Add Two Numbers Represented by Linked Lists | Set 3

Given two numbers represented by two linked lists, write a function that returns sum list. The sum list is linked list representation of addition of two input numbers. Expected Space Complexity O(1).

Examples:

Input:
L1 = 5 -> 6 -> 3 -> NULL
L2 = 8 -> 4 -> 2 -> NULL
Output: 1 -> 4 -> 0 -> 5 -> NULL

Input:
L1 = 1 -> 0 -> 0 -> NULL
L2 = 9 -> 1 -> NULL
Output: 1 -> 9 -> 1 -> NULL

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

Approach: We have discussed a solution here where we used recursion to reach to the least significant number in the lists, but due to the involvement of the stack, the space complexity of the solution becomes O(N)

Here the target is to do the sum inplace, and return the modified sum list.

The idea is to first reverse both the linked list, so new head of the list points to least significant number and and we can start adding as described here and instead of creating a new list, we modify the existing one and return the head of modified list.

Following are the steps:

1. Reverse List L1.
2. Reverse List L2.
3. Add the nodes of both the lists iteratively.
4. Reverse the resultant list and return its head.

Below is the implementation of the above approach:

C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `class` `LinkedList; ` ` `  `// Node class for the linked list ` `class` `Node { ` `    ``int` `data; ` `    ``Node* next; ` ` `  `    ``friend` `LinkedList; ` ` `  `public``: ` `    ``Node(); ` `    ``Node(``int` `x); ` `}; ` ` `  `Node::Node() ` `{ ` `    ``data = 0; ` `    ``next = NULL; ` `} ` ` `  `// Function to initialise ` `// a node with value x ` `Node::Node(``int` `x) ` `{ ` `    ``data = x; ` `    ``next = NULL; ` `} ` ` `  `// Linkedlist class with helper functions ` `class` `LinkedList { ` `public``: ` `    ``Node* head; ` ` `  `    ``LinkedList(); ` ` `  `    ``void` `insert(``int` `x); ` `    ``void` `reverse(); ` `    ``void` `traverse(); ` ` `  `    ``void` `sum(LinkedList*); ` `}; ` ` `  `LinkedList::LinkedList() ` `{ ` `    ``head = NULL; ` `} ` ` `  `// Function to insert a node at ` `// the head of the list ` `void` `LinkedList::insert(``int` `x) ` `{ ` `    ``Node* node = ``new` `Node(); ` `    ``node->data = x; ` ` `  `    ``if` `(head == NULL) ` `        ``head = node; ` `    ``else` `{ ` `        ``node->next = head; ` `        ``head = node; ` `    ``} ` `} ` ` `  `// Function to reverse the linked list ` `void` `LinkedList::reverse() ` `{ ` `    ``Node *prev = NULL, *curr = head; ` ` `  `    ``while` `(curr) { ` `        ``Node* temp = curr->next; ` `        ``curr->next = prev; ` `        ``prev = curr; ` `        ``curr = temp; ` `    ``} ` `    ``head = prev; ` `} ` ` `  `// Function to traverse and print the list ` `void` `LinkedList::traverse() ` `{ ` ` `  `    ``Node* temp = head; ` ` `  `    ``while` `(temp) { ` `        ``cout << temp->data << ``" -> "``; ` `        ``temp = temp->next; ` `    ``} ` `    ``cout << ``"NULL"``; ` `} ` ` `  `// Function to add two numbers ` `// represented as linked lists ` `void` `LinkedList::sum(LinkedList* l2) ` `{ ` `    ``reverse(); ` `    ``l2->reverse(); ` ` `  `    ``Node *start1 = head, *start2 = l2->head; ` ` `  `    ``Node* prev = NULL; ` `    ``int` `carry = 0; ` ` `  `    ``// While both lists exist ` `    ``while` `(start1 && start2) { ` ` `  `        ``// Current sum ` `        ``int` `temp = start1->data + start2->data + carry; ` ` `  `        ``// Handle carry ` `        ``start1->data = temp % 10; ` `        ``carry = temp / 10; ` `        ``prev = start1; ` ` `  `        ``// Get to next nodes ` `        ``start1 = start1->next; ` `        ``start2 = start2->next; ` `    ``} ` ` `  `    ``// If there are reamining digits ` `    ``// in any one of the lists ` `    ``if` `(start1 || start2) { ` ` `  `        ``if` `(start2) ` `            ``prev->next = start2; ` ` `  `        ``start1 = prev->next; ` ` `  `        ``// While first list has digits remaining ` `        ``while` `(start1) { ` `            ``int` `temp = start1->data + carry; ` `            ``start1->data = temp % 10; ` `            ``carry = temp / 10; ` `            ``prev = start1; ` `            ``start1 = start1->next; ` `        ``} ` `    ``} ` ` `  `    ``// If a new node needs to be ` `    ``// created due to carry ` `    ``if` `(carry > 0) { ` `        ``prev->next = ``new` `Node(carry); ` `    ``} ` ` `  `    ``// Reverse the resultant list ` `    ``reverse(); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` ` `  `    ``// Create first list ` `    ``LinkedList* l1 = ``new` `LinkedList(); ` `    ``l1->insert(3); ` `    ``l1->insert(6); ` `    ``l1->insert(5); ` ` `  `    ``// Create second list ` `    ``LinkedList* l2 = ``new` `LinkedList(); ` `    ``l2->insert(2); ` `    ``l2->insert(4); ` `    ``l2->insert(8); ` ` `  `    ``// Add the lists ` `    ``l1->sum(l2); ` ` `  `    ``// Print the resultant list ` `    ``l1->traverse(); ` ` `  `    ``return` `0; ` `} `

