用c++实现分数（fraction）类

这个想法已经有3周，于是今天将它实现了。

Step 1基础：

我们需要定义一个class——fraction，全部属性定义为public

class fraction{
public:};

现在，让我们添加2个元素，分子和分母——fz和fw

Step 1.1添加分子分母：

class fraction{
public:int fz,fw;
};

Step 2重载运算符：

首先是约分

static fraction teasy(fraction ans){int yf=__gcd(ans.fz,ans.fw);ans.fz/=yf;ans.fw/=yf;return ans;
}

接着是lcm（最小公倍数）

static int lcm(int x,int y){return x*y/__gcd(x,y);
}

其次是加减乘除，很简单


friend fraction operator+(fraction x,fraction y){fraction ans;ans.fz=x.fz*y.fw+y.fz*x.fw;ans.fw=x.fw*y.fw;return teasy(ans);
}
friend fraction operator-(fraction x,fraction y){fraction ans;ans.fz=x.fz*y.fw-y.fz*x.fw;ans.fw=x.fw*y.fw;return teasy(ans);
}
friend fraction operator*(fraction x,fraction y){fraction ans;ans.fz=x.fz*y.fz;ans.fw=x.fw*y.fw;return teasy(ans);
}
friend fraction operator/(fraction x,fraction y){fraction ans;swap(y.fz,y.fw);	ans.fz=x.fz*y.fz;ans.fw=x.fw*y.fw;return teasy(ans);
}
friend bool operator>(fraction x,fraction y){int thard=lcm(x.fw,y.fw);x.fz=x.fz*thard/x.fw;y.fz=y.fz*thard/y.fw;if(x.fz>y.fz)return 1;else return 0;
}

当然，逻辑运算符也不能忘记

friend bool operator>(fraction x,fraction y){int thard=lcm(x.fw,y.fw);x.fz=x.fz*thard/x.fw;y.fz=y.fz*thard/y.fw;if(x.fz>y.fz)return 1;else return 0;
}
friend bool operator==(fraction x,fraction y){int thard=lcm(x.fw,y.fw);x.fz=x.fz*thard/x.fw;y.fz=y.fz*thard/y.fw;if(x.fz==y.fz)return 1;else return 0;
}
friend bool operator<(fraction x,fraction y){int thard=lcm(x.fw,y.fw);x.fz=x.fz*thard/x.fw;y.fz=y.fz*thard/y.fw;if(x.fz<y.fz)return 1;else return 0;
}
friend bool operator<=(fraction x,fraction y){int thard=lcm(x.fw,y.fw);x.fz=x.fz*thard/x.fw;y.fz=y.fz*thard/y.fw;if(x.fz<=y.fz)return 1;else return 0;
}
friend bool operator>=(fraction x,fraction y){int thard=lcm(x.fw,y.fw);x.fz=x.fz*thard/x.fw;y.fz=y.fz*thard/y.fw;if(x.fz>=y.fz)return 1;else return 0;
}

输出函数


static void print(fraction x){if(x.fz==0)cout<<"0\n";else if(x.fw==1)cout<<x.fz<<"\n";else cout<<x.fz<<"/"<<x.fw<<"\n"; 
}

n次方函数

static fraction fipow(fraction x,int y){fraction ans=x;for(int i=0;i<y-1;i++)ans=ans*x;return teasy(ans);
}

绝对值

static fraction frabs(fraction x){if(x.fz*x.fw<1){x.fz=abs(x.fz);x.fw=abs(x.fw);}return x;
}

完整code：

class fraction{
public:int fz,fw;static fraction teasy(fraction ans){int yf=__gcd(ans.fz,ans.fw);ans.fz/=yf;ans.fw/=yf;return ans;}static int lcm(int x,int y){return x*y/__gcd(x,y);}friend fraction operator+(fraction x,fraction y){fraction ans;ans.fz=x.fz*y.fw+y.fz*x.fw;ans.fw=x.fw*y.fw;return teasy(ans);}friend fraction operator-(fraction x,fraction y){fraction ans;ans.fz=x.fz*y.fw-y.fz*x.fw;ans.fw=x.fw*y.fw;return teasy(ans);}friend fraction operator*(fraction x,fraction y){fraction ans;ans.fz=x.fz*y.fz;ans.fw=x.fw*y.fw;return teasy(ans);}friend fraction operator/(fraction x,fraction y){fraction ans;swap(y.fz,y.fw);ans.fz=x.fz*y.fz;ans.fw=x.fw*y.fw;return teasy(ans);}friend bool operator>(fraction x,fraction y){int thard=lcm(x.fw,y.fw);x.fz=x.fz*thard/x.fw;y.fz=y.fz*thard/y.fw;if(x.fz>y.fz)return 1;else return 0;}friend bool operator==(fraction x,fraction y){int thard=lcm(x.fw,y.fw);x.fz=x.fz*thard/x.fw;y.fz=y.fz*thard/y.fw;if(x.fz==y.fz)return 1;else return 0;}friend bool operator<(fraction x,fraction y){int thard=lcm(x.fw,y.fw);x.fz=x.fz*thard/x.fw;y.fz=y.fz*thard/y.fw;if(x.fz<y.fz)return 1;else return 0;}friend bool operator<=(fraction x,fraction y){int thard=lcm(x.fw,y.fw);x.fz=x.fz*thard/x.fw;y.fz=y.fz*thard/y.fw;if(x.fz<=y.fz)return 1;else return 0;}friend bool operator>=(fraction x,fraction y){int thard=lcm(x.fw,y.fw);x.fz=x.fz*thard/x.fw;y.fz=y.fz*thard/y.fw;if(x.fz>=y.fz)return 1;else return 0;}static fraction fipow(fraction x,int y){fraction ans=x;for(int i=0;i<y-1;i++)ans=ans*x;return teasy(ans);} static fraction ffpow(fraction x,fraction y){}static void print(fraction x){if(x.fz==0)cout<<"0\n";else if(x.fw==1)cout<<x.fz<<"\n";else cout<<x.fz<<"/"<<x.fw<<"\n"; }static fraction frabs(fraction x){if(x.fz*x.fw<1){x.fz=abs(x.fz);x.fw=abs(x.fw);}return x;}
};