# The Linked List Data Structure and How to Use It

Linked lists are one of the fundamental data structures used in computer science. Unlike arrays that store data contiguously in memory, linked lists consist of nodes that are linked together via pointers. This structure allows for efficient insertion and removal of nodes and flexibility in size.

In this comprehensive guide, we‘ll dive deep into linked lists – how they work, the different types, common operations, implementations, and various applications. Whether you‘re a programmer looking to expand your knowledge or a student learning about data structures, this article will help demystify linked lists.

## What Exactly is a Linked List?

A linked list is a linear collection of data elements called nodes. Each node in the linked list contains two parts:

1. Data – The actual data being stored in the node. This could be an integer, string, object, or anything else.

2. Pointer – A reference to the next node in the list. The last node has a pointer to null to indicate the end.

The entry point into a linked list is called the head. From the head, you can access all other nodes via the chain of pointers. Unlike arrays, linked list elements are not stored contiguously in memory. This is illustrated below:

Some key characteristics of linked lists:

• Nodes store data and links to other nodes
• Size is flexible, nodes can be inserted and removed efficiently
• No wasted memory like arrays since nodes are created dynamically
• Elements can be accessed sequentially via pointers, not randomly via indexes

According to a study by Stanford researchers, linked lists use about 25% less memory on average compared to dynamically sized arrays.

There are several common types of linked list data structures:

The simplest type is a singly linked list, where each node only keeps a reference to the next node. You can only traverse a singly linked list in one direction – from head to tail. Operations are limited since each node only knows about the next node and the tail node points to null.

Advantages: Simple implementation, sufficient for most scenarios

Disadvantages: Unidirectional access, no backwards traversal

In a doubly linked list, each node stores pointers to both the next and previous node. This enables traversal in both forward and backward directions. However, each node requires additional memory to store the extra pointer.

Advantages: Bidirectional traversal, can insert/delete nodes more efficiently

Disadvantages: Requires more memory per node

In circular linked lists, the tail node points back to the head node to create a continuous loop. This allows traversal indefinitely in either direction. Circular lists are useful for implementation of queues and other algorithms that require persistence across ends.

Advantages: Support endless traversal and queue operations

Disadvantages: No discernible end node, can result in infinite loops

This combines features of doubly linked lists and circular linked lists. Each node maintains pointers to both next and previous nodes while the head/tail nodes also point at each other. This provides full bidirectional traversal and persistence in a loop.

Advantages: Fastest traversal in either direction, easy to insert/delete nodes

Disadvantages: Highest memory requirements per node

Here is a summary comparison of the different types of linked list and their memory requirements:

Type Next Pointer Prev Pointer Head/Tail Pointers Memory
Singly Linked Yes No No Small
Doubly Linked Yes Yes No Medium
Circular Yes No Yes Small
Doubly Circular Yes Yes Yes Large

Once you‘ve chosen the type of linked list for your use case, understanding the common operations is crucial:

### Insertion

This involves inserting a new node into the linked list. For singly linked lists, you can insert at head or tail as well as after a known node. For doubly linked lists, you can also insert before a known position. Time complexity is O(1) for insertion at head and O(N) at tail.

``````# Insert at head in doubly linked list
new_node = Node(value)
new_node.prev = None

# Insert after specific node
def insert_after(node, value):
new_node = Node(value)
new_node.next = node.next
node.next = new_node
new_node.prev = node``````

### Deletion

Delete involves removing an existing node from the linked list. This requires updating the pointers of adjacent nodes properly. Time complexity is O(1) for head and O(N) for tail node.

``````# Delete head node
temp.next = None

# Delete arbitrary node
def delete(node):
node.prev.next = node.next
node.next.prev = node.prev
node.next = None
node.prev = None``````

### Traversal

To access each element, you need to traverse the linked list linearly node by node. Different traversal orders are possible depending on the list type.

``````def traverse(list):
while curr:
print(curr.data)
curr = curr.next``````

Time complexity is O(N) since each node is processed exactly once.

### Searching

Searching for a specific node involves linear traversal similar to traversal. Alternatively, doubly linked lists can search backwards. Optimized search is possible by having pointers to certain nodes.

``````def find(list, value):
while curr:
if curr.data == value:
return curr
curr = curr.next

Searching takes O(N) time in the worst case, but can be O(1) with index nodes.

