Insertion Sort for Doubly Linked List

Sort the doubly linked list using the insertion sort technique.

Initial doubly linked list 

Doubly Linked List after applying insertion sort 

Algorithm:
Below is a simple insertion sort algorithm for doubly-linked lists.
1) Create an empty sorted (or result) doubly linked list. 
2) Traverse the given doubly linked list, and do the following for every node. 
     a) Insert the current node in a sorted way in the sorted(or result) doubly linked list. 
3) Change the head of the given linked list to the head of the sorted (or result) list.
The main step is (2. a), which has been covered in the post below. 
Sorted Insert for Doubly Linked List

C++

// C++ implementation for insertion Sort
// on a doubly linked list
#include <bits/stdc++.h>

using namespace std;

// Node of a doubly linked list
struct Node {
    int data;
    struct Node* prev, *next;
};

// function to create and return a new node
// of a doubly linked list
struct Node* getNode(int data)
{
    // allocate node
    struct Node* newNode =
          (struct Node*)malloc(sizeof(struct Node));

    // put in the data
    newNode->data = data;
    newNode->prev = newNode->next = NULL;
    return newNode;
}

// function to insert a new node in sorted way in
// a sorted doubly linked list
void sortedInsert(struct Node** head_ref, struct Node* newNode)
{
    struct Node* current;

    // if list is empty
    if (*head_ref == NULL)
        *head_ref = newNode;

    // if the node is to be inserted at the beginning
    // of the doubly linked list
    else if ((*head_ref)->data >= newNode->data) {
        newNode->next = *head_ref;
        newNode->next->prev = newNode;
        *head_ref = newNode;
    }

    else {
        current = *head_ref;

        // locate the node after which the new node
        // is to be inserted
        while (current->next != NULL &&
               current->next->data < newNode->data)
            current = current->next;

        /*Make the appropriate links */

        newNode->next = current->next;

        // if the new node is not inserted
        // at the end of the list
        if (current->next != NULL)
            newNode->next->prev = newNode;

        current->next = newNode;
        newNode->prev = current;
    }
}

// function to sort a doubly linked list using insertion sort
void insertionSort(struct Node** head_ref)
{
    // Initialize 'sorted' - a sorted doubly linked list
    struct Node* sorted = NULL;

    // Traverse the given doubly linked list and
    // insert every node to 'sorted'
    struct Node* current = *head_ref;
    while (current != NULL) {

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

        // removing all the links so as to create 'current'
        // as a new node for insertion
        current->prev = current->next = NULL;

        // insert current in 'sorted' doubly linked list
        sortedInsert(&sorted, current);

        // Update current
        current = next;
    }

    // Update head_ref to point to sorted doubly linked list
    *head_ref = sorted;
}

// function to print the doubly linked list
void printList(struct Node* head)
{
    while (head != NULL) {
        cout << head->data << " ";
        head = head->next;
    }
}

// function to insert a node at the beginning of
// the doubly linked list
void push(struct Node** head_ref, int new_data)
{
    /* allocate node */
    struct Node* new_node =
         (struct Node*)malloc(sizeof(struct Node));

    /* put in the data  */
    new_node->data = new_data;

    /* Make next of new node as head and previous as NULL */
    new_node->next = (*head_ref);
    new_node->prev = NULL;

    /* change prev of head node to new node */
    if ((*head_ref) != NULL)
        (*head_ref)->prev = new_node;

    /* move the head to point to the new node */
    (*head_ref) = new_node;
}

// Driver program to test above
int main()
{
    /* start with the empty doubly linked list */
    struct Node* head = NULL;

    // insert the following data
    push(&head, 9);
    push(&head, 3);
    push(&head, 5);
    push(&head, 10);
    push(&head, 12);
    push(&head, 8);

    cout << "Doubly Linked List Before Sortingn";
    printList(head);

    insertionSort(&head);

    cout << "nDoubly Linked List After Sortingn";
    printList(head);

    return 0;
}

Java

// Java implementation for insertion Sort
// on a doubly linked list
class Solution
{

// Node of a doubly linked list
static class Node
{
    int data;
    Node prev, next;
};

