XOR Linked List – Find Nth Node from the end

Given a XOR linked list and an integer N, the task is to print the Nth node from the end of the given XOR linked list.

Examples:

Input: 4 –> 6 –> 7 –> 3, N = 1 
Output: 3 
Explanation: 1st node from the end is 3.
Input: 5 –> 8 –> 9, N = 4 
Output: Wrong Input 
Explanation: The given Xor Linked List contains only 3 nodes. 

Approach: Follow the steps below to solve the problem:

• Traverse the first N nodes of the Linked List using a pointer, say curr.
• Use another pointer, say curr1, and traverse the linked list incrementing curr and curr1 by a node after every iteration.
• Iterate until the pointer curr exceeds the end of the List, i.e.NULL. Once reached, print the value of the node curr1 as the required answer.

Below is the implementation of the above approach:

C++

// C++ program to implement
// the above approach
#include <bits/stdc++.h>
#include <inttypes.h>
using namespace std;

// Structure of a node
// in XOR linked list
struct Node {

    // Stores data value
    // of a node
    int data;

    // Stores XOR of previous
    // pointer and next pointer
    struct Node* nxp;
};

// Function to find the XOR of two nodes
struct Node* XOR(struct Node* a, struct Node* b)
{
    return (struct Node*)((uintptr_t)(a) ^ (uintptr_t)(b));
}

// Function to insert a node with
// given value at given position
struct Node* insert(struct Node** head, int value)
{

    // If XOR linked list is empty
    if (*head == NULL) {

        // Initialize a new Node
        struct Node* node = new Node;

        // Stores data value in
        // the node
        node->data = value;

        // Stores XOR of previous
        // and next pointer
        node->nxp = XOR(NULL, NULL);

        // Update pointer of head node
        *head = node;
    }

    // If the XOR linked list
    // is not empty
    else {

        // Stores the address
        // of current node
        struct Node* curr = *head;

        // Stores the address
        // of previous node
        struct Node* prev = NULL;

        // Initialize a new Node
        struct Node* node
            = new Node();

        // Update curr node address
        curr->nxp = XOR(node, XOR(NULL, curr->nxp));

        // Update new node address
        node->nxp = XOR(NULL, curr);

        // Update head
        *head = node;

        // Update data value of
        // current node
        node->data = value;
    }
    return *head;
}

// Function to print elements of
// the XOR Linked List
void printList(struct Node** head)
{
    // Stores XOR pointer
    // in current node
    struct Node* curr = *head;

    // Stores XOR pointer of
    // in previous Node
    struct Node* prev = NULL;

    // Stores XOR pointer of
    // in next node
    struct Node* next;

    // Traverse XOR linked list
    while (curr != NULL) {

        // Print current node
        cout << curr->data << " " ;

        // Forward traversal
        next = XOR(prev, curr->nxp);

        // Update prev
        prev = curr;

        // Update curr
        curr = next;
    }
}
struct Node* NthNode(struct Node** head, int N)
{
    int count = 0;

    // Stores XOR pointer
    // in current node
    struct Node* curr = *head;
    struct Node* curr1 = *head;

    // Stores XOR pointer of
    // in previous Node
    struct Node* prev = NULL;
    struct Node* prev1 = NULL;

    // Stores XOR pointer of
    // in next node
    struct Node* next;
    struct Node* next1;

    while (count < N && curr != NULL) {

        // Forward traversal
        next = XOR(prev, curr->nxp);

        // Update prev
        prev = curr;

        // Update curr
        curr = next;

        count++;
    }

    if (curr == NULL && count < N) {
       cout << "Wrong Input\n";
        return (uintptr_t)0;
    }
    else {
        while (curr != NULL) {

            // Forward traversal
            next = XOR(prev, curr->nxp);
            next1 = XOR(prev1, curr1->nxp);

            // Update prev
            prev = curr;
            prev1 = curr1;

            // Update curr
            curr = next;
            curr1 = next1;
        }
        cout << curr1->data << " ";
    }
}

