The Question
Coding

Add Two Numbers Represented by Linked Lists

You are given two non-empty linked lists representing two non-negative integers. The digits are stored in reverse order, such that the head of the list contains the least significant digit. Each node contains exactly one digit. Add the two numbers and return the sum as a new linked list. 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, except for the number 0 itself.
Java
Singly Linked List
Iterative Algorithm
Questions & Insights

Clarifying Questions

What is the maximum length of the linked lists? (Assumption: Up to 100 nodes, meaning the numbers can be much larger than what long or BigInteger should handle, necessitating a digit-by-digit approach).
Are negative numbers possible? (Assumption: No, the problem specifies non-negative integers).
Can the input lists have leading zeros? (Assumption: No, except for the number 0 itself represented as [0]).
Should we modify the original lists or return a new list? (Assumption: Return a new list to maintain the integrity of the input data).

Thinking Process

Simultaneous Traversal: Since the lists are stored in reverse order, the heads represent the least significant digits. We can iterate through both lists in a single pass, adding corresponding digits along with a carry from the previous position.
Carry Management: At each step, calculate the sum of the current nodes and the carry. The digit to store in the new node is sum % 10, and the carry for the next step is sum / 10.
Handling Unequal Lengths: If one list is shorter than the other, we treat the missing digits as 0. We must continue the process as long as either list has nodes remaining OR there is a non-zero carry left to append.
Dummy Head Pattern: Use a "dummy" node to represent the start of the result list. This simplifies the logic by avoiding null checks when appending the very first digit.
Implementation Breakdown

Problem Set

Functional Requirements:
Input: Two ListNode objects (heads of the lists).
Output: A ListNode representing the sum.
Constraints:
Number of nodes in each list is in the range [1, 100].
Node.val is in the range [0, 9].
The number does not contain any leading zeros, except the number 0 itself.

Approach

Algorithm: Iterative Linear Traversal.
Data Structure: Singly Linked List.
Complexity:
Time: O(\max(N, M)), where N and M are lengths of the two lists.
Space: O(\max(N, M)), as we create a new list to store the sum.

Implementation

Wrap Up

Advanced Topics

BigInteger Approach: If the lists were relatively short, one could convert them to integers, add them, and convert back. However, for lists with 100+ digits, the digit-by-digit approach is more efficient and avoids overflow issues.
In-place Addition: To optimize space complexity to O(1) (excluding the output), we could overwrite one of the input lists. However, this is generally discouraged in API design unless space is extremely constrained, as it destroys the input data.
Recursive Implementation: This problem can be solved recursively, which is elegant but risks a StackOverflowError if the linked lists are extremely deep (though 100 nodes is perfectly safe).
Follow-up: Digits in Forward Order: If the digits were in forward order, we would either need to reverse the lists first, or use a Stack/Recursion to process digits from right to left while building the result.