Circular Queue Implementation Using Array in DSA Python - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Circular Queue Enqueue and Dequeue Operations

What is the printed state of the circular queue after performing the following operations?

Initialize queue with size 5.
Enqueue 10, 20, 30.
Dequeue one element.
Enqueue 40, 50.
Dequeue two elements.
Enqueue 60, 70.

Print the queue elements from front to rear.

DSA Python

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

    def enqueue(self, data):
        if (self.rear + 1) % self.size == self.front:
            return "Queue is Full"
        elif self.front == -1:
            self.front = 0
            self.rear = 0
            self.queue[self.rear] = data
        else:
            self.rear = (self.rear + 1) % self.size
            self.queue[self.rear] = data

    def dequeue(self):
        if self.front == -1:
            return "Queue is Empty"
        data = self.queue[self.front]
        if self.front == self.rear:
            self.front = -1
            self.rear = -1
        else:
            self.front = (self.front + 1) % self.size
        return data

    def display(self):
        if self.front == -1:
            return []
        elements = []
        i = self.front
        while True:
            elements.append(self.queue[i])
            if i == self.rear:
                break
            i = (i + 1) % self.size
        return elements

cq = CircularQueue(5)
cq.enqueue(10)
cq.enqueue(20)
cq.enqueue(30)
cq.dequeue()
cq.enqueue(40)
cq.enqueue(50)
cq.dequeue()
cq.dequeue()
cq.enqueue(60)
cq.enqueue(70)
print(cq.display())

A [20, 30, 40, 50]

B [30, 40, 50, 60, 70]

C [40, 50, 60, 70]

D [10, 20, 30, 40]

💡 Hint

Remember that the circular queue wraps around when rear reaches the end of the array.

After the operations, the queue contains 40, 50, 60, 70 in order from front to rear. Earlier elements were dequeued.

🧠 Conceptual

intermediate

Understanding Circular Queue Full Condition

In a circular queue implemented using an array of size 6, which condition correctly checks if the queue is full?

A rear == size - 1

B front == 0 and rear == size - 1

C front == rear

D (rear + 1) % size == front

💡 Hint

Think about how the rear wraps around to the front in a circular queue.

The queue is full when the next position of rear (circularly) is front, meaning no space left.

🔧 Debug

advanced

Identify the Bug in Circular Queue Dequeue Method

What error will occur when running this dequeue method if the queue is empty?

DSA Python

def dequeue(self):
    if self.front == -1:
        return "Queue is Empty"
    data = self.queue[self.front]
    if self.front == self.rear:
        self.front = -1
        self.rear = -1
    else:
        self.front = (self.front + 1) % self.size
    return data

cq = CircularQueue(3)
cq.dequeue()

A Returns 'Queue is Empty' string

B IndexError: list index out of range

C TypeError: unsupported operand type(s)

D AttributeError: 'CircularQueue' object has no attribute 'queue'

💡 Hint

Check what happens when front is -1 and dequeue is called.

The method returns the string 'Queue is Empty' when the queue is empty, no error occurs.

❓ Predict Output

advanced

Result of Circular Queue After Wrap-Around Enqueue

Given a circular queue of size 4, what is the queue content after these operations?

Enqueue 1, 2, 3.
Dequeue one element.
Enqueue 4.
Enqueue 5.

Print the queue elements from front to rear.

DSA Python

cq = CircularQueue(4)
cq.enqueue(1)
cq.enqueue(2)
cq.enqueue(3)
cq.dequeue()
cq.enqueue(4)
cq.enqueue(5)
print(cq.display())

A [2, 3, 4, 5]

B [1, 2, 3, 4]

C [3, 4, 5]

D [2, 3, 4]

💡 Hint

Remember the queue size is 4 and it wraps around when full.

After dequeuing 1, the queue has 2,3. Enqueue 4 and 5 fills the queue to [2,3,4,5].

🚀 Application

expert

Maximum Number of Elements in Circular Queue

If a circular queue is implemented using an array of size N, what is the maximum number of elements it can hold without resizing?

A N

B N - 1

C N + 1

D N // 2

💡 Hint

One slot is kept empty to distinguish full and empty states.

To differentiate full and empty states, one slot remains unused, so max elements = N - 1.

Practice

1. What is the main advantage of using a circular queue over a simple linear queue when implemented using an array?

easy

A. It efficiently uses the available space by reusing freed slots.

B. It allows storing different data types in the same queue.

C. It automatically sorts the elements in the queue.

D. It eliminates the need for front and rear pointers.

Solution

1. Step 1: Understand linear queue limitation

   In a linear queue using an array, once rear reaches the end, no more elements can be added even if there is space at the front.

2. Step 2: Circular queue reuses space

   Circular queue connects the end of the array back to the front, allowing reuse of freed slots and efficient space usage.