Java

 `// Java implementation of the approach ` `import` `java.util.*; ` `class` `Node  ` `{ ` `    ``int` `data; ` `    ``Node next; ` `     `  `    ``// constructor ` `    ``Node(``int` `d) ` `    ``{ ` `        ``data = d; ` `        ``next = ``null``; ` `    ``} ` `}``// Node closes ` ` `  `class` `LinkedList ` `{ ` `    ``Node head; ` `     `  `    ``// Helper function to traverse ` `    ``void` `traverse(Node head)  ` `    ``{ ` `        ``while``(head != ``null``) ` `        ``{ ` `            ``System.out.print(head.data + ``"->"``); ` `            ``head = head.next; ` `        ``} ` `    ``} ` ` `  `    ``// Helper function to insert data in linked list ` `    ``void` `insert(``int` `x) ` `    ``{ ` `        ``Node temp = ``new` `Node(x); ` `        ``if``(head == ``null``) head = temp; ` `        ``else` `        ``{ ` `            ``temp.next = head; ` `            ``head = temp; ` `        ``} ` `    ``} ` ` `  `    ``// Helper function to reverse the list ` `    ``public` `static` `Node reverse(Node head) ` `    ``{ ` `        ``if``(head == ``null` `|| head.next == ``null``) ``return` `head; ` ` `  `        ``Node prev = ``null``; ` `        ``Node curr = head; ` `        ``while``(curr != ``null``) ` `        ``{ ` `            ``Node temp = curr.next; ` `            ``curr.next = prev; ` `            ``prev = curr; ` `            ``curr = temp; ` `        ``} ` `        ``head = prev; ` `        ``return` `head; ` `    ``} ` `     `  `    ``// Function to add two lists ` `    ``public` `static` `Node sum(Node l1, Node l2) ` `    ``{ ` `        ``if``(l2 == ``null``) ``return` `l1; ` `        ``if``(l1 == ``null``) ``return` `l2; ` ` `  `        ``// reverse l1 list ` `        ``l1 = reverse(l1); ` ` `  `        ``// reverse l2 list ` `        ``l2 = reverse(l2); ` ` `  `        ``// storing head whose reverse is to be returned ` `        ``// This is where which will be final node ` `        ``Node head = l1; ` `        ``Node prev = ``null``; ` `        ``int` `c = ``0``,sum; ` `        ``while``(l1 != ``null` `&& l2 != ``null``) ` `        ``{ ` `            ``sum = c + l1.data + l2.data; ` `            ``l1.data = sum % ``10``; ` `            ``c = sum / ``10``; ` `            ``prev = l1; ` `            ``l1 = l1.next; ` `            ``l2 = l2.next; ` `        ``} ` ` `  `        ``if``(l1 != ``null``||l2 != ``null``) ` `        ``{ ` `            ``if``(l2 != ``null``) prev.next = l2; ` `            ``l1 = prev.next; ` `            ``while``(l1 != ``null``) ` `            ``{ ` `                ``sum = c + l1.data; ` `                ``l1.data = sum % ``10``; ` `                ``c = sum / ``10``; ` `                ``prev = l1; ` `                ``l1 = l1.next; ` `            ``} ` `        ``} ` `        ``if``(c > ``0``) prev.next = ``new` `Node(c); ` `        ``return` `reverse(head); ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``LinkedList l1 = ``new` `LinkedList(); ` `        ``l1.insert(``3``); ` `        ``l1.insert(``6``); ` `        ``l1.insert(``5``); ` `        ``LinkedList l2 = ``new` `LinkedList(); ` `        ``l2.insert(``2``); ` `        ``l2.insert(``4``); ` `        ``l2.insert(``8``); ` `        ``LinkedList l3 = ``new` `LinkedList(); ` `        ``Node head = sum(l1.head, l2.head); ` `        ``l3.traverse(head); ` `        ``System.out.print(``"Null"``); ` `    ``} ` `} ` ` `  `// This code is contributed  ` `// by Devarshi Singh `