// function to create and return a new node
// of a doubly linked list
static Node getNode(int data)
{
    // allocate node
    Node newNode = new Node();

    // put in the data
    newNode.data = data;
    newNode.prev = newNode.next = null;
    return newNode;
}

// function to insert a new node in sorted way in
// a sorted doubly linked list
static Node sortedInsert(Node head_ref, Node newNode)
{
    Node current;

    // if list is empty
    if (head_ref == null)
        head_ref = newNode;

    // if the node is to be inserted at the beginning
    // of the doubly linked list
    else if ((head_ref).data >= newNode.data)
    {
        newNode.next = head_ref;
        newNode.next.prev = newNode;
        head_ref = newNode;
    }

    else
    {
        current = head_ref;

        // locate the node after which the new node
        // is to be inserted
        while (current.next != null &&
            current.next.data < newNode.data)
            current = current.next;

        //Make the appropriate links /

        newNode.next = current.next;

        // if the new node is not inserted
        // at the end of the list
        if (current.next != null)
            newNode.next.prev = newNode;

        current.next = newNode;
        newNode.prev = current;
    }
    return head_ref;
}

// function to sort a doubly linked list using insertion sort
static Node insertionSort(Node head_ref)
{
    // Initialize 'sorted' - a sorted doubly linked list
    Node sorted = null;

    // Traverse the given doubly linked list and
    // insert every node to 'sorted'
    Node current = head_ref;
    while (current != null)
    {

        // Store next for next iteration
        Node next = current.next;

        // removing all the links so as to create 'current'
        // as a new node for insertion
        current.prev = current.next = null;

        // insert current in 'sorted' doubly linked list
        sorted=sortedInsert(sorted, current);

        // Update current
        current = next;
    }

    // Update head_ref to point to sorted doubly linked list
    head_ref = sorted;

    return head_ref;
}

// function to print the doubly linked list
static void printList(Node head)
{
    while (head != null)
    {
        System.out.print(head.data + " ");
        head = head.next;
    }
}

// function to insert a node at the beginning of
// the doubly linked list
static Node push(Node head_ref, int new_data)
{
    // allocate node /
    Node new_node = new Node();

    // put in the data /
    new_node.data = new_data;

    // Make next of new node as head and previous as null /
    new_node.next = (head_ref);
    new_node.prev = null;

    // change prev of head node to new node /
    if ((head_ref) != null)
        (head_ref).prev = new_node;

    // move the head to point to the new node /
    (head_ref) = new_node;

    return head_ref;
}

// Driver code
public static void main(String args[])
{
    // start with the empty doubly linked list /
    Node head = null;

    // insert the following data
    head=push(head, 9);
    head=push(head, 3);
    head=push(head, 5);
    head=push(head, 10);
    head=push(head, 12);
    head=push(head, 8);

    System.out.println( "Doubly Linked List Before Sorting\n");
    printList(head);

    head=insertionSort(head);

    System.out.println("\nDoubly Linked List After Sorting\n");
    printList(head);

}
}

// This code is contributed by Arnab Kundu

Python3

# Python3 implementation for insertion Sort
# on a doubly linked list

# Node of a doubly linked list
class Node:

    def __init__(self, data):
        self.data = data
        self.prev = None
        self.next = None

# function to create and return a new node
# of a doubly linked list
def getNode(data):

    # allocate node
    newNode = Node(0)

    # put in the data
    newNode.data = data
    newNode.prev = newNode.next = None
    return newNode

# function to insert a new node in sorted way in
# a sorted doubly linked list
def sortedInsert(head_ref, newNode):

    current = None

    # if list is empty
    if (head_ref == None):
        head_ref = newNode

    # if the node is to be inserted at the beginning
    # of the doubly linked list
    elif ((head_ref).data >= newNode.data) :
        newNode.next = head_ref
        newNode.next.prev = newNode
        head_ref = newNode

    else :
        current = head_ref

        # locate the node after which the new node
        # is to be inserted
        while (current.next != None and
            current.next.data < newNode.data):
            current = current.next

