In computer programming, there are a wide variety of data structures that have their own unique set of properties and offer specialised ways to handle data. One such **data structure** is the** Linked List. **In this article, we will explore various use cases of a linked list in the context of programming and real-world problem-solving.

## Application of Linked list in Computer Science

Below is a list of applications of linked list in the world of computer science

**Representation of Polynomials****Arithmetic operations on Polynomials****Addition of Long Positive integers****Implementation of Queue Data structure****Implementation of Stack Data structure****Representation Adjacency List**

Let’s take a look at each one of them in detail.

## Representation of Polynomials

Polynomials are algebraic expressions that contain coefficients and variables. Linked lists can be used to represent polynomials in computer programs. For instance, to represent a polynomial like** 3x^2 + 2x + 5** we can use the below reference image of a linked list.

Considering the same polynomial** 3x^2 + 2x + 5****.** This polynomial can be represented as following in a linked list:

**3x^2 (coefficient = 3, exponent = 2)**

**2x^1 (coefficient = 2, exponent = 1)**

**5x^0 (coefficient = 5, exponent = 0)**

### Python Program to represent Polynomials

Now, to represent the above polynomial through a linked list, take a look at the Python code below.

# Node class representing a term in the polynomialclass Node: def __init__(self, coefficient, exponent): # Coefficient of the term self.coefficient = coefficient # Exponent of the term self.exponent = exponent # Reference to the next term in the polynomial self.next = None
# Polynomial class to manage the linked list of termsclass Polynomial: def __init__(self): # Initialize the head of the linked list self.head = None
# Method to add a new term to the polynomial def add_term(self, coefficient, exponent): # Create a new term node new_term = Node(coefficient, exponent) # If the polynomial is empty, set the new term as the head if not self.head: self.head = new_term else: # Traverse to the end of the list current = self.head while current.next: current = current.next # Add the new term at the end current.next = new_term
# Method to display the polynomial def display(self): current = self.head # String to store the polynomial representation polynomial_str = ""
while current: # Check if the term is non-zero if current.coefficient != 0: if current.exponent == 0: # Append constant term polynomial_str += str(current.coefficient) else: # Append other terms polynomial_str += str(current.coefficient) + "x^" + str(current.exponent) if current.next and current.next.coefficient > = 0: # Add '+' between terms if needed polynomial_str += " + " current = current.next
# Print the polynomial representation print(polynomial_str)
# Create a polynomial objectpoly = Polynomial()
# Add terms to the polynomialpoly.add_term(3, 2) # Add term 3x^2poly.add_term(2, 1) # Add term 2x^1poly.add_term(5, 0) # Add term 5x^0
# Display the polynomialpoly.display()

**Output**

*3x^2 + 2x^1 + 5*

## Arithmetic operations on Polynomials

To perform operations like addition, subtraction, multiplication and division among polynomials, we can also make use of a Linked list data structure.

### Python Program to Add Polynomials

class Node: def __init__(self, coef=0, exp=0): # Coefficient of the term self.coef = coef # Exponent of the term self.exp = exp # Reference to the next # term in the polynomial self.next = None
class Polynomial: def __init__(self): # Initialize the head # of the linked list self.head = None
# Method to add a new term # to the polynomial def add_term(self, coef, exp): # Create a new term node new_term = Node(coef, exp) # If the polynomial is empty, # set the new term as the head if not self.head: self.head = new_term else: current = self.head # Traverse to the end of the list while current.next: current = current.next # Add the new term at the end current.next = new_term
# Method to display the polynomial def display(self): current = self.head # String to store the # polynomial representation polynomial_str = "" while current: # Check if the term is non-zero if current.coef != 0: if current.exp == 0: # Append constant term polynomial_str += str(current.coef) else: # Append other terms polynomial_str += str(current.coef) + "x^" + str(current.exp) if current.next and current.next.coef > = 0: # Add '+' between terms if needed polynomial_str += " + " current = current.next # Print the polynomial representation print(polynomial_str)
# Method to add two polynomials def add(self, poly): result = Polynomial() current1 = self.head current2 = poly.head
while current1 and current2: # If exponent of current1 is greater if current1.exp > current2.exp: result.add_term(current1.coef, current1.exp) current1 = current1.next # If exponent of current2 is greater elif current1.exp < current2.exp: result.add_term(current2.coef, current2.exp) current2 = current2.next else: # If exponents are equal # Add coefficients new_coef = current1.coef + current2.coef result.add_term(new_coef, current1.exp) current1 = current1.next current2 = current2.next
# Append remaining terms if any while current1: result.add_term(current1.coef, current1.exp) current1 = current1.next
while current2: result.add_term(current2.coef, current2.exp) current2 = current2.next
return result # Create first polynomial 3x^2 + 2x + 5poly1 = Polynomial()poly1.add_term(3, 2)poly1.add_term(2, 1)poly1.add_term(5, 0)
# Create second polynomial 2x^2 - 4x - 1poly2 = Polynomial()poly2.add_term(2, 2)poly2.add_term(-4, 1)poly2.add_term(-1, 0)
# Perform additionprint("Addition:")result_add = poly1.add(poly2)result_add.display()

