Related Articles
Add two numbers represented by linked lists | Set 1
• Difficulty Level : Easy
• Last Updated : 10 Nov, 2020

Given two numbers represented by two lists, write a function that returns the sum list. The sum list is list representation of the addition of two input numbers.

Example:

Input:
List1: 5->6->3 // represents number 365
List2: 8->4->2 // represents number 248
Output:
Resultant list: 3->1->6 // represents number 613
Explanation: 365 + 248 = 613
Input:
List1: 7->5->9->4->6 // represents number 64957
List2: 8->4 // represents number 48
Output:
Resultant list: 5->0->0->5->6 // represents number 65005
Explanation: 64957 + 48 = 65005

Approach: Traverse both lists and One by one pick nodes of both lists and add the values. If the sum is more than 10 then make carry as 1 and reduce sum. If one list has more elements than the other then consider remaining values of this list as 0.

The steps are:

1. Traverse the two linked lists from start to end
2. Add the two digits each from respective linked lists.
3. If one of the list has reached the end then take 0 as its digit.
4. Continue it until both the lists end.
5. If the sum of two digits is greater than 9 then set carry as 1 and the current digit as sum % 10

Below is the implementation of this approach.

## C++

 `// C++ program to add two numbers``// represented by linked list``#include ``using` `namespace` `std;` `/* Linked list node */``class` `Node {``public``:``    ``int` `data;``    ``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;``}` `/* Function to insert a node at the``beginning of the Singly Linked List */``void` `push(Node** head_ref, ``int` `new_data)``{``    ``/* allocate node */``    ``Node* new_node = newNode(new_data);` `    ``/* link the old list off the new node */``    ``new_node->next = (*head_ref);` `    ``/* move the head to point to the new node */``    ``(*head_ref) = new_node;``}` `/* Adds contents of two linked lists and``return the head node of resultant list */``Node* addTwoLists(Node* first, Node* second)``{` `    ``// res is head node of the resultant list``    ``Node* res = NULL;``    ``Node *temp, *prev = NULL;``    ``int` `carry = 0, sum;` `    ``// while both lists exist``    ``while` `(first != NULL``           ``|| second != NULL) {``        ``// Calculate value of next``        ``// digit in resultant list.``        ``// The next digit is sum of``        ``// following things``        ``// (i) Carry``        ``// (ii) Next digit of first``        ``// list (if there is a next digit)``        ``// (ii) Next digit of second``        ``// list (if there is a next digit)``        ``sum = carry + (first ? first->data : 0)``              ``+ (second ? second->data : 0);` `        ``// update carry for next calulation``        ``carry = (sum >= 10) ? 1 : 0;` `        ``// update sum if it is greater than 10``        ``sum = sum % 10;` `        ``// Create a new node with sum as data``        ``temp = newNode(sum);` `        ``// if this is the first node then``        ``// set it as head of the resultant list``        ``if` `(res == NULL)``            ``res = temp;` `        ``// If this is not the first``        ``// node then connect it to the rest.``        ``else``            ``prev->next = temp;` `        ``// Set prev for next insertion``        ``prev = temp;` `        ``// Move first and second``        ``// pointers to next nodes``        ``if` `(first)``            ``first = first->next;``        ``if` `(second)``            ``second = second->next;``    ``}` `    ``if` `(carry > 0)``        ``temp->next = newNode(carry);` `    ``// return head of the resultant list``    ``return` `res;``}` `// A utility function to print a linked list``void` `printList(Node* node)``{``    ``while` `(node != NULL) {``        ``cout << node->data << ``" "``;``        ``node = node->next;``    ``}``    ``cout << endl;``}` `/* Driver code */``int` `main(``void``)``{``    ``Node* res = NULL;``    ``Node* first = NULL;``    ``Node* second = NULL;` `    ``// create first list 7->5->9->4->6``    ``push(&first, 6);``    ``push(&first, 4);``    ``push(&first, 9);``    ``push(&first, 5);``    ``push(&first, 7);``    ``printf``(``"First List is "``);``    ``printList(first);` `    ``// create second list 8->4``    ``push(&second, 4);``    ``push(&second, 8);``    ``cout << ``"Second List is "``;``    ``printList(second);` `    ``// Add the two lists and see result``    ``res = addTwoLists(first, second);``    ``cout << ``"Resultant list is "``;``    ``printList(res);` `    ``return` `0;``}` `// This code is contributed by rathbhupendra`

