Do Repeating Decimals Match

Hard

You get two strings first and second, each the notation of a non-negative rational number. Return True if they denote the same number and False otherwise. A notation takes one of three forms: - an integer part only: 7, 0, 250; - an integer part, a dot and an optional finite fractional part: 0.25, 3., 12.0408; - the same followed by a period in parentheses that repeats forever: 0.(6), 1.2(45), 5.(9). For instance, 0.1(6), 0.16(6) and 0.1(66) all mean 0.1666… = 1/6.

Example 1

first="0.(36)", second="0.3(63)" → True

Both stand for 0.363636…

Example 2

first="2.4(9)", second="2.5" → True

2.4999… with nines forever is exactly 2.5.

Example 3

first="0.(3)", second="0.33" → False

0.333… is 1/3, while 0.33 is a little less.

Constraints

Every part consists of digits
The integer part has 1 to 4 digits and no leading zeros (except the number 0 itself)
The fractional part before the parentheses has 0 to 4 digits
The period has 1 to 4 digits

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Topics

Math String

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Input

first="0.(36)", second="0.3(63)"

Expected

True

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