**Output**

*Addition:**5x^2-2x^1 + 4*

In the above code, we have generated two polynomials **poly1** that is equal to** 3x^2 + 2x + 5** and** poly2** that is equal to **2x^2 - 4x - 1**. When we add these to the polynomial we get a new polynomial equal to** 5x^2-2x^1 + 4**

### Python program to Subtract polynomials

class Node: def __init__(self, coef=0, exp=0): # Coefficient of the term self.coef = coef # Exponent of the term self.exp = exp # Reference to the next # term in the polynomial self.next = None
class Polynomial: def __init__(self): # Initialize the head # of the linked list self.head = None
# Method to add a new term # to the polynomial def add_term(self, coef, exp): # Create a new term node new_term = Node(coef, exp) # If the polynomial is empty, # set the new term as the head if not self.head: self.head = new_term else: current = self.head # Traverse to the end of the list while current.next: current = current.next # Add the new term at the end current.next = new_term
# Method to display the polynomial def display(self): current = self.head # String to store the # polynomial representation polynomial_str = "" while current: # Check if the term is non-zero if current.coef != 0: if current.exp == 0: # Append constant term polynomial_str += str(current.coef) else: # Append other terms polynomial_str += str(current.coef) + "x^" + str(current.exp) if current.next and current.next.coef > = 0: # Add '+' between terms if needed polynomial_str += " + " current = current.next # Print the polynomial representation print(polynomial_str)
# Method to subtract two polynomials def subtract(self, poly): result = Polynomial() current1 = self.head current2 = poly.head
while current1 and current2: # If exponent of current1 is greater if current1.exp > current2.exp: result.add_term(current1.coef, current1.exp) current1 = current1.next # If exponent of current2 is greater elif current1.exp < current2.exp: result.add_term(-current2.coef, current2.exp) current2 = current2.next else: # If exponents are equal # Subtract coefficients new_coef = current1.coef - current2.coef result.add_term(new_coef, current1.exp) current1 = current1.next current2 = current2.next
# Append remaining terms if any while current1: result.add_term(current1.coef, current1.exp) current1 = current1.next
while current2: result.add_term(-current2.coef, current2.exp) current2 = current2.next
return result # Create first polynomial 3x^2 + 2x + 5poly1 = Polynomial()poly1.add_term(3, 2)poly1.add_term(2, 1)poly1.add_term(5, 0)
# Create second polynomial 2x^2 - 4x - 1poly2 = Polynomial()poly2.add_term(2, 2)poly2.add_term(-4, 1)poly2.add_term(-1, 0)
# Perform subtractionprint("\nSubtraction:")result_subtract = poly1.subtract(poly2)result_subtract.display()

**Output**

*Subtraction:**1x^2 + 6x^1 + 6*

In the above code, we have generated two polynomials **poly1** that is equal to** 3x^2 + 2x + 5** and** poly2** that is equal to **2x^2 - 4x - 1**. When we subtract these from to polynomial, we get a new polynomial equal to** 1x^2 + 6x^1 + 6**

