Point to next higher value node in a linked list with an arbitrary pointer

Given singly linked list with every node having an additional “arbitrary” pointer that currently points to NULL. Need to make the “arbitrary” pointer point to the next higher value node.

listwithArbit

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A Simple Solution is to traverse all nodes one by one, for every node, find the node which has next greater value of the current node and changes the next pointer. Time Complexity of this solution is O(n2).

An Efficient Solution works in O(nLogn) time. The idea is to use Merge Sort for linked list.
1) Traverse input list and copy next pointer to arbit pointer for every node.
2) Do Merge Sort for the linked list formed by arbit pointers.



Below is the implementation of the above idea. All of the merger sort functions are taken from here. The taken functions are modified here so that they work on arbit pointers instead of next pointers.

C++

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// C++ program to populate arbit pointers 
// to next higher value using merge sort 
#include <bits/stdc++.h>
using namespace std;
  
/* Link list node */
class Node 
    public:
    int data; 
    Node* next, *arbit; 
}; 
  
/* function prototypes */
Node* SortedMerge(Node* a, Node* b); 
void FrontBackSplit(Node* source, 
                    Node** frontRef, Node** backRef); 
  
/* sorts the linked list formed by arbit pointers 
(does not change next pointer or data) */
void MergeSort(Node** headRef) 
    Node* head = *headRef; 
    Node* a, *b; 
  
    /* Base case -- length 0 or 1 */
    if ((head == NULL) || (head->arbit == NULL)) 
        return
  
    /* Split head into 'a' and 'b' sublists */
    FrontBackSplit(head, &a, &b); 
  
    /* Recursively sort the sublists */
    MergeSort(&a); 
    MergeSort(&b); 
  
    /* answer = merge the two sorted lists together */
    *headRef = SortedMerge(a, b); 
  
details of this function */
Node* SortedMerge(Node* a, Node* b) 
    Node* result = NULL; 
  
    /* Base cases */
    if (a == NULL) 
        return (b); 
    else if (b == NULL) 
        return (a); 
  
    /* Pick either a or b, and recur */
    if (a->data <= b->data) 
    
        result = a; 
        result->arbit = SortedMerge(a->arbit, b); 
    
    else
    
        result = b; 
        result->arbit = SortedMerge(a, b->arbit); 
    
  
    return (result); 
  
/* Split the nodes of the given list into front 
and back halves, and return the two lists using 
the reference parameters. If the length is odd, 
the extra node should go in the front list. 
Uses the fast/slow pointer strategy. */
void FrontBackSplit(Node* source, 
                    Node** frontRef, Node** backRef) 
    Node* fast, *slow; 
  
    if (source == NULL || source->arbit == NULL) 
    
        /* length < 2 cases */
        *frontRef = source; 
        *backRef = NULL; 
        return
    
  
    slow = source, fast = source->arbit; 
  
    /* Advance 'fast' two nodes, and 
    advance 'slow' one node */
    while (fast != NULL) 
    
        fast = fast->arbit; 
        if (fast != NULL) 
        
            slow = slow->arbit; 
            fast = fast->arbit; 
        
    
  
    /* 'slow' is before the midpoint in the list, 
     so split it in two at that point. */
    *frontRef = source; 
    *backRef = slow->arbit; 
    slow->arbit = NULL; 
  
/* Function to insert a node at the
beginging of the linked list */
void push(Node** head_ref, int new_data) 
    /* allocate node */
    Node* new_node = new Node();
  
    /* put in the data */
    new_node->data = new_data; 
  
    /* link the old list off the new node */
    new_node->next = (*head_ref); 
  
    new_node->arbit = NULL; 
  
    /* move the head to point to the new node */
    (*head_ref) = new_node; 
  
// Utility function to print result linked list 
void printListafter(Node *node, Node *anode) 
    cout<<"Traversal using Next Pointer\n"
    while (node!=NULL) 
    
        cout << node->data << ", "
        node = node->next; 
    
  
    printf("\nTraversal using Arbit Pointer\n"); 
    while (anode!=NULL) 
    
        cout << anode->data << ", "
        anode = anode->arbit; 
    
