fraction.hpp

[詳解]

#include"../../kyopro_library/template.hpp"
 
/// @brief 有理数構造体
template<typename T=ll>
struct Fraction {
    T upper,lower;
    Fraction()=default;
 
    /// @brief 有理数 a/b を宣言する
    Fraction(T a, T b) {
        T g=gcd(a,b);
        upper=a/g,lower=b/g;
        if(lower<0) upper*=-1,lower*=-1;
    }
 
    Fraction(T a=0) { upper=a,lower=1; }
 
    Fraction operator+(const Fraction& f) { return Fraction(upper*f.lower+f.upper*lower,lower*f.lower); }
    Fraction operator-(const Fraction& f) { return Fraction(upper*f.lower-f.upper*lower,lower*f.lower); }
    Fraction operator*(const Fraction& f) { return Fraction(upper*f.upper,lower*f.lower); }
    Fraction operator/(const Fraction& f) { return Fraction(upper*f.lower,lower*f.upper); }
 
    Fraction operator+=(const Fraction& f) { return *this=*this+f; }
    Fraction operator-=(const Fraction& f) { return *this=*this-f; }
    Fraction operator*=(const Fraction& f) { return *this=*this*f; }
    Fraction operator/=(const Fraction& f) { return *this=*this/f; }
 
    Fraction operator+(const T& f) { return Fraction(upper+f*lower,lower); }
    Fraction operator-(const T& f) { return Fraction(upper-f*lower,lower); }
    Fraction operator*(const T& f) { return Fraction(upper*f,lower); }
    Fraction operator/(const T& f) { return Fraction(upper,lower*f); }
 
    Fraction operator+=(const T& f) { return *this=*this+f; }
    Fraction operator-=(const T& f) { return *this=*this-f; }
    Fraction operator*=(const T& f) { return *this=*this*f; }
    Fraction operator/=(const T& f) { return *this=*this/f; }
 
    Fraction operator-() { return Fraction(-upper,lower); }
 
    bool operator==(const Fraction& f) const { return upper==f.upper&&lower==f.lower; }
    bool operator!=(const Fraction& f) const { return upper!=f.upper||lower!=f.lower; }
    bool operator<(const Fraction& f) const { return upper*f.lower<f.upper*lower; }
    bool operator<=(const Fraction& f) const { return upper*f.lower<=f.upper*lower; }
    bool operator>(const Fraction& f) const { return upper*f.lower>f.upper*lower; }
    bool operator>=(const Fraction& f) const { return upper*f.lower>=f.upper*lower; }
    bool operator==(const T& f) const {return upper==f&&lower==1; }
    bool operator!=(const T& f) const {return upper!=f||lower!=1; }
    bool operator<(const T& f) const {return upper<f*lower; }
    bool operator<=(const T& f) const {return upper<=f*lower; }
    bool operator>(const T& f) const {return upper>f*lower; }
    bool operator>=(const T& f) const {return upper>=f*lower; }
 
    friend ostream& operator<<(ostream& os, const Fraction& f) {
        os<<f.upper<<"/"<<f.lower;
        return os;
    }
 
private:
    T gcd(T a, T b) {
        while(b!=0) {
            T r=a%b;
            a=b;
            b=r;
        }
        return a;
    }
};