        """Make the appropriate links """
        newNode.next = current.next

        # if the new node is not inserted
        # at the end of the list
        if (current.next != None):
            newNode.next.prev = newNode

        current.next = newNode
        newNode.prev = current

    return head_ref;

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

    # Initialize 'sorted' - a sorted
    # doubly linked list
    sorted = None

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

        # Store next for next iteration
        next = current.next

        # removing all the links so as to create
        # 'current' as a new node for insertion
        current.prev = current.next = None

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

        # Update current
        current = next

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

    return head_ref

# function to print the doubly linked list
def printList(head):

    while (head != None) :
        print( head.data, end = " ")
        head = head.next

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

    """ allocate node """
    new_node = Node(0)

    """ put in the data """
    new_node.data = new_data

    """ Make next of new node as head
    and previous as None """
    new_node.next = (head_ref)
    new_node.prev = None

    """ change prev of head node to new node """
    if ((head_ref) != None):
        (head_ref).prev = new_node

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


# Driver Code
if __name__ == "__main__":

    """ start with the empty doubly linked list """
    head = None

    # insert the following data
    head = push(head, 9)
    head = push(head, 3)
    head = push(head, 5)
    head = push(head, 10)
    head = push(head, 12)
    head = push(head, 8)

    print( "Doubly Linked List Before Sorting")
    printList(head)

    head = insertionSort(head)

    print("\nDoubly Linked List After Sorting")
    printList(head)

# This code is contributed by Arnab Kundu

C#

// C# implementation for insertion Sort
// on a doubly linked list
using System;

class GFG
{

// Node of a doubly linked list
public class Node
{
    public int data;
    public Node prev, next;
};

// function to create and return a new node
// of a doubly linked list
static Node getNode(int data)
{
    // allocate node
    Node newNode = new Node();

    // put in the data
    newNode.data = data;
    newNode.prev = newNode.next = null;
    return newNode;
}

// function to insert a new node in sorted way
// in a sorted doubly linked list
static Node sortedInsert(Node head_ref,
                         Node newNode)
{
    Node current;

    // if list is empty
    if (head_ref == null)
        head_ref = newNode;

    // if the node is to be inserted at the beginning
    // of the doubly linked list
    else if ((head_ref).data >= newNode.data)
    {
        newNode.next = head_ref;
        newNode.next.prev = newNode;
        head_ref = newNode;
    }

    else
    {
        current = head_ref;

        // locate the node after which
        // the new node is to be inserted
        while (current.next != null &&
               current.next.data < newNode.data)
            current = current.next;

        //Make the appropriate links

        newNode.next = current.next;

        // if the new node is not inserted
        // at the end of the list
        if (current.next != null)
            newNode.next.prev = newNode;

        current.next = newNode;
        newNode.prev = current;
    }
    return head_ref;
}

// function to sort a doubly linked list
// using insertion sort
static Node insertionSort(Node head_ref)
{
    // Initialize 'sorted' - a sorted doubly linked list
    Node sorted = null;

    // Traverse the given doubly linked list and
    // insert every node to 'sorted'
    Node current = head_ref;
    while (current != null)
    {

        // Store next for next iteration
        Node next = current.next;

        // removing all the links so as to create
        // 'current' as a new node for insertion
        current.prev = current.next = null;

        // insert current in 'sorted' doubly linked list
        sorted = sortedInsert(sorted, current);

        // Update current
        current = next;
    }

    // Update head_ref to point to
    // sorted doubly linked list
    head_ref = sorted;

    return head_ref;
}

// function to print the doubly linked list
static void printList(Node head)
{
    while (head != null)
    {
        Console.Write(head.data + " ");
        head = head.next;
    }
}

// function to insert a node at the beginning of
// the doubly linked list
static Node push(Node head_ref, int new_data)
{
    // allocate node
    Node new_node = new Node();

    // put in the data
    new_node.data = new_data;

    // Make next of new node as head
    // and previous as null
    new_node.next = (head_ref);
    new_node.prev = null;

    // change prev of head node to new node
    if ((head_ref) != null)
        (head_ref).prev = new_node;

    // move the head to point to the new node
    (head_ref) = new_node;

    return head_ref;
}

// Driver code
public static void Main(String []args)
{

    // start with the empty doubly linked list
    Node head = null;

