# 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,end=" ")
            temp = node
            node = node.next
        print ("\nBackward Traversal using prev pointer")
        while(temp):
            print (temp.data,end=" ")
            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)

Time complexity: nlogn
Space complexity: constant