Insertion Sort for Singly Linked List

We have discussed Insertion Sort for arrays. In this article, we are going to discuss Insertion Sort for a linked list. 
Below is a simple insertion sort algorithm for a linked list. 

1) Create an empty sorted (or result) list
2) Traverse the given list, do following for every node.
......a) Insert current node in sorted way in sorted or result list.
3) Change head of given linked list to head of sorted (or result) list.

The main step is (2.a) which has been covered in the below post. 
Sorted Insert for Singly Linked List

Below is the implementation of the above algorithm

C

// C program to sort link list
// using insertion sort
#include <stdio.h>
#include <stdlib.h>

struct node {
    int data;
    struct node* next;
};

struct node* head = NULL;
struct node* sorted = NULL;

void push(int val)
{
    /* allocate node */
    struct node* newnode
        = (struct node*)malloc(sizeof(struct node));
    newnode->data = val;
    /* link the old list off the new node */
    newnode->next = head;
    /* move the head to point to the new node */
    head = newnode;
}

/*
 * function to insert a new_node in a list. Note that
 * this function expects a pointer to head_ref as this
 * can modify the head of the input linked list
 * (similar to push())
 */
void sortedInsert(struct node* newnode)
{
    /* Special case for the head end */
    if (sorted == NULL || sorted->data >= newnode->data) {
        newnode->next = sorted;
        sorted = newnode;
    }
    else {
        struct node* current = sorted;
        /* Locate the node before the point of insertion
         */
        while (current->next != NULL
               && current->next->data < newnode->data) {
            current = current->next;
        }
        newnode->next = current->next;
        current->next = newnode;
    }
}

// function to sort a singly linked list
// using insertion sort
void insertionsort()
{

    struct node* current = head;

    // Traverse the given linked list and insert every
    // node to sorted
    while (current != NULL) {

        // Store next for next iteration
        struct node* next = current->next;

        // insert current in sorted linked list
        sortedInsert(current);

        // Update current
        current = next;
    }
    // Update head to point to sorted linked list
    head = sorted;
}

/* Function to print linked list */
void printlist(struct node* head)
{
    while (head != NULL) {
        printf("%d->", head->data);
        head = head->next;
    }
    printf("NULL");
}

// Driver program to test above functions
int main()
{

    push(5);
    push(20);
    push(4);
    push(3);
    push(30);

    printf("Linked List before sorting:\n");
    printlist(head);
    printf("\n");

    insertionsort(head);

    printf("Linked List after sorting:\n");
    printlist(head);
}

// This code is contributed by Sornodeep Chandra

C++

// C++ program to sort link list
// using insertion sort
#include <bits/stdc++.h>
using namespace std;

struct Node {
    int val;
    struct Node* next;
    Node(int x)
    {
        val = x;
        next = NULL;
    }
};

class LinkedlistIS {

public:
    Node* head;
    Node* sorted;

    void push(int val)
    {
        /* allocate node */
        Node* newnode = new Node(val);
        /* link the old list off the new node */
        newnode->next = head;
        /* move the head to point to the new node */
        head = newnode;
    }

    // function to sort a singly linked list using insertion
    // sort
    void insertionSort(Node* headref)
    {
        // Initialize sorted linked list
        sorted = NULL;
        Node* current = headref;
        // Traverse the given linked list and insert every
        // node to sorted
        while (current != NULL) {
            // Store next for next iteration
            Node* next = current->next;
            // insert current in sorted linked list
            sortedInsert(current);
            // Update current
            current = next;
        }
        // Update head_ref to point to sorted linked list
        head = sorted;
    }

    /*
     * function to insert a new_node in a list. Note that
     * this function expects a pointer to head_ref as this
     * can modify the head of the input linked list
     * (similar to push())
     */
    void sortedInsert(Node* newnode)
    {
        /* Special case for the head end */
        if (sorted == NULL || sorted->val >= newnode->val) {
            newnode->next = sorted;
            sorted = newnode;
        }
        else {
            Node* current = sorted;
            /* Locate the node before the point of insertion
             */
            while (current->next != NULL
                   && current->next->val < newnode->val) {
                current = current->next;
            }
            newnode->next = current->next;
            current->next = newnode;
        }
    }
    /* Function to print linked list */
    void printlist(Node* head)
    {
        while (head != NULL) {
            cout << head->val << " ";
            head = head->next;
        }
    }
};
// Driver program to test above functions
int main()
{
    LinkedlistIS list;
    list.head = NULL;
    list.push(5);
    list.push(20);
    list.push(4);
    list.push(3);
    list.push(30);
    cout << "Linked List before sorting" << endl;
    list.printlist(list.head);
    cout << endl;
    list.insertionSort(list.head);
    cout << "Linked List After sorting" << endl;
    list.printlist(list.head);
}

