Implementation of Deque using circular array

Implement a deque Using a circular array:

Deque or Double Ended Queue is a generalized version of the Queue data structure that allows insert and delete at both ends

Operations on Deque: 

Mainly the following four basic operations are performed on queue: 

• insertFront(): Adds an item at the front of Deque.
• insertRear(): Adds an item at the rear of Deque. 
• deleteFront(): Deletes an item from front of Deque. 
• deleteRear(): Deletes an item from rear of Deque.

In addition to above operations, following operations are also supported 

• getFront(): Gets the front item from queue. 
• getRear(): Gets the last item from queue. 
• isEmpty(): Checks whether Deque is empty or not. 
• isFull(): Checks whether Deque is full or not. 
   

Circular array implementation of Deque:

For implementing deque, we need to keep track of two indices, front, and rear. We enqueue(push) an item at the rear or the front end of the dequeue and dequeue(pop) an item from both the rear and the front end. 

Working: 

Create an empty array ‘arr’ of size N
initialize front = -1 , rear = 0 
Inserting the First element in the deque, at either front or rear will lead to the same result:
 

Note: After inserting Front Points at 0 and Rear points at 0 

Insert Elements at the Rear end of Deque:

a). First we check deque if Full or Not 

b). IF Rear == Size-1 
     then reinitialize Rear = 0 ;
     Else increment Rear by ‘1’
     and push current key into Arr[ rear ] = key 
     Front remain same.      

Insert Elements at the Front end  of Deque:

a). First we check deque if Full or Not

b). IF Front == 0 || initial position, move Front
     to points last index of array
     front = size – 1
     Else decremented front by ‘1’ and push 
     current key into Arr[ Front] = key 
     Rear remain same

Delete Element From Rear end of Deque: 

First Check deque is Empty or Not

If deque has only one element
front = -1 ; rear =-1;

Else IF Rear points to the first index of array
it’s means we have to move rear to points 
last index [ now first inserted element at 
front end become rear end ]  

rear = size-1;
Else || decrease rear by ‘1’  rear = rear-1;

Delete Element From the Front end of Deque:

a). first Check deque is Empty or Not

b).  If deque has only one element
      front = -1 ; rear =-1 ;

Else IF front points to the last index of the array
it’s means we have no more elements in array so 
we move front to points first index of array
front = 0 ;

Else || increment Front by ‘1’  
front = front+1;

Below is the implementation of the above methods: 

Insert element at rear end  : 5 
insert element at rear end : 10 
get rear element  10
After delete rear element new rear become 5
inserting element at front end 
get front element  15
After delete front element new front become 5

Time Complexity: O(N)
Auxiliary Space: O(N)

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