### Python program to multiply Polynomials.

class Node: def __init__(self, coef=0, exp=0): # Coefficient of the term self.coef = coef # Exponent of the term self.exp = exp # Reference to the next # term in the polynomial self.next = None
class Polynomial: def __init__(self): # Initialize the head # of the linked list self.head = None
# Method to add a new term # to the polynomial def add_term(self, coef, exp): # Create a new term node new_term = Node(coef, exp) # If the polynomial is empty, # set the new term as the head if not self.head: self.head = new_term else: current = self.head # Traverse to the end of the list while current.next: current = current.next # Add the new term at the end current.next = new_term
# Method to display the polynomial def display(self): current = self.head # String to store the # polynomial representation polynomial_str = "" while current: # Check if the term is non-zero if current.coef != 0: if current.exp == 0: # Append constant term polynomial_str += str(current.coef) else: # Append other terms polynomial_str += str(current.coef) + "x^" + str(current.exp) if current.next and current.next.coef > = 0: # Add '+' between terms if needed polynomial_str += " + " current = current.next # Print the polynomial representation print(polynomial_str)
# Method to multiply two polynomials def multiply(self, poly): result = Polynomial() current1 = self.head
while current1: current2 = poly.head while current2: # Multiply coefficients new_coef = current1.coef * current2.coef # Add exponents new_exp = current1.exp + current2.exp result.add_term(new_coef, new_exp) current2 = current2.next current1 = current1.next
return result # Create first polynomial 3x^2 + 2x + 5poly1 = Polynomial()poly1.add_term(3, 2)poly1.add_term(2, 1)poly1.add_term(5, 0)
# Create second polynomial 2x^2 - 4x - 1poly2 = Polynomial()poly2.add_term(2, 2)poly2.add_term(-4, 1)poly2.add_term(-1, 0)
# Perform multiplicationprint("\nMultiplication(non-simplified):")result_multiply = poly1.multiply(poly2)result_multiply.display()

**Output**

*Multiplication(non-simplified):**6x^4-12x^3-3x^2 + 4x^3-8x^2-2x^1 + 10x^2-20x^1-5*

In the above code, we have generated two polynomials **poly1** that is equal to** 3x^2 + 2x + 5** and** poly2** that is equal to **2x^2 - 4x - 1**. When we multiply these to polynomial, we get a new polynomial equal to** 6x^4-12x^3-3x^2 + 4x^3-8x^2-2x^1 + 10x^2-20x^1-5** that, when simplified, can be written as** 6x^4-8x^3-21x^2+18x+5**.

