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C++ Program For Merge Sort For Doubly Linked List

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Given a doubly linked list, write a function to sort the doubly linked list in increasing order using merge sort.
For example, the following doubly linked list should be changed to 24810

Merge sort for singly linked list is already discussed. The important change here is to modify the previous pointers also when merging two lists.

Below is the implementation of merge sort for doubly linked list.  


// C++ program for merge sort on doubly 
// linked list 
#include <bits/stdc++.h>
using namespace std;
class Node 
    int data; 
    Node *next, *prev; 
Node *split(Node *head); 
// Function to merge two linked lists 
Node *merge(Node *first, Node *second) 
    // If first linked list is empty 
    if (!first) 
        return second; 
    // If second linked list is empty 
    if (!second) 
        return first; 
    // Pick the smaller value 
    if (first->data < second->data) 
        first->next = merge(first->next,
        first->next->prev = first; 
        first->prev = NULL; 
        return first; 
        second->next = merge(first,second->next); 
        second->next->prev = second; 
        second->prev = NULL; 
        return second; 
// Function to do merge sort 
Node *mergeSort(Node *head) 
    if (!head || !head->next) 
        return head; 
    Node *second = split(head); 
    // Recur for left and right halves 
    head = mergeSort(head); 
    second = mergeSort(second); 
    // Merge the two sorted halves 
    return merge(head,second); 
// A utility function to insert a new node 
// at the beginning of doubly linked list 
void insert(Node **head, int data) 
    Node *temp = new Node();
    temp->data = data; 
    temp->next = temp->prev = NULL; 
    if (!(*head)) 
        (*head) = temp; 
        temp->next = *head; 
        (*head)->prev = temp; 
        (*head) = temp; 
// A utility function to print a doubly 
// linked list in both forward and 
// backward directions 
void print(Node *head) 
    Node *temp = head; 
    cout << 
    "Forward Traversal using next pointer"
    while (head) 
        cout << head->data << " "
        temp = head; 
        head = head->next; 
    cout << 
    "Backward Traversal using prev pointer"
    while (temp) 
        cout << temp->data << " "
        temp = temp->prev; 
// Utility function to swap two integers 
void swap(int *A, int *B) 
    int temp = *A; 
    *A = *B; 
    *B = temp; 
// Split a doubly linked list (DLL) into
// 2 DLLs of half sizes 
Node *split(Node *head) 
    Node *fast = head,*slow = head; 
    while (fast->next && fast->next->next) 
        fast = fast->next->next; 
        slow = slow->next; 
    Node *temp = slow->next; 
    slow->next = NULL; 
    return temp; 
// Driver program 
int main(void
    Node *head = NULL; 
    insert(&head, 5); 
    insert(&head, 20); 
    insert(&head, 4); 
    insert(&head, 3); 
    insert(&head, 30); 
    insert(&head, 10); 
    head = mergeSort(head); 
    cout << "Linked List after sorting"
    return 0; 
// This is code is contributed by rathbhupendra


Linked List after sorting
Forward Traversal using next pointer
3 4 5 10 20 30
Backward Traversal using prev pointer
30 20 10 5 4 3

Time Complexity: Time complexity of the above implementation is same as time complexity of MergeSort for arrays. It takes Θ(nLogn) time. 

Space Complexity:O(1). We are only using constant amount of extra space.
You may also like to see QuickSort for doubly linked list
Please refer complete article on Merge Sort for Doubly Linked List for more details!

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Last Updated : 09 Dec, 2022
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