Why is deleting in a Singly Linked List O(1)?

How does deleting a node in Singly Linked List work?

To delete a node from a linked list we need to break the link between that node and the one pointing to that node. Assume node X needs to be deleted and node Y is the one pointing to X. So, we will need to break the link between X and Y and Y will point to the node which was being pointed by X.

Types of Deletion of a node from Linked List

There can be three types of deletions:

1. Deletion from the beginning of the linked list
2. Deletion from the end of the linked list
3. Deletion from in between the beginning and the end.

All the cases do not take O(1) time. Check the below section to find the time complexities of different operations.

Time Complexities of different deletion operations

Deletion from the beginning:

• Point head to the next node
• Time Complexity: O(1)

Deletion from the end:

• Traverse to the second last element
• Change its next pointer to NULL.
• Time Complexity: O(N)

Delete from the middle of a linked list

• Traverse to the element which is just before the element to be deleted
• Change the next pointers to exclude the node from the list
• Time Complexity: O(N)

When Deletion in a Singly Linked List takes O(1) time?

There are 3 cases when deleting in a singly linked list is O(1), because we do not have to traverse the list.

First case: When we have the pointer pointing to the node which needs to be deleted, let's call it prev. So, we have to do,

• curr = prev->next
• prev->next = curr->next
• curr->next = NULL
• delete curr

Since curr is the node that is deleted from the singly linked list.

Second case: When we have to delete the first/start/head node, let's call it head. So, we have to do,

• head = head->next

Hence head is pointing to the next node.

Third case: When we have to delete the last/end/tail node, let's call it tail. So, we have to do,

• tail = NULL

This is only possible if we maintain an extra pointer except the head i.e., tail for referencing the last node of the linked list. But we can do this only once because after doing this we lose the reference of the last node and there is no way to find the reference of the new last node in O(1) in a singly linked list. In a doubly linked list, it is possible as it contains the previous pointer.

Below is the implementation of different deletion operations in a singly linked list:

// C++ code to implement the approach

#include <iostream>
using namespace std;

// Creating a class Node
class Node {
public:
    int data;
    Node* next;
    Node(int d)
    {
        data = d;
        next = NULL;
    }
};

// Function to delete the start node
void deleteFromStart(Node*& head)
{
    head = head->next;
}

// Function to delete the middle node
void deleteGivenNode(Node*& head, int val)
{
    if (head->data == val) {
        head = head->next;
    }

    Node *temp = head, *prev = NULL;

    while (temp->data != val) {
        prev = temp;
        temp = temp->next;
    }
    prev->next = temp->next;
}

// Function to delete the last node
void deleteFromEnd(Node* head)
{
    Node* temp = head;

    while (temp->next->next != NULL) {
        temp = temp->next;
    }

    temp->next = NULL;
}

// Function to print the list
void printList(Node* head)
{
    Node* temp = head;
    while (temp != NULL) {
        cout << temp->data << " ";
        temp = temp->next;
    }
    cout << endl;
}

// Driver Code
int main()
{
    Node* head = new Node(10);
    Node* second = new Node(20);
    Node* third = new Node(30);
    Node* fourth = new Node(40);

    head->next = second;
    second->next = third;
    third->next = fourth;

    cout << "Original list: ";
    printList(head);

    deleteFromStart(head);
    cout << "List after deleting the starting node: ";
    printList(head);

    deleteFromEnd(head);
    cout << "List after deleting the ending node: ";
    printList(head);

    deleteGivenNode(head, 30);
    cout << "List after deleting the given node: ";
    printList(head);
}

// Java code to implement the approach

// Creating a class Node
class Node {
  public int data;
  public Node next;

  public Node(int d) {
    data = d;
    next = null;
  }
}

public class Main {
  // Function to delete the start node
  public static Node deleteFromStart(Node head) {
    head = head.next;
    return head;
  }

  // Function to delete the given node
  public static void deleteGivenNode(Node head, int val) {
    if (head.data == val) {
      head = head.next;
    }

    Node temp = head, prev = null;

    while (temp.data != val) {
      prev = temp;
      temp = temp.next;
    }
    prev.next = temp.next;
  }

  // Function to delete the last node
  public static void deleteFromEnd(Node head) {
    Node temp = head;

    while (temp.next.next != null) {
      temp = temp.next;
    }

    temp.next = null;
  }

  // Function to print the list
  public static void printList(Node head) {
    Node temp = head;
    while (temp != null) {
      System.out.print(temp.data + " ");
      temp = temp.next;
    }
    System.out.println();
  }

  // Driver Code
  public static void main(String[] args) {
    Node head = new Node(10);
    Node second = new Node(20);
    Node third = new Node(30);
    Node fourth = new Node(40);

    head.next = second;
    second.next = third;
    third.next = fourth;