### Python program to Divide Polynomials

class Node: def __init__(self, coef=0, exp=0): # Coefficient of the term self.coef = coef # Exponent of the term self.exp = exp # Reference to the next # term in the polynomial self.next = None
class Polynomial: def __init__(self): # Initialize the head # of the linked list self.head = None
# Method to add a new term # to the polynomial def add_term(self, coef, exp): # Create a new term node new_term = Node(coef, exp) # If the polynomial is empty, # set the new term as the head if not self.head: self.head = new_term else: current = self.head # Traverse to the end of the list while current.next: current = current.next # Add the new term at the end current.next = new_term
# Method to display the polynomial def display(self): current = self.head # String to store the # polynomial representation polynomial_str = "" while current: # Check if the term is non-zero if current.coef != 0: if current.exp == 0: # Append constant term polynomial_str += str(current.coef) else: # Append other terms polynomial_str += str(current.coef) + "x^" + str(current.exp) if current.next and current.next.coef > = 0: # Add '+' between terms if needed polynomial_str += " + " current = current.next # Print the polynomial representation print(polynomial_str) # Method to subtract two polynomials def subtract(self, poly): result = Polynomial() current1 = self.head current2 = poly.head
while current1 and current2: # If exponent of current1 is greater if current1.exp > current2.exp: result.add_term(current1.coef, current1.exp) current1 = current1.next # If exponent of current2 is greater elif current1.exp < current2.exp: result.add_term(-current2.coef, current2.exp) current2 = current2.next else: # If exponents are equal # Subtract coefficients new_coef = current1.coef - current2.coef result.add_term(new_coef, current1.exp) current1 = current1.next current2 = current2.next
# Append remaining terms if any while current1: result.add_term(current1.coef, current1.exp) current1 = current1.next
while current2: result.add_term(-current2.coef, current2.exp) current2 = current2.next
return result
# Method to multiply two polynomials def multiply(self, poly): result = Polynomial() current1 = self.head
while current1: current2 = poly.head while current2: # Multiply coefficients new_coef = current1.coef * current2.coef # Add exponents new_exp = current1.exp + current2.exp result.add_term(new_coef, new_exp) current2 = current2.next current1 = current1.next
return result
# Method to divide two polynomials def divide(self, poly): # Quotient polynomial quotient = Polynomial() # Remainder polynomial remainder = Polynomial() # Current node of the dividend polynomial current1 = self.head
while current1: # Current node of the # divisor polynomial current2 = poly.head # Temporary polynomial to # hold intermediate division results temp = Polynomial() # Initialize temp with the current term of dividend temp.add_term(current1.coef, current1.exp) while current2: # Coefficient division new_coef = current1.coef // current2.coef # Exponent subtraction new_exp = current1.exp - current2.exp # Temporary polynomial to # hold the term for subtraction temp2 = Polynomial() # Initialize temp2 with the term for subtraction temp2.add_term(new_coef, new_exp) # Subtract (temp2 * divisor) from temp temp = temp.subtract(temp2.multiply(poly)) # Move to the next term in the divisor current2 = current2.next # Add the new term to the quotient quotient.add_term(new_coef, new_exp) # Assign the remainder as the # result of the last subtraction remainder = temp # Move to the next term in the dividend current1 = current1.next # Return the quotient and # remainder polynomials return quotient, remainder # Create first polynomial 3x^2 + 2x + 5poly1 = Polynomial()poly1.add_term(3, 2)poly1.add_term(2, 1)poly1.add_term(5, 0)
# Create second polynomial 2x^2 - 4x - 1poly2 = Polynomial()poly2.add_term(2, 2)poly2.add_term(-4, 1)poly2.add_term(-1, 0)
# Perform divisionprint("\nDivision - Quotient:")result_quotient, result_remainder = poly1.divide(poly2)result_quotient.display()print("\nDivision - Remainder:")result_remainder.display()

**Output**

*Division - Quotient:**-3x^2-2x^1-5*

*Division - Remainder:**10x^2-16x^1-12 + 6x^-1 + 2x^-2*

In the above code, we have generated two polynomials **poly1** that is equal to** 3x^2 + 2x + 5** and** poly2** that is equal to **2x^2 - 4x - 1**. When we divide the first polynomial with the second one, we get a new quotient polynomial equal to** -3x^2-2x^1-5** and the remainder polynomial equal to** 10x^2-16x^1-12 + 6x^-1 + 2x^-2**.

## Addition of Long Positive Integers

In programming, a** long positive integer** refers to an integer that can have variable size, representing very large whole numbers.

Look at the Python program below to add long positive integers using Linked List.

### Python program to Add Long Positive Integers

class Node: def __init__(self, data): self.data = data self.next = None
class LinkedList: def __init__(self): self.head = None
def insert_at_head(self, data): new_node = Node(data) new_node.next = self.head self.head = new_node
def display(self): current = self.head while current: print(current.data, end="") current = current.next print()
def add_long_integers(self, num1, num2): carry = 0 self.head = None # Resetting head for the result list while num1 is not None or num2 is not None: digit1 = num1.data if num1 else 0 digit2 = num2.data if num2 else 0
if num1: num1 = num1.next if num2: num2 = num2.next
total = digit1 + digit2 + carry carry = total // 10 self.insert_at_head(total % 10)
if carry > 0: self.insert_at_head(carry)
def insert_number(self, number): for digit in str(number)[::-1]: self.insert_at_head(int(digit))
# Create and insert numbers correctlynum1 = LinkedList()num1.insert_number(954756)
num2 = LinkedList()num2.insert_number(689347)
# Display the numbers to be addedprint("First number:")num1.display()print("Second number:")num2.display()
# Calculate the sum of the numbers and display the resultresult = LinkedList()result.add_long_integers(num1.head, num2.head)print("Sum:")result.display()

**Output**

*First number:**954756**Second number:**689347**Sum:**1401445*

**Note: ** Python 3 eliminated the distinction between int and long types from Python 2, so integers in Python 3 automatically transition to long integers as needed, accommodating any integer size.