## C

 `#include ``#include ` `/* Linked list node */``struct` `Node {``    ``int` `data;``    ``struct` `Node* next;``};` `/* Function to create a new node with given data */``struct` `Node* newNode(``int` `data)``{``    ``struct` `Node* new_node``        ``= (``struct` `Node*)``malloc``(``sizeof``(``struct` `Node));``    ``new_node->data = data;``    ``new_node->next = NULL;``    ``return` `new_node;``}` `/* Function to insert a node``at the beginning of the Singly Linked List */``void` `push(``struct` `Node** head_ref, ``int` `new_data)``{``    ``/* allocate node */``    ``struct` `Node* new_node = newNode(new_data);` `    ``/* link the old list off the new node */``    ``new_node->next = (*head_ref);` `    ``/* move the head to point to the new node */``    ``(*head_ref) = new_node;``}` `/* Adds contents of two linked`` ``lists and return the head node`` ``of resultant list */``struct` `Node* addTwoLists(``struct` `Node* first,``                         ``struct` `Node* second)``{` `    ``// res is head node of the resultant list``    ``struct` `Node* res = NULL;``    ``struct` `Node *temp, *prev = NULL;``    ``int` `carry = 0, sum;` `    ``// while both lists exist``    ``while` `(first != NULL || second != NULL) {``        ``// Calculate value of next``        ``// digit in resultant list.``        ``// The next digit is sum``        ``// of following things``        ``// (i)  Carry``        ``// (ii) Next digit of first``        ``// list (if there is a next digit)``        ``// (ii) Next digit of second``        ``// list (if there is a next digit)``        ``sum = carry + (first ? first->data : 0)``              ``+ (second ? second->data : 0);` `        ``// Update carry for next calulation``        ``carry = (sum >= 10) ? 1 : 0;` `        ``// Update sum if it is greater than 10``        ``sum = sum % 10;` `        ``// Create a new node with sum as data``        ``temp = newNode(sum);` `        ``// if this is the first node then``        ``// set it as head of the resultant list``        ``if` `(res == NULL)``            ``res = temp;``        ``// If this is not the first node``        ``// then connect it to the rest.``        ``else``            ``prev->next = temp;` `        ``// Set prev for next insertion``        ``prev = temp;` `        ``// Move first and second``        ``// pointers to next nodes``        ``if` `(first)``            ``first = first->next;``        ``if` `(second)``            ``second = second->next;``    ``}` `    ``if` `(carry > 0)``        ``temp->next = newNode(carry);` `    ``// return head of the resultant list``    ``return` `res;``}` `// A utility function to print a linked list``void` `printList(``struct` `Node* node)``{``    ``while` `(node != NULL) {``        ``printf``(``"%d "``, node->data);``        ``node = node->next;``    ``}``    ``printf``(``"\n"``);``}` `/* Driver code */``int` `main(``void``)``{``    ``struct` `Node* res = NULL;``    ``struct` `Node* first = NULL;``    ``struct` `Node* second = NULL;` `    ``// create first list 7->5->9->4->6``    ``push(&first, 6);``    ``push(&first, 4);``    ``push(&first, 9);``    ``push(&first, 5);``    ``push(&first, 7);``    ``printf``(``"First List is "``);``    ``printList(first);` `    ``// create second list 8->4``    ``push(&second, 4);``    ``push(&second, 8);``    ``printf``(``"Second List is "``);``    ``printList(second);` `    ``// Add the two lists and see result``    ``res = addTwoLists(first, second);``    ``printf``(``"Resultant list is "``);``    ``printList(res);` `    ``return` `0;``}`

