# Point arbit pointer to greatest value right side node in a linked list

Given singly linked list with every node having an additional “arbitrary” pointer that currently points to NULL. We need to make the “arbitrary” pointer to greatest value node in a linked list on its right side. ## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

A Simple Solution is to traverse all nodes one by one. For every node, find the node which has greatest value on right side and change the next pointer. Time Complexity of this solution is O(n2).

An Efficient Solution can work in O(n) time. Below are steps.

2. Start traversing linked list and store maximum value node encountered so far. Make arbit of every node to point to max. If the data in current node is more than max node so far, update max.

Following is the implementation of above steps.

## C++

 `// C++ program to point arbit pointers to highest ` `// value on its right ` `#include ` `using` `namespace` `std; ` ` `  `/* Link list node */` `struct` `Node ` `{ ` `    ``int` `data; ` `    ``Node* next, *arbit; ` `}; ` ` `  `/* Function to reverse the linked list */` `Node* reverse(Node *head) ` `{ ` `    ``Node *prev = NULL, *current = head, *next; ` `    ``while` `(current != NULL) ` `    ``{ ` `        ``next  = current->next; ` `        ``current->next = prev; ` `        ``prev = current; ` `        ``current = next; ` `    ``} ` `    ``return` `prev; ` `} ` ` `  `// This function populates arbit pointer in every ` `// node to the greatest value to its right. ` `Node* populateArbit(Node *head) ` `{ ` `    ``// Reverse given linked list ` `    ``head = reverse(head); ` ` `  `    ``// Initialize pointer to maximum value node ` `    ``Node *max = head; ` ` `  `    ``// Traverse the reversed list ` `    ``Node *temp = head->next; ` `    ``while` `(temp != NULL) ` `    ``{ ` `        ``// Connect max through arbit pointer ` `        ``temp->arbit = max; ` ` `  `        ``// Update max if required ` `        ``if` `(max->data < temp->data) ` `            ``max = temp; ` ` `  `        ``// Move ahead in reversed list ` `        ``temp = temp->next; ` `    ``} ` ` `  `    ``// Reverse modified linked list and return ` `    ``// head. ` `    ``return` `reverse(head); ` `} ` ` `  `// Utility function to print result linked list ` `void` `printNextArbitPointers(Node *node) ` `{ ` `    ``printf``(``"Node\tNext Pointer\tArbit Pointer\n"``); ` `    ``while` `(node!=NULL) ` `    ``{ ` `        ``cout << node->data << ``"\t\t"``; ` ` `  `        ``if` `(node->next) ` `            ``cout << node->next->data << ``"\t\t"``; ` `        ``else` `cout << ``"NULL"` `<< ``"\t\t"``; ` ` `  `        ``if` `(node->arbit) ` `            ``cout << node->arbit->data; ` `        ``else` `cout << ``"NULL"``; ` ` `  `        ``cout << endl; ` `        ``node = node->next; ` `    ``} ` `} ` ` `  `/* Function to create a new node with given data */` `Node *newNode(``int` `data) ` `{ ` `    ``Node *new_node = ``new` `Node; ` `    ``new_node->data = data; ` `    ``new_node->next = NULL; ` `    ``return` `new_node; ` `} ` ` `  `/* Driver program to test above functions*/` `int` `main() ` `{ ` `    ``Node *head = newNode(5); ` `    ``head->next = newNode(10); ` `    ``head->next->next = newNode(2); ` `    ``head->next->next->next = newNode(3); ` ` `  `    ``head = populateArbit(head); ` ` `  `    ``printf``(``"Resultant Linked List is: \n"``); ` `    ``printNextArbitPointers(head); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to point arbit pointers to highest  ` `// value on its right  ` `class` `GfG  ` `{  ` ` `  `/* Link list node */` `static` `class` `Node  ` `{  ` `    ``int` `data;  ` `    ``Node next, arbit;  ` `} ` ` `  `/* Function to reverse the linked list */` `static` `Node reverse(Node head)  ` `{  ` `    ``Node prev = ``null``, current = head, next = ``null``;  ` `    ``while` `(current != ``null``)  ` `    ``{  ` `        ``next = current.next;  ` `        ``current.next = prev;  ` `        ``prev = current;  ` `        ``current = next;  ` `    ``}  ` `    ``return` `prev;  ` `}  ` ` `  `// This function populates arbit pointer in every  ` `// node to the greatest value to its right.  ` `static` `Node populateArbit(Node head)  ` `{  ` `    ``// Reverse given linked list  ` `    ``head = reverse(head);  ` ` `  `    ``// Initialize pointer to maximum value node  ` `    ``Node max = head;  ` ` `  `    ``// Traverse the reversed list  ` `    ``Node temp = head.next;  ` `    ``while` `(temp != ``null``)  ` `    ``{  ` `        ``// Connect max through arbit pointer  ` `        ``temp.arbit = max;  ` ` `  `        ``// Update max if required  ` `        ``if` `(max.data < temp.data)  ` `            ``max = temp;  ` ` `  `        ``// Move ahead in reversed list  ` `        ``temp = temp.next;  ` `    ``}  ` ` `  `    ``// Reverse modified linked list and return  ` `    ``// head.  ` `    ``return` `reverse(head);  ` `}  ` ` `  `// Utility function to print result linked list  ` `static` `void` `printNextArbitPointers(Node node)  ` `{  ` `    ``System.out.println(``"Node\tNext Pointer\tArbit Pointer"``);  ` `    ``while` `(node != ``null``)  ` `    ``{  ` `        ``System.out.print(node.data + ``"\t\t"``);  ` ` `  `        ``if` `(node.next != ``null``)  ` `            ``System.out.print(node.next.data + ``"\t\t"``);  ` `        ``else` `            ``System.out.print(``"NULL"` `+``"\t\t"``);  ` ` `  `        ``if` `(node.arbit != ``null``)  ` `            ``System.out.print(node.arbit.data);  ` `        ``else` `            ``System.out.print(``"NULL"``);  ` ` `  `        ``System.out.println();  ` `        ``node = node.next;  ` `    ``}  ` `}  ` ` `  `/* Function to create a new node with given data */` `static` `Node newNode(``int` `data)  ` `{  ` `    ``Node new_node = ``new` `Node();  ` `    ``new_node.data = data;  ` `    ``new_node.next = ``null``;  ` `    ``return` `new_node;  ` `}  ` ` `  `/* Driver code*/` `public` `static` `void` `main(String[] args)  ` `{  ` `    ``Node head = newNode(``5``);  ` `    ``head.next = newNode(``10``);  ` `    ``head.next.next = newNode(``2``);  ` `    ``head.next.next.next = newNode(``3``);  ` ` `  `    ``head = populateArbit(head);  ` ` `  `    ``System.out.println(``"Resultant Linked List is: "``);  ` `    ``printNextArbitPointers(head);  ` ` `  `} ` `}  ` ` `  `// This code is contributed by Prerna Saini. `