// Driver Code
int main()
{

    /* Create following XOR Linked List
    head -->7 –> 6 –>8 –> 11 –> 3 –> 1 –> 2 –> 0*/
    struct Node* head = NULL;

    insert(&head, 0);
    insert(&head, 2);
    insert(&head, 1);
    insert(&head, 3);
    insert(&head, 11);
    insert(&head, 8);
    insert(&head, 6);
    insert(&head, 7);

    NthNode(&head, 3);

    return (0);
}

C

// C program to implement
// the above approach
#include <inttypes.h>
#include <stdio.h>
#include <stdlib.h>

// Structure of a node
// in XOR linked list
struct Node {

    // Stores data value
    // of a node
    int data;

    // Stores XOR of previous
    // pointer and next pointer
    struct Node* nxp;
};

// Function to find the XOR of two nodes
struct Node* XOR(struct Node* a,
                 struct Node* b)
{
    return (struct Node*)((uintptr_t)(a)
                          ^ (uintptr_t)(b));
}

// Function to insert a node with
// given value at given position
struct Node* insert(
    struct Node** head, int value)
{

    // If XOR linked list is empty
    if (*head == NULL) {

        // Initialize a new Node
        struct Node* node
            = (struct Node*)malloc(
                sizeof(struct Node));

        // Stores data value in
        // the node
        node->data = value;

        // Stores XOR of previous
        // and next pointer
        node->nxp = XOR(NULL, NULL);

        // Update pointer of head node
        *head = node;
    }

    // If the XOR linked list
    // is not empty
    else {

        // Stores the address
        // of current node
        struct Node* curr = *head;

        // Stores the address
        // of previous node
        struct Node* prev = NULL;

        // Initialize a new Node
        struct Node* node
            = (struct Node*)malloc(
                sizeof(struct Node));

        // Update curr node address
        curr->nxp = XOR(node,
                        XOR(NULL, curr->nxp));

        // Update new node address
        node->nxp = XOR(NULL, curr);

        // Update head
        *head = node;

        // Update data value of
        // current node
        node->data = value;
    }
    return *head;
}

// Function to print elements of
// the XOR Linked List
void printList(struct Node** head)
{
    // Stores XOR pointer
    // in current node
    struct Node* curr = *head;

    // Stores XOR pointer of
    // in previous Node
    struct Node* prev = NULL;

    // Stores XOR pointer of
    // in next node
    struct Node* next;

    // Traverse XOR linked list
    while (curr != NULL) {

        // Print current node
        printf("%d ", curr->data);

        // Forward traversal
        next = XOR(prev, curr->nxp);

        // Update prev
        prev = curr;

        // Update curr
        curr = next;
    }
}
struct Node* NthNode(struct Node** head,
                     int N)
{
    int count = 0;

    // Stores XOR pointer
    // in current node
    struct Node* curr = *head;
    struct Node* curr1 = *head;

    // Stores XOR pointer of
    // in previous Node
    struct Node* prev = NULL;
    struct Node* prev1 = NULL;

    // Stores XOR pointer of
    // in next node
    struct Node* next;
    struct Node* next1;

    while (count < N && curr != NULL) {

        // Forward traversal
        next = XOR(prev, curr->nxp);

        // Update prev
        prev = curr;

        // Update curr
        curr = next;

        count++;
    }

    if (curr == NULL && count < N) {
        printf("Wrong Input");
        return (uintptr_t)0;
    }
    else {
        while (curr != NULL) {

            // Forward traversal
            next = XOR(prev,
                       curr->nxp);
            next1 = XOR(prev1,
                        curr1->nxp);

            // Update prev
            prev = curr;
            prev1 = curr1;

            // Update curr
            curr = next;
            curr1 = next1;
        }
        printf("%d", curr1->data);
    }
}

