分数类

#include<iostream>
#include<math.h>
using namespace std;
class Fract
{
public:
    Fract(){num=0;den=1;}
    Fract(int a=0,int b)
    {
        if(b==0)
        {
            cout<<"invalid fraction!!please check it!";
        }
        else
        {
            if(a*b<0)
            {
                num=-abs(a);
                den=abs(b);
            }
            else
            {
                num=abs(a);
                den=abs(b);
            }
            if(num!=0)
            cutit(num,den);
        }

    }//构造 
    Fract(const Fract &t){num=t.num;den=t.den;}//复制构造
    ~Fract(){}

     void Show()const;//show函数 
     void Input();//input函数 
     void cutit(int &a,int &b);
     friend  Fract operator + (const Fract &a,const Fract &b);
    friend  Fract operator - (const Fract &a,const Fract &b);
    friend  Fract operator * (const Fract &a,const Fract &b);    
    friend  Fract operator / (const Fract &a,const Fract &b);    
    friend  Fract operator - (const Fract &a);//前置负号 
    Fract operator ++ ();//前置 ++ 
    Fract operator ++ (int i);//后置++ 
    
    void operator += (const Fract &b);//混合赋值+=
     void operator -= (const Fract &b);//混合赋值-=
    friend ostream &operator <<(ostream &out,const Fract &k);//重载<< 
    friend istream &operator >>(istream &in,Fract &a);//重载>> 
     friend    Fract operator * (const Fract &a,int i);//分数乘整数
     friend    Fract operator * (int i,const Fract &a);//整数乘分数
     friend    Fract operator / (const Fract &a,int i);//分数除以整数
     friend    Fract operator / (int i,const Fract &a);//整数除以分数 
     double doublef(){return (double)num/den;}//分数转double 

    friend  bool operator == (const Fract &a,const Fract &b);
    friend  bool operator != (const Fract &a,const Fract &b);    
    friend  bool operator > (const Fract &a,const Fract &b);
    friend  bool operator < (const Fract &a,const Fract &b);                    
private:

   int num;   //分子

   int den;  //分母
   
};
void Fract::cutit(int &a,int &b)
{
    int c,t;
    int k1=abs(a),k2=abs(b);
    if(k2>k1)
    {
        t=k1;
        k1=k2;
        k2=t;
    }
    do
    {
        c=k1%k2;
        k1=k2;
        k2=c;
    }while(c!=0);
    a=a/k1;
    b=b/k1;
}
void Fract::Show()const
{
    int a=num,b=den;
    if(a==0)
    cout<<"0"<<endl;
    else if(a==b)
    cout<<"1"<<endl;
    else if(b==1)
    cout<<num<<endl;
    else
    {
        cout<<num<<"/"<<den<<endl;
    }
}
void Fract::Input()
{
    int a, b;
    cin>>a>>b;
    while(b==0)
    {
        cout<<"invalid fraction!!please rebuild it!";
        cin>>a>>b;
    }
    if(b!=0)
    {
        if(a*b<0)
        {
            num=-abs(a);
            den=abs(b);
        }
        else
        {
            num=abs(a);
            den=abs(b);
        }
        cutit(num,den);
    }
}
Fract operator+(const Fract &a,const Fract &b)
{
    int k1,k2;
    k1=a.num*b.den+b.num*a.den;
    k2=a.den*b.den;
    return Fract(k1,k2);
}
Fract operator-(const Fract &a,const Fract &b)
{
    int k1,k2;
    k1=a.num*b.den-b.num*a.den;
    k2=a.den*b.den;
    return Fract(k1,k2);
}
Fract operator*(const Fract &a,const Fract &b)
{
    return Fract(a.num*b.num,a.den*b.den);
}
Fract operator/(const Fract &a,const Fract &b)
{
    return Fract(a.num*b.den,a.den*b.num);
}
Fract operator - (const Fract &a)
{
    return Fract(-a.num,a.den);
}
Fract Fract::operator ++ ()
{
    num+=den;
    return Fract(num,den);
}
Fract Fract::operator ++ (int i)
{
    int a=num,b=den;
    num+=den;
    return Fract(a,b);
}
bool operator == (const Fract &a,const Fract &b)
{
    double j1,j2;
    j1=a.num/a.den;
    j2=b.num/b.den;
    if(j1-j2>-0.000001&&j1-j2<0.000001)
    return 1;
    else
    return 0;
}
bool operator != (const Fract &a,const Fract &b)
{
    double j1,j2;
    j1=a.num/a.den;
    j2=b.num/b.den;
    if(j1-j2>-0.000001&&j1-j2<0.000001)
    return 0;
    else
    return 1;
}
 bool operator > (const Fract &a,const Fract &b)
 {
    double j1,j2;
    j1=a.num/a.den;
    j2=b.num/b.den;
    if(j1>j2)
    return 1;
    else
    return 0;
 }
 bool operator < (const Fract &a,const Fract &b)
 {
    double j1,j2;
    j1=a.num/a.den;
    j2=b.num/b.den;
    if(j1<j2)
    return 1;
    else
    return 0;
 }
 void Fract::operator += (const Fract &b)
 {
    int k1,k2;
    k1=num*b.den+b.num*den;
    k2=den*b.den;
    cutit(k1,k2);
    num=k1;
    den=k2;
 }
 void Fract::operator -= (const Fract &b)
 {
    int k1,k2;
    k1=num*b.den-b.num*den;
    k2=den*b.den;
    cutit(k1,k2);
    num=k1;
    den=k2;
 }
 Fract operator * (const Fract &a,int i)
 {
     return Fract(a.num*i,a.den);
 }
 Fract operator * (int i,const Fract &a)
 {
     return Fract(a.num*i,a.den);
 }
 Fract operator / (const Fract &a,int i)
 {
     return Fract(a.num,a.den*i);
 }
 Fract operator / (int i,const Fract &a)
 {
     return Fract(i*a.den,a.num);
 }
/*
Fract Fract::operator =(double &k)
{
    return a.num/a.den;
}*/
ostream &operator <<(ostream &out,const Fract &k)
{
    int a=k.num,b=k.den;
    if(a==0)
    cout<<"0"<<endl;
    else if(a==b)
    cout<<"1"<<endl;
    else if(b==1)
    cout<<k.num<<endl;
    else
    {
        cout<<k.num<<"/"<<k.den<<endl;
    }
    return out;
}
istream &operator >>(istream &in,Fract &a)
{
    int k1,k2;
    in>>k1>>k2;
    a=Fract(k1,k2);
    return in;
}
int main()