3. Final Answer:

   It efficiently uses the available space by reusing freed slots. -> Option A

4. Quick Check:

   Space reuse = Advantage [OK]

Hint: Circular queue reuses space unlike linear queue [OK]

Common Mistakes:

• Thinking circular queue sorts elements
• Believing circular queue removes need for pointers
• Assuming it stores multiple data types automatically

2. Which of the following is the correct way to check if a circular queue is full when using an array of size max_size with front and rear pointers?

easy

A. if rear == max_size - 1

B. if rear == front

C. if front == -1

D. if (rear + 1) % max_size == front

Solution

1. Step 1: Understand full condition in circular queue

   The queue is full when the next position of rear (circularly) is front.

2. Step 2: Use modulo for circular increment

   Using modulo operator, (rear + 1) % max_size gives the next position circularly.

3. Final Answer:

   if (rear + 1) % max_size == front -> Option D

4. Quick Check:

   Full condition = (rear + 1) % max_size == front [OK]

Hint: Full when next rear equals front using modulo [OK]

Common Mistakes:

• Checking rear == front means full (actually empty)
• Using rear == max_size - 1 ignores circular wrap
• Checking front == -1 means empty, not full

3. Consider this circular queue code snippet with max_size = 5:

front = 0
rear = 3
queue = [10, 20, 30, 40, None]

# Enqueue operation
rear = (rear + 1) % 5
queue[rear] = 50

# Dequeue operation
front = (front + 1) % 5

print(queue)

What will be the printed output?

medium

A. [10, 20, 30, 40, 50] with front=1 and rear=4

B. [10, 20, 30, 40, None]

C. [10, 20, 30, 40, 50]

D. [10, 20, 30, 40, 50] with front=0 and rear=4

Solution

1. Step 1: Perform enqueue operation

   rear moves from 3 to (3+1)%5 = 4; queue[4] = 50; queue becomes [10, 20, 30, 40, 50]

2. Step 2: Perform dequeue operation

   front moves from 0 to (0+1)%5 = 1; front=1, rear=4

3. Final Answer:

   [10, 20, 30, 40, 50] with front=1 and rear=4 -> Option A

4. Quick Check:

   Enqueue rear=4, Dequeue front=1 [OK]

Hint: Track front and rear updates carefully after enqueue/dequeue [OK]

Common Mistakes:

• Ignoring front and rear pointer updates
• Assuming queue content changes on dequeue
• Confusing front and rear positions

4. The following code snippet for dequeue operation in a circular queue has a bug:

def dequeue(queue, front, rear, max_size):
    if front == -1:
        return None, front, rear  # Queue empty
    data = queue[front]
    if front == rear:
        front = rear = -1
    else:
        front = (front + 1) % max_size
    return data, front, rear

# Initial state
queue = [10, 20, 30, 40, 50]
front = 0
rear = 4

# Dequeue call
value, front, rear = dequeue(queue, front, rear, 5)
print(value, front, rear)

What is the bug in this code?

medium

A. The condition to check empty queue should be rear == -1, not front == -1.

B. The function does not update the queue after dequeue.

C. The function does not handle the case when queue is full.

D. The function incorrectly resets front and rear to -1 when queue becomes empty.

Solution

1. Step 1: Check queue update after dequeue

   The dequeue operation removes the element logically by moving front, but the queue array still holds the old value.

2. Step 2: Identify missing update

   To avoid stale data, the dequeued position should be cleared or updated (e.g., set to None) after dequeue.

3. Final Answer:

   The function does not update the queue after dequeue. -> Option B

4. Quick Check:

   Queue array update after dequeue [OK]

Hint: Dequeue should clear or update the dequeued slot [OK]

Common Mistakes:

• Checking only front for empty queue
• Not resetting pointers correctly after last dequeue
• Ignoring queue full condition in dequeue

5. You have a circular queue of size 6 (indices 0 to 5). Initially, front = 4 and rear = 2. The queue array is:
[70, 80, 90, None, 40, 50]

Which of the following sequences of operations will correctly enqueue 100 and dequeue two elements, updating front and rear properly?

hard

A. Enqueue: rear = (rear + 1) % 6; queue[rear] = 100; Dequeue: front = (front + 1) % 6

B. Enqueue: rear = (rear + 2) % 6; queue[rear] = 100; Dequeue: front = (front + 1) % 6; front = (front + 1) % 6

C. Enqueue: rear = (rear + 1) % 6; queue[rear] = 100; Dequeue: front = (front + 1) % 6; front = (front + 1) % 6

D. Enqueue: rear = (rear + 1) % 6; queue[rear] = 100; Dequeue: front = (front + 2) % 6

Solution

1. Step 1: Enqueue operation

   rear = (2 + 1) % 6 = 3; queue[3] = 100; queue becomes [70, 80, 90, 100, 40, 50]

2. Step 2: Dequeue two elements

   front moves twice: front = (4 + 1) % 6 = 5, then front = (5 + 1) % 6 = 0

3. Final Answer:

   Enqueue: rear = (rear + 1) % 6; queue[rear] = 100; Dequeue: front = (front + 1) % 6; front = (front + 1) % 6 -> Option C

4. Quick Check:

   One enqueue + two dequeues update pointers correctly [OK]

Hint: Increment pointers modulo size for each enqueue/dequeue [OK]

Common Mistakes:

• Incrementing rear or front by more than 1 at once
• Not using modulo for circular wrap
• Dequeueing fewer or more times than asked