《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)

  1 #!/usr/bib/env python
  2 # -*- coding:utf-8 -*-
  3
  4 """
  5 ADT Rational:                           #定义有理数的抽象数据类型
  6     Rational(self, int num, int den)    #构造有理数num/den
  7     +(self, Rational r2)                #求出本对象加r2的结果
  8     -(self, Rational r2)                #求出本对象减r2的结果
  9     *(self, Rational r2)                #求出本对象乘以r2的结果
 10     /(self, Rational r2)                #求出本对象除以r2的结果
 11     num(self)                           #取出本对象的分子
 12     den(self)                           #取出本对象的分母
 13     int(self)                           #取整
 14     float(self)                         #取浮点数
 15     ==(self,Rational r2)
 16     !=(self,Rational r2)
 17     >(self,Rational r2)
 18     <(self,Rational r2)
 19     >=(self,Rational r2)
 20     >=(self,Rational r2)
 21 """
 22
 23 class Rational(object):
 24     __slots__ = (‘_num‘, ‘_den‘)
 25
 26     @staticmethod
 27     def _gcd(m,n):
 28         while 1:
 29             temp = n % m
 30             if temp == 0:
 31                 return m
 32             else:
 33                 n = m
 34                 m = temp
 35
 36     def __init__(self, num, den=1):
 37         if not isinstance(num, int) or not isinstance(num, int):
 38             raise   TypeError
 39         if den == 0:
 40             raise ZeroDivisionError
 41         sign = 1
 42         if num < 0:
 43             num, sign = -num, -sign
 44         if den < 0:
 45             den, sign = -den, -sign
 46         g = Rational._gcd(num, den)
 47         self._num = sign*(num//g)
 48         self._den = den//g
 49
 50         #float
 51         x = self._num / self._den
 52         self._num = x.as_integer_ratio()[0]
 53         self._den = x.as_integer_ratio()[1]
 54
 55     def __add__(self, other):
 56         den = self._den * other._den
 57         num = self._den * other._num + self._num * other._den
 58         return Rational(num, den)
 59
 60     def __sub__(self, other):
 61         den = self._den * other._den
 62         num = self._num * other._den - self._den * other._num
 63         return Rational(num, den)
 64
 65     def __mul__(self, other):
 66         den = self._den * other._den
 67         num = self._num * other._num
 68         return Rational(num, den)
 69
 70     def __floordiv__(self, other):
 71         den = self._den * other._num
 72         num = self._num * other._den
 73         return Rational(num, den)
 74
 75     def __int__(self):
 76         return self._num // self._den
 77
 78     def __float__(self):
 79         return self._num / self._den
 80
 81     def __eq__(self, other):
 82         return self._num * other._den == self._den * other._num
 83
 84     def __ne__(self, other):
 85         return self._num * other._den != self._den * other._num
 86
 87     def __lt__(self, other):
 88         return self._num * other._den < self._den * other._num
 89
 90     def __le__(self, other):
 91         return self._num * other._den <= self._den * other._num
 92
 93     def __gt__(self, other):
 94         return self._num * other._den > self._den * other._num
 95
 96     def __ge__(self, other):
 97         return self._num * other._den >= self._den * other._num
 98
 99
100     def __str__(self):
101         return str(self._num) + "/" + str(self._den)
102
103     def print(self):
104         print(self._num, "/", self._den)
105
106     def num(self):
107         return self._num
108     def den(self):
109         return self._den
110
111 if __name__ == ‘__main__‘:
112     a = Rational(10,5)
113     b = Rational(1,1000000)
114     print(a)
115     print(b)
116     print("==")
117     print(a+b)
118     print(a!=b)
119     print(int(a))
120     print(int(b))