// Driver Code
int main()
{

    /* Create following XOR Linked List
    head -->7 –> 6 –>8 –> 11 –> 3 –> 1 –> 2 –> 0*/
    struct Node* head = NULL;

    insert(&head, 0);
    insert(&head, 2);
    insert(&head, 1);
    insert(&head, 3);
    insert(&head, 11);
    insert(&head, 8);
    insert(&head, 6);
    insert(&head, 7);

    NthNode(&head, 3);

    return (0);
}

Python3

# Python implementation of the above approach.
import ctypes


# Structure of a node in XOR linked list
class Node:

    def __init__(self, value):
        self.value = value
        self.npx = 0


# create linked list class
class XorLinkedList:

    # constructor
    def __init__(self):
        self.head = None
        self.tail = None
        self.__nodes = []


    # Function to insert a node with given value at given position
    def insert(self, value):

        # Initialize a new Node
        node = Node(value)

        # Check If XOR linked list is empty
        if self.head is None:

            # Update pointer of head node
            self.head = node

            # Update pointer of tail node
            self.tail = node

        else:

            # Update curr node address
            self.head.npx = id(node) ^ self.head.npx

            # Update new node address
            node.npx = id(self.head)

            # Update head
            self.head = node

        # push node
        self.__nodes.append(node)


    # method to get length of linked list
    def Length(self):
        if not self.isEmpty():
            prev_id = 0
            node = self.head
            next_id = 1
            count = 1
            while next_id:
                next_id = prev_id ^ node.npx
                if next_id:
                    prev_id = id(node)
                    node = self.__type_cast(next_id)
                    count += 1
                else:
                    return count
        else:
            return 0

    def NthNode(self, N):
        count = 1

        # Stores XOR pointer of
        # in previous Node
        prev_id = 0
        prev1_id = 0

        # Stores XOR pointer
        # in current node
        node = self.head
        node1 = self.head

        # Stores XOR pointer of
        # in next node
        next_id = 1
        next1_id = 1

        while(next_id  and count < N):

            # Forward traversal
            next_id = prev_id ^ node.npx
            if next_id:

                # Update prev
                prev_id = id(node)

                # Update curr
                node = self.__type_cast(next_id)

                count = count + 1

        # Move 1 step forward because in python, prev1_id and next1_id are
        # starting from 0 and 1 respectively, and not with None.
        next_id = prev_id ^ node.npx
        prev_id = id(node)
        node = self.__type_cast(next_id)

        if not next_id and count < N:
            print("Wrong Input")
            return

        while next_id:

            # Forward Traversal
            next_id = prev_id ^ node.npx
            next1_id = prev1_id ^ node1.npx

            # Update prev
            if next_id:
                prev_id = id(node)
                node = self.__type_cast(next_id)

            # Update curr
            if next_id:
                prev1_id = id(node1)
                node1 = self.__type_cast(next1_id)

        node1 = self.__type_cast(next1_id)
        print(node1.value)


    # Function to print elements of the XOR Linked List
    def printList(self):


        if self.head != None:
            prev_id = 0
            node = self.head
            next_id = 1
            print(node.value, end=' ')

            # Traverse XOR linked list
            while next_id:

                # Forward traversal
                next_id = prev_id ^ node.npx

                if next_id:

                    # Update prev
                    prev_id = id(node)

                    # Update curr
                    node = self.__type_cast(next_id)

                    # Print current node
                    print(node.value, end=' ')
                else:
                    return


    # method to check if the linked list is empty or not
    def isEmpty(self):
        if self.head is None:
            return True
        return False

    # method to return a new instance of type
    def __type_cast(self, id):
        return ctypes.cast(id, ctypes.py_object).value


# Create following XOR Linked List
# head -->7 –> 6 –>8 –> 11 –> 3 –> 1 –> 2 –> 0
head = XorLinkedList()
head.insert(0)
head.insert(2)
head.insert(1)
head.insert(3)
head.insert(11)
head.insert(8)
head.insert(6)
head.insert(7)

head.NthNode(3)


# This code is contributed by Nidhi goel.

Output:

1

Time Complexity: O(N) 
Auxiliary Space: O(1)