《数据结构与算法Python语言描述》习题第二章第三题（python版）

ADT Rational: #定义有理数的抽象数据类型
    Rational(self, int num, int den)    #构造有理数num/den
    +(self, Rational r2)                #求出本对象加r2的结果
    -(self, Rational r2)                #求出本对象减r2的结果
    *(self, Rational r2)                #求出本对象乘以r2的结果
    /(self, Rational r2)                #求出本对象除以r2的结果
    num(self)                           #取出本对象的分子
    den(self)                           #取出本对象的分母
    int(self)                           #取整
    float(self)                         #取浮点数
    ==(self,Rational r2)
    !=(self,Rational r2)
    >(self,Rational r2)
    <(self,Rational r2)
    >=(self,Rational r2)
    >=(self,Rational r2)

 #!/usr/bib/env python
 # -*- coding:utf-8 -*-

 """
 ADT Rational:                           #定义有理数的抽象数据类型
     Rational(self, int num, int den)    #构造有理数num/den
     +(self, Rational r2)                #求出本对象加r2的结果
     -(self, Rational r2)                #求出本对象减r2的结果
     *(self, Rational r2)                #求出本对象乘以r2的结果
     /(self, Rational r2)                #求出本对象除以r2的结果
     num(self)                           #取出本对象的分子
     den(self)                           #取出本对象的分母
     int(self)                           #取整
     float(self)                         #取浮点数
     ==(self,Rational r2)
     !=(self,Rational r2)
     >(self,Rational r2)
     <(self,Rational r2)
     >=(self,Rational r2)
     >=(self,Rational r2)
 """

 class Rational(object):
     __slots__ = ('_num', '_den')

     @staticmethod
     def _gcd(m,n):
         while 1:
             temp = n % m
             if temp == 0:
                 return m
             else:
                 n = m
                 m = temp

     def __init__(self, num, den=1):
         if not isinstance(num, int) or not isinstance(num, int):
             raise   TypeError
         if den == 0:
             raise ZeroDivisionError
         sign = 1
         if num < 0:
             num, sign = -num, -sign
         if den < 0:
             den, sign = -den, -sign
         g = Rational._gcd(num, den)
         self._num = sign*(num//g)
         self._den = den//g

         #float
         x = self._num / self._den
         self._num = x.as_integer_ratio()[0]
         self._den = x.as_integer_ratio()[1]

     def __add__(self, other):
         den = self._den * other._den
         num = self._den * other._num + self._num * other._den
         return Rational(num, den)

     def __sub__(self, other):
         den = self._den * other._den
         num = self._num * other._den - self._den * other._num
         return Rational(num, den)

     def __mul__(self, other):
         den = self._den * other._den
         num = self._num * other._num
         return Rational(num, den)

     def __floordiv__(self, other):
         den = self._den * other._num
         num = self._num * other._den
         return Rational(num, den)

     def __int__(self):
         return self._num // self._den

     def __float__(self):
         return self._num / self._den

     def __eq__(self, other):
         return self._num * other._den == self._den * other._num

     def __ne__(self, other):
         return self._num * other._den != self._den * other._num

     def __lt__(self, other):
         return self._num * other._den < self._den * other._num

     def __le__(self, other):
         return self._num * other._den <= self._den * other._num

     def __gt__(self, other):
         return self._num * other._den > self._den * other._num

     def __ge__(self, other):
         return self._num * other._den >= self._den * other._num

     def __str__(self):
         return str(self._num) + "/" + str(self._den)

     def print(self):
         print(self._num, "/", self._den)

     def num(self):
         return self._num
     def den(self):
         return self._den

 if __name__ == '__main__':
     a = Rational(10,5)
     b = Rational(1,1000000)
     print(a)
     print(b)
     print("==")
     print(a+b)
     print(a!=b)
     print(int(a))
     print(int(b))