《C++语言基础》实践参考——分数类中的运算符重载

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【项目3-分数类中的运算符重载】
　　（1）实现分数类中的运算符重载，在分数类中可以完成分数的加减乘除（运算后再化简）、比较（6种关系）的运算。可以在第4周分数类代码的基础上开始工作。

class CFraction{private:    int nume;  // 分子    int deno;  // 分母public:    //构造函数及运算符重载的函数声明};//重载函数的实现及用于测试的main()函数

[参考解答]

#include <iostream>#include <Cmath>using namespace std;class CFraction{private:    int nume;  // 分子    int deno;  // 分母public:    CFraction(int nu=0,int de=1):nume(nu),deno(de) {}    void simplify();    void display();    CFraction operator+(const CFraction &c);  //两个分数相加，结果要化简    CFraction operator-(const CFraction &c);  //两个分数相减，结果要化简    CFraction operator*(const CFraction &c);  //两个分数相乘，结果要化简    CFraction operator/(const CFraction &c);  //两个分数相除，结果要化简    bool operator>(const CFraction &c);    bool operator<(const CFraction &c);    bool operator==(const CFraction &c);    bool operator!=(const CFraction &c);    bool operator>=(const CFraction &c);    bool operator<=(const CFraction &c);};// 分数化简void CFraction::simplify(){    int m,n,r;    m=fabs(deno);             //此处存在bug，请参看评论1楼    n=fabs(nume);    while(r=m%n)  // 求m，n的最大公约数    {        m=n;        n=r;    }    deno/=n;     // 化简    nume/=n;    if (deno<0)  // 将分母转化为正数    {        deno=-deno;        nume=-nume;    }}//显示分数void CFraction::display(){    cout<<"("<<nume<<"/"<<deno<<")"<<endl;}// 分数相加CFraction CFraction::operator+(const CFraction &c){    CFraction t;    t.nume=nume*c.deno+c.nume*deno;    t.deno=deno*c.deno;    t.simplify();    return t;}// 分数相减CFraction CFraction:: operator-(const CFraction &c){    CFraction t;    t.nume=nume*c.deno-c.nume*deno;    t.deno=deno*c.deno;    t.simplify();    return t;}// 分数相乘CFraction CFraction:: operator*(const CFraction &c){    CFraction t;    t.nume=nume*c.nume;    t.deno=deno*c.deno;    t.simplify();    return t;}// 分数相除CFraction CFraction:: operator/(const CFraction &c){    CFraction t;    if (!c.nume) return *this;   //除法无效时，这种情况需要考虑，但这种处理仍不算合理    t.nume=nume*c.deno;    t.deno=deno*c.nume;    t.simplify();    return t;}// 分数比较大小bool CFraction::operator>(const CFraction &c){    int this_nume,c_nume,common_deno;    this_nume=nume*c.deno;        // 计算分数通分后的分子，同分母为deno*c.deno    c_nume=c.nume*deno;    common_deno=deno*c.deno;    //if (this_nume>c_nume) return true; 无法应对common_deno<0的情形    //下面的语句更简练的一种写法if ((this_nume-c_nume)*common_deno>0) return true;    if ((this_nume>c_nume&&common_deno>0)||(this_nume<c_nume&&common_deno<0)) return true; // 将通分后的分子比较大小    return false;}// 分数比较大小bool CFraction::operator<(const CFraction &c){    int this_nume,c_nume,common_deno;    this_nume=nume*c.deno;    c_nume=c.nume*deno;    common_deno=deno*c.deno;    if ((this_nume-c_nume)*common_deno<0) return true;    return false;}// 分数比较大小bool CFraction::operator==(const CFraction &c){    if (*this!=c) return false;    return true;}// 分数比较大小bool CFraction::operator!=(const CFraction &c){    if (*this>c || *this<c) return true;    return false;}// 分数比较大小bool CFraction::operator>=(const CFraction &c){    if (*this<c) return false;    return true;}// 分数比较大小bool CFraction::operator<=(const CFraction &c){    if (*this>c) return false;    return true;}int main(){    CFraction x(1,3),y(-5,10),s;    cout<<"分数x=1/3      y=-5/10"<<endl;    s=x+y;    cout<<"x+y=";    s.display();    s=x-y;    cout<<"x-y=";    s.display();    s=x*y;    cout<<"x*y=";    s.display();    s=x/y;    cout<<"x/y=";    s.display();    x.display();    if (x>y) cout<<"大于"<<endl;    if (x<y) cout<<"小于"<<endl;    if (x==y) cout<<"等于"<<endl;    y.display();    cout<<endl;    return 0;}

