In a simple array-based queue, once the tail reaches the end, you can't insert back at the beginning even if space is freed. A **Circular Queue** solves this by connecting the end back to the start.

The Magic Formula

next_index = (current + 1) % capacity

This simple modulo operation creates an infinite loop effect, recycling memory perfectly.

The Ring Buffer

Circular Queue simulation

HEAD

TAIL

Wraps around to 0

Priority Queue

Here, the "Fairness" rule changes. Every element has a **priority**. Highest priority items jump the line. Essential for hospital ERs and system interrupts.

O(log n) Insertion

Deque (Double-Ended)

The Swiss Army Knife of linear structures. You can Enqueue and Dequeue from **BOTH** ends. It can act as a Stack AND a Queue simultaneously.

Hybrid Structure

Implementation Matrix

Type	Primary Advantage	Memory Use
Linear Queue	Simple to implement	Wasteful (Dead space)
Circular Queue	Memory Recycling	Optimized
Priority Queue	Importance Based	Moderate (Heap based)
Deque	Maximum Flexibility	Moderate

Queue Fundamentals Real Use Cases