# Find pairs with given product in a sorted Doubly Linked List

Given a sorted doubly linked list of positive distinct elements, the task is to find pairs in the doubly linked list whose product is equal to given value x, without using any extra space.

Examples:

```Input : List = 1 <=> 2 <=> 4 <=> 5 <=> 6 <=> 8 <=> 9
x = 8
Output: (1, 8), (2, 4)

Input : List = 1 <=> 2 <=> 3 <=> 4 <=> 5 <=> 6 <=> 7
x = 6
Output: (1, 6), (2, 3)
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

A Simple Approach for this problem is to traverse the linked list using two nested loops and find all pairs and check for the pairs with product equals to x. Time complexity for this problem will be O(n^2), n is total number of nodes in doubly linked list.

An Efficient Solution for this problem is same as this article. Here is the algorithm :

• Initialize two pointer variables to find the candidate elements in the sorted doubly linked list. Initialize first with start of doubly linked list i.e; first=head and initialize second with last node of doubly linked list i.e; second=last_node.
• We initialize first and second pointers as first and last nodes. Here we don’t have random access, so to find second pointer, we traverse the list to initialize second.
• If current product of first and second is less than x, then we move first in forward direction. If current product of first and second element is greater than x, then we move second in backward direction.
• Loop termination conditions are also different from arrays. The loop terminates when either of two pointers become NULL, or they cross each other (second->next = first), or they become same (first == second)

Below is the implementation of the above approach:

## C++

 `// C++ program to find a pair with ` `// given product x in sorted Doubly ` `// Linked List ` `#include ` `using` `namespace` `std; ` ` `  `// Doubly Linked List Node ` `struct` `Node { ` `    ``int` `data; ` `    ``struct` `Node *next, *prev; ` `}; ` ` `  `// Function to find pair whose product ` `// equal to given value x ` `void` `pairProduct(``struct` `Node* head, ``int` `x) ` `{ ` `    ``// Set two pointers, ` `    ``// first to the beginning of DLL ` `    ``// and second to the end of DLL. ` `    ``struct` `Node* first = head; ` `    ``struct` `Node* second = head; ` `    ``while` `(second->next != NULL) ` `        ``second = second->next; ` ` `  `    ``// To track if we find a pair or not ` `    ``bool` `found = ``false``; ` ` `  `    ``// The loop terminates when either of two pointers ` `    ``// become NULL, or they cross each other (second->next ` `    ``// == first), or they become same (first == second) ` `    ``while` `(first != NULL && second != NULL && first != second ` `           ``&& second->next != first) { ` `        ``// pair found ` `        ``if` `((first->data * second->data) == x) { ` `            ``found = ``true``; ` `            ``cout << ``"("` `<< first->data << ``", "` `                 ``<< second->data << ``")"` `<< endl; ` ` `  `            ``// move first in forward direction ` `            ``first = first->next; ` ` `  `            ``// move second in backward direction ` `            ``second = second->prev; ` `        ``} ` `        ``else` `{ ` `            ``if` `((first->data * second->data) < x) ` `                ``first = first->next; ` `            ``else` `                ``second = second->prev; ` `        ``} ` `    ``} ` ` `  `    ``// if pair is not present ` `    ``if` `(found == ``false``) ` `        ``cout << ``"No pair found"``; ` `} ` ` `  `// A utility function to insert a new node at the ` `// beginning of doubly linked list ` `void` `insert(``struct` `Node** head, ``int` `data) ` `{ ` `    ``struct` `Node* temp = ``new` `Node; ` `    ``temp->data = data; ` `    ``temp->next = temp->prev = NULL; ` `    ``if` `(!