用C++编写功能强大，完整的有理数类_168 ufc168完整视频

分享人:追逐白月光来源:互联网29

一、头文件函数定义：

//Rational.h

#ifndef RATIONAl_CLASS
#define RATIONAl_CLASS

class Rational
{
private:
int P,Q;
voidStandardize();//将有理数化为标准形式
int gcd (int m,intn);//求两个数的最大公约数
public:
Rational (int p=0, intq=1);//构造有理数分数，分子默认为0，分母默认为1
Rational (Rational&r);//拷贝构造函数
Rational (doublera);//构造函数，将实数转换为标准形式的有理数

virtual ~Rational(void);//虚析构函数

void Reduce();//将分数化为最简形式

intGetNumerator();//取分数的分子
intGetDenominator();//取分数的分母

Rational& operator=(Rational& r); //将一个有理数对象赋值给另一个对象
Rational& operator= (doublera); //将一个实数赋值给一个有理数对象
Rational operator-();//将一个有理数取反
friend double Float(Rational&r); //强制转换一个有理数对象为一个实数

//以下为两个有理数对象、一个有理数对象和一个实数、一个实数和一个有理数对象
//之间的关系运算符的重载
int operator== (Rational& r)const;
int operator== (double ra) const;
friend int operator== (double ra,Rational& r);

int operator!= (Rational& r)const;
int operator!= (double ra) const;
friend int operator!= (double ra,Rational& r);

int operator<(Rational& r) const;
int operator< (double ra)const;
friend int operator< (double ra,Rational& r);

int operator<=(Rational& r) const;
int operator<= (double ra)const;
friend int operator<= (double ra,Rational& r);

int operator>(Rational& r) const;
int operator> (double ra)const;
friend int operator> (double ra,Rational& r);

int operator>=(Rational& r) const;
int operator>= (double ra)const;
friend int operator>= (double ra,Rational& r);

//以下两个有理数对象、一个有理数对象和一个实数
//之间的普通四则运算的重载
Rational operator+ (Rational& r)const;
Rational operator+ (double ra) const;
void operator+= (Rational&r);
void operator+= (double ra);

Rational operator- (Rational&r) const;
Rational operator- (double ra) const;
void operator-= (Rational&r);
void operator-= (double ra);

Rational operator* (Rational&r) const;
Rational operator* (double ra) const;
void operator*= (Rational&r);
void operator*= (double ra);

Rational operator/ (Rational&r) const;
Rational operator/ (double ra) const;
void operator/= (Rational&r);
void operator/= (double ra);

//输入输出流的重载，输出为最简形式
friend ostream&operator<<(ostream&output,Rational &obj);
friendistream&operator>>(istream&input,Rational &obj);

int Iegal(void)const;//判断有理数对象的值是否合法
};

//一个实数和一个有理数对象之间的四则运算重载
Rational operator+ (double ra, Rational& r);
Rational operator- (double ra, Rational& r);
Rational operator* (double ra, Rational& r);
Rational operator/ (double ra, Rational& r);

void PrintMixedNumber(RationalX);//将一个有理数对象转换为带分数形式
Rational SolveEquation(Rational a,Rational b,Rationalc); //求解一般的分数方程

#endif

二、函数实现部分：

//Rational.cpp

#include <iostream>
using namespace std;
#include "Rational.h"

void Rational::Standardize()//将有理数化为标准形式
{
if(Q == 0)
{
cout<<"Error!"<<endl;
exit(1);
}
else
if(Q < 0)
{
P= -P;
Q= -Q;
}
}

int Rational::gcd (int m,intn)//求两个数的最大公约数
{
int i,t;
if(m==0 || n==0)
{
cout<<"Error!"<<endl;
exit(1);
}
if(n>m ||n<-m)
{
t=n;
n=m;
m=t;
}
i=m%n;
if(i!=0)
do
{
m=n;
n=i;
i=m%n;
}while(m%n!=0);
return ((n>0)? n : -n);
}

Rational::Rational (int p, intq)//构造有理数分数，分子默认为0，分母默认为1
{
P=p;
Q=q;
Standardize();
}

Rational::Rational (Rational&r)//拷贝构造函数
{
P=r.P;
Q=r.Q;
Standardize();
}

Rational::Rational (doublera)//构造函数，将实数转换为标准形式的有理数
{
int base=1;
while(ra-(int)ra !=0)
{
ra=ra*10;
base=base*10;
}
P=ra;
Q=base;
}

Rational::~Rational(void)//虚析构函数
{}

void Rational::Reduce()//将分数化为最简形式
{
int max=gcd(P,Q);
P= P/max;
Q= Q/max;
}

intRational::GetNumerator()//取分数的分子
{
return P;
}
intRational::GetDenominator()//取分数的分母
{
return Q;
}