## Python

 `# Python Program to point arbit pointers to highest ` `# value on its right ` ` `  `# Node class  ` `class` `Node:  ` ` `  `    ``# Constructor to initialize the node object  ` `    ``def` `__init__(``self``, data):  ` `        ``self``.data ``=` `data  ` `        ``self``.``next` `=` `None` `        ``self``.arbit ``=` `None` ` `  `# Function to reverse the linked list  ` `def` `reverse(head): ` ` `  `    ``prev ``=` `None` `    ``current ``=` `head ` `    ``next` `=` `None` `    ``while` `(current !``=` `None``): ` `     `  `        ``next` `=` `current.``next` `        ``current.``next` `=` `prev ` `        ``prev ``=` `current ` `        ``current ``=` `next` `     `  `    ``return` `prev ` ` `  `# This function populates arbit pointer in every ` `# node to the greatest value to its right. ` `def` `populateArbit(head): ` ` `  `    ``# Reverse given linked list ` `    ``head ``=` `reverse(head) ` ` `  `    ``# Initialize pointer to maximum value node ` `    ``max` `=` `head ` ` `  `    ``# Traverse the reversed list ` `    ``temp ``=` `head.``next` `    ``while` `(temp !``=` `None``): ` `     `  `        ``# Connect max through arbit pointer ` `        ``temp.arbit ``=` `max` ` `  `        ``# Update max if required ` `        ``if` `(``max``.data < temp.data): ` `            ``max` `=` `temp ` ` `  `        ``# Move ahead in reversed list ` `        ``temp ``=` `temp.``next` `     `  `    ``# Reverse modified linked list and return ` `    ``# head. ` `    ``return` `reverse(head) ` ` `  `# Utility function to print result linked list ` `def` `printNextArbitPointers(node): ` ` `  `    ``print``(``"Node\tNext Pointer\tArbit Pointer\n"``) ` `    ``while` `(node !``=` `None``): ` `     `  `        ``print``( node.data , ``"\t\t"``,end ``=` `"") ` ` `  `        ``if` `(node.``next` `!``=` `None``): ` `            ``print``( node.``next``.data , ``"\t\t"``,end ``=` `"") ` `        ``else` `: ` `            ``print``( ``"None"` `, ``"\t\t"``,end ``=` `"") ` ` `  `        ``if` `(node.arbit !``=` `None``): ` `            ``print``( node.arbit.data,end ``=` `"") ` `        ``else` `: ` `            ``print``( ``"None"``,end ``=` `"") ` `         `  `        ``print``(``"\n"``) ` `        ``node ``=` `node.``next` `     `  `# Function to create a new node with given data  ` `def` `newNode(data): ` ` `  `    ``new_node ``=` `Node(``0``) ` `    ``new_node.data ``=` `data ` `    ``new_node.``next` `=` `None` `    ``return` `new_node ` ` `  `# Driver code ` ` `  `head ``=` `newNode(``5``) ` `head.``next` `=` `newNode(``10``) ` `head.``next``.``next` `=` `newNode(``2``) ` `head.``next``.``next``.``next` `=` `newNode(``3``) ` ` `  `head ``=` `populateArbit(head) ` ` `  `print``(``"Resultant Linked List is: \n"``) ` `printNextArbitPointers(head) ` ` `  `# This code is contributed by Arnab Kundu `

