C++ Program For Merge Sort For Doubly Linked List

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++

// C++ program for merge sort on doubly
// linked list
#include <bits/stdc++.h>
using namespace std;
class Node
{
    public:
    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,
                            second);
        first->next->prev = first;
        first->prev = NULL;
        return first;
    }
    else
    {
        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;
    else
    {
        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";
    print(head);
    return 0;
}
// This is code is contributed by rathbhupendra

Output:

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!