Rational& Rational::operator=(Rational&r)//将一个有理数对象赋值给另一个对象
{
P=r.GetNumerator();
Q=r.GetDenominator();
return *this;
}

Rational& Rational::operator= (doublera)//将一个实数赋值给一个有理数对象
{
Rational temp(ra);
*this=temp;
return *this;
}

Rational Rational::operator-()//将一个有理数取反
{
Rationaltemp(-GetNumerator(),GetDenominator());
return temp;
}

double Float(Rational&r)//强制转换一个有理数对象为一个实数
{
return(1.0*r.GetNumerator()/r.GetDenominator());
}

//以下为两个有理数对象、一个有理数对象和一个实数、一个实数和一个有理数对象
//之间的关系运算符的重载
int Rational::operator== (Rational& r) const
{
int r_p=r.GetNumerator(),r_q=r.GetDenominator();
return (P*r_q==r_p*Q);
}

int Rational::operator== (double ra) const
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
return (P*temp_q==temp_p*Q);
}

int operator== (double ra, Rational& r)
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
int r_p=r.GetNumerator(),r_q=r.GetDenominator();
r_p=r_p*temp_q;
temp_p=temp_p*r_q;
return (r_p==temp_p);
}

int Rational::operator!= (Rational& r) const
{
int r_p=r.GetNumerator(),r_q=r.GetDenominator();
return !(P*r_q==r_p*Q);
}

int Rational::operator!= (double ra) const
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
return !(P*temp_q==temp_p*Q);
}

int operator!= (double ra, Rational& r)
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
int r_p=r.GetNumerator(),r_q=r.GetDenominator();
r_p=r_p*temp_q;
temp_p=temp_p*r_q;
return !(r_p==temp_p);
}

int Rational::operator< (Rational&r) const
{
int r_p=r.GetNumerator(),r_q=r.GetDenominator();
return (P*r_q<r_p*Q);
}

int Rational::operator< (double ra) const
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
return (P*temp_q<temp_p*Q);
}

int operator< (double ra,Rational& r)
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
int r_p=r.GetNumerator(),r_q=r.GetDenominator();
r_p=r_p*temp_q;
temp_p=temp_p*r_q;
return (r_p<temp_p);
}

int Rational::operator<= (Rational&r) const
{
int r_p=r.GetNumerator(),r_q=r.GetDenominator();
return (P*r_q<=r_p*Q);
}

int Rational::operator<= (double ra) const
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
return (P*temp_q<=temp_p*Q);
}

int operator<= (double ra,Rational& r)
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
int r_p=r.GetNumerator(),r_q=r.GetDenominator();
r_p=r_p*temp_q;
temp_p=temp_p*r_q;
return (r_p<=temp_p);
}

int Rational::operator>(Rational& r) const
{
int r_p=r.GetNumerator(),r_q=r.GetDenominator();
return (P*r_q>r_p*Q);
}

int Rational::operator> (double ra) const
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
return (P*temp_q>temp_p*Q);
}

int operator> (double ra,Rational& r)
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
int r_p=r.GetNumerator(),r_q=r.GetDenominator();
r_p=r_p*temp_q;
temp_p=temp_p*r_q;
return (r_p>temp_p);
}

int Rational::operator>= (Rational&r) const
{
int r_p=r.GetNumerator(),r_q=r.GetDenominator();
return (P*r_q>=r_p*Q);
}

int Rational::operator>= (double ra) const
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
return (P*temp_q>=temp_p*Q);
}

int operator>= (double ra,Rational& r)
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
int r_p=r.GetNumerator(),r_q=r.GetDenominator();
r_p=r_p*temp_q;
temp_p=temp_p*r_q;
return (r_p>=temp_p);
}

//以下为两个有理数对象、一个有理数对象和一个实数
//之间的普通四则运算的重载
Rational Rational::operator+ (Rational& r)const
{
int r_p=r.GetNumerator(),r_q=r.GetDenominator();
Rational obj(P*r_q+r_p*Q,Q*r_q);
return obj;
}

Rational Rational::operator+ (double ra) const
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
Rational obj(P*temp_q+temp_p*Q,Q*temp_q);
return obj;
}

void Rational::operator+= (Rational& r)
{
P=P+r.GetNumerator();
Q=Q+r.GetDenominator();
}

void Rational::operator+= (double ra)
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
P=P*temp_q+temp_p*Q;
Q=temp_q*Q;
}

Rational Rational::operator- (Rational& r)const
{
int r_p=r.GetNumerator(),r_q=r.GetDenominator();
Rational obj(P*r_q-r_p*Q,Q*r_q);
return obj;
}

Rational Rational::operator- (double ra) const
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
Rational obj(P*temp_q-temp_p*Q,Q*temp_q);
return obj;
}

void Rational::operator-= (Rational& r)
{
P=P-r.GetNumerator();
Q=Q-r.GetDenominator();
}

void Rational::operator-= (double ra)
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
P=P*temp_q-temp_p*Q;
Q=temp_q*Q;
}

