Add two integer strings using digit-adder

Q: Add two integer strings using digit-adder

This question evaluates proficiency in string-based arithmetic, digit-wise addition, carry propagation, and management of arbitrarily large non-negative integers without converting entire strings to native numeric types.

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Question

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Coding Prompt

You are given a helper function:

addDigits(a, b) -> (sumDigit, carry)
- a and b are single decimal digits (characters '0' … '9' or integers 0…9).
- It returns the ones digit of a + b and the carry (0 or 1).
- Example: addDigits(7, 8) -> (5, 1) .

Task

Implement addStrings(num1, num2) -> string that returns the decimal string representing num1 + num2.

Requirements

num1 and num2 are non-negative integers represented as strings (no leading + / - ).
You may not convert the entire strings to built-in integer types (assume very long inputs).
You may only use the provided addDigits helper for digit-wise addition.

Examples

addStrings("11", "123") = "134"
addStrings("999", "1") = "1000"
addStrings("0", "0") = "0"

Constraints

Length of each string can be up to at least $10^5$ characters.
Time should be linear in the total number of digits.