求高手解答，用C++设计一个有理数运算

#includeiostream

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using namespace std;

//numerator 分子

//denominator分母

int gcd(int m,int n) //求最大公约数函数,用于约分

{

if(n==0)return m;

return gcd(n,m%n);

}

class fraction

{

private:

int numer;

int denom;

public:

fraction(int n=0,int d=1)//带默认参数的构造函数，整数与分数的运算迎刃而解

{

numer=n;

denom=d;

}

void rev(fraction a){numer=a.denom;denom=a.numer;}//倒数

friend ostream operator(std::ostream, const fraction); //重载输出

friend istream operator(std::istream, fraction); //重载输入

friend bool operator==(const fraction, const fraction); //判断有理数是否相等，以下类似

friend bool operator(const fraction, const fraction);

friend bool operator(const fraction, const fraction);

friend bool operator=(const fraction, const fraction);

friend bool operator=(const fraction, const fraction);

friend fraction operator +(const fraction,const fraction);//重载运算符

friend fraction operator -(const fraction,const fraction);

friend fraction operator *(const fraction,const fraction);

friend fraction operator /(const fraction,const fraction);

friend bool operator!=(const fraction, const fraction);

};

fraction operator +(const fraction a,const fraction b)

{

fraction p;

p.numer=a.numer*b.denom+b.numer*a.denom;

p.denom=a.denom*b.denom;

return p;

}

fraction operator -(const fraction a,const fraction b)

{

fraction p;

p.numer=a.numer*b.denom-b.numer*a.denom;

p.denom=a.denom*b.denom;

return p;

}

fraction operator *(const fraction a,const fraction b)

{

fraction p;

p.numer=a.numer*b.numer;

p.denom=a.denom*b.denom;

return p;

}

fraction operator /(const fraction a,const fraction b)

{

fraction p;

p.numer=a.numer*b.denom;

p.denom=a.denom*b.numer;

return p;

}

ostream operator(ostream output,const fraction num)

{

int a=gcd(num.numer,num.denom);

if((num.denom/a)==1)

outputnum.numer/a;

else if(num.denom/a0)

output-num.numer/a"/"-num.denom/a;

else outputnum.numer/a"/"num.denom/a;

return output;

}

istream operator(istreaminput, fraction num)

{

inputnum.numernum.denom;

return input;

}

bool operator==(const fractionnum1, const fractionnum2)

{

return (num1.numer*num2.denom)==(num2.numer*num1.denom);

}

bool operator!=(const fraction num1, const fraction num2)

{

return (num1.numer*num2.denom)!=(num2.numer*num1.denom);

}

bool operator(const fractiona, const fractionb)

{

return (a.numer*b.denom)(b.numer*a.denom);

}

bool operator(const fractiona, const fractionb)

{

return (a.numer*b.denom)(b.numer*a.denom);

}

bool operator=(const fractiona, const fractionb)

{

return (a.numer*b.denom)=(b.numer*a.denom);

}

bool operator=(const fractiona, const fractionb)

{

return (a.numer*b.denom)=(b.numer*a.denom);

}

int main()

{

fraction zrf(1,7),ssh(26,65);

fraction p;

p.rev(ssh);

cout"ssh="ssh"\n1/ssh="pendl;

cout"zrf="zrf"\nssh="ssh'\n' ;

cout"(zrf==ssh)="(zrf==ssh)"\n(zrfssh)="(zrfssh)endl ;

cout"zrf+ssh="zrf+sshendl;

cout"zrf*ssh="zrf*sshendl;

cout"ssh-zrf="ssh-zrfendl;

cout"zrf-ssh="zrf-sshendl;

cout"zrf/ssh="zrf/sshendl;

return 0;

}

c++定义一个有理数类，实现有理数的加减乘除以及化简成最简分数等，要代码。问题解决了还会加分。

//Rational.h

#ifndef RATIONAl_CLASS

#define RATIONAl_CLASS

class Rational

{

private:

int P,Q;

void Standardize(); //将有理数化为标准形式

int gcd (int m,int n); //求两个数的最大公约数

public:

Rational (int p=0, int q=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 (double ra); //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

int GetNumerator(); //取分数的分子

int GetDenominator(); //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= (double ra); //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);

friend istream 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(Rational X); //将一个有理数对象转换为带分数形式

Rational SolveEquation(Rational a,Rational b,Rational c); //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,int n) //求两个数的最大公约数