## C#

 `// C# program to point arbit pointers   ` `// to highest value on its right ` `using` `System; ` ` `  `class` `GfG  ` `{  ` ` `  `    ``/* Link list node */` `    ``class` `Node  ` `    ``{  ` `        ``public` `int` `data;  ` `        ``public` `Node next, arbit;  ` `    ``} ` ` `  `    ``/* Function to reverse the linked list */` `    ``static` `Node reverse(Node head)  ` `    ``{  ` `        ``Node prev = ``null``, current = head, next = ``null``;  ` `        ``while` `(current != ``null``)  ` `        ``{  ` `            ``next = current.next;  ` `            ``current.next = prev;  ` `            ``prev = current;  ` `            ``current = next;  ` `        ``}  ` `        ``return` `prev;  ` `    ``}  ` ` `  `    ``// This function populates arbit pointer in every  ` `    ``// node to the greatest value to its right.  ` `    ``static` `Node populateArbit(Node head)  ` `    ``{  ` `        ``// Reverse given linked list  ` `        ``head = reverse(head);  ` ` `  `        ``// Initialize pointer to maximum value node  ` `        ``Node max = head;  ` ` `  `        ``// Traverse the reversed list  ` `        ``Node temp = head.next;  ` `        ``while` `(temp != ``null``)  ` `        ``{  ` `            ``// Connect max through arbit pointer  ` `            ``temp.arbit = max;  ` ` `  `            ``// Update max if required  ` `            ``if` `(max.data < temp.data)  ` `                ``max = temp;  ` ` `  `            ``// Move ahead in reversed list  ` `            ``temp = temp.next;  ` `        ``}  ` ` `  `        ``// Reverse modified linked list   ` `        ``// and return head.  ` `        ``return` `reverse(head);  ` `    ``}  ` ` `  `    ``// Utility function to print result linked list  ` `    ``static` `void` `printNextArbitPointers(Node node)  ` `    ``{  ` `        ``Console.WriteLine(``"Node\tNext Pointer\tArbit Pointer"``);  ` `        ``while` `(node != ``null``)  ` `        ``{  ` `            ``Console.Write(node.data + ``"\t\t"``);  ` ` `  `            ``if` `(node.next != ``null``)  ` `                ``Console.Write(node.next.data + ``"\t\t"``);  ` `            ``else` `                ``Console.Write(``"NULL"` `+``"\t\t"``);  ` ` `  `            ``if` `(node.arbit != ``null``)  ` `                ``Console.Write(node.arbit.data);  ` `            ``else` `                ``Console.Write(``"NULL"``);  ` ` `  `            ``Console.WriteLine();  ` `            ``node = node.next;  ` `        ``}  ` `    ``}  ` ` `  `    ``/* Function to create a new node with given data */` `    ``static` `Node newNode(``int` `data)  ` `    ``{  ` `        ``Node new_node = ``new` `Node();  ` `        ``new_node.data = data;  ` `        ``new_node.next = ``null``;  ` `        ``return` `new_node;  ` `    ``}  ` ` `  `    ``/* Driver code*/` `    ``public` `static` `void` `Main(String[] args)  ` `    ``{  ` `        ``Node head = newNode(5);  ` `        ``head.next = newNode(10);  ` `        ``head.next.next = newNode(2);  ` `        ``head.next.next.next = newNode(3);  ` ` `  `        ``head = populateArbit(head);  ` ` `  `        ``Console.WriteLine(``"Resultant Linked List is: "``);  ` `        ``printNextArbitPointers(head);  ` `    ``} ` `} ` ` `  `/* This code is contributed by 29AjayKumar */`

Output:

```Resultant Linked List is:
Node    Next Pointer    Arbit Pointer
5               10              10
10              2               3
2               3               3
3               NULL            NULL
```

Recursive Solution:
We can recursively reach the last node and traverse the linked list from end. Recursive solution doesn’t require reversing of linked list. We can also use a stack in place of recursion to temporarily hold nodes. Thanks to Santosh Kumar Mishra for providing this solution.

