LeetCode 2: Add Two Numbers — Python Solution

Solve LeetCode 2: Add Two Numbers in Python with a digitwise carry approach. The key is to make the state invariant explicit, so the implementation and complexity follow naturally.

This guide paraphrases the task and does not reproduce LeetCode’s prompt. Use the official page for the complete statement, examples, constraints, and submission runner.

What the problem is testing

Walk both reverse-order digit lists, add available digits plus carry, and append the ones digit while carrying the tens digit.

Algorithm

1. Walk both reverse-order digit lists, add available digits plus carry, and append the ones digit while carrying the tens digit.
2. Maintain this invariant: The output prefix represents the exact sum of the processed digit positions.
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

LeetCode provides the list, tree, or graph node definition used by the method.

from collections import Counter, defaultdict, deque, OrderedDict
import random

class Solution:
    def addTwoNumbers(self, l1, l2):
        dummy = tail = ListNode()
        carry = 0
        while l1 or l2 or carry:
            total = carry
            if l1: total += l1.val; l1 = l1.next
            if l2: total += l2.val; l2 = l2.next
            carry, digit = divmod(total, 10)
            tail.next = ListNode(digit)
            tail = tail.next
        return dummy.next

Why this is correct

The proof follows the maintained state: The output prefix represents the exact sum of the processed digit positions. Each iteration preserves that claim while permanently resolving at least one position, node, interval, or search state. When the loop or recursion ends, every candidate required by the problem has therefore been included or ruled out, so the returned value is correct.

Complexity

O(max(m,n)) time and O(max(m,n)) output space. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

A final carry creates a new node; lists can have different lengths.

Tested reference code

This implementation is included in the site’s downloadable 100-solution Python library. The complete suite compiles every solution and runs a behavioral assertion for every problem before publication.

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