(*head)) ` `        ``(*head) = temp; ` `    ``else` `{ ` `        ``temp->next = *head; ` `        ``(*head)->prev = temp; ` `        ``(*head) = temp; ` `    ``} ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``// Create Doubly Linked List ` `    ``struct` `Node* head = NULL; ` `    ``insert(&head, 9); ` `    ``insert(&head, 8); ` `    ``insert(&head, 6); ` `    ``insert(&head, 5); ` `    ``insert(&head, 4); ` `    ``insert(&head, 2); ` `    ``insert(&head, 1); ` ` `  `    ``int` `x = 8; ` ` `  `    ``pairProduct(head, x); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find a pair with ` `// given product x in sorted Doubly ` `// Linked List ` ` `  `class` `GFG { ` ` `  `    ``// Doubly Linked List Node ` `    ``static` `class` `Node { ` `        ``int` `data; ` `        ``Node next, prev; ` `    ``}; ` ` `  `    ``// Function to find pair whose product ` `    ``// equal to given value x ` `    ``static` `void` `pairProduct(Node head, ``int` `x) ` `    ``{ ` `        ``// Set two pointers, ` `        ``// first to the beginning of DLL ` `        ``// and second to the end of DLL. ` `        ``Node first = head; ` `        ``Node second = head; ` `        ``while` `(second.next != ``null``) ` `            ``second = second.next; ` ` `  `        ``// To track if we find a pair or not ` `        ``boolean` `found = ``false``; ` ` `  `        ``// The loop terminates when either of two pointers ` `        ``// become null, or they cross each other (second.next ` `        ``// == first), or they become same (first == second) ` `        ``while` `(first != ``null` `&& second != ``null` `&& first != second ` `               ``&& second.next != first) { ` `            ``// pair found ` `            ``if` `((first.data * second.data) == x) { ` `                ``found = ``true``; ` `                ``System.out.println(``"("` `+ first.data + ``", "` `                                   ``+ second.data + ``")"``); ` ` `  `                ``// move first in forward direction ` `                ``first = first.next; ` ` `  `                ``// move second in backward direction ` `                ``second = second.prev; ` `            ``} ` `            ``else` `{ ` `                ``if` `((first.data * second.data) < x) ` `                    ``first = first.next; ` `                ``else` `                    ``second = second.prev; ` `            ``} ` `        ``} ` ` `  `        ``// if pair is not present ` `        ``if` `(found == ``false``) ` `            ``System.out.println(``"No pair found"``); ` `    ``} ` ` `  `    ``// A utility function to insert a new node at the ` `    ``// beginning of doubly linked list ` `    ``static` `Node insert(Node head, ``int` `data) ` `    ``{ ` `        ``Node temp = ``new` `Node(); ` `        ``temp.data = data; ` `        ``temp.next = temp.prev = ``null``; ` `        ``if` `((head) == ``null``) ` `            ``(head) = temp; ` `        ``else` `{ ` `            ``temp.next = head; ` `            ``(head).prev = temp; ` `            ``(head) = temp; ` `        ``} ` `        ``return` `head; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``// Create Doubly Linked List ` `        ``Node head = ``null``; ` `        ``head = insert(head, ``9``); ` `        ``head = insert(head, ``8``); ` `        ``head = insert(head, ``6``); ` `        ``head = insert(head, ``5``); ` `        ``head = insert(head, ``4``); ` `        ``head = insert(head, ``2``); ` `        ``head = insert(head, ``1``); ` ` `  `        ``int` `x = ``8``; ` ` `  `        ``pairProduct(head, x); ` `    ``} ` `} ` ` `  `// This code is contributed by Arnab Kundu `

## Python3

 `# Python3 program to find a pair with ` `# given product x in sorted Doubly ` `# Linked List ` ` `  `# Node of the doubly linked list  ` `class` `Node:  ` `     `  `    ``def` `__init__(``self``, data):  ` `        ``self``.data ``=` `data  ` `        ``self``.prev ``=` `None` `        ``self``.``next` `=` `None` ` `  `# Function to find pair whose product ` `# equal to given value x ` `def` `pairProduct(head, x): ` ` `  `    ``# Set two pointers, ` `    ``# first to the beginning of DLL ` `    ``# and second to the end of DLL. ` `    ``first ``=` `head ` `    ``second ``=` `head ` `    ``while` `(second.``next` `!``=` `None``): ` `        ``second ``=` `second.``next` ` `  `    ``# To track if we find a pair or not ` `    ``found ``=` `False` ` `  `    ``# The loop terminates when either of two pointers ` `    ``# become None, or they cross each other (second.next ` `    ``# == first), or they become same (first == second) ` `    ``while` `(first !``=` `None` `and` `second !``=` `None` `and`  `           ``first !``=` `second ``and` `second.``next` `!``=` `first) : ` `        ``# pair found ` `        ``if` `((first.data ``*` `second.data) ``=``=` `x) : ` `            ``found ``=` `True` `            ``print``(``"("``, first.data, ``", "``, second.data, ``")"``) ` ` `  `            ``# move first in forward direction ` `            ``first ``=` `first.``next` ` `  `            ``# move second in backward direction ` `            ``second ``=` `second.prev ` `         `  `        ``else` `: ` `            ``if` `((first.data ``*` `second.data) < x): ` `                ``first ``=` `first.