    System.out.print("Original list: ");
    printList(head);

    head = deleteFromStart(head);
    System.out.print("List after deleting the starting node: ");
    printList(head);

    deleteFromEnd(head);
    System.out.print("List after deleting the ending node: ");
    printList(head);

    deleteGivenNode(head, 30);
    System.out.print("List after deleting the given node: ");
    printList(head);
  }
}

# Python code to implement the approach

# Creating a class Node
class Node:
    def __init__(self,val):
        self.val = val
        self.next = None
    
# Function to delete the start node
def deleteFromStart(head):
  if head != None:
    head = head.next
  return head
  
#  Function to delete the middle node
def deleteGivenNode(head,val):
  if head.val == val: head = head.next
  curr = head
  prev = None
  while curr and curr.val != val:
    prev = curr
    curr = curr.next
  prev.next = curr.next
  
# Function to delete the last node
def deleteFromEnd(head):
  curr = head
  while curr.next and curr.next.next != None:
    curr = curr.next
  curr.next = None

# Prints the stack
def printList(head):
  if head == None:
    print('List is Empty')
    return
  curr = head
  while curr != None:
    print(curr.val,end = ' ')
    curr = curr.next
  print()

# Driver code
head =  Node(10)
second = Node(20)
third = Node(30)
fourth = Node(40)

head.next = second 
second.next = third 
third.next = fourth 

print("Original list: ")
printList(head) 

head = deleteFromStart(head) 
print("List after deleting the starting node: " )
printList(head) 

deleteFromEnd(head) 
print("List after deleting the ending node: " )
printList(head) 

deleteGivenNode(head, 30) 
print("List after deleting the given node: ")
printList(head) 

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;

// C# code to implement the approach

// Creating a class Node
class Node {
  public int data;
  public Node next;

  public Node(int d) {
    data = d;
    next = null;
  }
}

class HelloWorld {

    // Function to delete the start node
    public static Node deleteFromStart(Node head) {
        head = head.next;
        return head;
    }

    // Function to delete the given node
    public static void deleteGivenNode(Node head, int val) {
        if (head.data == val) {
          head = head.next;
        }

        Node temp = head, prev = null;

        while (temp.data != val) {
            prev = temp;
            temp = temp.next;
        }
        prev.next = temp.next;
    }

    // Function to delete the last node
    public static void deleteFromEnd(Node head) {
        Node temp = head;

        while (temp.next.next != null) {
          temp = temp.next;
        }

        temp.next = null;
    }

    // Function to print the list
    public static void printList(Node head) {
        Node temp = head;
        while (temp != null) {
          Console.Write(temp.data + " ");
          temp = temp.next;
        }
        Console.WriteLine();
    }
    
    static void Main() {
        Node head = new Node(10);
        Node second = new Node(20);
        Node third = new Node(30);
        Node fourth = new Node(40);

        head.next = second;
        second.next = third;
        third.next = fourth;

        Console.Write("Original list: ");
        printList(head);

        head = deleteFromStart(head);
        Console.Write("List after deleting the starting node: ");
        printList(head);

        deleteFromEnd(head);
        Console.Write("List after deleting the ending node: ");
        printList(head);

        deleteGivenNode(head, 30);
        Console.Write("List after deleting the given node: ");
        printList(head);
    }
}

// The code is contributed by Nidhi goel

<script>

// javascript code to implement the approach

// Creating a class Node
class Node {

    constructor(val){
        this.data = val;
        this.next = null;
    }
}

// Function to delete the start node
function deleteFromStart(head)
{
    head = head.next;
    return head;
    
}

// Function to delete the middle node
function deleteGivenNode(head, val)
{
    if (head.data == val) {
        head = head.next;
    }

    let temp = head;
    let prev = null;

    while (temp.data != val) {
        prev = temp;
        temp = temp.next;
    }
    prev.next = temp.next;
}

// Function to delete the last node
function deleteFromEnd(head)
{
    let temp = head;

    while (temp.next.next != null) {
        temp = temp.next;
    }

    temp.next = null;
}

// Function to print the list
function printList(head)
{
    let temp = head;
    while (temp != null) {
        document.write(temp.data + " ");
        temp = temp.next;
    }
    document.write("\n");
}

// Driver Code
let head = new Node(10);
let second = new Node(20);
let third = new Node(30);
let fourth = new Node(40);

head.next = second;
second.next = third;
third.next = fourth;

document.write("Original list: ");
printList(head);

head = deleteFromStart(head);
document.write("List after deleting the starting node: ");
printList(head);

deleteFromEnd(head);
document.write("List after deleting the ending node: ");
printList(head);

deleteGivenNode(head, 30);
document.write("List after deleting the given node: ");
printList(head);

// The code is contributed by Nidhi goel. 

</script> 

Original list: 10 20 30 40 
List after deleting the starting node: 20 30 40 
List after deleting the ending node: 20 30 
List after deleting the given node: 20