### Sorting

Sorting a linked list requires dynamically re-arranging nodes. Insertion sort is commonly used with time complexity of O(N^2). Faster sorts like merge sort are possible by using auxiliary space.

``````def insertion_sort(list):
# Start from 2nd node
while curr:
prev = curr.prev
# Shift if value is less than prev
if curr.data < prev.data:
prev.next = curr.next
curr.next = prev
curr.prev = None

else:
# Insert between nodes
curr.next = prev
prev.prev.next = curr
curr.prev = prev.prev

curr = curr.next``````

### Reversing

Reversing a linked list involves rearranging pointers so they point backwards. Used in some linked list algorithms.

``````def reverse(list):
prev = None

while curr:
# Save next node
next = curr.next
# Reverse pointer
curr.next = prev
# Update other pointers
prev = curr
curr = next

Time complexity is O(N).

### Concatenation

Merging two linked lists into one combined list requires rearranging pointers between the tails and heads.

``````def concat(list1, list2):
# Pointer from list1 tail to list2 head

# Update tail reference
list1.tail = list2.tail``````

Runs in O(1) time.

So in summary, the most common linked list operations are insertion, deletion, traversal, searching, sorting, reversing and concatenation.

Linked lists are natively supported by many programming languages. Here are some examples of basic singly linked list implementations:

Python

``````class Node:
# Constructor to create node
def __init__(self, data):
self.data = data
self.next = None

def __init__(self):

def insert(self, data):
newNode = Node(data)

# Print
def printll(self):
while curr:
print(curr.data)
curr = curr.next

ll.insert(3)
ll.insert(2)
ll.insert(1)
ll.printll()``````

Java

``````class Node{
int data;
Node next;

Node(int x){
data = x;
next = null;
}
}

public void insert(int x){
Node newNode = new Node(x);
}

// Print
public void print(){
while(curr != null){
System.out.print(curr.data + " ");
curr = curr.next;
}
}

public static void main(String args[]){
list.insert(3);
list.insert(2);
list.insert(1);
list.print();
}
}``````

JavaScript

``````class Node {
constructor(data) {
this.data = data;
this.next = null;
}
}

constructor() {
}

insert(data) {
let node = new Node(data);
}

// Print
print() {
while (curr) {
console.log(curr.data);
curr = curr.next;
}
}
}

ll.insert(3);
ll.insert(2);
ll.insert(1);
ll.print(); ``````

These all share the same basic structure – a Node class to represent each node and a LinkedList class to handle list operations. Variations exist for different programming languages.

Linked lists are extensively used in computer science for building complex data structures and algorithms. Some examples include:

• Stacks and Queues – Linked lists allow efficient LIFO and FIFO operations for stacks and queues.

• Adjacency Lists – Graphs use linked lists to represent connections between vertices.

• Dynamic Memory Allocation – OS kernels use linked lists of free blocks to handle memory allocation.

• Music Playlists – Songs in playlists are stored and reordered via linked lists.

• Hash Table Collision Chaining – Linked lists resolve hash collisions by chaining entries that hash to the same slot.

• Browser History – Browsers use singly linked lists to store visited pages and allow backwards/forwards navigation.

According to a survey published in Communications of the ACM, linked lists are the 3rd most commonly used data structure behind arrays and records. Their flexibility and efficiency for rearranging data makes them a versatile tool for programmers.

The two main options for implementing linear data structures are linked lists and arrays. They have complementary strengths and weaknesses:

Indexing Sequential access via pointers Random access via indexes
Size Flexible size, no need to preallocate Fixed size, requires preallocation
Insertion/Deletion O(1) at head, O(N) at tail O(N) at head/tail – requires shifting
Memory Only requires space for existing elements Contiguous block of memory required
Caching Poor cache performance due to unpredictable memory access Good cache performance from contiguous memory

In summary, linked lists allow efficient insertion and deletion and flexible sizing while arrays provide better caching and indexing. Choosing the right one depends on the use case and tradeoffs around access patterns and modifications.

## Conclusion

Linked lists are fundamental data structures used across computer science disciplines and applications ranging from operating systems to web browsers. Their principal benefit is efficient insertion and removal of nodes anywhere in the list.

There are several types of linked lists such as singly, doubly, and circularly linked lists. Each type provides different tradeoffs between memory usage and traversal flexibility. Mastering common linked list operations like insertion, deletion and traversal is crucial.

Understanding linked lists will equip you with a versatile data structure for solving problems in efficient space and time complexities. They serve as the basis for more complex data structures like graphs, stacks, and queues. Whether you‘re looking to prepare for technical interviews or enhance your programming skills, linked lists are essential knowledge.