C++只提供了整数类和浮点数类,但是没有有理数类,所以需要自己写一个有理数类。
我们将使用分数来表示一个有理数。即Rational类有两个数据域,分子叫做 numerator,分母叫做denominator,且分母不能为0。
同时,一个有理数可能又很多表现形式,比如1/4可以表示为3/12,2/8等,我们统一用化简后的形式表示这个数,比如1/4。
#ifndef RATIONAL_H
#define RATIONAL_H
#include <ostream>
#include <istream>
class Rational
{
public:
Rational(int numerator = 0, int denominator = 1);
Rational(const Rational &other);
~Rational();
int getNumerator() const;
int getDenominator() const;
void setNumerator(int numerator);
void setDenominator(int denominator);
Rational operator+(const Rational &other) const;
Rational operator-(const Rational &other) const;
Rational operator*(const Rational &other) const;
Rational operator/(const Rational &other) const;
Rational operator%(const Rational &other) const;
Rational operator-() const;
Rational &operator=(const Rational &other);
Rational &operator+=(const Rational &other);
Rational &operator-=(const Rational &other);
Rational &operator*=(const Rational &other);
Rational &operator/=(const Rational &other);
Rational &operator%=(const Rational &other);
bool operator==(const Rational &other) const;
bool operator!=(const Rational &other) const;
bool operator<(const Rational &other) const;
bool operator>(const Rational &other) const;
bool operator<=(const Rational &other) const;
bool operator>=(const Rational &other) const;
friend std::ostream &operator<<(std::ostream &out, const Rational &r);
friend std::istream &operator>>(std::istream &in, Rational &r);
private:
int numerator; // 分子
int denominator; // 分母
void reduce(); // 约分
};
#endif // RATIONAL_H
#include "rational.h"
#include <iostream>
static int gcd(int a, int b)
{
if (b == 0)
return a;
return gcd(b, a % b);
}
Rational::Rational(int numerator, int denominator)
{
if (denominator == 0)
{
std::cout << "denominator can't be zero!" << std::endl;
exit(1);
}
this->numerator = numerator;
this->denominator = denominator;
reduce();
}
Rational::Rational(const Rational &other)
{
numerator = other.numerator;
denominator = other.denominator;
}
Rational::~Rational()
{
}
int Rational::getNumerator() const
{
return numerator;
}
int Rational::getDenominator() const
{
return denominator;
}
void Rational::setNumerator(int numerator)
{
this->numerator = numerator;
}
void Rational::setDenominator(int denominator)
{
this->denominator = denominator;
}
Rational Rational::operator+(const Rational &other) const
{
Rational result;
result.numerator = numerator * other.denominator + denominator * other.numerator;
result.denominator = denominator * other.denominator;
result.reduce();
return result;
}
Rational Rational::operator-(const Rational &other) const
{
Rational result;
result.numerator = numerator * other.denominator - denominator * other.numerator;
result.denominator = denominator * other.denominator;
result.reduce();
return result;
}
Rational Rational::operator*(const Rational &other) const
{
Rational result;
result.numerator = numerator * other.numerator;
result.denominator = denominator * other.denominator;
result.reduce();
return result;
}
Rational Rational::operator/(const Rational &other) const
{
Rational result;
result.numerator = numerator * other.denominator;
result.denominator = denominator * other.numerator;
result.reduce();
return result;
}
Rational Rational::operator%(const Rational &other) const
{
Rational result;
result.numerator = numerator * other.denominator;
result.denominator = denominator * other.numerator;
result.reduce();
return result;
}
Rational Rational::operator-() const
{
Rational result;
result.numerator = -numerator;
result.denominator = denominator;
result.reduce();
return result;
}
Rational &Rational::operator=(const Rational &other)
{
if (this != &other)
{
numerator = other.numerator;
denominator = other.denominator;
}
return *this;
}
Rational &Rational::operator+=(const Rational &other)
{
numerator = numerator * other.denominator + denominator * other.numerator;
denominator = denominator * other.denominator;
reduce();
return *this;
}
Rational &Rational::operator-=(const Rational &other)
{
numerator = numerator * other.denominator - denominator * other.numerator;
denominator = denominator * other.denominator;
reduce();
return *this;
}
Rational &Rational::operator*=(const Rational &other)
{
numerator = numerator * other.numerator;
denominator = denominator * other.denominator;
reduce();
return *this;
}
Rational &Rational::operator/=(const Rational &other)
{
numerator = numerator * other.denominator;
denominator = denominator * other.numerator;
reduce();
return *this;
}
Rational &Rational::operator%=(const Rational &other)
{
numerator = numerator * other.denominator;
denominator = denominator * other.numerator;
reduce();
return *this;
}
bool Rational::operator==(const Rational &other) const
{
return numerator == other.numerator && denominator == other.denominator;
}
bool Rational::operator!=(const Rational &other) const
{
return numerator != other.numerator || denominator != other.denominator;
}
bool Rational::operator<(const Rational &other) const
{
return numerator * other.denominator < denominator * other.numerator;
}
bool Rational::operator>(const Rational &other) const
{
return numerator * other.denominator > denominator * other.numerator;
}
bool Rational::operator<=(const Rational &other) const
{
return numerator * other.denominator <= denominator * other.numerator;
}
bool Rational::operator>=(const Rational &other) const
{
return numerator * other.denominator >= denominator * other.numerator;
}
std::ostream &operator<<(std::ostream &os, const Rational &r)
{
os << r.numerator << "/" << r.denominator;
return os;
}
std::istream &operator>>(std::istream &is, Rational &r)
{
is >> r.numerator >> r.denominator;
r.reduce();
return is;
}
void Rational::reduce()
{
int divisor = gcd(numerator, denominator);
numerator /= divisor;
denominator /= divisor;
}
#include "rational.h"
#include <iostream>
int main()
{
Rational r1(1, 2);
Rational r2(2, 3);
std::cout << r1 << " + " << r2 << " = " << r1 + r2 << std::endl;
std::cout << r1 << " - " << r2 << " = " << r1 - r2 << std::endl;
std::cout << r1 << " * " << r2 << " = " << r1 * r2 << std::endl;
std::cout << r1 << " / " << r2 << " = " << r1 / r2 << std::endl;
std::cout << r1 << " % " << r2 << " = " << r1 % r2 << std::endl;
return 0;
}