Circular Queue Implementation Using Array in DSA Python - Time & Space Complexity

Time Complexity: Circular Queue Implementation Using Array

O(1)

Understanding Time Complexity

We want to understand how fast operations run in a circular queue using an array.

Specifically, how the time to add or remove items changes as the queue grows.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

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

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

This code adds (enqueue) and removes (dequeue) items in a circular queue using an array.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Single-step index update and assignment in enqueue and dequeue.
• How many times: Each enqueue or dequeue runs once per call, no loops inside.

How Execution Grows With Input

Each enqueue or dequeue does a fixed number of steps regardless of queue size.

Input Size (n)	Approx. Operations
10	5-6 steps per operation
100	5-6 steps per operation
1000	5-6 steps per operation

Pattern observation: The number of steps stays about the same no matter how big the queue is.

Final Time Complexity

Time Complexity: O(1)

This means adding or removing an item takes the same short time no matter how many items are in the queue.

Common Mistake

[X] Wrong: "Because the queue uses an array, enqueue or dequeue must check many elements, so it takes longer as the queue grows."

[OK] Correct: The circular queue uses index math to jump directly to the right spot, so it does not scan or loop through elements.

Interview Connect

Understanding constant time operations in data structures like circular queues shows you can design efficient systems that handle data smoothly.

Self-Check

"What if we changed the circular queue to a normal queue using a list that shifts elements on dequeue? How would the time complexity change?"

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