Add Two Numbers

Problem Statement

You are given two non-empty linked lists representing two non-negative integers. The digits are stored in reverse order, and each of their nodes contains a single digit. Add the two numbers and return the sum as a linked list.

You may assume the two numbers do not contain any leading zero, except the number 0 itself.

Examples

Example 1:

Input: l1 = [2,4,3], l2 = [5,6,4]
Output: [7,0,8]
Explanation: 342 + 465 = 807.

Example 2:

Input: l1 = [0], l2 = [0]
Output: [0]

Example 3:

Input: l1 = [9,9,9,9,9,9,9], l2 = [9,9,9,9]
Output: [8,9,9,9,0,0,0,1]

Constraints

• The number of nodes in each linked list is in the range [1, 100].
• 0 <= Node.val <= 9
• It is guaranteed that the list represents a number that does not have leading zeros.

Solution Approach

Understanding the Problem

The key insight is that the digits are stored in reverse order:

• [2,4,3] represents 342 (2 + 40 + 300)
• [5,6,4] represents 465 (5 + 60 + 400)
• The result [7,0,8] represents 807

Algorithm

1. Initialize a dummy head node and a carry variable
2. Traverse both lists simultaneously
3. At each position:
   • Add values from both lists (0 if one list is shorter)
   • Add the carry from the previous addition
   • Create a new node with the digit (sum % 10)
   • Update carry for the next iteration (sum / 10)
4. Continue until both lists are exhausted and carry is 0
5. Return the list starting from dummy.next

Edge Cases to Consider

1. Different lengths: One list may be longer than the other
2. Carry at the end: Final carry may create an additional digit
3. Single digit: Lists with only one node
4. Large numbers: Multiple carries in sequence