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# Find pairs with given sum in doubly linked list

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

Example:

```Input : head : 1 <-> 2 <-> 4 <-> 5 <-> 6 <-> 8 <-> 9
x = 7
Output: (6, 1), (5,2)```

The expected time complexity is O(n) and auxiliary space is O(1).

A simple approach for this problem is to one by one pick each node and find a second element whose sum is equal to x in the remaining list by traversing in the forward direction. The time complexity for this problem will be O(n^2), n is the total number of nodes in the doubly linked list.

An efficient solution for this problem is the 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 the start of the doubly linked list i.e; first=head and initialize second with the last node of the 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 the second pointer, we traverse the list to initialize the second.
• If current sum of first and second is less than x, then we move first in forward direction. If current sum 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 two pointers cross each other (second->next = first), or they become the same (first == second).
• The case when no pairs are present will be handled by the condition “first==second”

Implementation:

## C++

 `// C++ program to find a pair with given sum x. ` `#include ` `using` `namespace` `std; `   `// structure of node of doubly linked list ` `struct` `Node ` `{ ` `    ``int` `data; ` `    ``struct` `Node *next, *prev; ` `}; `   `// Function to find pair whose sum equal to given value x. ` `void` `pairSum(``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 two pointers ` `    ``// cross each other (second->next ` `    ``// == first), or they become same (first == second) ` `    ``while` `(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 program ` `int` `main() ` `{ ` `    ``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 = 7; `   `    ``pairSum(head, x); `   `    ``return` `0; ` `} `

## Java

 `// Java program to find a` `// pair with given sum x.` `import` `java.io.*;` `import` `java.util.*;`   `public` `class` `GFG {`   `    ``// structure of node of` `    ``// doubly linked list` `    ``static` `class` `Node {` `        ``int` `data;` `        ``Node next, prev;` `    ``};`   `    ``// Function to find pair whose` `    ``// sum equal to given value x.` `    ``static` `void` `pairSum(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` `        ``// they cross each other (second.next` `        ``// == first), or they become same` `        ``// (first == second)` `        ``while` `(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` `temp;` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `main(String args[])` `    ``{` `        ``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 = ``7``;`   `        ``pairSum(head, x);` `    ``}` `}`   `// This code is contributed` `// by Arnab Kundu`

## Python3

 `# Python3 program to find a pair with` `# given sum x.`   `# Structure of node of doubly linked list` `class` `Node:` `    `  `    ``def` `__init__(``self``, x):` `        `  `        ``self``.data ``=` `x` `        ``self``.``next` `=` `None` `        ``self``.prev ``=` `None`   `# Function to find pair whose sum ` `# equal to given value x.` `def` `pairSum(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 they` `    ``# cross each other (second.next == ` `    ``# first), or they become same ` `    ``# (first == second)` `    ``while` `(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(data)` `    `  `    ``if` `not` `head:` `        ``head ``=` `temp` `    ``else``:` `        ``temp.``next` `=` `head` `        ``head.prev ``=` `temp` `        ``head ``=` `temp` `        `  `    ``return` `head`   `# Driver code` `if` `__name__ ``=``=` `'__main__'``:` `    `  `    ``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 ``=` `7`   `    ``pairSum(head, x)`   `# This code is contributed by mohit kumar 29`

## C#

 `// C# program to find a ` `// pair with given sum x.` `using` `System; `   `class` `GFG ` `{ `   `    ``// structure of node of ` `    ``// doubly linked list ` `    ``class` `Node ` `    ``{ ` `        ``public` `int` `data; ` `        ``public` `Node next, prev; ` `    ``}; `   `    ``// Function to find pair whose ` `    ``// sum equal to given value x. ` `    ``static` `void` `pairSum( 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  ` `        ``// they cross each other (second.next ` `        ``// == first), or they become same ` `        ``// (first == second) ` `        ``while` `(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` `temp; ` `    ``} `   `    ``// Driver Code ` `    ``public` `static` `void` `Main(String []args) ` `    ``{ ` `        ``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 = 7; `   `        ``pairSum(head, x); ` `    ``} ` `} `   `// This code is contributed by 29AjayKumar`

## Javascript

 ``

Output

```(1, 6)
(2, 5)```

Time complexity : O(n)
Auxiliary space : O(1)

If linked list is not sorted, then we can sort the list as a first step. But in that case overall time complexity would become O(n Log n). We can use Hashing in such cases if extra space is not a constraint. The hashing based solution is same as method 2 here.

This article is contributed by Shashank Mishra ( Gullu ). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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