**Implementation of Queue Data structure**

A queue is a linear data structure with both ends open for operations and follows the principle of First In, First Out (FIFO).

According to the First In, First Out (FIFO) concept, the first element to enter a queue (enqueue) must also be the first element to exit the queue (dequeue). To better understand a queue, picture a queue of people waiting to get on a bus. The person in the queue will get on the bus first, and vice versa.

Take a look at the image below for reference.

Now that we know what a queue Data structure is let’s take a look at the implementation of a queue using a linked list in Python.

This implementation will follow the below algorithm

### Algorithm

The algorithm would look like the below for the above-mentioned steps

**Step 1:** [START] CREATE NEW_NODE, SET FRONT = NULL, SET REAR = NULL

**Step 2:** SET DATA = VALUE, NEW_NODE NEXT = NULL

**Step 3: **If FRONT is NULL (Queue is empty)

* SET FRONT = NEW_NODE*

* SET REAR = NEW_NODE*

* Else*

* SET REAR NEXT = NEW_NODE*

* SET REAR = NEW_NODE*

**Step 4**: EXIT

### Python program to Implement Queue using Linked List

# initialize a nodeclass Node: def __init__(self, value): self.data = value self.next = None
class Queue: def __init__(self): self.front = None self.rear = None
def do_enqueue(self, value): # Create a new node new_node = Node(value) # If queue is empty, set # new node as front and rear if self.front is None: self.front = new_node self.rear = new_node else: # If queue is not empty, # add new node at the rear self.rear.next = new_node self.rear = new_node
def display(self): # Display the elements in the queue current = self.front if current is None: print("Queue is empty") return while current is not None: print(current.data, end=" < - ") current = current.next print("rear")
def do_dequeue(self): # Check if queue is empty if self.front is None: print("Queue is empty, cannot dequeue") return None else: # dequeue the front element temp = self.front self.front = self.front.next if self.front is None: self.rear = None return temp.data
# Example usequeue = Queue()queue.do_enqueue(1)queue.do_enqueue(2)queue.do_enqueue(3)
# Display the elements in the queuequeue.display() dequeued_value = queue.do_dequeue()print(f"Dequeued value: {dequeued_value}")
# Display the elements after do_dequeuequeue.display()

**Output**

*1 <- 2 <- 3 <- rear**Dequeued value: 1**2 <- 3 <- rear*

**Implementation of Stack Data structure**

A stack is a linear data structure with one end open for operations and follows the First In, Last Out (FILO) principle.

The FILO principle states that the first element getting inside a stack(i.e., push) has to be the last element that gets out of the stack(i.e., pop). To better understand a stack, think of a stack of books placed above one another. The first book that can be taken out of the stack should be at the top and has to be placed last in that stack and vice-versa.

Take a look at the image below for reference.

Now that we know what a stack Data structure is, let’s take a look at the implementation of a stack using a linked list in Python.

This implementation will follow the below algorithm:

