What is the optimal time complexity of solving Add Two Numbers?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Add Two Numbers?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Add Two Numbers?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Add Two Numbers?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Add Two Numbers

Learn how to solve the 'Add Two Numbers' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

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.

The linked lists are represented as Python lists. Implement a function addTwoNumbers(l1: list, l2: list) -> list that returns the sum as a list in reverse digit order.

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

Examples

Example 1

Input

[2,4,3], [5,6,4]

Output

[7,0,8]

Explanation

342 + 465 = 807. Represented in reverse: [7,0,8].

Example 2

Input

[0], [0]

Output

[0]

Explanation

0 + 0 = 0.

Example 3

Input

[9,9,9,9,9,9,9], [9,9,9,9]

Output

[8,9,9,9,0,0,0,1]

Explanation

9999999 + 9999 = 10009998. Represented in reverse: [8,9,9,9,0,0,0,1].

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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