Python 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.  

Python

# Program for merge sort on doubly linked list
# A node of the doubly linked list
class Node:

    # Constructor to create a new node
    def __init__(self, data):
        self.data = data
        self.next = None
        self.prev = None

class DoublyLinkedList:

     # Constructor for empty Doubly
     # Linked List
    def __init__(self):
        self.head = None

    # Function to merge two linked list
    def merge(self, first, second):

        # If first linked list is empty
        if first is None:
            return second

        # If second linked list is empty
        if second is None:
            return first

        # Pick the smaller value
        if first.data < second.data:
            first.next = self.merge(first.next,
                                    second)
            first.next.prev = first
            first.prev = None
            return first
        else:
            second.next = self.merge(first,
                                     second.next)
            second.next.prev = second
            second.prev = None
            return second

    # Function to do merge sort
    def mergeSort(self, tempHead):
        if tempHead is None:
            return tempHead
        if tempHead.next is None:
            return tempHead

        second = self.split(tempHead)

        # Recur for left and right halves
        tempHead = self.mergeSort(tempHead)
        second = self.mergeSort(second)

        # Merge the two sorted halves
        return self.merge(tempHead, second)

    # Split the doubly linked list (DLL) into
    # two DLLs of half sizes
    def split(self, tempHead):
        fast = slow =  tempHead
        while(True):
            if fast.next is None:
                break
            if fast.next.next is None:
                break
            fast = fast.next.next
            slow = slow.next

        temp = slow.next
        slow.next = None
        return temp


    # Given a reference to the head of a list and an
    # integer,inserts a new node on the front of list
    def push(self, new_data):

        # 1. Allocates node
        # 2. Put the data in it
        new_node = Node(new_data)

        # 3. Make next of new node as head and
        # previous as None (already None)
        new_node.next = self.head

        # 4. change prev of head node to new_node
        if self.head is not None:
            self.head.prev = new_node

        # 5. move the head to point to the new node
        self.head = new_node


    def printList(self, node):
        temp = node
        print "Forward Traversal using next pointer"
        while(node is not None):
            print node.data,
            temp = node
            node = node.next
        print "
Backward Traversal using prev pointer"
        while(temp):
            print temp.data,
            temp = temp.prev

# Driver program to test the above functions
dll = DoublyLinkedList()
dll.push(5)
dll.push(20);
dll.push(4);
dll.push(3);
dll.push(30)
dll.push(10);
dll.head = dll.mergeSort(dll.head)
print "Linked List after sorting"
dll.printList(dll.head)

# This code is contributed by Nikhil Kumar Singh(nickzuck_007)

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!