Implement round() From String + Round-to-Precision

Two-part string-arithmetic problem: (1) reimplement Python's `round()` on a string input — no float conversion — with all the edge cases that exposes; (2) round a numeric string `s` to a precision specified by another string `p` (e.g. `p='100'` rounds to the hundreds, `p='0.1'` rounds to one decimal). Requirements Part 1. Implement round(s: str) -> str from scratch. Input is a decimal-number string. Round to the nearest integer using banker's rounding (round-half-to-even) or standard half-up — clarify with the interviewer which. Part 2. Implement roundTo(s: str, p: str) -> str where p describes the precision as a power-of-ten string: s='12567', p='100' → '12600' s='1234.678', p='0.1' → '1234.7' No floating-point conversion — strings only. Examples round("2.5") → "2" or "3" (depending on rounding mode) round("-.2") → "0" round("2.") → "2" round("1e300") → defined? (clarify overflow behavior) roundTo("12567", "100") → "12600" roundTo("1234.678", "0.1") → "1234.7" Notes The interviewer will hammer on edge cases — clarify them upfront before writing code: leading -, leading +, leading . with no whole part ('-.2'), trailing . with no fractional part ('2.'), scientific notation ('1e3'), float-overflow strings ('1e300'), and the empty string. For Part 1, parse the input into (sign, integer-part-digits, fractional-part-digits). To round to the nearest integer, inspect the first fractional digit: if < 5 truncate; if > 5 increment the integer-part-digits (with carry propagation); if == 5, look at downstream fractional digits and apply your chosen tie-break rule. Carry propagation across digit boundaries is the most-bugged part: rounding '999.5' up should yield '1000', not '9910'. Practice the carry loop on '999', '9999', and '9'. This also surfaces in the SWE onsite loop, framed as "round the last digit of a non-negative decimal/integer" with heavy case-splitting — same carry-and-edge-case core, no negative sign there. For Part 2, normalize p to a precision integer = ±exponent of 10 (e.g. '100' → +2, '0.1' → −1). Then shift the decimal point in s by that exponent, round to integer using Part 1, and shift back. Preparation Spend the first 5 minutes enumerating edge cases out loud; this is graded as part of the signal. Implement digit-string addition with carry once before this round — it is the workhorse for every increment-after-rounding operation. Practice on the example inputs above plus three of your own (negative numbers, very long fractional parts, rounding precision larger than the input).