Looks simple until you realize you can't just convert to int and call it a day.
Clarify that the problem is essentially string-based addition, similar to manual addition, and that you'll simulate the process digit by digit from right to left while handling carries. Then outline an algorithm that iterates through both strings, computes the sum and carry at each position, and builds the result string, ensuring to handle edge cases like different lengths and leading zeros.
Pro tip: Mention that you can optimize space by using a StringBuilder and appending digits, then reversing at the end, and that you should discuss potential follow-ups like handling negative numbers or decimal points to show depth.
Ask if the numbers are non-negative, if they can have leading zeros, and if the result should also be a string without leading zeros. Confirm that the numbers are too large for standard integer types.
Explain that you'll process digits from least significant to most significant, maintaining a carry. At each step, sum the digits (or 0 if one string is exhausted) plus the carry, then append the result digit to a StringBuilder.
Use two pointers starting at the end of each string and decrement them until both are exhausted. After the loop, if there's a remaining carry, append it to the result.
Since digits are appended in reverse order, reverse the StringBuilder to get the final sum. Optionally, strip any leading zeros (though the algorithm naturally avoids them except for the case of '0').
State that time complexity is O(max(n, m)) and space complexity is O(max(n, m)) for the result. Discuss edge cases: one string empty, both empty, carry propagation, and very long strings.
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