封装分数类

namespace std{
	template<class T=int>class frac{
	private:
		T Numerator=0,Denominator=1;
		T gcd(T a,T b){return (!b)?a:gcd(b,a%b);}
		void simplify(){
			if(Denominator==0)
				throw std::runtime_error("Denominator cannot be zero");
			if(Numerator==0){
				Denominator=1;
				return;
			}
			if(Denominator<0){
				Numerator=-Numerator;
				Denominator=-Denominator;
			}
			int common_divisor=gcd(std::abs(Numerator),Denominator);
			Numerator/=common_divisor;
			Denominator/=common_divisor;
		}
	public:
		frac(int num=0,int denom=1):Numerator(num),
		Denominator(denom){simplify();}
		T numerator(){return Numerator;}
		T denominator(){return Denominator;}
		frac operator+(const frac&other)const{
			T new_num=Numerator*other.denominator()+other.numerator()*Denominator;
			T new_denom=Denominator*other.denominator();
			return frac(new_num,new_denom);
		}
    	frac operator-(const frac&other)const{
			T new_num=Numerator*other.denominator()-other.numerator()*Denominator;
			T new_denom=Denominator*other.denominator();
			return frac(new_num,new_denom);
    	}
		frac operator*(const frac&other)const{
			int new_num=Numerator*other.numerator();
			int new_denom=Denominator*other.denominator();
			return frac(new_num,new_denom);
		}
    	frac operator/(const frac&other)const{
			if(other.numerator()==0)
				throw std::runtime_error("Cannot divide by zero");
			int new_num=Numerator*other.denominator();
			int new_denom=Denominator*other.numerator();
			return frac(new_num,new_denom);
    	}
    	frac operator+=(const frac&other){return *this=*this+other;}
    	frac operator-=(const frac&other){return *this=*this-other;}
    	frac operator*=(const frac&other){return *this=*this*other;}
    	frac operator/=(const frac&other){return *this=*this/other;}
    	frac abs()const{return frac(std::abs(Numerator),Denominator);}
    	frac operator-()const{return frac(-Numerator,Denominator);}
		bool operator==(const frac&other)const{return Numerator==other.numerator()&&Denominator==other.denominator();}
		bool operator!=(const frac&other)const{return !(*this==other);}
		bool operator< (const frac&other)const{return Numerator*other.denominator()<other.numerator()*Denominator;}
		bool operator> (const frac&other)const{return Numerator*other.denominator()>other.numerator()*Denominator;}
		bool operator<=(const frac&other)const{return !(*this>other);}
		bool operator>=(const frac&other)const{return !(*this<other);}
		double toDouble()const{return static_cast<double>(Numerator)/Denominator;}
		T toInt()const{return Numerator/Denominator;}
		friend ostream& operator<<(ostream&os,const frac&fraction){
			if(fraction.Denominator==1)os<<fraction.Numerator;
			else os<<fraction.Numerator<<"/"<<fraction.Denominator;
			return os;
		}
		friend istream& operator>>(istream&is,frac&fraction){
			char slash;
			is>>fraction.Numerator>>slash>>fraction.Denominator;
			if(slash!='/'){
				is.setstate(ios::failbit);
				fraction=frac();
			}
			else fraction.simplify();
			return is;
		}
	};
}