Condition required to detect queue full and queue empty-quiz question asked in interviews

For the operations given below in a circular queue of (n-1) capacity is implemented with an array of n elements. Condition required to detect queue full and queue empty are:

//initializing index
int FRONT=0
int REAR=0
Insertion and deletion is carried out using FRONT and REAR as array indices

A) Full: (REAR+1) mod n == FRONT, empty: REAR == FRONT

B) Full: (REAR+1) mod n == FRONT, empty: (FRONT+1) mod n == REAR

C) Full: REAR == FRONT, empty: (REAR+1) mod n == FRONT

D) Full: (FRONT+1) mod n == REAR, empty: REAR == FRONT

Correct answer: Option A

Suppose we start filling the queue.

Let the maxQueueSize ( Capacity of the Queue) is 4.
So the size of the array which is used to implement 
this circular queue is 5, which is n.

In the beginning when the queue is empty, FRONT and REAR 
point to 0 index in the array.

REAR represents insertion at the REAR index.
FRONT represents deletion from the FRONT index.

enqueue("a"); REAR = (REAR+1)%5; ( FRONT = 0, REAR = 1)
enqueue("b"); REAR = (REAR+1)%5; ( FRONT = 0, REAR = 2)
enqueue("c"); REAR = (REAR+1)%5; ( FRONT = 0, REAR = 3)
enqueue("d"); REAR = (REAR+1)%5; ( FRONT = 0, REAR = 4)

Now the queue size is 4 which is equal to the maxQueueSize. 
Hence overflow condition is reached.

Now, we can check for the conditions.

When Queue Full :

( REAR+1)%n = (4+1)%5 = 0

FRONT is also 0.

Hence ( REAR + 1 ) %n is equal to FRONT.

When Queue Empty :

REAR was equal to FRONT when empty ( because in the starting 
before filling the queue FRONT = REAR = 0 )

Hence Option A is correct.

Thanks for Reading

Placewit grows the best engineers by providing an interactive classroom experience and by helping them develop their skills and get placed in amazing companies.

Learn more at Placewit. Follow us on Instagram and Facebook for daily learning.