## Introduction

Linked lists are linear data structures. The data is stored in consecutive memory locations. Every element in the data structure has a unique predecessor and unique successor. In this, elements are stored in a sequential form. A linked list is among the simplest and most common data structures used to store similar data types in memory. It is a linear collection of data elements called nodes, where the linear order is given using pointers. Every node has two parts: the first contains the information/data, and the second contains the link/address of the next node in the list.

## What is a Linked List?

A linked list is a linear data structure representing a sequence of nodes, with the head node pointing to the start and the tail node pointing to the end. The elements of a linked list are not stored in contiguous memory addresses. Each node is allocated memory dynamically and is linked together using links or pointers. In this article, we will understand the applications of linked lists in detail.

## Applications of Linked List in Computer Science

**Stacks and Queues**

The stack and queues data structure is implemented using a linked list.

**Stack (Last In First Out - LIFO):**

**Push Operation (INSERT_IN_BEGINNING):**Add an item to the top of the stack.**Pop Operation (DELETE_IN_BEGINNING):**Remove and return the item from the top of the stack.**Used for:**Function call tracking (call stack), expression evaluation, undo functionality, backtracking in algorithms, and more.**Time Complexity:**O(1) for both push and pop operations.

**Queue (First In First Out - FIFO):**

**Enqueue Operation (INSERT_IN_END):**Add an item to the end of the queue.**Dequeue Operation (DELETE_IN_BEGINNING):**Remove and return the item from the front of the queue.**Used for:**Task scheduling, print job management, breadth-first search in graphs, handling requests in web servers, and more.**Time Complexity:**O(1) for both enqueue and dequeue operations.

**Graph**

There are mainly two ways to represent a graph. One of the most widely used representations is the *Adjacency List Representation*, which is nothing but a combination of array and linked list data structure.

**Application of Graph:**

- Used to represent friendships or connections between individuals.

- Each person is a node, and edges indicate relationships.

- Applied in GPS systems and network routing algorithms.

- Nodes represent locations, and edges represent roads or connections.

- Used in recommending products or content to users.

- Nodes represent users or items, and edges indicate user interactions.

**Sparse Matrix**

Itβs a matrix that is comprised of mostly zeros. The sparse matrix can also be represented by a linked list. This prevents using extra unnecessary memory.** Application of Sparse Matrix:**

- In Finite Element Analysis (FEA) simulations, matrices representing physical systems can be sparse. This leads to efficient memory usage in structural analysis and simulations.

- In image processing, images often contain many blank or near-zero pixels. Sparse matrices are used to store image data efficiently.

- Electronic circuit simulators use sparse matrices to analyze complex electrical networks efficiently.

**Hash Tables**

A hash table is a data structure where every value is mapped to a key using a hash function. But in some cases, the key for two or more values of the input is the same. In this case, we store all these values corresponding to the same key using a linked list.

**Application of Hash Tables:**

- Compilers use hash tables to manage variables, functions, and symbols during code compilation.

- Passwords stored in hash tables are more secure because they're not stored in plain text.

- Hash tables distribute workloads evenly in load-balancing systems by mapping requests to servers.

**Polynomial**

The linked list can also represent polynomials.

**Application of Polynomial:**

- Integration of polynomials can also be performed using linked lists. You can integrate each term and build a new linked list representing the integral.

- Linked lists are efficient for sparse polynomials with many zero or negligible terms since you only need to store non-zero terms.

- Linked lists make it easy to display polynomials in a readable format, showing terms in descending order of exponents.

**Dynamic memory allocation**

Nodes of a linked list are not stored in contiguous memory and are created dynamically at runtime which is why linked lists are often used in dynamic memory allocation.

**Application of Dynamic memory allocation:**

- Linked lists are fundamental for building more complex data structures like stacks, queues, and hash tables.

- Linked lists consume memory only for data and pointers, making them efficient when memory usage is a concern.

- In database systems, linked lists are used to implement data structures like indexes, lists, and linked records.

## Applications of Linked List in the Real World

**Image Viewer-**When you open an image in the image viewer on your computer, you can use the Next button to navigate to the next image. Although the pictures are not stored in a contiguous memory location, the linked list allows you to scroll through them.**History in Web Browser-**When you move through the web pages, you have the option to revert to the previous web page and again move to the next one in a web browser. This functionality is achieved using a doubly-linked list.**Music Player-**Same as we can scroll through pictures in an image viewer, we can scroll through our songs in a music player using a linked list.**Switching Between Applications on the Computer-**Using**alt+tab**on Windows and**command+tab**on mac, you can swap between running applications. This is achieved using a circular linked list.**Phone Books-**When inserting values in between, the linked list is generally the ideal data structure to use. In the instance of a phone book, we need to insert values in between as the numbers are stored in alphabetical order, therefore we utilize a linked list to do so.**Undo Function-**In Photoshop and Word documents, a doubly-linked list is also used to implement the undo function. Every modification you make to a document or file is saved as nodes in a doubly-linked list. We can return to the previous state of the document by pressing 'Ctrl+Z.'

