Data Structures – Linked lists


title: Linked Lists

Linked Lists

A Linked List is a simple linear-access data structure.

A linked list is a simple data structure, but it can be used to implement more complicated Data Structures like Queues, Stacks, etc. There are three types of Linked Lists:

  1. Simple Linked List
  2. Doubly Linked List (or Double Ended Linked List)
  3. Circular Linked Lists (Ring Buffer)

Linked List | (Introduction)
Like arrays, Linked List is a linear data structure. Unlike arrays, linked list elements are not stored at contiguous location; the elements are linked using pointers or like in the example using JavaScript, a reference to the next node.

If you want to understand Linked Lists, it helps to understand Arrays.

To recap, an array is traditionally a static linear data structure that supports constant time random access. Insertions and Deletions are not always constant time.

Advantages over arrays
1) Dynamic size
2) Ease of insertion/deletion

static = size fixed at creation time linear = stored linearly in memory as a single block

Arrays have the following disadvantages:-

  1. Arrays are static structures and therefore cannot be easily extended or reduced to fit the data set.
  2. Arrays are also expensive to maintain new insertions and deletions.

Linked Lists address some of the limitations of arrays. Unlike an array, where all the elements are stored in a contiguous block of memory, in a linked list each element is a separate object and has a link to the next element in sequence. This allows a linked list to start with space for only one element, and grow to accomodate an arbitrary number of elements by allocating memory as and when needed.

Deleting elements is also simply handled by manipulating links.

Once you understand the Simple Linked List (which from here on will be referred as ‘List’), you can move on to the Doubly Linked List.

A List as illustrated below is made up of the following components:-

head | | +---+---+ +---+---+ +----+------+ | 1 | o----->| 2 | o-----> | 3 | φ | +---+---+ +---+---+ +----+------+ | | tail
NodeSignificance
HEADBeginning of the List
Node(s)Dynamically allocated self-referential block contain 1 Data element and a link to the next node
TAILEnd of the List

Most common operations available on List are,

  1. AddFirst – Inserts an element at the front of the List.
  2. AddLast – Inserts an element at the tail of the List.
  3. InsertAfter – Inserts an element after an existing element in the List.
  4. InsertBefore – Inserts an element before an existing element in the List.
  5. Remove – Remove an existing element from the List.
  6. Access / Peek – Access an existing element from the List.
  7. Size / Count – Returns the number of elements currently present in the List.
  8. IsEmpty – Check whether the List is empty or not.
  9. Reverse – Reversing a linear linked list.

Doubly/Singly Linked List Time Complexity

AccessSearchInsertionDeletion
O(n)O(n)O(1)O(1)

Implementation of a Simple Linked List in C++

#include<iostream> using namespace std; struct Number { int num; struct Number *tail; }; typedef struct Number N; class List { private: N *head,*end; int count; public: void display(); void insertBefore(int); void deleteNode(int); List(); }; List :: List() { head=NULL; end=NULL; count=0; } void List :: insertBefore(int data) { N *node; node= new N; node->num=data; node->tail=NULL; if(!head){ head=end=node; } else{ node->tail=head; head=node; } count++; } void List :: deleteNode(int loc) { //delete first node if(loc == 1 || count == 1) { N *node = new N; node = head; head = head->tail; delete node; } //delete last node else if(loc == count) { N *curr = new N; N *prev = new N; curr = head; while(curr->tail != NULL) { prev = curr; curr = curr->tail; } prev->tail = NULL; end = prev; delete curr; } //delete in between else { N *curr=new N; N *prev=new N; curr=head; for(int i=1;i<loc;i++) { prev=curr; curr=curr->tail; } prev->tail=curr->tail; } count--; } void List :: display() { cout<<"Number of nodes in the list = "<<count<<endl; N *node; node=head; while(node) { cout<<node->num<<endl; node=node->tail; } } int main() { List l1; l1.insertBefore(10); l1.insertBefore(20); l1.insertBefore(30); l1.insertBefore(40); l1.insertBefore(50); l1.display(); l1.deleteNode(3); l1.display(); return 0; }

OUTPUT

Number of nodes in the list = 5 50 40 30 20 10 Number of nodes in the list = 4 50 40 20 10

Explanation

struct Number { int num; struct Number *tail; };

Declaration of a structure(node) with 2 data members

  • num holds the integer data value
  • *tail pointer points to the next node in the List
class List { private: N *head,*end; int count; public: void display(); void insertBefore(int); List(); };

The List class declares the Linked List.

  • *head points to the first node in the List
  • *end points to the last node in the List
  • count holds the value for number of nodes in the list
  • display() is used to print the complete list on the console
  • insertBefore() is used to insert a new node
  • List() is a defualt constructor
List :: List() { head=NULL; end=NULL; count=0; }

The default constructor is used to initialize the data members of the List class with default values

void List :: insertBefore(int data) { N *node; node= new N; node->num=data; node->tail=NULL; if(!head){ head=end=node; } else{ node->tail=head; head=node; } count++; }
  • A new node is created.
  • num is assigned the value of data.
  • tail is pointing to Null.
  • The if(!head) condition is true only when there are no elements in the List.
  • When this is the case, head and end are both pointing to the newly created node.
  • Control will move to the else section, when there is at least one node in the list.
  • In this case, tail pointer in the newly created node is made to point to the head(first) node.
  • The head pointer then points to the newly created node to make it the first node in the list.
  • count is incremented by 1 as each new node is added.
void List :: display() { N *node; node=head; while(node) { cout<<node->num<<endl; node=node->tail; } }

The display function is used to run through the list and print the total number of nodes and values of num on the console.

