Add Two Large Numbers Represented as Strings

Problem Statement

Given two non-negative integers represented as strings, return their sum, also as a string.

You must not use any BigInteger library or convert the entire input to an integer directly (the numbers can be arbitrarily large — beyond 64-bit range).

Constraints

• 1 <= num1.length, num2.length <= 10^4
• Both strings contain only digits 0-9
• No leading zeros (except the number "0" itself)
• Cannot use built-in big-number libraries

Example

Input: num1 = "9999999999999999999", num2 = "1"

Output: "10000000000000000000"

Input: num1 = "456", num2 = "77"

Output: "533"

What the Interviewer Expects

1. Simulate grade-school addition — process digits from right to left.
2. Track carry — sum each pair of digits + carry, append sum % 10, carry sum / 10.
3. Handle different lengths — use pointers and treat missing digits as 0.
4. Final carry — don't forget to append a leading 1 if carry remains.
5. Build result efficiently — append to a list/StringBuilder and reverse at the end (avoid O(n²) string concatenation).

Follow-ups

1. How would you extend this to multiply two large numbers as strings?
2. How would you handle subtraction (including negative results)?
3. What if the numbers are in a base other than 10 (e.g., hexadecimal)?
4. How would you handle decimal points (floating-point strings)?