Queue Implementation: The Circular Buffer

Efficient Queue Implementation: The Circular Buffer

A standard array-based queue requires $O(N)$ time complexity for the dequeue operation because all subsequent elements must be shifted forward. To achieve efficient $O(1)$ operation time, we use a Circular Buffer (or Ring Queue).

The Circular Buffer uses a fixed-size array (Capacity) and two pointers: front (for dequeue) and rear (for enqueue). The array acts as a continuous loop using the modulo operator (%) to handle index wrapping.

Operation	Pointer Logic	Effect
Enqueue (Add)	rear = (rear + 1) % Capacity	Inserts at the next available spot.
Dequeue (Remove)	front = (front + 1) % Capacity	Moves the starting point forward.

Benefit: This structure ensures both insertion and removal take constant time, regardless of the queue size.

Performance Analysis (Circular Buffer)

The primary advantage of the Circular Buffer is achieving $O(1)$ time complexity for all core operations, making it highly suitable for real-time systems and fixed-memory constraints.

Operation	Time Complexity	Space Complexity	Details
Enqueue	$O(1)$	$O(N)$ Fixed	Constant time addition.
Dequeue	$O(1)$	$O(N)$ Fixed	Constant time removal (no shifting).
Peek (Front)	$O(1)$	$O(1)$	Directly accesses front index.

Implementation Caveats: Full vs. Empty

A major challenge in circular buffer implementation is that both an empty queue and a full queue can result in front == rear.

Two Common Solutions:

1. The Sentinel Approach: Always leave one slot empty. The queue is full when (rear + 1) % Capacity == front.
2. The Counter Approach: Maintain an explicit integer count variable. If count == 0, it is empty; if count == Capacity, it is full. This removes the need to waste a slot.