分数类
struct Fraction
{
ll num,den;
Fraction(ll n=0,ll d=1):num(n),den(d)
{
d=__gcd(num,den),num/=d,den/=d;
if(den<0)num=-num,den=-den;
}
friend Fraction operator+(const Fraction& A,const Fraction& B)
{
ll d=__gcd(A.den,B.den);
return Fraction(B.den/d*A.num+A.den/d*B.num,A.den/d*B.den);
}
Fraction& operator+=(const Fraction &c)
{
return *this=*this+c;
}
Fraction operator-()const
{
Fraction r(*this);
return r.num=-r.num,r;
}
friend Fraction operator-(const Fraction &a,const Fraction &c)
{
return -c+a;
}
Fraction& operator-=(const Fraction &c)
{
return *this=*this-c;
}
friend Fraction operator*(const Fraction& A,const Fraction& B)
{
return Fraction(A.num*B.num,A.den*B.den);
}
Fraction& operator*=(const Fraction &c)
{
return *this=*this*c;
}
friend Fraction operator/(const Fraction& A,const Fraction& B)
{
return Fraction(A.num*B.den,A.den*B.num);
}
Fraction& operator/=(const Fraction &c)
{
return *this=*this/c;
}
friend Fraction operator%(const Fraction &a,const Fraction &c)
{
return Fraction(a.num*c.den%(c.num*a.den),a.den*c.den);
}
Fraction& operator%=(const Fraction &c)
{
return *this=*this%c;
}
friend bool operator==(const Fraction &a,const Fraction &b)
{
return a.num*b.den==a.den*b.num;
}
friend bool operator!=(const Fraction &a,const Fraction &b)
{
return !(a==b);
}
friend bool operator<(const Fraction &a,const Fraction &b)
{
return a.num*b.den<a.den*b.num;
}
friend bool operator>(const Fraction &a,const Fraction &b)
{
return b<a;
}
friend bool operator<=(const Fraction &a,const Fraction &b)
{
return !(a>b);
}
friend bool operator>=(const Fraction &a,const Fraction &b)
{
return !(a<b);
}
friend Fraction abs(Fraction f)
{
if(f.num<0)f.num=-f.num;
return f;
}
friend ostream& operator<<(ostream &os,const Fraction &f)
{
return !f.num?os<<0:
f.den==1?os<<f.num:
os<<f.num<<'/'<<f.den;
}
};