  
// This function populates arbit pointer in every node to the 
// next higher value. And returns pointer to the node with 
// minimum value 
Node* populateArbit(Node *head) 
    // Copy next pointers to arbit pointers 
    Node *temp = head; 
    while (temp != NULL) 
    
        temp->arbit = temp->next; 
        temp = temp->next; 
    
  
    // Do merge sort for arbitrary pointers 
    MergeSort(&head); 
  
    // Return head of arbitrary pointer linked list 
    return head; 
  
/* Driver program to test above functions*/
int main() 
    /* Start with the empty list */
    Node* head = NULL; 
  
    /* Let us create the list shown above */
    push(&head, 3); 
    push(&head, 2); 
    push(&head, 10); 
    push(&head, 5); 
  
    /* Sort the above created Linked List */
    Node *ahead = populateArbit(head); 
  
    cout << "Result Linked List is: \n"
    printListafter(head, ahead); 
    return 0; 
  
// This is code is contributed by rathbhupendra

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C

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// C program to populate arbit pointers to next higher value
// using merge sort
#include<stdio.h>
#include<stdlib.h>
  
/* Link list node */
struct Node
{
    int data;
    struct Node* next, *arbit;
};
  
/* function prototypes */
struct Node* SortedMerge(struct Node* a, struct Node* b);
void FrontBackSplit(struct Node* source,
                    struct Node** frontRef, struct Node** backRef);
  
/* sorts the linked list formed by arbit pointers
  (does not change next pointer or data) */
void MergeSort(struct Node** headRef)
{
    struct Node* head = *headRef;
    struct Node* a, *b;
  
    /* Base case -- length 0 or 1 */
    if ((head == NULL) || (head->arbit == NULL))
        return;
  
    /* Split head into 'a' and 'b' sublists */
    FrontBackSplit(head, &a, &b);
  
    /* Recursively sort the sublists */
    MergeSort(&a);
    MergeSort(&b);
  
    /* answer = merge the two sorted lists together */
    *headRef = SortedMerge(a, b);
}
  
/* See https://www.geeksforgeeks.org/?p=3622 for details of this
   function */
struct Node* SortedMerge(struct Node* a, struct Node* b)
{
    struct Node* result = NULL;
  
    /* Base cases */
    if (a == NULL)
        return (b);
    else if (b==NULL)
        return (a);
  
    /* Pick either a or b, and recur */
    if (a->data <= b->data)
    {
        result = a;
        result->arbit = SortedMerge(a->arbit, b);
    }
    else
    {
        result = b;
        result->arbit = SortedMerge(a, b->arbit);
    }
  
    return (result);
}
  
/* Split the nodes of the given list into front and back halves,
   and return the two lists using the reference parameters.
   If the length is odd, the extra node should go in the front list.
   Uses the fast/slow pointer strategy.  */
void FrontBackSplit(struct Node* source,
                    struct Node** frontRef, struct Node** backRef)
{
    struct Node* fast, *slow;
  
    if (source==NULL || source->arbit==NULL)
    {
        /* length < 2 cases */
        *frontRef = source;
        *backRef = NULL;
        return;
    }
  
    slow = source,  fast = source->arbit;
  
    /* Advance 'fast' two nodes, and advance 'slow' one node */
    while (fast != NULL)
    {
        fast = fast->arbit;
        if (fast != NULL)
        {
            slow = slow->arbit;
            fast = fast->arbit;
        }
    }
  
    /* 'slow' is before the midpoint in the list, so split it in two
      at that point. */
    *frontRef = source;
    *backRef = slow->arbit;
    slow->arbit = NULL;
}
  
/* Function to insert a node at the beginging of the linked list */
void push(struct Node** head_ref, int new_data)
{
    /* allocate node */
    struct Node* new_node =
        (struct Node*) malloc(sizeof(struct Node));
  
    /* put in the data  */
    new_node->data  = new_data;
  
    /* link the old list off the new node */
    new_node->next = (*head_ref);
  
    new_node->arbit = NULL;
  
