# XOR Linked List – A Memory Efficient Doubly Linked List | Set 2

Last Updated : 17 Apr, 2024

In the previous post, we discussed how a Doubly Linked can be created using only one space for the address field with every node. In this post, we will discuss the implementation of a memory-efficient doubly linked list. We will mainly discuss the following two simple functions.

1. A function to insert a new node at the beginning.
2. A function to traverse the list in a forwarding direction.
Recommended Practice

In the following code, insert() function inserts a new node at the beginning. We need to change the head pointer of Linked List, that is why a double pointer is used (See this). Let us first discuss a few things again that have been discussed in the previous post. We store XOR of the next and previous nodes with every node and we call it npx, which is the only address member we have with every node. When we insert a new node at the beginning, npx of the new node will always be XOR of NULL and the current head. And npx of the current head must be changed to XOR of the new node and node next to the current head.
printList() traverses the list in a forwarding direction. It prints data values from every node. To traverse the list, we need to get a pointer to the next node at every point. We can get the address of next node by keeping track of the current node and previous node. If we do XOR of curr->npx and prev, we get the address of next node.

Implementation:

C++ ```/* C++ Implementation of Memory efficient Doubly Linked List */ #include <bits/stdc++.h> #include <cinttypes> using namespace std; // Node structure of a memory // efficient doubly linked list class Node { public: int data; Node* npx; /* XOR of next and previous node */ }; /* returns XORed value of the node addresses */ Node* XOR (Node *a, Node *b) { return reinterpret_cast<Node *>( reinterpret_cast<uintptr_t>(a) ^ reinterpret_cast<uintptr_t>(b)); } /* Insert a node at the beginning of the XORed linked list and makes the newly inserted node as head */ void insert(Node **head_ref, int data) { // Allocate memory for new node Node *new_node = new Node(); new_node->data = data; /* Since new node is being inserted at the beginning, npx of new node will always be XOR of current head and NULL */ new_node->npx = *head_ref; /* If linked list is not empty, then npx of current head node will be XOR of new node and node next to current head */ if (*head_ref != NULL) { // *(head_ref)->npx is XOR of NULL and next. // So if we do XOR of it with NULL, we get next (*head_ref)->npx = XOR(new_node, (*head_ref)->npx); } // Change head *head_ref = new_node; } // prints contents of doubly linked // list in forward direction void printList (Node *head) { Node *curr = head; Node *prev = NULL; Node *next; cout << "Following are the nodes of Linked List: \n"; while (curr != NULL) { // print current node cout<<curr->data<<" "; // get address of next node: curr->npx is // next^prev, so curr->npx^prev will be // next^prev^prev which is next next = XOR (prev, curr->npx); // update prev and curr for next iteration prev = curr; curr = next; } } // Driver code int main () { /* Create following Doubly Linked List head-->40<-->30<-->20<-->10 */ Node *head = NULL; insert(&head, 10); insert(&head, 20); insert(&head, 30); insert(&head, 40); // print the created list printList (head); return (0); } // This code is contributed by rathbhupendra ``` C ```/* C Implementation of Memory efficient Doubly Linked List */ #include <stdio.h> #include <stdlib.h> #include <inttypes.h> // Node structure of a memory // efficient doubly linked list struct Node { int data; struct Node* npx; /* XOR of next and previous node */ }; /* returns XORed value of the node addresses */ struct Node* XOR (struct Node *a, struct Node *b) { return (struct Node*) ((uintptr_t) (a) ^ (uintptr_t) (b)); } /* Insert a node at the beginning of the XORed linked list and makes the newly inserted node as head */ void insert(struct Node **head_ref, int data) { // Allocate memory for new node struct Node *new_node = (struct Node *) malloc (sizeof (struct Node) ); new_node->data = data; /* Since new node is being inserted at the beginning, npx of new node will always be XOR of current head and NULL */ new_node->npx = *head_ref; /* If linked list is not empty, then npx of current head node will be XOR of new node and node next to current head */ if (*head_ref != NULL) { // *(head_ref)->npx is XOR of NULL and next. // So if we do XOR of it with NULL, we get next (*head_ref)->npx = XOR(new_node, (*head_ref)->npx); } // Change head *head_ref = new_node; } // prints contents of doubly linked // list in forward direction void printList (struct Node *head) { struct Node *curr = head; struct Node *prev = NULL; struct Node *next; printf ("Following are the nodes of Linked List: \n"); while (curr != NULL) { // print current node printf ("%d ", curr->data); // get address of next node: curr->npx is // next^prev, so curr->npx^prev will be // next^prev^prev which is next next = XOR (prev, curr->npx); // update prev and curr for next iteration prev = curr; curr = next; } } // Driver program to test above functions int main () { /* Create following Doubly Linked List head-->40<-->30<-->20<-->10 */ struct Node *head = NULL; insert(&head, 10); insert(&head, 20); insert(&head, 30); insert(&head, 40); // print the created list printList (head); return (0); } ``` Python3 ```# Python3 implementation of Memory # efficient Doubly Linked List # library for providing C # compatible data types import ctypes # Node class for memory # efficient doubly linked list class Node: def __init__(self, data): self.data = data # XOR of next and previous node self.npx = 0 class XorLinkedList: def __init__(self): self.head = None self.