Given two strings S and T, each of which represents a non-negative rational number, return True if and only if they represent the same number. The strings may use parentheses to denote the repeating part of the rational number.
In general a rational number can be represented using up to three parts: an integer part, a non-repeating part, and a repeating part. The number will be represented in one of the following three ways:

<IntegerPart> (e.g. 0, 12, 123)
<IntegerPart><.><NonRepeatingPart>  (e.g. 0.5, 1., 2.12, 2.0001)
<IntegerPart><.><NonRepeatingPart><(><RepeatingPart><)> (e.g. 0.1(6), 0.9(9), 0.00(1212))

The repeating portion of a decimal expansion is conventionally denoted within a pair of round brackets.  For example:
1 / 6 = 0.16666666... = 0.1(6) = 0.1666(6) = 0.166(66)
Both 0.1(6) or 0.1666(6) or 0.166(66) are correct representations of 1 / 6.
 
Example 1:
Input: S = "0.(52)", T = "0.5(25)"
Output: true
Explanation:
Because "0.(52)" represents 0.52525252..., and "0.5(25)" represents 0.52525252525..... , the strings represent the same number.


Example 2:
Input: S = "0.1666(6)", T = "0.166(66)"
Output: true


Example 3:
Input: S = "0.9(9)", T = "1."
Output: true
Explanation: 
"0.9(9)" represents 0.999999999... repeated forever, which equals 1.  [See this link for an explanation.]
"1." represents the number 1, which is formed correctly: (IntegerPart) = "1" and (NonRepeatingPart) = "".
 


Note:

Each part consists only of digits.
The <IntegerPart> will not begin with 2 or more zeros.  (There is no other restriction on the digits of each part.)
1 <= <IntegerPart>.length <= 4 
0 <= <NonRepeatingPart>.length <= 4 
1 <= <RepeatingPart>.length <= 4

Source: leetcode | Difficulty: MEDIUM_HARD
Tags: String algorithms

Mathematics

Starter code: class Solution:
    def isRationalEqual(self, S: str, T: str) -> bool:
        

Solutions:
import math

class Solution:

	def isRationalEqual(self, S: str, T: str) -> bool:
		if len(S) == 0 or len(T) == 0:
			return False

		def process(s):
			if s[-1] == '.':
				s = s[:-1]
			(stack, repeat_9) = ([], False)
			for (i, x) in enumerate(s):
				if x != ')':
					stack.append(x)
				else:
					tmp = ''
					while stack[-1] != '(':
						tmp += stack.pop()
					if len(tmp) == tmp.count('9'):
						repeat_9 = True
					stack.pop()
					return (''.join(stack) + tmp[::-1] * (24 // len(tmp)), repeat_9)
			return (''.join(stack), repeat_9)
		(x, y) = (process(S), process(T))
		if x[0].count('.') == 0 or y[0].count('.') == 0:
			return float(x[0]) == float(y[0])
		l = max(len(x[0]), len(y[0]))
		if x[0][:17] == y[0][:17]:
			return True
		if x[1] or y[1]:
			m = min(len(x[0].split('.')[1]), len(y[0].split('.')[1]))
			if round(float(x[0]), m) == round(float(y[0]), m):
				return True
		return False