Rational Number
コードについての説明
有理数型のコード. 計算幾何や確率の問題で誤差落ちが怖いときに用いたくなるかもしれない(実際に使ったことはない).
整数型との演算も Rational Number にキャストされて上手く行えるはず.
(コンストラクタ)
$Rational Number$<T>$(num)$: 整数 $num$ の有理数型を構築
$Rational Number$<T>$(num, den)$: 有理数 $num / den$ の有理数型を構築
コード
template<typename T> class Rational {
private:
static Rational make(const T& x, const T& y){
Rational m; return m.num = x, m.den = y, m;
}
public:
friend ostream& operator<<(ostream& os, const Rational& rn) {
return (os << rn.num << " / " << rn.den);
}
Rational& operator=(T val){ return *this = Rational(val); }
bool operator<(const Rational& val) const { return num*val.den < den*val.num; }
bool operator<(const T val) const { return *this < Rational(val); }
friend bool operator<(const T val1, const Rational& val2){ return Rational(val1) < val2; }
bool operator>(const Rational& val) const { return val < *this; }
bool operator>(const T val) const { return *this > Rational(val); }
friend bool operator>(const T val1, const Rational& val2){ return Rational(val1) > val2; }
bool operator<=(const Rational& val) const { return !(*this > val); }
bool operator<=(const T val) const { return *this <= Rational(val); }
friend bool operator<=(const T val1, const Rational& val2){ return Rational(val1) <= val2; }
bool operator>=(const Rational& val) const { return !(*this < val); }
bool operator>=(const T val) const { return *this >= Rational(val); }
friend bool operator>=(const T val1, const Rational& val2){ return Rational(val1) >= val2; }
bool operator==(const Rational& val) const { return num*val.den == den*val.num; }
bool operator==(const T val) const { return *this == Rational(val); }
friend bool operator==(const T val1, const Rational& val2){ return Rational(val1) == val2; }
bool operator!=(const Rational& val) const { return !(*this == val); }
bool operator!=(const T val) const { return *this != Rational(val); }
friend bool operator!=(const T val1, const Rational& val2){ return Rational(val1) != val2; }
explicit operator bool() const noexcept { return num; }
bool operator!() const noexcept { return !static_cast<bool>(*this); }
Rational operator+() const { return *this; }
Rational operator-() const { return make(-num, den); }
friend Rational abs(const Rational& val){ return make(abs(val.num), val.den); }
Rational operator+(const Rational& val) const { return make(num*val.den+val.num*den, den*val.den); }
Rational operator+(T val) const { return *this + Rational(val); }
friend Rational operator+(T a, const Rational& b){ return b + a; }
Rational& operator+=(const Rational& val){ return *this = *this + val; }
Rational& operator+=(const T& val){ return *this = *this + val; }
Rational& operator++(){ return *this += 1; }
Rational operator++(int){ return make(num + den, den); }
Rational operator-(const Rational& val) const { return make(num*val.den-val.num*den, den*val.den); }
Rational operator-(T val) const { return *this - Rational(val); }
friend Rational operator-(T a, const Rational& b){ return Rational(a) - b; }
Rational& operator-=(const Rational& val){ return *this = *this - val; }
Rational& operator-=(const T& val){ return *this = *this - val; }
Rational& operator--(){ return *this -= 1; }
Rational operator--(int){ return make(num - den, den); }
Rational operator*(const Rational& val) const { return make(num*val.num, den*val.den); }
Rational operator*(T val) const { return *this * Rational(val); }
friend Rational operator*(T a, const Rational& b){ return b * a; }
Rational& operator*=(const Rational& val){ return *this = *this * val;}
Rational& operator*=(const T& val){ return *this = *this * val; }
Rational operator/(const Rational& val) const { return make(num*val.den, den*val.num); }
Rational operator/(T val) const { return *this / Rational(val); }
friend Rational operator/(T a, const Rational& b){ return Rational(a) / b; }
Rational& operator/=(const Rational& val){ return *this / val; }
Rational& operator/=(const T& val){ return *this = *this / val; }
T num, den;
Rational(){}
Rational(T num_) : num(num_), den(1){}
Rational(T num_, T den_) : num(num_), den(den_){ if(den < 0) num = -num, den = -den; }
};
verify 用の問題
AOJ : Unit Fraction Partition
提出コード
Codeforces : Power Transmission (Hard Edition)
提出コード
(掛け算や割り算は verify していません)