{

//测试默认构造函数与输出函数

  Fract f1;

  f1.Show();       //输出：0

//测试构造函数与输出函数

  Fract f2(2,4);
  Fract f3(-2,-4);
  Fract f4(2,-5);
  Fract f5(-2,5);
  Fract f6(2,2);
  Fract f7(0,8);
  Fract f8(4,-2);

  f2.Show();    //输出：1/2

  f3.Show();    //输出：1/2

  f4.Show();    //输出：-2/5

  f5.Show();    //输出：-2/5

  f6.Show();    //输出：1

  f7.Show();    //输出：0

  f8.Show();    //输出：-2

//测试复制构造函数

  Fract f9(f2);

  f9.Show();    //输出：1/2

//测试输入函数

  f1.Input();   //输入：  2   6

  f2.Input();   //输入：  1   8

  f1.Show();    //输出：  1/3

  f2.Show();    //输出：  1/8

//测试加减乘除 

  f3 = f1+f2;

  f3.Show();     //输出：11/24

  f4 = f1-f2;

  f4.Show();      //输出：5/24
  
  f3 = f1*f2; 
 
 f3.Show();  //输出 1/24
 
 f4 = f4 / f3;
 
 f4.Show(); //输出 5 

//测试分数的负(-)、自增（前后置++)

  f3 = -f1;

  f3.Show();        //输出：-1/3

  f3 = ++f1;

  f1.Show();        //输出：4/3

  f3.Show();        //输出：4/3

  f3 = f1++;

  f1.Show();        //输出：7/3

  f3.Show();        //输出：4/3

//测试关系运算符== != > <以及分数与整数的  乘  除 运算 
    //对应数据 f1=7/3 f2=1/8 f3=4/3 f4=5 f5=-2/5 f6=1 f7=0 f8=-2 f9=1/2 
    if(f2*40==f4) 
    {
        cout<<"yes1"<<endl; //验证分数乘整数 == 
    }
    if(40*f2==f4)
    {
        cout<<"yes2"<<endl;//验证整数乘分数== 
    }
    if((f2/3)==(f3/32))
    {
        cout<<"yes3"<<endl;//验证分数除以整数== 
    }
    if(4/f3!=f3)
    {
        cout<<"yes4"<<endl;//验证整数除以分数！= 
    }
    if(f6>f9)
    {
        cout<<"yes5"<<endl;//验证大于 
    }
    if(f9<f6)
    {
        cout<<"yes6"<<endl;//验证小于 
    }
    //验证+= -=
    f2+=f3;
    
    f2.Show(); //输出 35/24
    
    f4-=f5;
    
    f4.Show();//输出 27/5 
    
    //验证 分数转double 
    double q=f4.doublef();
    cout<<q<<endl; 
    //验证 >> <<
    cin>>f1;   //输入  5 10
    cout<<f1;   //输出 1/2 
    
return 0;
}