Python3

 `# Python3 implementation of the approach ` ` `  `# Linked List Node ` `class` `Node: ` `     `  `    ``def` `__init__(``self``, data): ` `         `  `        ``self``.data ``=` `data ` `        ``self``.``next` `=` `None` ` `  `# Handle list operations ` `class` `LinkedList: ` `     `  `    ``def` `__init__(``self``): ` `         `  `        ``self``.head ``=` `None` ` `  `    ``# Method to traverse list and ` `    ``# return it in a format ` `    ``def` `traverse(``self``): ` `         `  `        ``linkedListStr ``=` `"" ` `        ``temp ``=` `self``.head ` `         `  `        ``while` `temp: ` `            ``linkedListStr ``+``=` `str``(temp.data) ``+` `" -> "` `            ``temp ``=` `temp.``next` `             `  `        ``return` `linkedListStr ``+` `"NULL"` ` `  `    ``# Method to insert data in linked list ` `    ``def` `insert(``self``, data): ` `         `  `        ``newNode ``=` `Node(data) ` `         `  `        ``if` `self``.head ``is` `None``: ` `            ``self``.head ``=` `newNode ` `        ``else``: ` `            ``newNode.``next` `=` `self``.head ` `            ``self``.head ``=` `newNode ` ` `  `# Helper function to reverse the list ` `def` `reverse(Head): ` `     `  `    ``if` `(Head ``is` `None` `and`  `        ``Head.``next` `is` `None``): ` `        ``return` `Head ` `         `  `    ``prev ``=` `None` `    ``curr ``=` `Head ` `     `  `    ``while` `curr: ` `        ``temp ``=` `curr.``next` `        ``curr.``next` `=` `prev ` `        ``prev ``=` `curr ` `        ``curr ``=` `temp ` `         `  `    ``Head ``=` `prev ` `    ``return` `Head ` ` `  `# Function to add two lists ` `def` `listSum(l1, l2): ` ` `  `    ``if` `l1 ``is` `None``: ` `        ``return` `l1 ` `    ``if` `l2 ``is` `None``: ` `        ``return` `l2 ` ` `  `    ``# Reverse first list ` `    ``l1 ``=` `reverse(l1) ` ` `  `    ``# Reverse second list ` `    ``l2 ``=` `reverse(l2) ` ` `  `    ``# Storing head whose reverse  ` `    ``# is to be returned This is  ` `    ``# where which will be final node ` `    ``head ``=` `l1 ` `    ``prev ``=` `None` `    ``c ``=` `0` `    ``sum` `=` `0` `     `  `    ``while` `l1 ``is` `not` `None` `and` `l2 ``is` `not` `None``: ` `        ``sum` `=` `c ``+` `l1.data ``+` `l2.data ` `        ``l1.data ``=` `sum` `%` `10` `        ``c ``=` `int``(``sum` `/` `10``) ` `        ``prev ``=` `l1 ` `        ``l1 ``=` `l1.``next` `        ``l2 ``=` `l2.``next` `         `  `    ``if` `l1 ``is` `not` `None` `or` `l2 ``is` `not` `None``: ` `        ``if` `l2 ``is` `not` `None``: ` `            ``prev.``next` `=` `l2 ` `        ``l1 ``=` `prev.``next` `         `  `        ``while` `l1 ``is` `not` `None``: ` `            ``sum` `=` `c ``+` `l1.data ` `            ``l1.data ``=` `sum` `%` `10` `            ``c ``=` `int``(``sum` `/` `10``) ` `            ``prev ``=` `l1 ` `            ``l1 ``=` `l1.``next` `             `  `    ``if` `c > ``0``: ` `        ``prev.``next` `=` `Node(c) ` `         `  `    ``return` `reverse(head) ` `     `  `# Driver code ` `linkedList1 ``=` `LinkedList() ` `linkedList1.insert(``3``) ` `linkedList1.insert(``6``) ` `linkedList1.insert(``5``) ` ` `  `linkedList2 ``=` `LinkedList() ` `linkedList2.insert(``2``) ` `linkedList2.insert(``4``) ` `linkedList2.insert(``8``) ` ` `  `linkedList3 ``=` `LinkedList() ` `linkedList3.head ``=` `listSum(linkedList1.head, ` `                           ``linkedList2.head) ` `                            `  `print``(linkedList3.traverse()) ` ` `  `# This code is contributed by Debidutta Rath `

