#include<math.h>
#include<iostream.h>
class rational
{
int numerator,denominator;
void optimization();
public:
rational(int x=0,int y=1); //声明带默认值的构造函数
friend rational operator +(rational &num1,rational &num2);
//声明重载运算符"+"
friend rational operator -(rational &num1,rational &num2);
friend rational operator *(rational &num1,rational &num2);
friend rational operator /(rational &num1,rational &num2);
friend bool operator==(rational &num1,rational &num2);
//声明比较运算符"=="重载函数
friend double real(rational& x); //声明将分数转换为浮点数的函数
friend ostream &operator<<(ostream&,rational &); //声明"<<"重载
friend istream &operator>>(istream&,rational &); //声明">>"重载
};
void rational::optimization()
{
int gcd,min,max;
if(numerator==0)
{ //如分子为0，则置分母为1后返回
denominator=1;
return;
}
gcd=(abs(numerator)>abs(denominator)?abs(denominator):abs(numerator));
if(gcd==0) return;
/*//也可如此用循环求最大公约数
for(max=gcd;max>1;max--)
if((numerator%max==0)&&(denominator%max==0))
break;
*/
//以下用辗转相除法求最大公约数，此方法较好
if(abs(numerator)>abs(denominator))
{max=numerator;min=denominator;}
else
{min=numerator;max=denominator;}
do{
gcd=max%min;
max=min;
min=gcd;
}while(gcd!=0);
numerator/=max;
denominator/=max;
if(numerator<0 && denominator<0)
{
numerator=-numerator;
denominator=-denominator;
}
else if(numerator<0 || denominator<0)
{
numerator=-abs(numerator);
denominator=abs(denominator);
}
}
rational::rational(int x,int y)
{
numerator=x;
denominator=y;
optimization();
}
rational operator +(rational &num1,rational &num2)
{
rational temp;
temp.denominator=num1.denominator*num2.denominator;
temp.numerator=num1.numerator*num2.denominator+
num1.denominator*num2.numerator;
temp.optimization();
return temp;
}
rational operator -(rational &num1,rational &num2)
{
rational temp;
temp.denominator=num1.denominator*num2.denominator;
temp.numerator=num1.numerator*num2.denominator-
num1.denominator*num2.numerator;
temp.optimization();
return temp;
}
rational operator *(rational &num1,rational &num2)
{
rational temp;
temp.denominator=num1.denominator*num2.denominator;
temp.numerator=num1.numerator*num2.numerator;
temp.optimization();
return temp;
}
rational operator /(rational &num1,rational &num2)
{
rational temp;
temp.denominator=num1.denominator*num2.numerator;
temp.numerator=num1.numerator*num2.denominator;
temp.optimization();
return temp;
}
bool operator==(rational &num1,rational &num2)
{
if(num1.numerator==num2.numerator &&
num1.denominator==num2.denominator)
return true;
else
return false;
}
double real(rational& x)
{
return (double(x.numerator))/(x.denominator);
}
ostream &operator<<(ostream& out,rational &obj)
{
out<<obj.numerator;
if(obj.numerator!=0 && obj.denominator!=1 &&obj.denominator!=0)
cout<<"/"<<obj.denominator<<"\n";
else if(obj.denominator==0)
cout<<"ERROR!The denominator is equal to 0.\n";
else cout<<"\n";
return out;
}
istream &operator>>(istream& in,rational &obj)
{
cout<<"Input the numerator ,denominator of the rational:\n";
in>>obj.numerator;
in>>obj.denominator;
obj.optimization();
return in;
}
void main()
{
rational r1,r2,r3;
cin>>r1;
cin>>r2;
cout<<"r1="<<r1;
cout<<"r2="<<r2;
r3=r1+r2;
cout<<"r1+r2=";cout<<r3;
r3=r1-r2;
cout<<"r1-r2=";cout<<r3;
r3=r1*r2;
cout<<"r1*r2=";cout<<r3;
r3=r1/r2;
cout<<"r1/r2=";cout<<r3;
if(r1==r2)
cout<<"r2 is equal to r1.\n";
else
cout<<"r2 isn't equal to r1.\n";
}
c++程序设计技能百练
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2009-09-22
10:16:03
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c++程序设计技能百练 （200个子文件） 
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