　　（2）在（1）的基础上，实现分数类中的对象和整型数的四则运算。分数类中的对象可以和整型数进行四则运算，且运算符合交换律。例如：CFraction a(1,3),b; int i=2; 可以完成b=a+i;。同样，可以完成i+a, 45+a, a*27, 5/a等各种运算。

[参考解答]

#include <iostream>using namespace std;class CFraction{private:    int nume;  // 分子    int deno;  // 分母public:    CFraction(int nu=0,int de=1):nume(nu),deno(de) {}    void simplify();    void display();    friend CFraction operator+(const CFraction &c1, const CFraction &c2);  //两个分数相加，结果要化简    friend CFraction operator-(const CFraction &c1, const CFraction &c2);  //两个分数相减，结果要化简    friend CFraction operator*(const CFraction &c1, const CFraction &c2);  //两个分数相乘，结果要化简    friend CFraction operator/(const CFraction &c1, const CFraction &c2);  //两个分数相除，结果要化简    friend CFraction operator+(const CFraction &c, int i);    friend CFraction operator+(int i, const CFraction &c );    friend CFraction operator-(const CFraction &c, int i);    friend CFraction operator-(int i, const CFraction &c );    friend CFraction operator*(const CFraction &c, int i);    friend CFraction operator*(int i, const CFraction &c );    friend CFraction operator/(const CFraction &c, int i);    friend CFraction operator/(int i, const CFraction &c );    CFraction operator+();  //取正一目运算    CFraction operator-();  //取反一目运算    friend bool operator>(const CFraction &c1, const CFraction &c2);    friend bool operator<(const CFraction &c1, const CFraction &c2);    friend bool operator==(const CFraction &c1, const CFraction &c2);    friend bool operator!=(const CFraction &c1, const CFraction &c2);    friend bool operator>=(const CFraction &c1, const CFraction &c2);    friend bool operator<=(const CFraction &c1, const CFraction &c2);    friend bool operator>(const CFraction &c, int i);    friend bool operator>(int i, const CFraction &c);    friend bool operator<(const CFraction &c, int i);    friend bool operator<(int i, const CFraction &c);    friend bool operator==(const CFraction &c, int i);    friend bool operator==(int i, const CFraction &c);    friend bool operator!=(const CFraction &c, int i);    friend bool operator!=(int i, const CFraction &c);    friend bool operator>=(const CFraction &c, int i);    friend bool operator>=(int i, const CFraction &c);    friend bool operator<=(const CFraction &c, int i);    friend bool operator<=(int i, const CFraction &c);};// 分数化简void CFraction::simplify(){    int m,n,r;    m=abs(deno);    n=abs(nume);    while(r=m%n)  // 求m，n的最大公约数    {        m=n;        n=r;    }    deno/=n;     // 化简    nume/=n;    if (deno<0)  // 将分母转化为正数    {        deno=-deno;        nume=-nume;    }}//显示分数void CFraction::display(){    cout<<"("<<nume<<"/"<<deno<<")"<<endl;}// 分数相加CFraction operator+(const CFraction &c1, const CFraction &c2){    CFraction t;    t.nume=c1.nume*c2.deno+c2.nume*c1.deno;    t.deno=c1.deno*c2.deno;    t.simplify();    return t;}// 分数相减CFraction operator-(const CFraction &c1, const CFraction &c2){    CFraction t;    t.nume=c1.nume*c2.deno-c2.nume*c1.deno;    t.deno=c1.deno*c2.deno;    t.simplify();    return t;}// 分数相乘CFraction operator*(const CFraction &c1, const CFraction &c2){    CFraction t;    t.nume=c1.nume*c2.nume;    t.deno=c1.deno*c2.deno;    t.simplify();    return t;}// 分数相除CFraction operator/(const CFraction &c1, const CFraction &c2){    CFraction t;    if (!c2.nume) return c1;    t.nume=c1.nume*c2.deno;    t.deno=c1.deno*c2.nume;    t.simplify();    return t;}CFraction operator+(const CFraction &c, int i){    CFraction c1(c.nume+i*c.deno,c.deno);    c1.simplify();    return c1;}CFraction operator+(int i, const CFraction &c ){    CFraction c1(c.nume+i*c.deno,c.deno);    c1.simplify();    return c1;}CFraction operator-(const CFraction &c, int i){    CFraction c1(c.nume-i*c.deno,c.deno);    c1.simplify();    