    // insert the following data
    head = push(head, 9);
    head = push(head, 3);
    head = push(head, 5);
    head = push(head, 10);
    head = push(head, 12);
    head = push(head, 8);

    Console.WriteLine("Doubly Linked List Before Sorting");
    printList(head);

    head = insertionSort(head);

    Console.WriteLine("\nDoubly Linked List After Sorting");
    printList(head);
}
}

// This code is contributed by Princi Singh

Javascript

<script>
    // javascript implementation for insertion Sort
    // on a doubly linked list

    // Node of a doubly linked list
    class Node {
        constructor(val) {
            this.data = val;
            this.prev = null;
            this.next = null;
        }
    }
    // function to create and return a new node
    // of a doubly linked list
    function getNode(data) {
        // allocate node
        var newNode = new Node();

        // put in the data
        newNode.data = data;
        newNode.prev = newNode.next = null;
        return newNode;
    }

    // function to insert a new node in sorted way in
    // a sorted doubly linked list
    function sortedInsert(head_ref,  newNode) {
        var current;

        // if list is empty
        if (head_ref == null)
            head_ref = newNode;

        // if the node is to be inserted at the beginning
        // of the doubly linked list
        else if ((head_ref).data >= newNode.data) {
            newNode.next = head_ref;
            newNode.next.prev = newNode;
            head_ref = newNode;
        }

        else {
            current = head_ref;

            // locate the node after which the new node
            // is to be inserted
            while (current.next != null && current.next.data < newNode.data)
                current = current.next;

            // Make the appropriate links /

            newNode.next = current.next;

            // if the new node is not inserted
            // at the end of the list
            if (current.next != null)
                newNode.next.prev = newNode;

            current.next = newNode;
            newNode.prev = current;
        }
        return head_ref;
    }

    // function to sort a doubly linked list using insertion sort
    function insertionSort(head_ref) {
        // Initialize 'sorted' - a sorted doubly linked list
        var sorted = null;

        // Traverse the given doubly linked list and
        // insert every node to 'sorted'
        var current = head_ref;
        while (current != null) {

            // Store next for next iteration
            var next = current.next;

            // removing all the links so as to create 'current'
            // as a new node for insertion
            current.prev = current.next = null;

            // insert current in 'sorted' doubly linked list
            sorted = sortedInsert(sorted, current);

            // Update current
            current = next;
        }

        // Update head_ref to point to sorted doubly linked list
        head_ref = sorted;

        return head_ref;
    }

    // function to print the doubly linked list
    function printList(head) {
        while (head != null) {
            document.write(head.data + " ");
            head = head.next;
        }
    }

    // function to insert a node at the beginning of
    // the doubly linked list
    function push(head_ref , new_data) {
        // allocate node /
        var new_node = new Node();

        // put in the data /
        new_node.data = new_data;

        // Make next of new node as head and previous as null /
        new_node.next = (head_ref);
        new_node.prev = null;

        // change prev of head node to new node /
        if ((head_ref) != null)
            (head_ref).prev = new_node;

        // move the head to point to the new node /
        (head_ref) = new_node;

        return head_ref;
    }

    // Driver code

    // start with the empty doubly linked list /
    var head = null;

    // insert the following data
    head = push(head, 9);
    head = push(head, 3);
    head = push(head, 5);
    head = push(head, 10);
    head = push(head, 12);
    head = push(head, 8);

    document.write("Doubly Linked List Before Sorting<br/>");
    printList(head);

    head = insertionSort(head);

    document.write("<br/>Doubly Linked List After Sorting<br/>");
    printList(head);


// This code contributed by umadevi9616
</script>

Output:

Doubly Linked List Before Sorting
8 12 10 5 3 9
Doubly Linked List After Sorting
3 5 8 9 10 12

Time Complexity: O(n*n), as we are using a loop to traverse n times and in each traversal, we are calling the function sortedInsert which costs O(n) time (as we are traversing n time to insert the node). Where n is the number of nodes in the linked list.

Auxiliary Space: O(1), as we are not using any extra space.

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