C#

 `// C# implementation of the above approach ` `using` `System; ` `     `  `public` `class` `Node  ` `{ ` `    ``public` `int` `data; ` `    ``public` `Node next; ` `     `  `    ``// constructor ` `    ``public` `Node(``int` `d) ` `    ``{ ` `        ``data = d; ` `        ``next = ``null``; ` `    ``} ` `} ` ` `  `// Node closes ` `public` `class` `LinkedList ` `{ ` `    ``Node head; ` `     `  `    ``// Helper function to traverse ` `    ``void` `traverse(Node head)  ` `    ``{ ` `        ``while``(head != ``null``) ` `        ``{ ` `            ``Console.Write(head.data + ``"->"``); ` `            ``head = head.next; ` `        ``} ` `    ``} ` ` `  `    ``// Helper function to insert data in linked list ` `    ``void` `insert(``int` `x) ` `    ``{ ` `        ``Node temp = ``new` `Node(x); ` `        ``if``(head == ``null``) head = temp; ` `        ``else` `        ``{ ` `            ``temp.next = head; ` `            ``head = temp; ` `        ``} ` `    ``} ` ` `  `    ``// Helper function to reverse the list ` `    ``public` `static` `Node reverse(Node head) ` `    ``{ ` `        ``if``(head == ``null` `||  ` `           ``head.next == ``null``) ``return` `head; ` ` `  `        ``Node prev = ``null``; ` `        ``Node curr = head; ` `        ``while``(curr != ``null``) ` `        ``{ ` `            ``Node temp = curr.next; ` `            ``curr.next = prev; ` `            ``prev = curr; ` `            ``curr = temp; ` `        ``} ` `        ``head = prev; ` `        ``return` `head; ` `    ``} ` `     `  `    ``// Function to add two lists ` `    ``public` `static` `Node sum(Node l1, Node l2) ` `    ``{ ` `        ``if``(l2 == ``null``) ``return` `l1; ` `        ``if``(l1 == ``null``) ``return` `l2; ` ` `  `        ``// reverse l1 list ` `        ``l1 = reverse(l1); ` ` `  `        ``// reverse l2 list ` `        ``l2 = reverse(l2); ` ` `  `        ``// storing head whose reverse is  ` `        ``// to be returned. This is where  ` `        ``// which will be final node ` `        ``Node head = l1; ` `        ``Node prev = ``null``; ` `        ``int` `c = 0,sum; ` `        ``while``(l1 != ``null` `&& l2 != ``null``) ` `        ``{ ` `            ``sum = c + l1.data + l2.data; ` `            ``l1.data = sum % 10; ` `            ``c = sum / 10; ` `            ``prev = l1; ` `            ``l1 = l1.next; ` `            ``l2 = l2.next; ` `        ``} ` ` `  `        ``if``(l1 != ``null``||l2 != ``null``) ` `        ``{ ` `            ``if``(l2 != ``null``) prev.next = l2; ` `            ``l1 = prev.next; ` `            ``while``(l1 != ``null``) ` `            ``{ ` `                ``sum = c + l1.data; ` `                ``l1.data = sum % 10; ` `                ``c = sum / 10; ` `                ``prev = l1; ` `                ``l1 = l1.next; ` `            ``} ` `        ``} ` `        ``if``(c > 0) prev.next = ``new` `Node(c); ` `        ``return` `reverse(head); ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `Main(String[] args) ` `    ``{ ` `        ``LinkedList l1 = ``new` `LinkedList(); ` `        ``l1.insert(3); ` `        ``l1.insert(6); ` `        ``l1.insert(5); ` `        ``LinkedList l2 = ``new` `LinkedList(); ` `        ``l2.insert(2); ` `        ``l2.insert(4); ` `        ``l2.insert(8); ` `        ``LinkedList l3 = ``new` `LinkedList(); ` `        ``Node head = sum(l1.head, l2.head); ` `        ``l3.traverse(head); ` `        ``Console.Write(``"Null"``); ` `    ``} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```1 -> 4 -> 0 -> 5 -> NULL
```

Time Complexity: O(max(m, n)) where m and n are number of nodes in list l1 and list l2 respectively.
Space Complexity: O(1)

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