Rational Rational::operator* (Rational& r)const
{
Rational temp(P*r.GetNumerator(),Q*r.GetDenominator());
return temp;
}

Rational Rational::operator* (double ra) const
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
Rational obj(P*temp_p,Q*temp_q);
return obj;
}

void Rational::operator*= (Rational& r)
{
P=P*r.GetNumerator();
Q=Q*r.GetDenominator();
}

void Rational::operator*= (double ra)
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
P=P*temp_p;
Q=temp_q*Q;
}

Rational Rational::operator/ (Rational& r)const
{
Rationaltemp(P*r.GetDenominator(),Q*r.GetNumerator());
return temp;
}

Rational Rational::operator/ (double ra) const
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
Rational obj(P*temp_q,Q*temp_p);
return obj;
}

void Rational::operator/= (Rational& r)
{
P=P*r.GetDenominator();
Q=Q*r.GetNumerator();
}

void Rational::operator/= (double ra)
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
P=P*temp_q;
Q=temp_p*Q;
}

//输入输出流的重载，输出为最简形式
ostream&operator<<(ostream&output,Rational &obj)
{
obj.Reduce();
output<<obj.GetNumerator();
output<<"/"<<obj.GetDenominator();
returnoutput;
}

istream&operator>>(istream&input,Rational &obj)
{
intnum,den;
char oper;
input>>num;
input>>oper;
input>>den;
Rationaltemp(num,den);
obj=temp;
returninput;
}

int Rational::Iegal(void)const//判断有理数对象的值是否合法
{
if(Q==0)
return 0;
else
return 1;
}

//一个实数和一个有理数对象之间的四则运算重载
Rational operator+ (double ra, Rational& r)
{
Rational temp(ra);
temp=temp+r;
return temp;
}

Rational operator- (double ra, Rational&r)
{
Rational temp(ra);
temp=temp-r;
return temp;
}

Rational operator* (double ra, Rational&r)
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
int r_p=r.GetNumerator(),r_q=r.GetDenominator();
Rational obj(temp_p*r_p,r_q*temp_q);
return obj;
}

Rational operator/ (double ra, Rational&r)
{
Rational temp(ra);
int temp_p=temp.GetNumerator(),temp_q=temp.GetDenominator();
int r_p=r.GetNumerator(),r_q=r.GetDenominator();
Rational obj(temp_p*r_q,r_p*temp_q);
return obj;
}

void PrintMixedNumber(RationalX)//将一个有理数对象转换为带分数形式
{
int t;
X.Reduce();
t=X.GetNumerator()/X.GetDenominator();
cout<<t<<"("<<(X.GetNumerator()-t*X.GetDenominator())<<"/"<<X.GetDenominator()<<")"<<endl;
}

Rational SolveEquation(Rational a,Rational b,Rationalc) //求解一般的分数方程
{
Rational temp;
if(a.GetNumerator()==0)
{
cout<<"Error!"<<endl;
exit(1);
}
temp=(c-b)/a;
temp.Reduce();
return temp;
}

三、主函数（测试部分）:

#include <iostream>
using namespace std;
#include "Rational.h"

void main()
{
Rational A(-4,-8),C,D;
Rational B(10.05);
Rational E(B);
cout<<"Please inputC: ";
cin>>C;
D=43.9;
cout<<"A ="<<A<<endl;
cout<<"B ="<<B<<endl;
cout<<"E ="<<E<<endl;
cout<<"B = E ?"<<(B==E)<<endl;
cout<<"A != B ?"<<(A!=B)<<endl;
cout<<"-B ="<<(-B)<<endl;
cout<<"D(43.9) ="<<D<<endl;
cout<<"A+B ="<<(A+B)<<endl;
cout<<"A-B ="<<(A-B)<<endl;
cout<<"A+1.5 ="<<(A+1.5)<<endl;
cout<<"1.5+A ="<<(1.5+A)<<endl;
cout<<"A*1.5 ="<<(A*1.5)<<endl;
cout<<"1.5*A ="<<(1.5*A)<<endl;
cout<<"A/B ="<<(A/B)<<endl;
cout<<"A/1.5 ="<<(A/1.5)<<endl;
cout<<"1.5/A ="<<(1.5/A)<<endl;
A*=1.5;
cout<<"A*=1.5 ="<<A<<endl;
cout<<"float(A) ="<<Float(A)<<endl;
cout<<"E 的带分数形式为:";
PrintMixedNumber(E);
Rational X;
cout<<"A*X+B=C 解得:";
X=SolveEquation(A,C,E);
cout<<"X ="<<X<<endl;
}

  
有理数ppt课件完整版 ufc168完整视频 

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