Recurring Decimal Without Division | Dataford Interview Questions

Cruise autonomy software may need exact decimal formatting for diagnostic values without relying on floating-point arithmetic. Given a fraction, determine whether its decimal expansion terminates or repeats, and return the exact representation.

You must not use division or multiplication operators anywhere in your algorithm. Bit shifts, addition, subtraction, comparisons, dictionaries, and string operations are allowed.

Formal Specification

Implement fraction_to_decimal(numerator, denominator).

numerator is an integer.
denominator is a nonzero integer.
Return a string containing the decimal representation.
Enclose the repeating sequence in parentheses.
Return terminating decimals without parentheses.
Preserve a leading negative sign when exactly one input is negative.
Do not include unnecessary trailing zeros.

Constraints

-10^9 <= numerator <= 10^9
-10^9 <= denominator <= 10^9
denominator != 0
Do not use division or multiplication operators
The result must use parentheses only around the repeating fractional sequence

Function Signature

def fraction_to_decimal(numerator, denominator):

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