{

int i,t;

if(m==0 || n==0)

{

cout"Error!"endl;

exit(1);

}

if(nm || 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 ((n0)? n : -n);

}

Rational::Rational (int p, int q) //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 (double ra) //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;

}

int Rational::GetNumerator() //取分数的分子

{

return P;

}

int Rational::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= (double ra) //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

{

Rational temp(-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_qr_p*Q);

}

int Rational::operator (double ra) const

{

Rational temp(ra);

int temp_p=temp.GetNumerator(), temp_q=temp.GetDenominator();

return (P*temp_qtemp_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_ptemp_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_qr_p*Q);

}

int Rational::operator (double ra) const

{

Rational temp(ra);

int temp_p=temp.GetNumerator(), temp_q=temp.GetDenominator();

return (P*temp_qtemp_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_ptemp_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

{

Rational temp(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();

outputobj.GetNumerator();

output"/"obj.GetDenominator();

return output;

}

istream operator(istream input,Rational obj)

{

int num,den;

char oper;

inputnum;

inputoper;

inputden;

Rational temp(num,den);

obj=temp;

return input;

}

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(Rational X) //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();

coutt"("(X.GetNumerator()-t*X.GetDenominator())"/"X.GetDenominator()")"endl;

}

Rational SolveEquation(Rational a,Rational b,Rational c) //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 input C: ";

cinC;

D=43.9;

cout"A = "Aendl;

cout"B = "Bendl;

cout"E = "Eendl;

cout"B = E ? "(B==E)endl;

cout"A != B ? "(A!=B)endl;

cout"-B = "(-B)endl;

cout"D(43.9) = "Dendl;

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 = "Aendl;

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 = "Xendl;

}

C++编程题 定义一个有理数类。

1 有理数类

class Fraction

{

private:

int _Numerator; //分子

int _Denominator; //分母

public:

Fraction(){}

Fraction(const int Numerator,const int Denominator);

friend Fraction operator+(const Fraction frac1,const Fraction frac2);

friend Fraction operator-(const Fraction frac1,const Fraction frac2);

friend Fraction operator*(const Fraction frac1,const Fraction frac2);

friend Fraction operator/(const Fraction frac1,const Fraction frac2);

bool operator(const Fraction frac);

bool operator(const Fraction frac);

bool operator==(const Fraction frac);

bool operator!=(const Fraction frac);

void simp();

friend ostream operator(ostream out,Fraction frac);

};

2 包含类

class A

{

class B // B类属于A类的成员

{

//成员

};

//A类的其他成员

};

3 派生类

class A

{

};

//Book是从PrintedDocument中派生的

class B:A

{

//成员表

};

希望对你有所帮助！

c语言中有理数怎么表示

结构体定义有理数及其操作

#includeiostreamusing namespace std;struct RationalT { // 有理数类型的定义 int num; // 分子 int den; // 分母};RationalT CreateRational(int num, int den) // 创建一个有理数{ RationalT r; r.num = num; r.den = den; return r;}RationalT AddRational(RationalT r1, RationalT r2) // 有理数加法{ RationalT r; int fac; r.num = r1.num * r2.den + r2.num * r1.den; r.den = r1.den * r2.den; fac = r.num r.den ? r.num : r.den; // 将结果化成最简分式 while (r.num % fac != 0 || r.den % fac != 0) -- fac; r.num /= fac; r.den /= fac; return r;}RationalT MultiplyRational(RationalT r1, RationalT r2) // 有理数乘法{ RationalT r; int fac; r.num = r1.num * r2.num; r.den = r1.den * r2.den; fac = r.num r.den ? r.num : r.den; // 将结果化成最简分式 while (r.num % fac != 0 || r.den % fac != 0) -- fac; r.num /= fac; r.den /= fac; return r;}double GetRational(RationalT r) // 将有理数转换成小数{ return double(r.num) / r.den;}void PrintRational(RationalT r) // 以分数形式输出有理数{ cout r.num "/" r.den endl;}void main(){ struct RationalT r1,r2,r3,r4; r1 = CreateRational(2,3); r2 = CreateRational(3,8); r3 = AddRational(r1,r2); r4 = MultiplyRational(r1,r2); PrintRational(r3); PrintRational(r4); coutGetRational(r4)endl; cin.get();cin.get();}/*25/241/40.25*/

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