Circular Queue

How It Works

A circular queue implements FIFO on a fixed array by letting the front and rear positions wrap around with modulo arithmetic. Enqueue writes at the rear and advances it by (rear + 1) mod capacity; dequeue reads at the front and advances it the same way. Wrapping means dequeued slots at the start of the array get reused, so the structure never shifts elements — every operation is O(1) with zero allocation after construction.

The subtle design question is telling full from empty, since front == rear describes both. Standard fixes: keep an explicit size counter, or allocate one extra slot and declare the queue full when (rear + 1) mod capacity == front. This layout is called a ring buffer in systems code.

Step-by-Step Visualization

Code

class CircularQueue {
  int[] arr;
  int front = 0, rear = -1, size = 0, cap;

  CircularQueue(int k) { arr = new int[k]; cap = k; }

  boolean enqueue(int val) {
    if (size == cap) return false;
    rear = (rear + 1) % cap;
    arr[rear] = val;
    size++;
    return true;
  }

  boolean dequeue() {
    if (size == 0) return false;
    front = (front + 1) % cap;
    size--;
    return true;
  }
}

Tips & Gotchas

Practice Problems

• 1Design Circular Queue
• 2Design Circular Deque
• 3Moving Average from Data Stream

About the Queue Design Pattern

Classic design problems that test your understanding of how queues work internally.

Common Queue / Deque Interview Problems

• Binary Tree Level Order Traversal
• Sliding Window Maximum
• Rotting Oranges
• Shortest Path in Binary Matrix
• Implement Queue using Stacks

Frequently Asked Questions

Other Queue Design Techniques