__nodes = [] # Returns XORed value of the node addresses def XOR(self, a, b): return a ^ b # Insert a node at the beginning of the # XORed linked list and makes the newly # inserted node as head def insert(self, data): # New node node = Node(data) # Since new node is being inserted at # the beginning, npx of new node will # always be XOR of current head and NULL node.npx = id(self.head) # If linked list is not empty, then # npx of current head node will be # XOR of new node and node next to # current head if self.head is not None: # head.npx is XOR of None and next. # So if we do XOR of it with None, # we get next self.head.npx = self.XOR(id(node), self.head.npx) self.__nodes.append(node) # Change head self.head = node # Prints contents of doubly linked # list in forward direction def printList(self): if self.head != None: prev_id = 0 curr = self.head next_id = 1 print("Following are the nodes " "of Linked List:") while curr is not None: # Print current node print(curr.data, end = ' ') # Get address of next node: curr.npx is # next^prev, so curr.npx^prev will be # next^prev^prev which is next next_id = self.XOR(prev_id, curr.npx) # Update prev and curr for next iteration prev_id = id(curr) curr = self.__type_cast(next_id) # Method to return a new instance of type # which points to the same memory block. def __type_cast(self, id): return ctypes.cast(id, ctypes.py_object).value # Driver code if __name__ == '__main__': obj = XorLinkedList() # Create following Doubly Linked List # head-->40<-->30<-->20<-->10 obj.insert(10) obj.insert(20) obj.insert(30) obj.insert(40) # Print the created list obj.printList() # This code is contributed by MuskanKalra1 ``` C# ```using System; // Node structure of a doubly linked list class Node { public int data; public Node prev; public Node next; } class Program { // Insert a node at the beginning of the linked list static void Insert(ref Node head_ref, int data) { // Allocate memory for new node Node new_node = new Node(); new_node.data = data; // Set the next of the new node as the current head new_node.next = head_ref; // If the current head is not null, set the previous of the head as the new node if (head_ref != null) head_ref.prev = new_node; // Set the new node as the head head_ref = new_node; } // Prints the contents of the linked list in forward direction static void PrintList(Node head) { Console.WriteLine("Following are the nodes of Linked List: "); while (head != null) { Console.Write(head.data + " "); head = head.next; } } // Driver code static void Main(string[] args) { /* Create following Doubly Linked List head-->40<-->30<-->20<-->10 */ Node head = null; Insert(ref head, 10); Insert(ref head, 20); Insert(ref head, 30); Insert(ref head, 40); // Print the created list PrintList(head); // This code is contributed by Shivam Tiwari } } ``` Javascript ```// Node structure of a memory // efficient doubly linked list class Node { constructor(data, npx) { this.data = data; this.npx = npx; } } /* returns XORed value of the node addresses */ function XOR(a, b) { return (a ^ b); } /* Insert a node at the beginning of the XORed linked list and makes the newly inserted node as head */ function insert(head_ref, data) { // Allocate memory for new node let new_node = new Node(data, null); /* Since new node is being inserted at the beginning, npx of new node will always be XOR of current head and NULL */ new_node.npx = head_ref; /* If linked list is not empty, then npx of current head node will be XOR of new node and node next to current head */ if (head_ref != null) { // head_ref.npx is XOR of NULL and next. // So if we do XOR of it with NULL, we get next head_ref.npx = XOR(new_node, head_ref.npx); } // Change head head_ref = new_node; } // prints contents of doubly linked // list in forward direction function printList(head) { let curr = head; let prev = null; let next; console.log("Following are the nodes of Linked List: "); while (curr != null) { // print current node console.log(curr.data); // get address of next node: curr.npx is // next^prev, so curr.npx^prev will be // next^prev^prev which is next next = XOR(prev, curr.npx); // update prev and curr for next iteration prev = curr; curr = next; } } // Driver code let head = null; insert(head, 10); insert(head, 20); insert(head, 30); insert(head, 40); // print the created list printList(head); ```

Output
```Following are the nodes of Linked List:
40 30 20 10

```

Time Complexity: O(n), Where n is the total number of nodes in the given Doubly Linked List
Auxiliary Space: O(1)

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