// This code is contributed by nirajgusain5

Java

// Java program to sort link list
// using insertion sort

public class LinkedlistIS
{
    node head;
    node sorted;

    class node
    {
        int val;
        node next;

        public node(int val)
        {
            this.val = val;
        }
    }

    void push(int val)
    {
        /* allocate node */
        node newnode = new node(val);
        /* link the old list off the new node */
        newnode.next = head;
        /* move the head to point to the new node */
        head = newnode;
    }

    // function to sort a singly linked list using insertion sort
    void insertionSort(node headref)
    {
        // Initialize sorted linked list
        sorted = null;
        node current = headref;
        // Traverse the given linked list and insert every
        // node to sorted
        while (current != null)
        {
            // Store next for next iteration
            node next = current.next;
            // insert current in sorted linked list
            sortedInsert(current);
            // Update current
            current = next;
        }
        // Update head_ref to point to sorted linked list
        head = sorted;
    }

    /*
     * function to insert a new_node in a list. Note that
     * this function expects a pointer to head_ref as this
     * can modify the head of the input linked list
     * (similar to push())
     */
    void sortedInsert(node newnode)
    {
        /* Special case for the head end */
        if (sorted == null || sorted.val >= newnode.val)
        {
            newnode.next = sorted;
            sorted = newnode;
        }
        else
        {
            node current = sorted;
            /* Locate the node before the point of insertion */
            while (current.next != null && current.next.val < newnode.val)
            {
                current = current.next;
            }
            newnode.next = current.next;
            current.next = newnode;
        }
    }

    /* Function to print linked list */
    void printlist(node head)
    {
        while (head != null)
        {
            System.out.print(head.val + " ");
            head = head.next;
        }
    }

    // Driver program to test above functions
    public static void main(String[] args)
    {
        LinkedlistIS list = new LinkedlistIS();
        list.push(5);
        list.push(20);
        list.push(4);
        list.push(3);
        list.push(30);
        System.out.println("Linked List before Sorting..");
        list.printlist(list.head);
        list.insertionSort(list.head);
        System.out.println("\nLinkedList After sorting");
        list.printlist(list.head);
    }
}

// This code is contributed by Rishabh Mahrsee

Python

# Python implementation of above algorithm

# Node class
class Node:

    # Constructor to initialize the node object
    def __init__(self, data):
        self.data = data
        self.next = None

# function to sort a singly linked list using insertion sort
def insertionSort(head_ref):

    # Initialize sorted linked list
    sorted = None

    # Traverse the given linked list and insert every
    # node to sorted
    current = head_ref
    while (current != None):

        # Store next for next iteration
        next = current.next

        # insert current in sorted linked list
        sorted = sortedInsert(sorted, current)

        # Update current
        current = next

    # Update head_ref to point to sorted linked list
    head_ref = sorted
    return head_ref

# function to insert a new_node in a list. Note that this
# function expects a pointer to head_ref as this can modify the
# head of the input linked list (similar to push())
def sortedInsert(head_ref, new_node):

    current = None

    # Special case for the head end */
    if (head_ref == None or (head_ref).data >= new_node.data):

        new_node.next = head_ref
        head_ref = new_node

    else:

        # Locate the node before the point of insertion
        current = head_ref
        while (current.next != None and
            current.next.data < new_node.data):

            current = current.next

        new_node.next = current.next
        current.next = new_node

    return head_ref

# BELOW FUNCTIONS ARE JUST UTILITY TO TEST sortedInsert

# Function to print linked list */
def printList(head):

    temp = head
    while(temp != None):

        print( temp.data, end = " ")
        temp = temp.next

# A utility function to insert a node
# at the beginning of linked list
def push( head_ref, new_data):

    # allocate node
    new_node = Node(0)

    # put in the data
    new_node.data = new_data

    # link the old list off the new node
    new_node.next = (head_ref)

    # move the head to point to the new node
    (head_ref) = new_node
    return head_ref

# Driver program to test above functions

a = None
a = push(a, 5)
a = push(a, 20)
a = push(a, 4)
a = push(a, 3)
a = push(a, 30)

print("Linked List before sorting ")
printList(a)

a = insertionSort(a)

print("\nLinked List after sorting ")
printList(a)

