用C++语言描述分数类，并进行各种运算

#include <iostream.h> class fraction{ public: fraction() {}; fraction (int n,int d); fraction operator-(const fraction &Y); //分数的减法 fraction operator+(const fraction &Y); //分数的加法 fraction operator*(const fraction &Y); //分数的乘法 fraction operator/(const fraction &Y); //分数的除法 fraction operator*(int i); //分数与整数相乘 bool operator>(fraction &Y); //分数大小的比较 bool operator<(fraction &Y); bool operator>=(fraction &Y); bool operator<=(fraction &Y); bool operator!=(fraction &Y); bool operator ==(fraction &Y){ return(num==Y.num&&denom==Y.denom); } friend istream & operator>>(istream &input,fraction &Y); //分数的输入 friend ostream & operator<<(ostream &output,fraction &Y); //分数的输出 fraction operator++(); //加1运算 void display() { cout<<num<<'/'<<denom<<endl; } bool iszero(){ return (denom==1&&num==0); } bool isone(){ return (denom==1&&num==1); } bool isint(){return denom==1;} int floor(); int ceding; void reciprocal(); //倒数运算 fraction makefraction(int n,unsigned d) { fraction ans; ans.num=n; ans.denom=d; return ans; } private: int num; //分子 int denom; //分母 }; istream & operator>>(istream &input,fraction &Y) // 分数的输入 友元函数 { cout<<"input numerator and denominator:"; input>>Y.num>>Y.denom; return input; } ostream & operator<<(ostream & output,fraction &Y) //分数的输出 友元函数 { output<<Y.num<<'/'<<Y.denom; return output; } void swap(int &a, int &b) //交换函数 非成员函数 { int c = a; a = b; b = c; } int gcd(int a, int b) //求最大公约数函数 非成员函数数 { if(0 == a){ return b; } if(0 == b){ return a; } if(a > b){ swap(a, b); } int c; for(c = a % b ; c > 0 ; c = a % b){ a = b; b = c; } return b; } fraction::fraction(int n,int d) //分数 { if(d==0){cout<<"fraction:denominator is 0"<<endl;} //exit(1); if(n==0){num=0; denom=1; return; } if (d<0) {n=-n; d=-d; } int g; if((g=gcd(n,d))!=1) //进行约分操作 { num=n/g;denom=d/g; } else {num=n;denom=d;} } fraction fraction::operator+(const fraction &Y) //分数的加法 { if (num==0) return makefraction(Y.num,Y.denom); else if (Y.num==0) return *this; else return (fraction(num*Y.denom+Y.num*denom,denom*Y.denom)); } fraction fraction::operator-(const fraction &Y) //分数的减法 { if (num==0) return makefraction(-Y.num,Y.denom); else if (Y.num==0) return *this ; else return (fraction(num*Y.denom-Y.num*denom,denom*Y.denom)); } fraction fraction::operator *(const fraction &Y) //分数的乘法 { return (fraction(num*Y.num,denom*Y.denom)); } fraction fraction::operator /(const fraction &Y) //分数的除法 { return (fraction(num*Y.denom,denom*Y.num)); } fraction fraction::operator*(int i) //分数与整数的相乘 { return fraction(num*i,denom); } void fraction::reciprocal() //分数的倒数运算 { if(num!=0) { int temp=num; num=denom; denom=temp;} } bool fraction::operator < (fraction &Y) //比较大小 { return (num*Y.denom<Y.num*denom); } bool fraction::operator <=(fraction &Y) { return (num*Y.denom<=Y.num*denom) ; } bool fraction::operator >(fraction &Y) { return (num*Y.denom>Y.num*denom); } bool fraction::operator >=(fraction &Y) { return (num*Y.denom>=Y.num*denom); } bool fraction::operator !=(fraction &Y) { return (!(num==Y.num&&denom==Y.denom)); } fraction fraction::operator++() { return (fraction(num+denom,denom)); } void main() { fraction X(1,2); fraction Y(3,4); X.display(); // cout<<X.num<<"/"<<X.denom; fraction A; A=X+Y; A.display(); // cout<<A.num<<"/"<<A.denom; fraction B; B=X-Y; B.display(); // cout<<B.num<<"/"<<B.denom; fraction C; C=X*Y; C.display(); // fraction D; D=X/Y; D.display(); fraction E; E=Y*3; E.display(); // fraction Z(4,5); Z.reciprocal(); Z.display(); // fraction G; G=X+Y*4; G.display(); cout<<(X<=Y)<<endl; cout<<(X>Y)<<endl; cout<<(X==Y)<<endl; cout<<(X!=Y)<<endl; fraction H(2,3); fraction J; J=++H; J.display(); // fraction F; cin>>F; cout<<"F="<<F<<endl; }