    /* move the head to point to the new node */
    (*head_ref)    = new_node;
}
  
// Utility function to print result linked list
void printListafter(struct Node *node, struct Node *anode)
{
    printf("Traversal using Next Pointer\n");
    while (node!=NULL)
    {
        printf("%d, ", node->data);
        node = node->next;
    }
  
    printf("\nTraversal using Arbit Pointer\n");
    while (anode!=NULL)
    {
        printf("%d, ", anode->data);
        anode = anode->arbit;
    }
}
  
// This function populates arbit pointer in every node to the
// next higher value. And returns pointer to the node with
// minimum value
struct Node* populateArbit(struct Node *head)
{
    // Copy next pointers to arbit pointers
    struct Node *temp = head;
    while (temp != NULL)
    {
        temp->arbit = temp->next;
        temp = temp->next;
    }
  
    // Do merge sort for arbitrary pointers
    MergeSort(&head);
  
    // Return head of arbitrary pointer linked list
    return head;
}
  
/* Drier program to test above functions*/
int main()
{
    /* Start with the empty list */
    struct Node* head = NULL;
  
    /* Let us create the list shown above */
    push(&head, 3);
    push(&head, 2);
    push(&head, 10);
    push(&head, 5);
  
    /* Sort the above created Linked List */
    struct Node *ahead = populateArbit(head);
  
    printf("\nResult Linked List is: \n");
    printListafter(head, ahead);
  
    getchar();
    return 0;
}

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Java

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// Java program to populate arbit pointers 
// to next higher value using merge sort
class LinkedList
{
  
    static Node head;
  
    /* Link list node */
    static class Node
    {
        int data;
        Node next, arbit;
  
        Node(int data) 
        {
            this.data = data;
            next = null;
            arbit = null;
        }
    }
  
    // Utility function to print result linked list
    void printList(Node node, Node anode)
    {
        System.out.println("Traversal using Next Pointer");
        while (node != null)
        {
            System.out.print(node.data + " ");
            node = node.next;
        }
  
        System.out.println("\nTraversal using Arbit Pointer");
        while (anode != null)
        {
            System.out.print(anode.data + " ");
            anode = anode.arbit;
        }
    }
  
    // This function populates arbit pointer in every node to the 
    // next higher value. And returns pointer to the node with 
    // minimum value
    private Node populateArbit(Node start)
    {
  
        Node temp = start;
  
        // Copy next pointers to arbit pointers
        while (temp != null)
        {
            temp.arbit = temp.next;
            temp = temp.next;
        }
  
        // Do merge sort for arbitrary pointers and
        // return head of arbitrary pointer linked list
        return MergeSort(start);
    }
  
    /* sorts the linked list formed by arbit pointers 
    (does not change next pointer or data) */
    private Node MergeSort(Node start)
    {
          
        /* Base case -- length 0 or 1 */
        if (start == null || start.arbit == null)
        {
            return start;
        }
  
        /* Split head into 'middle' and 'nextofmiddle' sublists */
        Node middle = getMiddle(start);
        Node nextofmiddle = middle.arbit;
  
        middle.arbit = null;
  
        /* Recursively sort the sublists */
        Node left = MergeSort(start);
        Node right = MergeSort(nextofmiddle);
  
        /* answer = merge the two sorted lists together */
        Node sortedlist = SortedMerge(left, right);
  
        return sortedlist;
    }
  
    // Utility function to get the middle of the linked list
    private Node getMiddle(Node source)
    {
        // Base case
        if (source == null)
            return source;
        Node fastptr = source.arbit;
        Node slowptr = source;
  
        // Move fastptr by two and slow ptr by one 
        // Finally slowptr will point to middle node
        while (fastptr != null)
        {
            fastptr = fastptr.arbit;
            if (fastptr != null)
            {
                slowptr = slowptr.arbit;
                fastptr = fastptr.arbit;
            }
        }
        return slowptr;
    }
  
    private Node SortedMerge(Node a, Node b)
    {
        Node result = null;
  
        /* Base cases */
        if (a == null)
            return b;
        else if (b == null)
            return a;
  
        /* Pick either a or b, and recur */
        if (a.data <= b.data)
        {
            result = a;
            result.arbit = SortedMerge(a.arbit, b);
        }
        else
        {
            result = b;
            result.arbit = SortedMerge(a, b.arbit);
        }
  
        return result;
    }
  
    // Driver code
    public static void main(String[] args)
    {
        LinkedList list = new LinkedList();
  