### Algorithm

The algorithm would look like the below for the above-mentioned steps

**Step 1:** [START] Initialize Node, Create an empty stack

**Step 2:** Set TOP = NULL

**Step 3:** Define PUSH(value) to add an element

* Create a new node with the value*

* If TOP is NULL*

* Set TOP to the new node*

* Else*

* Set new node's NEXT to TOP*

* Update TOP to the new node*

**Step 4:** Define POP() to remove an element

* If TOP is NULL*

* Display "Stack is empty"*

* Else*

* Set TEMP to TOP*

* Move TOP to the next node*

* Free memory for TEMP*

**Step 5:** Define PEEK() to return top element

* If TOP is NULL*

* Display "Stack is empty"*

* Else*

* Return data of TOP*

**Step 6:** Define DISPLAY() to print stack elements

* Start from TOP*

* While current node is not NULL*

* Print data of current node*

* Move to the next node*

**Step 7:** [END]

### Python program to Implement Stack using Linked List

# Node class represents each node in the linked listclass Node: def __init__(self, data): # Data stored in the node self.data = data # Pointer to the next node self.next = None
# LinkedList class manages the linked list operationsclass Stack: def __init__(self): # Initialize the top of the stack self.top = None
# Method to push (add) an element onto the stack def push(self, data): # Create a new node new_node = Node(data) # Point the new node to the current top new_node.next = self.top # Update the top to the new node self.top = new_node
# Method to pop (remove) an element from the stack def pop(self): if self.top is None: # If stack is empty, return None return None else: # Get the data from the top node popped = self.top.data # Move the top to the next node self.top = self.top.next # Return the popped element return popped
# Method to peek at the top element without removing it def peek(self): if self.top is None: # If stack is empty, return None return None else: # Return the data of the top node return self.top.data
# Method to display the elements of the stack def display(self): current = self.top while current: # Print the data of each node print(current.data, end=" ") current = current.next print()
# Create a stack objectstack = Stack()
# Push elements onto the stackstack.push(10)stack.push(20)stack.push(30)
# Display the elements of the stackprint("Stack elements:")stack.display()
# Peek at the top elementprint("Top element (Peek):", stack.peek())
# Pop an element from the stackprint("Popped element:", stack.pop())
# Display the elements of the stack after poppingprint("Stack elements after pop:")stack.display()

**Output**

*Stack elements:**30 20 10 **Top element (Peek): 30**Popped element: 30**Stack elements after pop:**20 10 *

## Representation of Adjancey List

An adjacency list is a way to represent the connections between vertices in a graph. In this type of representation, for each vertex in the graph, a list of adjacent vertices are also maintained. It's one of the two main ways to represent a graph, with the other being the *adjacency matrix*.

A**djacency** list has 3 key components.

**Vertices:**In a graph, nodes are often referred to as vertices.**Edges:**Connections between these vertices are known as edges.**Adjacency List:**For each vertex in the graph, an adjacency list holds a list of vertices adjacent to it, i.e., vertices that are connected to it by an edge.

### Python program to represent Adjacency list using Linked list

# Node class represents each node# in the linked listclass Node: def __init__(self, data): self.data = data self.next = None
# Graph class manages the# adjacency list representationclass Graph: def __init__(self, vertices): self.V = vertices # Initialize the adjacency # list with V vertices self.adj_list = [None] * self.V
# Function to add an edge between # vertices src and dest def add_edge(self, src, dest): # Create a new node for the destination new_node = Node(dest) # Insert the new node at the beginning # of the adjacency list for source vertex new_node.next = self.adj_list[src] self.adj_list[src] = new_node
# For undirected graph, # also add an edge from dest to src new_node = Node(src) new_node.next = self.adj_list[dest] self.adj_list[dest] = new_node
# Function to print the # adjacency list representation of the graph def print_graph(self): for i in range(self.V): print(f"Adjacency list of vertex {i}:") temp = self.adj_list[i] while temp: print(f" - > {temp.data}", end="") temp = temp.next print(" \n")
# Create a graph with 4 verticesV = 4graph = Graph(V)
# Add edges to the graphgraph.add_edge(0, 1)graph.add_edge(0, 2)graph.add_edge(1, 2)graph.add_edge(2, 3)
# Display the adjacency list# representation of the graphgraph.print_graph()

**Output**

*Adjacency list of vertex 0:** -> 2 -> 1 *

*Adjacency list of vertex 1:** -> 2 -> 0 *

*Adjacency list of vertex 2:**-> 3 -> 1 -> 0 *

*Adjacency list of vertex 3:** -> 2 *

The above code creates a graph with four vertices and implements an adjacency list using linked lists for each vertex. The ** add_edge **method adds edges between vertices, and

**displays the adjacency list representation.**

*print_graph*## Application of Linked list in Real World

Linked lists can have a wide variety of use cases in real-world applications. We will further discuss a couple of those use cases in detail in the article.

