Queues are essential data structures that follow the First-In-First-Out (FIFO) principle. They're used in various applications, from task scheduling to breadth-first search algorithms, ensuring elements are processed in the order they're received.

Queue operations like enqueue and dequeue are performed in constant time, making them efficient for managing collections of elements. Understanding queues is crucial for implementing fair and orderly processing in many real-world scenarios.

Queue ADT and Its Applications

Queue abstract data type

• Represents a collection of elements where items are inserted at one end (rear) and removed from the other end (front)
• Follows the FIFO principle ensures elements are processed in the order they are received (first-come, first-served)
• Provides essential operations for adding and removing elements (enqueue and dequeue) in constant time $O(1)$
• Supports additional operations like checking the front element (front), determining if the queue is empty (isEmpty), and retrieving the number of elements (size)
• Commonly implemented using an array or linked list data structure

FIFO principle in queues

• Fundamental characteristic of queues states that the first element added will be the first one removed (first-in, first-out)
• Ensures elements are processed in the same order they are received preserves the original order of elements
• Implies that elements at the front of the queue have been waiting the longest and will be serviced next
• Contrasts with the LIFO (last-in, first-out) principle used in stack data structures (stack of plates)
• Useful for modeling real-world scenarios where fairness and order of arrival are important (waiting line, ticket counter)

Applications of queues

• Task scheduling manages tasks or processes in a system by executing them in the order they are received (CPU scheduling, print spooler)
• Breadth-First Search (BFS) traverses a graph or tree structure by exploring all neighboring nodes at the current level before moving to the next level (web crawler, social network analysis)
• Message passing in distributed systems enables communication between components by sending messages through a queue (message queue, event bus)
• Event handling in GUI applications maintains a queue of user actions or system events to be processed in the order they occur (keyboard input, mouse clicks)
• Cache management in web browsers uses a queue to store recently accessed web pages and evict the least recently used items when the cache is full (browser history, page caching)

Time complexity of queue operations

• Enqueue operation adds an element to the rear of the queue in constant time $O(1)$ by appending the element to the end of the underlying data structure (array or linked list)
• Dequeue operation removes and returns the element at the front of the queue in constant time $O(1)$ by removing the first element from the underlying data structure
• Front operation returns the element at the front of the queue without removing it in constant time $O(1)$ by accessing the first element of the underlying data structure
• IsEmpty operation checks if the queue is empty in constant time $O(1)$ by comparing the size of the queue to zero or checking if the front and rear pointers are equal
• Size operation returns the number of elements in the queue in constant time $O(1)$ by maintaining a size variable that is updated during enqueue and dequeue operations