        /* Let us create the list shown above */
        list.head = new Node(5);
        list.head.next = new Node(10);
        list.head.next.next = new Node(2);
        list.head.next.next.next = new Node(3);
  
        /* Sort the above created Linked List */
        Node ahead = list.populateArbit(head);
  
        System.out.println("Result Linked List is:");
        list.printList(head, ahead);
    }
}
  
// This code is contributed by shubham96301    

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// C# program to populate arbit pointers 
// to next higher value using merge sort
using System;
public class LinkedList
{
   
    public Node head;
   
    /* Link list node */
    public class Node
    {
        public int data;
        public Node next, arbit;
   
        public Node(int data) 
        {
            this.data = data;
            next = null;
            arbit = null;
        }
    }
   
    // Utility function to print result linked list
    void printList(Node node, Node anode)
    {
        Console.WriteLine("Traversal using Next Pointer");
        while (node != null)
        {
            Console.Write(node.data + " ");
            node = node.next;
        }
   
        Console.WriteLine("\nTraversal using Arbit Pointer");
        while (anode != null)
        {
            Console.Write(anode.data + " ");
            anode = anode.arbit;
        }
    }
   
    // This function populates arbit pointer in every node to the 
    // next higher value. And returns pointer to the node with 
    // minimum value
    private Node populateArbit(Node start)
    {
   
        Node temp = start;
   
        // Copy next pointers to arbit pointers
        while (temp != null)
        {
            temp.arbit = temp.next;
            temp = temp.next;
        }
   
        // Do merge sort for arbitrary pointers and
        // return head of arbitrary pointer linked list
        return MergeSort(start);
    }
   
    /* sorts the linked list formed by arbit pointers 
    (does not change next pointer or data) */
    private Node MergeSort(Node start)
    {
           
        /* Base case -- length 0 or 1 */
        if (start == null || start.arbit == null)
        {
            return start;
        }
   
        /* Split head into 'middle' and 'nextofmiddle' sublists */
        Node middle = getMiddle(start);
        Node nextofmiddle = middle.arbit;
   
        middle.arbit = null;
   
        /* Recursively sort the sublists */
        Node left = MergeSort(start);
        Node right = MergeSort(nextofmiddle);
   
        /* answer = merge the two sorted lists together */
        Node sortedlist = SortedMerge(left, right);
   
        return sortedlist;
    }
   
    // Utility function to get the middle of the linked list
    private Node getMiddle(Node source)
    {
        // Base case
        if (source == null)
            return source;
        Node fastptr = source.arbit;
        Node slowptr = source;
   
        // Move fastptr by two and slow ptr by one 
        // Finally slowptr will point to middle node
        while (fastptr != null)
        {
            fastptr = fastptr.arbit;
            if (fastptr != null)
            {
                slowptr = slowptr.arbit;
                fastptr = fastptr.arbit;
            }
        }
        return slowptr;
    }
   
    private Node SortedMerge(Node a, Node b)
    {
        Node result = null;
   
        /* Base cases */
        if (a == null)
            return b;
        else if (b == null)
            return a;
   
        /* Pick either a or b, and recur */
        if (a.data <= b.data)
        {
            result = a;
            result.arbit = SortedMerge(a.arbit, b);
        }
        else
        {
            result = b;
            result.arbit = SortedMerge(a, b.arbit);
        }
   
        return result;
    }
   
    // Driver code
    public static void Main(String[] args)
    {
        LinkedList list = new LinkedList();
   
        /* Let us create the list shown above */
        list.head = new Node(5);
        list.head.next = new Node(10);
        list.head.next.next = new Node(2);
        list.head.next.next.next = new Node(3);
   
        /* Sort the above created Linked List */
        Node ahead = list.populateArbit(list.head);
   
        Console.WriteLine("Result Linked List is:");
        list.printList(list.head, ahead);
    }
}
  
/* This code contributed by PrinciRaj1992 */

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Output:

Result Linked List is:
Traversal using Next Pointer
5, 10, 2, 3,
Traversal using Arbit Pointer
2, 3, 5, 10,

This article is contributed by Saurabh Bansal. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above



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