### Use of Linked List in Operation System

Linked lists are widely utilised in several fundamental operating system functions, like improving system performance and resource management, as described below:

**Process Management: The OS manages multiple processes using linked lists. A process's information is contained in each process control block (PCB), which can link to other PCBs to create a linked list. These linked lists are further used to support resource allocation, manage the process schedules, and end the process as needed.****File Management: To hold data about files, including their locations, permissions, and other characteristics, directories are kept up to date as linked lists. Linked lists are used to control disc space allocation in File Allocation Tables (FAT).****Memory Management:**Linked lists are used by OS memory management to maintain track of allocated and free memory blocks. Allocation techniques such as First, Best, and Worst Fit efficiently allocate and deallocate memory using linked lists of memory blocks.

### Use of Linked List in Database System

In database systems, linked lists are essential for effective data organisation and retrieval. The following are some database areas where linked lists are used:

**Indexing: Linked lists are used to implement indexing structures like linked lists of pointers, skip lists, or inverted lists. These structures allow quick access to the indexed data, further reducing the database query execution time and load to the database.****Avoid Collision:**Linked lists are used in the hash table structures used by databases to handle collisions. In Databases, there may occur an event where a bucket in the hash table may contain a linked list of entries that hash to the same index here, linked lists can be used to allow efficient handling of collisions.**Database Transactions: Linked lists help maintain atomicity and consistency in database transactions by making reorganising pointers or data blocks easier during transactional operations (such as insertions, deletions, and updates).**

### Use of Linked Lists in Music Players

For playlist management and song sequencing control, linked lists are commonly utilised in music players. Linked lists are used in music player software in the following ways:

**Playlist Management: Linked lists are a popular way to display music playlists, with each list node representing a song. Playlist administration, maintenance, and traversal are made simple by the linked list structure.****Playback Control: Linked lists make handling playback functions like shuffle, repeat, and skip easier. To play songs in a different order, shuffle a playlist, for instance, by randomly rearranging the nodes in the linked list.****Memory management: Linked lists allow for dynamic memory allocation, which improves memory efficiency when managing playlists. No set amount of RAM is needed when songs are added or removed.**

### Use of Linked Lists in Web Browsers

Web browsers use linked lists to store browsing history and enable forward and backward navigation features. Web browsers use linked lists in the following ways:

**Browsing History: Linked lists are used to keep track of web pages that have been visited over time. Every page visit is tracked as a node in the linked list, where the metadata is stored along with the URL, title, and timestamp.****Forward & Backward navigation: By going through the linked list in reverse order, you can enable the backward navigation capability in most browsers. In the same way, another linked list or stack is kept up to date to record the pages viewed after going backwards to enable forward navigation.****Tab Management: Tabs in a browser can be managed and organized using linked lists. Users can flip among tabs in sequential order by representing each open tab as a node in a linked list.****Session Management:**Linked lists also help with session history management, which includes the order in which pages were seen during a browsing session. This history can be used to restore sessions.

### Use of Linked List in Graphics Development

Linked lists are widely used in applications that generate images or videos to manage frame data or pixel data. This has been further elaborated in the below points:

**Pixel Data Management: Linked lists are useful for organising pixel data in image processing. Every node might stand in for a pixel, holding properties like colour.****Vertex And Edge in 3D Graphics: Linked lists are used in 3D graphics to maintain geometric shape vertex and edge data. For the purpose of efficiently rendering 3D models, these lists record coordinates, normals, and connection information.****Texture Management: In graphics applications, texture data can be managed using linked lists. Information regarding textures, their positions, and mapping specifics may be stored by each node.**

**Conclusion**

Thus, linked lists are a fundamental data structure in computer science, widely used for their dynamic and efficient management of data. They excel in scenarios requiring frequent insertions and deletions, as they offer flexibility and memory efficiency, making them ideal for implementing abstract data types like stacks, queues, and even more complex structures like graphs and hash tables.**Contributed by: Raju Kumar**

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