return c1;}CFraction operator-(int i, const CFraction &c ){    CFraction c1(i*c.deno-c.nume,c.deno);    c1.simplify();    return c1;}CFraction operator*(const CFraction &c, int i){    CFraction c1(c.nume*i,c.deno);    c1.simplify();    return c1;}CFraction operator*(int i, const CFraction &c ){    CFraction c1(c.nume*i,c.deno);    c1.simplify();    return c1;}CFraction operator/(const CFraction &c, int i){    CFraction c1(c.nume,c.deno*i);    c1.simplify();    return c1;}CFraction operator/(int i, const CFraction &c ){    CFraction c1(i*c.deno,c.nume);    c1.simplify();    return c1;}// 分数取正号CFraction CFraction:: operator+(){    return *this;}// 分数取负号CFraction CFraction:: operator-(){    CFraction c;    c.nume=-nume;    c.deno=-deno;    return c;}// 分数比较大小bool operator>(const CFraction &c1, const CFraction &c2){    int c1_nume,c2_nume,common_deno;    c1_nume=c1.nume*c2.deno;        // 计算分数通分后的分子，同分母为c1.deno*c2.deno    c2_nume=c2.nume*c1.deno;    common_deno=c1.deno*c2.deno;    //if (c1_nume>c2_nume) return true; 无法应对common_deno<0的情形    //下面的语句更简练的一种写法if ((c1_nume-c2_nume)*common_deno>0) return true;    if (c1_nume>c2_nume&&common_deno>0||c1_nume<c2_nume&&common_deno<0) return true; // 将通分后的分子比较大小    return false;}// 分数比较大小bool operator<(const CFraction &c1, const CFraction &c2){    int c1_nume,c2_nume,common_deno;    c1_nume=c1.nume*c2.deno;    c2_nume=c2.nume*c1.deno;    common_deno=c1.deno*c2.deno;    if ((c1_nume-c2_nume)*common_deno<0) return true;    return false;}// 分数比较大小bool operator==(const CFraction &c1, const CFraction &c2){    if (c1!=c2) return false;    return true;}// 分数比较大小bool operator!=(const CFraction &c1, const CFraction &c2){    if (c1>c2 || c1<c2) return true;    return false;}// 分数比较大小bool operator>=(const CFraction &c1, const CFraction &c2){    if (c1<c2) return false;    return true;}// 分数比较大小bool operator<=(const CFraction &c1, const CFraction &c2){    if (c1>c2) return false;    return true;}bool operator>(const CFraction &c, int i){    if(c.deno>0)        return c.nume>(i*c.deno);    else        return c.nume<(i*c.deno);}bool operator>(int i, const CFraction &c){    if(c.deno>0)        return (i*c.deno)>c.nume;    else        return (i*c.deno)<c.nume;}bool operator<(const CFraction &c, int i){    if(c.deno>0)        return c.nume<(i*c.deno);    else        return c.nume>(i*c.deno);}bool operator<(int i, const CFraction &c){    if(c.deno>0)        return (i*c.deno)<c.nume;    else        return (i*c.deno)>c.nume;}bool operator==(const CFraction &c, int i){    return c.nume==(i*c.deno);}bool operator==(int i, const CFraction &c){    return c.nume==(i*c.deno);}bool operator!=(const CFraction &c, int i){    return c.nume!=(i*c.deno);}bool operator!=(int i, const CFraction &c){    return c.nume!=(i*c.deno);}bool operator>=(const CFraction &c, int i){    return !(c<i);}bool operator>=(int i, const CFraction &c){    return !(i<c);}bool operator<=(const CFraction &c, int i){    return !(c>i);}bool operator<=(int i, const CFraction &c){    return !(i>c);}int main(){    CFraction x(1,3),y(-5,10),s;    cout<<"分数x=1/3      y=-5/10"<<endl;    s=+x+y;    cout<<"+x+y=";    s.display();    s=x-y;    cout<<"x-y=";    s.display();    s=x*y;    cout<<"x*y=";    s.display();    s=x/y;    cout<<"x/y=";    s.display();    s=-x+y;    cout<<"-x+y=";    s.display();    x.display();    if (x>y) cout<<"大于"<<endl;    if (x<y) cout<<"小于"<<endl;    if (x==y) cout<<"等于"<<endl;    y.display();    cout<<endl;    CFraction c1(5,3),c2;    //以下建议在调试环境中完成测试，    c2=c1+5;    c2=5+c1;    c2=c1-5;    c2=5-c1;    c2=c1*5;    c2=5*c1;    c2=c1/5;    c2=5/c1;    bool b;    b=(c1>2);    b=(2>c1);    return 0;}

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