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1012. Equal Rational Numbers

My accepted Python solution to LeetCode problem 1012, Equal Rational Numbers, running in 0ms.

  • Difficulty: Hard
  • Python
  • Runtime 0ms
  • Memory 17.4MB

Read the problem on LeetCode View on GitHub

The problem statement is LeetCode’s and stays on their site. What follows is my accepted solution.

Python

Accepted on LeetCode — runtime 0ms, memory 17.4MB, accepted 2026-01-01.

python
class Solution:
    def isRationalEqual(self, s: str, t: str) -> bool:
        from fractions import Fraction
        
        def parse(s):
            if '(' not in s:
                return Fraction(s).limit_denominator()
            
            # Split into integer.non_repeating(repeating)
            idx_paren = s.index('(')
            idx_dot = s.index('.') if '.' in s else len(s)
            
            integer = s[:idx_dot]
            non_repeat = s[idx_dot+1:idx_paren]
            repeat = s[idx_paren+1:-1]
            
            # Convert to fraction
            # x = integer.non_repeat + 0.000...repeat_repeat_repeat...
            # Let y = 0.non_repeat_repeat_repeat_repeat...
            # y * 10^len(non_repeat) = non_repeat.repeat_repeat_repeat...
            # y * 10^len(non_repeat) * 10^len(repeat) = non_repeat_repeat.repeat_repeat...
            # y * 10^(a+b) - y * 10^a = non_repeat_repeat - non_repeat (where a=len(non_repeat), b=len(repeat))
            
            a, b = len(non_repeat), len(repeat)
            
            if b == 0:
                return Fraction(s[:idx_paren]).limit_denominator()
            
            # (10^(a+b) - 10^a) * y = int(non_repeat + repeat) - int(non_repeat or 0)
            nr = int(non_repeat) if non_repeat else 0
            nrr = int(non_repeat + repeat) if non_repeat else int(repeat)
            
            numerator = nrr - nr
            denominator = (10 ** (a + b)) - (10 ** a)
            
            return Fraction(int(integer), 1) + Fraction(numerator, denominator)
        
        return abs(float(parse(s)) - float(parse(t))) < 1e-9

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