enQueue(2)
cq.enQueue(3)
cq.display()  # Output: 1 2 3 
cq.deQueue()
cq.display()  # Output: 2 3
cq.enQueue(4)
cq.enQueue(5)
cq.enQueue(6)  # Output: Queue is full

In this example, we have designed a circular queue using a doubly linked list in Python. The CircularQueue class provides methods for enqueuing, dequeuing, checking if the queue is full or empty, and displaying the elements of the queue. The key operations have been implemented such that they maintain the circular nature of the queue using the properties of the doubly linked list.