2. Add Two Numbers

Problem Description

You are given two non-empty linked lists representing two non-negative integers. The digits are stored in reverse order, and each node 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.

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

Solution Approach

We can solve this problem by simulating the addition process digit by digit:

1. Initialize a dummy head node to simplify the edge cases
2. Maintain a current pointer and a carry value
3. Iterate through both lists simultaneously:
• Get values from current nodes or 0 if a list ends
• Calculate sum: v1 + v2 + carry
• Update carry and the digit for the current node
• Move to the next nodes in both lists
4. After iteration, if there's a remaining carry, add one more node
5. Return the linked list starting from dummy.next

Python Implementation:

class ListNode:
    def __init__(self, val=0, next=None):
        self.val = val
        self.next = next

class Solution:
    def addTwoNumbers(self, l1: ListNode, l2: ListNode) -> ListNode:
        dummy = ListNode(0)
        cur, carry = dummy, 0
        
        while l1 or l2 or carry:
            v1 = l1.val if l1 else 0
            v2 = l2.val if l2 else 0
            
            # Calculate new digit and carry
            carry, out = divmod(v1 + v2 + carry, 10)
            
            # Create new node with the calculated digit
            cur.next = ListNode(out)
            cur = cur.next
            
            # Move to next nodes
            l1 = l1.next if l1 else None
            l2 = l2.next if l2 else None
            
        return dummy.next