## C++

 `// C++ program to point arbit pointers to highest ` `// value on its right ` `#include ` `using` `namespace` `std; ` ` `  `/* Link list node */` `struct` `Node ` `{ ` `    ``int` `data; ` `    ``Node* next, *arbit; ` `}; ` ` `  `// This function populates arbit pointer in every ` `// node to the greatest value to its right. ` `void` `populateArbit(Node *head) ` `{ ` `    ``// using static maxNode to keep track of maximum ` `    ``// orbit node address on right side ` `    ``static` `Node *maxNode; ` ` `  `    ``// if head is null simply return the list ` `    ``if` `(head == NULL) ` `        ``return``; ` ` `  `    ``/* if head->next is null it means we reached at ` `       ``the last node just update the max and maxNode */` `    ``if` `(head->next == NULL) ` `    ``{ ` `        ``maxNode = head; ` `        ``return``; ` `    ``} ` ` `  `    ``/* Calling the populateArbit to the next node */` `    ``populateArbit(head->next); ` ` `  `    ``/* updating the arbit node of the current ` `     ``node with the maximum value on the right side */` `    ``head->arbit = maxNode; ` ` `  `    ``/* if current Node value id greater then ` `     ``the previous right node then  update it */` `    ``if` `(head->data > maxNode->data) ` `        ``maxNode = head; ` ` `  `   ``return``; ` `} ` ` `  `// Utility function to print result linked list ` `void` `printNextArbitPointers(Node *node) ` `{ ` `    ``printf``(``"Node\tNext Pointer\tArbit Pointer\n"``); ` `    ``while` `(node!=NULL) ` `    ``{ ` `        ``cout << node->data << ``"\t\t"``; ` ` `  `        ``if``(node->next) ` `            ``cout << node->next->data << ``"\t\t"``; ` `        ``else` `cout << ``"NULL"` `<< ``"\t\t"``; ` ` `  `        ``if``(node->arbit) ` `            ``cout << node->arbit->data; ` `        ``else` `cout << ``"NULL"``; ` ` `  `        ``cout << endl; ` `        ``node = node->next; ` `    ``} ` `} ` ` `  `/* Function to create a new node with given data */` `Node *newNode(``int` `data) ` `{ ` `    ``Node *new_node = ``new` `Node; ` `    ``new_node->data = data; ` `    ``new_node->next = NULL; ` `    ``return` `new_node; ` `} ` ` `  `/* Driver program to test above functions*/` `int` `main() ` `{ ` `    ``Node *head = newNode(5); ` `    ``head->next = newNode(10); ` `    ``head->next->next = newNode(2); ` `    ``head->next->next->next = newNode(3); ` ` `  `    ``populateArbit(head); ` ` `  `    ``printf``(``"Resultant Linked List is: \n"``); ` `    ``printNextArbitPointers(head); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to point arbit pointers to highest ` `// value on its right ` `class` `GfG ` `{ ` ` `  `    ``/* Link list node */` `    ``static` `class` `Node ` `    ``{ ` `        ``int` `data; ` `        ``Node next, arbit; ` `    ``} ` ` `  `    ``static` `Node maxNode; ` ` `  `    ``// This function populates arbit pointer in every ` `    ``// node to the greatest value to its right. ` `    ``static` `void` `populateArbit(Node head) ` `    ``{ ` ` `  `        ``// if head is null simply return the list ` `        ``if` `(head == ``null``) ` `            ``return``; ` ` `  `        ``/* if head->next is null it means we reached at ` `        ``the last node just update the max and maxNode */` `        ``if` `(head.next == ``null``) ` `        ``{ ` `            ``maxNode = head; ` `            ``return``; ` `        ``} ` ` `  `        ``/* Calling the populateArbit to the next node */` `        ``populateArbit(head.next); ` ` `  `        ``/* updating the arbit node of the current ` `        ``node with the maximum value on the right side */` `        ``head.arbit = maxNode; ` ` `  `        ``/* if current Node value id greater then ` `        ``the previous right node then update it */` `        ``if` `(head.data > maxNode.data) ` `            ``maxNode = head; ` ` `  `        ``return``; ` `    ``} ` ` `  `    ``// Utility function to print result linked list ` `    ``static` `void` `printNextArbitPointers(Node node) ` `    ``{ ` `        ``System.out.println(``"Node\tNext Pointer\tArbit Pointer"``); ` `        ``while` `(node != ``null``) ` `        ``{ ` `            ``System.out.print(node.data + ``"\t\t\t"``); ` ` `  `            ``if` `(node.next != ``null``) ` `                ``System.out.print(node.next.data + ``"\t\t\t\t"``); ` `            ``else` `                ``System.out.print(``"NULL"` `+``"\t\t\t"``); ` ` `  `            ``if` `(node.arbit != ``null``) ` `                ``System.out.print(node.arbit.data); ` `            ``else` `                ``System.out.print(``"NULL"``); ` ` `  `            ``System.out.println(); ` `            ``node = node.next; ` `        ``} ` `    ``} ` ` `  `    ``/* Function to create a new node with given data */` `    ``static` `Node newNode(``int` `data) ` `    ``{ ` `        ``Node new_node = ``new` `Node(); ` `        ``new_node.data = data; ` `        ``new_node.next = ``null``; ` `        ``return` `new_node; ` `    ``} ` ` `  `    ``/* Driver code*/` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``Node head = newNode(``5``); ` `        ``head.next = newNode(``10``); ` `        ``head.next.next = newNode(``2``); ` `        ``head.next.next.next = newNode(``3``); ` ` `  `        ``populateArbit(head); ` ` `  `        ``System.out.println(``"Resultant Linked List is: "``); ` `        ``printNextArbitPointers(head); ` ` `  `    ``} ` `} ` ` `  `// This code is contributed by shubham96301     `