## Applications of Doubly Linked List

- Used in back and forward button in browser and file explorer.
- Undo and Redo functionality in Text editor.
- Can be applied in other data structures, such as Stack and Binary Trees.
- Web browsers use doubly linked lists to maintain the history of visited web pages.
- Doubly linked lists can be used in navigation systems to represent paths or routes between locations.
- Job scheduling algorithms use doubly linked lists.

## Applications of Circular Linked List

- Useful in implementing a queue.
- Circular linked lists are used in round-robin scheduling algorithms for task scheduling.
- Useful in applications where you need to go around quite often.
- Circular Double Linked List is used to implement high-level data structures like a Fibonacci Heap.
- Circular linked lists are often used to create circular playlists in music and media players.
- Circular linked lists are useful in managing and allocating resources.

## Polynomial Manipulation

Polynomial manipulation, using a linked list, is a common mathematical application. In this situation, each node of the linked list represents a polynomial equation. The node stores two values: the coefficient (e.g., 2 for 4x) and the exponent (e.g., 1 for x^3). By linking these nodes, you create a polynomial expression.

Operations include adding, subtracting, multiplying, or dividing polynomials, as well as evaluating them for specific values. Linked lists are properly appropriate for this task. They allow the dynamic advent of terms and efficient manipulation, inclusive of adding or putting off terms without wasting memory. This approach simplifies complicated mathematical calculations involving polynomials in computer applications.

### Polynomial of Multiple Variables

We can have polynomials with more than a single variable. Using a linked list as a data structure, a polynomial with several variables can be represented, with each term being stored as a node in the linked list. Each node of the linked list stores the exponent of each variable. So, if there are a total of three variables in the polynomial there will be three parts of exponents.

Let us look at the representation:

For example, if we have a polynomial 5 x^{2}y^{3}z + 4x y^{3} z^{2} + 8 xz + 2, the representation of the polynomial using linked list will look like:

**Simple C++ program to multiply two polynomials**

Let us look at the simple C++ program to multiply two polynomials:

**Output**

```
First polynomial is
2 + 4x^1 + 1x^2 + 5x^3
Second polynomial is
1 + 7x^1 + 3x^2
Product of two polynomial is
2 + 18x^1 + 35x^2 + 24x^3 + 38x^4 + 15x^5
```

**Explanation**

In the above example, we have multiplied two polynomials first 2 + 4x^1 + 1x^2 + 5x^3 and second 1 + 7x^1 + 3x^2. We printed the product of the multiplication of these two polynomials and the result is 2 + 18x^1 + 35x^2 + 24x^3 + 38x^4 + 15x^5.

**Time Complexity**

The time complexity of the program will be O( m+n ), where m is the size of the first array and n is the size of the second array.

## Advantages of Linked Lists over Arrays

Linked lists have several advantages over arrays, including:

**Dynamic siz**e: Linked lists can grow or shrink in size dynamically as needed, whereas arrays have a fixed size that must be declared at the time of creation.**Efficient insertion and deletion:**In a linked list, inserting or deleting an element in the middle of the list can be done efficiently by simply changing the pointers, whereas, in an array, elements must be shifted to accommodate the change, which can be a time-consuming process.**Easy to implement:**Linked lists are easy to implement and don't require knowledge of advanced data structures, whereas arrays can be more complex to work with, especially when dealing with multi-dimensional arrays.**Memory allocation:**Linked lists allocate memory dynamically, meaning that only the necessary amount of memory is used, while arrays require a fixed amount of memory to be allocated even if it's not fully used, which can waste memory resources.

## Frequently Asked Questions

**What are the applications of a linked list?**

Linked lists are used in a lot of places in the world of computer programming. It's used in addition of long integers, representation of sparse metrics, Polynomial representation, implementing stack and queues, hash tables, Undo and Redo buttons in browsers, and next and previous buttons in image viewers.

**What are the applications of Linkedlists in real life?**

In real life, linked lists are used in a lot of places, such as the back and forward buttons in a browser. It is also used in the Image viewer, where you get the functionality to go to the next and previous images.

**What is linked list and its application in data structure?**

A linked list is a linear data structure where each element (node) points to the next, forming a chain. It's used in data structures for tasks like dynamic memory allocation and implementing data containers like stacks and queues.

## Conclusion

We've discussed the various linked list applications. The linked list is one of the hot topics to study for coding interviews. I hope you enjoyed reading this blog. There are other such exciting blogs on the linked list, and other data structures are on Coding Ninjas Studio.

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Thank you for reading.