Add Two Strings with a Single-Digit Adder

Given only a helper that can add two single digits, implement addition for two non-negative integer strings. The live round expects careful carry handling and time/space complexity explanation. Requirements You are given a function that can add two single digits. Use it to implement addition for two number strings. Expected behavior: Inputs are strings representing non-negative integers. Add from right to left. Maintain carry. Return the sum as a string. Explain time and space complexity. Notes This is a straightforward implementation round, but it appears inside a broader QR / statistics interview day, so do not ignore coding basics. Clarify whether inputs may contain leading zeros, signs, decimals, or invalid characters. The natural baseline assumes non-negative integer strings. Time is O(max(m, n)); output space is O(max(m, n)). Preparation Write the reverse-iteration implementation without converting the full strings to integers. Test 0 + 0, different lengths, final carry, leading zeros, and very long inputs. Practice giving the complexity answer while coding, since candidates were explicitly asked to explain it.