Applications

  • Base Data Structure for Vector, Array, Queue, Stack, etc
  • Polynomial Representation
  • Ring Buffer

Drawbacks:
1) Random access is not allowed. We have to access elements sequentially starting from the first node. So we cannot do binary search with linked lists.
2) Extra memory space for a pointer is required with each element of the list

Types:
1) (Singly) linked lists contain nodes which have a data field as well as a ‘next’ field, which points to the next node in line of nodes. Operations that can be performed on singly linked lists include insertion, deletion and traversal.

2) (Doubly) In a ‘doubly linked list’, each node contains, besides the next-node link, a second link field pointing to the ‘previous’ node in the sequence. The two links may be called ‘forward(‘s’) and ‘backwards’, or ‘next’ and ‘prev'(‘previous’).

Example in JavaScript:

function LinkedList () { this.head = null; this.tail = null; } // Node has three properties value, next, prev function Node (value, next, prev) { this.value = value; // A 'pointer' referencing to the next Node (if present) otherwise null this.next = next; // A 'pointer' referencing the previous Node, otherwise null this.prev = prev; } LinkedList.prototype.addToHead = function(value) { let newNode = new Node(value, this.head, null); if (this.head) this.head.prev = newNode; else this.tail = newNode; this.head = newNode; }

Now Execute code

let LL = new LinkedList(); LL.addToHead(100); LL.addToHead(200); console.log(LL);

Representation in C:
A linked list is represented by a pointer to the first node of the linked list. The first node is called head. If the linked list is empty, then value of head is NULL.
Each node in a list consists of at least two parts:
1) data
2) pointer to the next node
In C, we can represent a node using structures. Below is an example of a linked list node with an integer data.
In Java, LinkedList can be represented as a class and a Node as a separate class. The LinkedList class contains a reference of Node class type

// A linked list node struct Node { int data; struct Node *next; };

Linked List with three elements

// A simple C program to introduce // a linked list #include<stdio.h> #include<stdlib.h> struct Node { int data; struct Node *next; }; // Program to create a simple linked // list with 3 nodes int main() { struct Node* head = NULL; struct Node* second = NULL; struct Node* third = NULL; // allocate 3 nodes in the heap head = (struct Node*)malloc(sizeof(struct Node)); second = (struct Node*)malloc(sizeof(struct Node)); third = (struct Node*)malloc(sizeof(struct Node)); /* Three blocks have been allocated dynamically. We have pointers to these three blocks as first, second and third head second third | | | | | | +---+-----+ +----+----+ +----+----+ | # | # | | # | # | | # | # | +---+-----+ +----+----+ +----+----+ # represents any random value. Data is random because we haven’t assigned anything yet */ head->data = 1; //assign data in first node head->next = second; // Link first node with the second node /* data has been assigned to data part of first block (block pointed by head). And next pointer of first block points to second. So they both are linked. head second third | | | | | | +---+---+ +----+----+ +-----+----+ | 1 | o----->| # | # | | # | # | +---+---+ +----+----+ +-----+----+ */ second->data = 2; //assign data to second node second->next = third; // Link second node with the third node /* data has been assigned to data part of second block (block pointed by second). And next pointer of the second block points to third block. So all three blocks are linked. head second third | | | | | | +---+---+ +---+---+ +----+----+ | 1 | o----->| 2 | o-----> | # | # | +---+---+ +---+---+ +----+----+ */ third->data = 3; //assign data to third node third->next = NULL; /* data has been assigned to data part of third block (block pointed by third). And next pointer of the third block is made NULL to indicate that the linked list is terminated here. We have the linked list ready. head | | +---+---+ +---+---+ +----+------+ | 1 | o----->| 2 | o-----> | 3 | NULL | +---+---+ +---+---+ +----+------+ Note that only head is sufficient to represent the whole list. We can traverse the complete list by following next pointers. */ return 0; }

Implementation of a Simple Linked List in Java

class Node { int data; Node next; Node(int d) { data = d; next = null; } } class LinkedList { // Create a linked list with atleast one node Node head; LinkedList(int data) { head = new Node(data); } public void addNode(int data) { Node temp = new Node(data); temp.next = head; head = temp; } public void reverseLinkedList() { // No need for changes or reversal. if (head == null || head.next == null) { return; } else { Node temp = head; Node curr = head.next; temp.next = null; while (curr != null && curr.next != null) { Node newNode = curr.next; curr.next = temp; temp = curr; curr = newNode; } curr.next = temp; head = curr; } } public void printLinkedList() { Node temp = head; System.out.println(); while (temp != null) { System.out.print(temp.data + " "); temp = temp.next; } System.out.println(); } } public class LinkedListWork { public static void main(String[] args) { LinkedList ll = new LinkedList(1); ll.addNode(2); ll.addNode(3); ll.addNode(4); ll.addNode(5); ll.printLinkedList(); ll.reverseLinkedList(); ll.printLinkedList(); } }

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