53-C++ CH08 01

http://lx.lanqiao.cn/problem.page?gpid=T407

算法训练 C++ CH08 01  

时间限制：1.0s   内存限制：256.0MB

问题描述

已知一个有理数类Zrf_Ratio，实现如下的操作符重载形式：
　　friend std::ostream& operator<<(std::ostream&, const zrf_Ratio&);//输出最简分数
　　friend std::istream& operator>>(std::istream&, zrf_Ratio&);
　　friend bool operator==(const zrf_Ratio&, const zrf_Ratio&);
　　friend bool operator<(const zrf_Ratio&, const zrf_Ratio&);

测试

测试时主程序会输入四个整数a, b, c, d，表示两个分数a/b和c/d。要求输出最简分数以及两个分数相等和大小的比较结果。

样例输入

1 7 26 25

样例输出

zrf is:1/7; ssh is:26/25
(zrf==ssh) is:0; (zrf<ssh) is:1

思路：就是补充四个重载函数，纯c++内容，只需提交一下代码：

ostream& operator<<(ostream& os, const zrf_Ratio& zrf_Ratio){os << zrf_Ratio.num << "/" << zrf_Ratio.den;return os;
}istream& operator>>(istream& in, zrf_Ratio& zrf_Ratio){in >> zrf_Ratio.num >> zrf_Ratio.den;return in;
}
bool operator==(const zrf_Ratio& z1, const zrf_Ratio& z2){if(z1.num == z2.num && z1.den == z2.den)return true;return false;
}
bool operator<(const zrf_Ratio& z1, const zrf_Ratio& z2){if(z1.num * z2.den < z2.num * z1.den)return true;return false;
}

　　完整的程序：

#include <iostream> 
#include <cassert> 
using namespace std;
class zrf_Ratio
{friend std::ostream& operator<<(std::ostream&, const zrf_Ratio&);friend std::istream& operator>>(std::istream&, zrf_Ratio&);friend bool operator==(const zrf_Ratio&, const zrf_Ratio&);friend bool operator<(const zrf_Ratio&, const zrf_Ratio&);
public:zrf_Ratio(int=0,int=1);zrf_Ratio(const zrf_Ratio&);private:int num;int den;void reduce();//化为最简分数
};
//补充函数： 
ostream& operator<<(ostream& os, const zrf_Ratio& zrf_Ratio){os << zrf_Ratio.num << "/" << zrf_Ratio.den;return os;
}istream& operator>>(istream& in, zrf_Ratio& zrf_Ratio){in >> zrf_Ratio.num >> zrf_Ratio.den;return in;
}
bool operator==(const zrf_Ratio& z1, const zrf_Ratio& z2){if(z1.num == z2.num && z1.den == z2.den)return true;return false;
}
bool operator<(const zrf_Ratio& z1, const zrf_Ratio& z2){if(z1.num * z2.den < z2.num * z1.den)return true;return false;
}
//公有成员函数:
zrf_Ratio::zrf_Ratio(int num, int den) : num(num), den(den)
{reduce();
}zrf_Ratio::zrf_Ratio(const zrf_Ratio& r) : num(r.num), den(r.den)
{}//私有成员函数:
void swap(int &m, int &n)
{   int t;       t=m;    m=n;    n=t;
}int zrf_Gcd(int m, int n)
{if (m<n)swap(m,n);assert(n>=0);while (n>0) {int r=m%n;  m = n;   n = r;}return m;
}void zrf_Ratio::reduce()
{if (num == 0 || den == 0) {num = 0;  den = 1;  return; }if (den < 0){den *= -1;  num *= -1;}if (num == 1)return;int sgn = (num<0?-1:1);int g = zrf_Gcd(sgn*num,den);num /= g; den /= g;
}int main()
{int a = 0, b = 0, c = 0, d = 0;cin >> a >> b >> c >> d;zrf_Ratio zrf(a, b),ssh(c, d);std::cout<<"zrf is:"<<zrf<<"; ssh is:"<<ssh<<'\n' ;std::cout<<"(zrf==ssh) is:"<<(zrf==ssh)<<"; (zrf<ssh) is:"<<(zrf<ssh) <<endl;return 0;}