## Java

 `// Java program to add two numbers``// represented by linked list` `class` `LinkedList {` `    ``static` `Node head1, head2;` `    ``static` `class` `Node {` `        ``int` `data;``        ``Node next;` `        ``Node(``int` `d)``        ``{``            ``data = d;``            ``next = ``null``;``        ``}``    ``}` `    ``/* Adds contents of two linked``lists and return the head node``of resultant list */``    ``Node addTwoLists(Node first, Node second)``    ``{``        ``// res is head node of the resultant list``        ``Node res = ``null``;``        ``Node prev = ``null``;``        ``Node temp = ``null``;``        ``int` `carry = ``0``, sum;` `        ``// while both lists exist``        ``while` `(first != ``null` `|| second != ``null``) {``            ``// Calculate value of next``            ``// digit in resultant list.``            ``// The next digit is sum``            ``// of following things``            ``// (i)  Carry``            ``// (ii) Next digit of first``            ``// list (if there is a next digit)``            ``// (ii) Next digit of second``            ``// list (if there is a next digit)``            ``sum = carry + (first != ``null` `? first.data : ``0``)``                  ``+ (second != ``null` `? second.data : ``0``);` `            ``// update carry for next calulation``            ``carry = (sum >= ``10``) ? ``1` `: ``0``;` `            ``// update sum if it is greater than 10``            ``sum = sum % ``10``;` `            ``// Create a new node with sum as data``            ``temp = ``new` `Node(sum);` `            ``// if this is the first node then set``            ``// it as head of the resultant list``            ``if` `(res == ``null``) {``                ``res = temp;``            ``}` `            ``// If this is not the first``            ``// node then connect it to the rest.``            ``else` `{``                ``prev.next = temp;``            ``}` `            ``// Set prev for next insertion``            ``prev = temp;` `            ``// Move first and second pointers``            ``// to next nodes``            ``if` `(first != ``null``) {``                ``first = first.next;``            ``}``            ``if` `(second != ``null``) {``                ``second = second.next;``            ``}``        ``}` `        ``if` `(carry > ``0``) {``            ``temp.next = ``new` `Node(carry);``        ``}` `        ``// return head of the resultant list``        ``return` `res;``    ``}``    ``/* Utility function to print a linked list */` `    ``void` `printList(Node head)``    ``{``        ``while` `(head != ``null``) {``            ``System.out.print(head.data + ``" "``);``            ``head = head.next;``        ``}``        ``System.out.println(``""``);``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``LinkedList list = ``new` `LinkedList();` `        ``// creating first list``        ``list.head1 = ``new` `Node(``7``);``        ``list.head1.next = ``new` `Node(``5``);``        ``list.head1.next.next = ``new` `Node(``9``);``        ``list.head1.next.next.next = ``new` `Node(``4``);``        ``list.head1.next.next.next.next = ``new` `Node(``6``);``        ``System.out.print(``"First List is "``);``        ``list.printList(head1);` `        ``// creating seconnd list``        ``list.head2 = ``new` `Node(``8``);``        ``list.head2.next = ``new` `Node(``4``);``        ``System.out.print(``"Second List is "``);``        ``list.printList(head2);` `        ``// add the two lists and see the result``        ``Node rs = list.addTwoLists(head1, head2);``        ``System.out.print(``"Resultant List is "``);``        ``list.printList(rs);``    ``}``}` `// this code has been contributed by Mayank Jaiswal`

## Python

 `# Python program to add two numbers represented by linked list` `# Node class`  `class` `Node:` `    ``# Constructor to initialize the node object``    ``def` `__init__(``self``, data):``        ``self``.data ``=` `data``        ``self``.``next` `=` `None`  `class` `LinkedList:` `    ``# Function to initialize head``    ``def` `__init__(``self``):``        ``self``.head ``=` `None` `    ``# Function to insert a new node at the beginning``    ``def` `push(``self``, new_data):``        ``new_node ``=` `Node(new_data)``        ``new_node.``next` `=` `self``.head``        ``self``.head ``=` `new_node` `    ``# Add contents of two linked lists and return the head``    ``# node of resultant list``    ``def` `addTwoLists(``self``, first, second):``        ``prev ``=` `None``        ``temp ``=` `None``        ``carry ``=` `0` `        ``# While both list exists``        ``while``(first ``is` `not` `None` `or` `second ``is` `not` `None``):` `            ``# Calculate the value of next digit in``            ``# resultant list``            ``# The next digit is sum of following things``            ``# (i) Carry``            ``# (ii) Next digit of first list (if ther is a``            ``# next digit)``            ``# (iii) Next digit of second list ( if there``            ``# is a next digit)``            ``fdata ``=` `0` `if` `first ``is` `None` `else` `first.data``            ``sdata ``=` `0` `if` `second ``is` `None` `else` `second.data``            ``Sum` `=` `carry ``+` `fdata ``+` `sdata` `            ``# update carry for next calculation``            ``carry ``=` `1` `if` `Sum` `>``=` `10` `else` `0` `            ``# update sum if it is greater than 10``            ``Sum` `=` `Sum` `if` `Sum` `< ``10` `else` `Sum` `%` `10` `            ``# Create a new node with sum as data``            ``temp ``=` `Node(``Sum``)` `            ``# if this is the first node then set it as head``            ``# of resultant list``            ``if` `self``.head ``is` `None``:``                ``self``.head ``=` `temp``            ``else``:``                ``prev.``next` `=` `temp` `            ``# Set prev for next insertion``            ``prev ``=` `temp` `            ``# Move first and second pointers to next nodes``            ``if` `first ``is` `not` `None``:``                ``first ``=` `first.``next``            ``if` `second ``is` `not` `None``:``                ``second ``=` `second.``next` `        ``if` `carry > ``0``:``            ``temp.``next` `=` `Node(carry)` `    ``# Utility function to print the linked LinkedList``    ``def` `printList(``self``):``        ``temp ``=` `self``.head``        ``while``(temp):``            ``print` `temp.data,``            ``temp ``=` `temp.``next`  `# Driver code``first ``=` `LinkedList()``second ``=` `LinkedList()` `# Create first list``first.push(``6``)``first.push(``4``)``first.push(``9``)``first.push(``5``)``first.push(``7``)``print` `"First List is "``,``first.printList()` `# Create second list``second.push(``4``)``second.push(``8``)``print` `"\nSecond List is "``,``second.printList()` `# Add the two lists and see result``res ``=` `LinkedList()``res.addTwoLists(first.head, second.head)``print` `"\nResultant list is "``,``res.printList()` `# This code is contributed by Nikhil Kumar Singh(nickzuck_007)`

