You are given a Double Link List with one pointer of each node pointing to the next node just like in a single link list. The second pointer however CAN point to any node in the list and not just the previous node. Now write a program in** O(n) time **to duplicate this list. That is, write a program which will create a copy of this list.

Let us call the second pointer as arbit pointer as it can point to any arbitrary node in the linked list.

Figure 1

Arbitrary pointers are shown in red and next pointers in black

**Method 1 (Uses O(n) extra space)**

This method stores the next and arbitrary mappings (of original list) in an array first, then modifies the original Linked List (to create copy), creates a copy. And finally restores the original list.

1) Create all nodes in copy linked list using next pointers.

2) Store the node and its next pointer mappings of original linked list.

3) Change next pointer of all nodes in original linked list to point to the corresponding node in copy linked list.

Following diagram shows status of both Linked Lists after above 3 steps. The red arrow shows arbit pointers and black arrow shows next pointers.

Figure 2

4) Change the arbit pointer of all nodes in copy linked list to point to corresponding node in original linked list.

5) Now construct the arbit pointer in copy linked list as below and restore the next pointer of nodes in the original linked list.

copy_list_node->arbit = copy_list_node->arbit->arbit->next; copy_list_node = copy_list_node->next;

6) Restore the next pointers in original linked list from the stored mappings(in step 2).

Time Complexity: O(n)

Auxiliary Space: O(n)

**Method 2 (Uses Constant Extra Space)**

Thanks to Saravanan Mani for providing this solution. This solution works using constant space.

1) Create the copy of node 1 and insert it between node 1 & node 2 in original Linked List, create the copy of 2 and insert it between 2 & 3.. Continue in this fashion, add the copy of N afte the Nth node

2) Now copy the arbitrary link in this fashion

original->next->arbitrary = original->arbitrary->next; /*TRAVERSE TWO NODES*/

This works because original->next is nothing but copy of original and Original->arbitrary->next is nothing but copy of arbitrary.

3) Now restore the original and copy linked lists in this fashion in a single loop.

original->next = original->next->next; copy->next = copy->next->next;

4) Make sure that last element of original->next is NULL.

Refer below post for implementation of this method.**Clone a linked list with next and random pointer in O(1) space**

Time Complexity: O(n)

Auxiliary Space: O(1)

Refer Following Post for Hashing based Implementation.

Clone a linked list with next and random pointer | Set 2

Asked by Varun Bhatia. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready.

## Recommended Posts:

- Clone a linked list with next and random pointer | Set 2
- Clone a linked list with next and random pointer in O(1) space
- Correct the Random Pointer in Doubly Linked List
- Insertion in a sorted circular linked list when a random pointer is given
- Point to next higher value node in a linked list with an arbitrary pointer
- Clone a Binary Tree with Random Pointers
- Given only a pointer/reference to a node to be deleted in a singly linked list, how do you delete it?
- How to write C functions that modify head pointer of a Linked List?
- Point arbit pointer to greatest value right side node in a linked list
- Delete multiple occurrences of key in Linked list using double pointer
- Given only a pointer to a node to be deleted in a singly linked list, how do you delete it?
- Delete a Node from linked list without head pointer
- XOR Linked List - A Memory Efficient Doubly Linked List | Set 1
- XOR Linked List – A Memory Efficient Doubly Linked List | Set 2
- Select a Random Node from a Singly Linked List
- Sum of nodes in a linked list which are greater than next node
- Next greater element in the Linked List
- Difference between Singly linked list and Doubly linked list
- Merge a linked list into another linked list at alternate positions
- Convert singly linked list into circular linked list