# This code is contributed by Arnab Kundu

C#

// C# program to sort link list
// using insertion sort
using System;

public class LinkedlistIS
{
    public node head;
    public node sorted;

    public class node
    {
        public int val;
        public node next;

        public node(int val)
        {
            this.val = val;
        }
    }

    void push(int val)
    {
        /* allocate node */
        node newnode = new node(val);

        /* link the old list off the new node */
        newnode.next = head;

        /* move the head to point to the new node */
        head = newnode;
    }

    // function to sort a singly
    // linked list using insertion sort
    void insertionSort(node headref)
    {
        // Initialize sorted linked list
        sorted = null;
        node current = headref;

        // Traverse the given
        // linked list and insert every
        // node to sorted
        while (current != null)
        {
            // Store next for next iteration
            node next = current.next;

            // insert current in sorted linked list
            sortedInsert(current);

            // Update current
            current = next;
        }

        // Update head_ref to point to sorted linked list
        head = sorted;
    }

    /*
    * function to insert a new_node in a list. Note that
    * this function expects a pointer to head_ref as this
    * can modify the head of the input linked list
    * (similar to push())
    */
    void sortedInsert(node newnode)
    {
        /* Special case for the head end */
        if (sorted == null || sorted.val >= newnode.val)
        {
            newnode.next = sorted;
            sorted = newnode;
        }
        else
        {
            node current = sorted;

            /* Locate the node before the point of insertion */
            while (current.next != null &&
                    current.next.val < newnode.val)
            {
                current = current.next;
            }
            newnode.next = current.next;
            current.next = newnode;
        }
    }

    /* Function to print linked list */
    void printlist(node head)
    {
        while (head != null)
        {
            Console.Write(head.val + " ");
            head = head.next;
        }
    }

    // Driver code
    public static void Main(String[] args)
    {
        LinkedlistIS list = new LinkedlistIS();
        list.push(5);
        list.push(20);
        list.push(4);
        list.push(3);
        list.push(30);
        Console.WriteLine("Linked List before Sorting..");
        list.printlist(list.head);
        list.insertionSort(list.head);
        Console.WriteLine("\nLinkedList After sorting");
        list.printlist(list.head);
    }
}

// This code contributed by Rajput-Ji

Javascript

<script>
// javascript program to sort link list
// using insertion sort

var head = null;
    var sorted = null;

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


    function push(val) {
        /* allocate node */
        var newnode = new node(val);
        /* link the old list off the new node */
        newnode.next = head;
        /* move the head to point to the new node */
        head = newnode;
    }

    // function to sort a singly linked list using insertion sort
    function insertionSort( headref) {
        // Initialize sorted linked list
        var sorted = null;
        var current = headref;
        // Traverse the given linked list and insert every
        // node to sorted
        while (current != null) {
            // Store next for next iteration
            var next = current.next;
            // insert current in sorted linked list
            sortedInsert(current);
            // Update current
            current = next;
        }
        // Update head_ref to point to sorted linked list
        head = sorted;
    }

    /*
     * function to insert a new_node in a  Note that this function expects a
     * pointer to head_ref as this can modify the head of the input linked list
     * (similar to push())
     */
    function sortedInsert( newnode) {
        /* Special case for the head end */
        if (sorted == null || sorted.val >= newnode.val) {
            newnode.next = sorted;
            sorted = newnode;
        } else {
            var current = sorted;
            /* Locate the node before the point of insertion */
            while (current.next != null && current.next.val < newnode.val) {
                current = current.next;
            }
            newnode.next = current.next;
            current.next = newnode;
        }
    }

    /* Function to print linked list */
    function printlist( head) {
        while (head != null) {
            document.write(head.val + " ");
            head = head.next;
        }
    }

    // Driver program to test above functions


        push(5);
        push(20);
        push(4);
        push(3);
        push(30);
        document.write("Linked List before Sorting..<br/>");
        printlist(head);
        insertionSort(head);
        document.write("<br/>LinkedList After sorting<br/>");
        printlist(sorted);

// This code contributed by aashish1995
</script>

Output:

Linked List before sorting
30  3  4  20  5
Linked List after sorting
3  4  5  20  30

Time and space complexity analysis: 

In the worst case, we might have to traverse all nodes of the sorted list for inserting a node. And there are “n” such nodes.

Thus Time Complexity: O(n)*O(n)=O(n^2)

Space Complexity: No extra space is required depending on the size of the input. Thus Space complexity is constant- O(1).

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