Suppose a circular queue of capacity (n – 1) elements is implemented with an array of n elements. Assume that the insertion and deletion operation are carried out using REAR and FRONT as array index variables, respectively. Initially, REAR = FRONT = 0. The conditions to detect queue full and queue empty area)Full: (REAR+1) mod n == FRONT, empty: REAR == FRONTb)Full: (REAR+1) mod n == FRONT, empty: (FRONT+1) mod n == REARc)Full: REAR == FRONT, empty: (REAR+1) mod n == FRONTd)Full: (FRONT+1) mod n == REAR, empty: REAR == FRONTCorrect answer is option 'A'. Can you explain this answer?

Question

Suppose a circular queue of capacity (n &ndash; 1) elements is implemented with an array of n elements. Assume that the insertion and deletion operation are carried out using REAR and FRONT as array index variables, respectively. Initially, REAR = FRONT = 0. The conditions to detect queue full and queue empty area)Full: (REAR+1) mod n == FRONT, empty: REAR == FRONTb)Full: (REAR+1) mod n == FRONT, empty: (FRONT+1) mod n == REARc)Full: REAR == FRONT, empty: (REAR+1) mod n == FRONTd)Full: (FRONT+1) mod n == REAR, empty: REAR == FRONTCorrect answer is option 'A'. Can you explain this answer?

Answer

A circular queue is a data structure that follows the FIFO (First In First Out) principle and has a fixed capacity. It is implemented using a circular array, which means that the last element is connected to the first element, forming a circle.

To implement a circular queue of capacity (n), we need to define the following:

1. A circular array of size n to hold the elements of the queue.
2. Two pointers - front and rear, to keep track of the elements in the queue.
3. A variable - count, to keep track of the number of elements in the queue.

Initially, both front and rear pointers are set to -1, indicating an empty queue. Whenever an element is added to the queue, the rear pointer is incremented by 1, and the element is added to the array at the rear index. If the rear pointer exceeds the array size, it is set to 0, indicating that the queue has wrapped around.

Similarly, whenever an element is removed from the queue, the front pointer is incremented by 1, and the element at the front index is removed from the array. If the front pointer exceeds the array size, it is set to 0, indicating that the queue has wrapped around.

To check if the queue is full, we need to compare the count variable with the capacity (n). If count is equal to n, the queue is full. To check if the queue is empty, we need to check if both front and rear pointers are -1. If they are, the queue is empty.

Here is the implementation of a circular queue of capacity (n) in Python:

```
class CircularQueue:
def __init__(self, capacity):
self.capacity = capacity
self.queue = [None] * capacity
self.front = -1
self.rear = -1
self.count = 0

def enqueue(self, item):
if self.is_full():
print('Queue is full')
return
if self.front == -1:
self.front = 0
self.rear = (self.rear + 1) % self.capacity
self.queue[self.rear] = item
self.count += 1

def dequeue(self):
if self.is_empty():
print('Queue is empty')
return
item = self.queue[self.front]
self.queue[self.front] = None
if self.front == self.rear:
self.front = -1
self.rear = -1
else:
self.front = (self.front + 1) % self.capacity
self.count -= 1
return item

def is_full(self):
return self.count == self.capacity

def is_empty(self):
return self.front == -1

def size(self):
return self.count
```

In this implementation, the enqueue() function adds an element to the rear of the queue, and the dequeue() function removes an element from the front of the queue. The is_full() function checks if the queue is full, and the is_empty() function checks if the queue is empty. The size() function returns the number of elements in the queue.

Note that the modulo operator (%) is used to wrap around the rear and front pointers when they exceed the array size. This ensures that the circular queue works correctly even if the front pointer is ahead of the rear pointer in

Answer

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.

Similar Computer Science Engineering (CSE) Doubts

A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are performed efficiently. Which one of the following statements is CORRECT (n refers to the number of items in the queu e)?

A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are performed efficiently. Which one of the following statements is CORRECT ( nrefers to the number of items in the queu e)?

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