1216.md

题目：有理数。为有理数实现一个不可变数据类型 Rational，支持加减乘除操作。

解答： 分数的加减乘除操作，结合欧几里得消除公约数。在 初始化方法中，再加入对数字溢出的判断更合理，也即1.2.17题目。

class Rational:
    def __init__(self, numerator:int, denominator:int):
        super().__init__()
        if denominator == 0:
            raise ValueError('denominator can not be zero')
            
        gcd = self._gcd(numerator, denominator)
        self.numerator = numerator//gcd
        self.denominator = denominator//gcd
    
    def plus(self, b):
        return Rational(self.numerator*b.denominator+b.numerator*self.denominator, self.denominator*b.denominator)
    
    def minus(self, b):
        return Rational(self.numerator*b.denominator-b.numerator*self.denominator, self.denominator*b.denominator)
    
    def times(self, b):
        return Rational(self.numerator*b.numerator, self.denominator*b.denominator)
    
    def divides(self, b):
        # a1/b1 / a2/b2 = a1/b1 * b2/a2
        return Rational(self.numerator*b.denominator, self.denominator*b.numerator)
    
    def equals(self, b):
        return self.numerator == b.numerator and self.denominator == b.denominator
    
    def _gcd(self,p, q):
        if q == 0:
            return p
        r = p % q
        return self._gcd(q, r)