``next` `            ``else``: ` `                ``second ``=` `second.prev ` `         `  `    ``# if pair is not present ` `    ``if` `(found ``=``=` `False``): ` `        ``print``( ``"No pair found"``) ` ` `  `# A utility function to insert a new node at the ` `# beginning of doubly linked list ` `def` `insert(head, data): ` ` `  `    ``temp ``=` `Node(``0``) ` `    ``temp.data ``=` `data ` `    ``temp.``next` `=` `temp.prev ``=` `None` `    ``if` `(head ``=``=` `None``): ` `        ``(head) ``=` `temp ` `    ``else` `: ` `        ``temp.``next` `=` `head ` `        ``(head).prev ``=` `temp ` `        ``(head) ``=` `temp ` `    ``return` `head ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"``:  ` ` `  `    ``# Create Doubly Linked List ` `    ``head ``=` `None` `    ``head ``=` `insert(head, ``9``) ` `    ``head ``=` `insert(head, ``8``) ` `    ``head ``=` `insert(head, ``6``) ` `    ``head ``=` `insert(head, ``5``) ` `    ``head ``=` `insert(head, ``4``) ` `    ``head ``=` `insert(head, ``2``) ` `    ``head ``=` `insert(head, ``1``) ` ` `  `    ``x ``=` `8` ` `  `    ``pairProduct(head, x) ` ` `  `# This code is contributed by Arnab Kundu `

## C#

 `// C# program to find a pair with ` `// given product x in sorted Doubly ` `// Linked List ` `using` `System; ` ` `  `class` `GFG { ` ` `  `    ``// Doubly Linked List Node ` `    ``public` `class` `Node { ` `        ``public` `int` `data; ` `        ``public` `Node next, prev; ` `    ``}; ` ` `  `    ``// Function to find pair whose product ` `    ``// equal to given value x ` `    ``static` `void` `pairProduct(Node head, ``int` `x) ` `    ``{ ` `        ``// Set two pointers, ` `        ``// first to the beginning of DLL ` `        ``// and second to the end of DLL. ` `        ``Node first = head; ` `        ``Node second = head; ` `        ``while` `(second.next != ``null``) ` `            ``second = second.next; ` ` `  `        ``// To track if we find a pair or not ` `        ``bool` `found = ``false``; ` ` `  `        ``// The loop terminates when either of two pointers ` `        ``// become null, or they cross each other (second.next ` `        ``// == first), or they become same (first == second) ` `        ``while` `(first != ``null` `&& second != ``null` `&& first != second ` `               ``&& second.next != first) { ` `            ``// pair found ` `            ``if` `((first.data * second.data) == x) { ` `                ``found = ``true``; ` `                ``Console.WriteLine(``"("` `+ first.data + ``", "` `                                  ``+ second.data + ``")"``); ` ` `  `                ``// move first in forward direction ` `                ``first = first.next; ` ` `  `                ``// move second in backward direction ` `                ``second = second.prev; ` `            ``} ` `            ``else` `{ ` `                ``if` `((first.data * second.data) < x) ` `                    ``first = first.next; ` `                ``else` `                    ``second = second.prev; ` `            ``} ` `        ``} ` ` `  `        ``// if pair is not present ` `        ``if` `(found == ``false``) ` `            ``Console.WriteLine(``"No pair found"``); ` `    ``} ` ` `  `    ``// A utility function to insert a new node at the ` `    ``// beginning of doubly linked list ` `    ``static` `Node insert(Node head, ``int` `data) ` `    ``{ ` `        ``Node temp = ``new` `Node(); ` `        ``temp.data = data; ` `        ``temp.next = temp.prev = ``null``; ` `        ``if` `((head) == ``null``) ` `            ``(head) = temp; ` `        ``else` `{ ` `            ``temp.next = head; ` `            ``(head).prev = temp; ` `            ``(head) = temp; ` `        ``} ` `        ``return` `head; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `Main(String[] args) ` `    ``{ ` `        ``// Create Doubly Linked List ` `        ``Node head = ``null``; ` `        ``head = insert(head, 9); ` `        ``head = insert(head, 8); ` `        ``head = insert(head, 6); ` `        ``head = insert(head, 5); ` `        ``head = insert(head, 4); ` `        ``head = insert(head, 2); ` `        ``head = insert(head, 1); ` ` `  `        ``int` `x = 8; ` ` `  `        ``pairProduct(head, x); ` `    ``} ` `} ` ` `  `// This code contributed by Rajput-Ji `

Output:

```(1, 8)
(2, 4)
```

Time complexity : O(n)

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