## C#

 `// C# program to add two numbers``// represented by linked list``using` `System;` `public` `class` `LinkedList {` `    ``Node head1, head2;` `    ``public` `class` `Node {``        ``public` `int` `data;``        ``public` `Node next;` `        ``public` `Node(``int` `d)``        ``{``            ``data = d;``            ``next = ``null``;``        ``}``    ``}` `    ``/* Adds contents of two linked lists``    ``and return the head node of resultant list */``    ``Node addTwoLists(Node first, Node second)``    ``{``        ``// res is head node of the resultant list``        ``Node res = ``null``;``        ``Node prev = ``null``;``        ``Node temp = ``null``;``        ``int` `carry = 0, sum;` `        ``// while both lists exist``        ``while` `(first != ``null` `|| second != ``null``) {``            ``// Calculate value of next digit in resultant``            ``// list. The next digit is sum of following``            ``// things (i) Carry (ii) Next digit of first``            ``// list (if there is a next digit) (ii) Next``            ``// digit of second list (if there is a next``            ``// digit)``            ``sum = carry + (first != ``null` `? first.data : 0)``                  ``+ (second != ``null` `? second.data : 0);` `            ``// update carry for next calulation``            ``carry = (sum >= 10) ? 1 : 0;` `            ``// update sum if it is greater than 10``            ``sum = sum % 10;` `            ``// Create a new node with sum as data``            ``temp = ``new` `Node(sum);` `            ``// if this is the first node then set it as head``            ``// of the resultant list``            ``if` `(res == ``null``) {``                ``res = temp;``            ``}` `            ``// If this is not the first``            ``// node then connect it to the rest.``            ``else` `{``                ``prev.next = temp;``            ``}` `            ``// Set prev for next insertion``            ``prev = temp;` `            ``// Move first and second pointers to next nodes``            ``if` `(first != ``null``) {``                ``first = first.next;``            ``}``            ``if` `(second != ``null``) {``                ``second = second.next;``            ``}``        ``}` `        ``if` `(carry > 0) {``            ``temp.next = ``new` `Node(carry);``        ``}` `        ``// return head of the resultant list``        ``return` `res;``    ``}``    ``/* Utility function to print a linked list */` `    ``void` `printList(Node head)``    ``{``        ``while` `(head != ``null``) {``            ``Console.Write(head.data + ``" "``);``            ``head = head.next;``        ``}``        ``Console.WriteLine(``""``);``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``LinkedList list = ``new` `LinkedList();` `        ``// creating first list``        ``list.head1 = ``new` `Node(7);``        ``list.head1.next = ``new` `Node(5);``        ``list.head1.next.next = ``new` `Node(9);``        ``list.head1.next.next.next = ``new` `Node(4);``        ``list.head1.next.next.next.next = ``new` `Node(6);``        ``Console.Write(``"First List is "``);``        ``list.printList(list.head1);` `        ``// creating seconnd list``        ``list.head2 = ``new` `Node(8);``        ``list.head2.next = ``new` `Node(4);``        ``Console.Write(``"Second List is "``);``        ``list.printList(list.head2);` `        ``// add the two lists and see the result``        ``Node rs = list.addTwoLists(list.head1, list.head2);``        ``Console.Write(``"Resultant List is "``);``        ``list.printList(rs);``    ``}``}` `// This code contributed by Rajput-Ji`
Output
```First List is 7 5 9 4 6
Second List is 8 4
Resultant list is 5 0 0 5 6
```

Complexity Analysis:

• Time Complexity: O(m + n), where m and n are number of nodes in first and second lists respectively.
The lists needs to be traversed only once.
• Space Complexity: O(m + n).
A temporary linked list is needed to store the output number
https://www.youtube.com/watch?v=LLPuC5kWD8U

Related Article: Add two numbers represented by linked lists | Set 2

Please write comments if you find the above codes/algorithms incorrect, or find other ways to solve the same problem.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up