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Rational.hpp
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Rational.hpp
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#pragma once
#include <cctype>
#include <iosfwd>
#include <iostream>
#include <stdexcept>
template <typename T>
class Rational {
T mNum;
T mDen;
void reduce(T &num, T &den) {
T g = gcd(abs(num), abs(den));
num /= g;
den /= g;
if (den < 0) {
den = -den;
num = -num;
if (num == 0) {
den = 1;
}
}
}
T gcd(T a, T b) { return b == 0 ? a : gcd(b, a % b); }
public:
Rational() : mNum(0), mDen(1) {}
Rational(const T &num, const T &den) : mNum(num), mDen(den) {
if (mDen == 0) {
throw std::runtime_error("Rational: denominator can't be 0!");
}
reduce(mNum, mDen);
}
const T &num() const { return mNum; }
const T &den() const { return mDen; }
};
template <typename T>
Rational<T> operator+(const Rational<T> &r1, const Rational<T> &r2) {
T num = r2.den() * r1.num() + r1.den() * r2.num();
T den = r1.den() * r2.den();
return Rational<T>(num, den);
}
template <typename T>
Rational<T> operator-(const Rational<T> &r1, const Rational<T> &r2) {
T num = r2.den() * r1.num() - r1.den() * r2.num();
T den = r1.den() * r2.den();
return Rational<T>(num, den);
}
template <typename T>
Rational<T> operator*(const Rational<T> &r1, const Rational<T> &r2) {
T num = r1.num() * r2.num();
T den = r1.den() * r2.den();
return Rational<T>(num, den);
}
template <typename T>
Rational<T> operator/(const Rational<T> &r1, const Rational<T> &r2) {
if (r2.num() == 0) {
throw std::runtime_error("Rational: can't divide by 0 (0/1)!");
}
T num = r1.num() * r2.den();
T den = r1.den() * r2.num();
return Rational<T>(num, den);
}
template <typename T>
bool operator<(const Rational<T> &r1, const Rational<T> &r2) {
return r1.num() * r2.den() < r2.num() * r1.den();
}
template <typename T>
bool operator>(const Rational<T> &r1, const Rational<T> &r2) {
return r2 < r1;
}
template <typename T>
bool operator==(const Rational<T> &r1, const Rational<T> &r2) {
return r1.num() * r2.den() == r2.num() * r1.den();
}
template <typename T>
bool operator!=(const Rational<T> &r1, const Rational<T> &r2) {
return !(r1 == r2);
}
template <typename T>
bool operator<=(const Rational<T> &r1, const Rational<T> &r2) {
return !(r1 > r2);
}
template <typename T>
bool operator>=(const Rational<T> &r1, const Rational<T> &r2) {
return !(r1 < r2);
}
template <typename T>
std::ostream &operator<<(std::ostream &out, const Rational<T> &r) {
out << r.num() << "/" << r.den();
return out;
}
template <typename T>
std::istream &operator>>(std::istream &in, Rational<T> &r) {
T num, den;
char ch;
if (!(in >> num)) return in;
if (!in.get(ch)) return in;
if (ch != '/') {
in.setstate(std::ios_base::failbit);
return in;
}
if (!in.get(ch)) return in;
if (ch != '+' && ch != '-' && !isdigit(ch)) {
in.setstate(std::ios_base::failbit);
return in;
}
in.putback(ch);
if (!(in >> den)) return in;
r = Rational<T>(num, den);
return in;
}