Linked lists are a fundamental data structure in computer science, providing a versatile way to store and manipulate collections of data. They offer flexibility in memory usage and ease of insertion and deletion operations, making them particularly useful in various real-world applications. This article explores several key applications of linked lists, illustrating how they are employed in different domains, from software design to database management.

Prerequisite: Fundamentals of Linked List Data Structure.

## Implementation of Stacks and Queues

Stacks and Queues are abstract data structures in computer science, each with distinct characteristics and use cases. A stack data structure follows the Last-In-First-Out (LIFO) principle, where the most recently added element is always at the top and is the first to be removed. This behavior is analogous to a stack of plates, where you can only add or remove plates from the top. Queue data structure, on the other hand, follow the First-In-First-Out (FIFO) principle, resembling a line of people waiting for a service. In a queue, elements are added at one end (called the rear or tail) and removed from the other end (called the front or head).

Linked lists are particularly well-suited for implementing stacks and queues due to the following points:

**Dynamic size**: Linked lists can easily grow or shrink as elements are added or removed, without needing to reallocate memory. This is ideal for stacks and queues, which frequently change in size.**Efficient insertions and deletions**: Linked lists allow for constant-time`O(1)`

insertions and deletions at the beginning (for stacks) or at both ends (for queues). This makes operations like push, pop, enqueue, and dequeue highly efficient.**No size limitations**: Unlike array-based implementations, linked lists don’t require predicting the maximum size in advance. This flexibility is perfect for stacks and queues that may need to accommodate an unknown number of elements.**Memory efficiency**: Linked lists only use memory for the actual elements stored, plus a small overhead for pointers. This can be more memory-efficient than arrays, which might reserve more space than needed.**Simple implementation**: The implementation of stacks and queues using linked lists is straightforward. The implementation of queues using arrays is little complex and difficult to understand.

These features make linked lists a good choice for implementing stacks and queues, especially when the size stored elements may vary significantly during program execution.

Related articles: Stack Data Structure, Implementing a Stack using linked list, Queue Data Structure, Implementing a Queue using linked list.

## Undo/Redo Functionality in Software

Linked lists are useful in implementing undo/redo features in software applications like text editors and graphic design tools. In such systems, each action taken by the user is stored as a node in a linked list along with a function to revert the action. This feature allows users to reverse or reapply their actions. When the user performs an “undo,” the program traverses the list backward, reverting the action. A “redo” operation moves forward through the list, reapplying actions.

In an undo/redo system implementation, each user action is stored as a node in the linked list. When a user performs an “undo,” the program simply moves backward through the list, reverting the most recent action. Conversely, a “redo” operation traverses the list forward, reapplying previously undone actions. This requires bidirectional movement and doubly linked lists are well suited for this, where each node contains references to both its predecessor and successor actions. To further optimize memory usage, older entries in the list can be deleted after a certain count or when they become irrelevant.

Similarly, linked lists are employed in web browsers for implementing forward and backward navigation. As users navigate between web pages, each visited page is stored in a node. Going back in history simply involves moving to the previous node, while forward navigation moves to the next.

## Hash Tables with Chaining

Hash tables are a popular data structure for implementing associative arrays or dictionaries, where each key is mapped to a specific value/index. However, collisions can occur when two different keys hash to the same index. Linked lists are used to handle these collisions through a method called chaining.

In chaining, each index of the hash table points to a linked list that contains all the elements hashing to that index. When a collision occurs, the new element is simply added to the list at that index. This approach ensures that the hash table can still operate efficiently, even when collisions occur, as the linked list allows for quick insertion and search operations.

Related Resources: Hash Table Data Structure, Collisions in Hash Tables, Collision Resolution By Separate Chaining

## Polynomial Arithmetic & Sparse Matrix Representations

Polynomials, which are expressions of the form `ax^n+bx^(n-1)+cx^(n-2)...`

, can be efficiently represented using linked lists. Each term in the polynomial can be stored as a node in a linked list, where the node contains the coefficient and exponent of the term.

This representation allows for efficient addition and multiplication of polynomials. For addition, we can traverse both polynomial lists simultaneously, comparing exponents and adding coefficients where necessary. New terms can be easily inserted into the result list. For multiplication, we can iterate through one polynomial, multiplying each term with every term of the other polynomial, and insert the resulting terms into a new list. This process is more memory-efficient and easier to manage with linked lists compared to fixed-size arrays, especially for sparse polynomials with many zero coefficients.

Similar linked list representations are used for memory-efficient sparse matrix data structures and adjacency lists in graph theory. For sparse matrices, non-zero elements can be stored as nodes, saving memory compared to full matrix storage using arrays. In adjacency lists, each vertex’s neighbors are stored as a linked list, allowing for efficient graph traversal and efficient addition/removal of nodes, particularly for sparse graphs.

Related Resources: Representing Graph using Adjacency List.

## Job Scheduling in Operating Systems

Job scheduling is a critical function in operating systems, ensuring that CPU time is allocated to all processes in a fair and efficient manner. Round-robin scheduling is a common technique where each process is given a fixed time slice (CPU processing time) before moving on to the next process in line.

Circular linked lists are ideal for implementing round-robin scheduling, as they allow the operating system to easily cycle through processes. Each node in the circular list represents a process, and once the last node is reached, the scheduler simply moves back to the head of the list, ensuring a continuous loop of execution. This structure also provides efficient mechanisms for adding new processes and removing completed ones:

**Adding new processes**: When a new process needs to be added, it can be inserted at any point in the circular linked list with`O(1)`

time complexity. Typically, it’s added right after the current process or at the end of the list. This operation only requires adjusting two pointers, making it very efficient.**Removing completed processes**: When a process completes its execution, it can be easily removed from the circular list. This operation also has`O(1)`

time complexity, as it only involves adjusting the pointers of the previous and next nodes to bypass the completed process.

The loopy nature of the Circular linked list ensures that the scheduling algorithm can continue seamlessly even as processes are dynamically added or removed, maintaining the round-robin behavior without any disruption.

## Other Applications

**Caching Implementations, LRU Caches**: Linked lists are used to efficiently store and retrieve frequently accessed data, improving system performance.**DataBases, File System Management**: Linked lists are used to organize and manage large amounts of data and files, enabling quick access and efficient storage.**Memory Management in Operating Systems**: Linked lists are used to allocate and deallocate memory resources, while ensuring optimal use of available system memory.**Blockchain Implementations**: Store and verify transactions in a decentralized and secure manner, supporting cryptocurrencies and other applications.