## C#

 `// C# program to point arbit pointers to highest ` `// value on its right ` `using` `System; ` `     `  `class` `GfG ` `{ ` ` `  `    ``/* Link list node */` `    ``public` `class` `Node ` `    ``{ ` `        ``public` `int` `data; ` `        ``public` `Node next, arbit; ` `    ``} ` ` `  `    ``static` `Node maxNode; ` ` `  `    ``// This function populates arbit pointer in every ` `    ``// node to the greatest value to its right. ` `    ``static` `void` `populateArbit(Node head) ` `    ``{ ` ` `  `        ``// if head is null simply return the list ` `        ``if` `(head == ``null``) ` `            ``return``; ` ` `  `        ``/* if head->next is null it means we reached at ` `        ``the last node just update the max and maxNode */` `        ``if` `(head.next == ``null``) ` `        ``{ ` `            ``maxNode = head; ` `            ``return``; ` `        ``} ` ` `  `        ``/* Calling the populateArbit to the next node */` `        ``populateArbit(head.next); ` ` `  `        ``/* updating the arbit node of the current ` `        ``node with the maximum value on the right side */` `        ``head.arbit = maxNode; ` ` `  `        ``/* if current Node value id greater then ` `        ``the previous right node then update it */` `        ``if` `(head.data > maxNode.data) ` `            ``maxNode = head; ` ` `  `        ``return``; ` `    ``} ` ` `  `    ``// Utility function to print result linked list ` `    ``static` `void` `printNextArbitPointers(Node node) ` `    ``{ ` `        ``Console.WriteLine(``"Node\tNext Pointer\tArbit Pointer"``); ` `        ``while` `(node != ``null``) ` `        ``{ ` `            ``Console.Write(node.data + ``"\t\t\t"``); ` ` `  `            ``if` `(node.next != ``null``) ` `                ``Console.Write(node.next.data + ``"\t\t\t\t"``); ` `            ``else` `                ``Console.Write(``"NULL"` `+``"\t\t\t"``); ` ` `  `            ``if` `(node.arbit != ``null``) ` `                ``Console.Write(node.arbit.data); ` `            ``else` `                ``Console.Write(``"NULL"``); ` ` `  `            ``Console.WriteLine(); ` `            ``node = node.next; ` `        ``} ` `    ``} ` ` `  `    ``/* Function to create a new node with given data */` `    ``static` `Node newNode(``int` `data) ` `    ``{ ` `        ``Node new_node = ``new` `Node(); ` `        ``new_node.data = data; ` `        ``new_node.next = ``null``; ` `        ``return` `new_node; ` `    ``} ` ` `  `    ``/* Driver code*/` `    ``public` `static` `void` `Main(String[] args) ` `    ``{ ` `        ``Node head = newNode(5); ` `        ``head.next = newNode(10); ` `        ``head.next.next = newNode(2); ` `        ``head.next.next.next = newNode(3); ` ` `  `        ``populateArbit(head); ` ` `  `        ``Console.WriteLine(``"Resultant Linked List is: "``); ` `        ``printNextArbitPointers(head); ` ` `  `    ``} ` `} ` ` `  `/* This code contributed by PrinciRaj1992 */`

Output:

```Resultant Linked List is:
Node    Next Pointer    Arbit Pointer
5               10              10
10              2               3
2               3               3
3               NULL            NULL
```