Rational number
(Mylib/Number/Rational/rational.cpp)

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• Last update: 2021-04-23 23:44:44+09:00

Operations

Requirements

Notes

Problems

References

Verified with

• test/aoj/1300/main.test.cpp

Code

#pragma once
#include <cmath>
#include <iostream>
#include <numeric>

namespace haar_lib {
  class rational {
    int64_t nume_, deno_;

  public:
    rational() : nume_(0), deno_(1) {}
    rational(int64_t nume) : nume_(nume), deno_(1) {}
    rational(int64_t nume, int64_t deno) {
      const int64_t g = std::gcd(nume, deno);
      nume_           = nume / g;
      deno_           = deno / g;
      if (deno_ < 0) {
        nume_ = -nume_;
        deno_ = -deno_;
      }
    }

    int64_t numerator() const { return nume_; }
    int64_t denominator() const { return deno_; }

    auto operator+(const rational &b) {
      int64_t l = std::lcm((*this).deno_, b.deno_);
      return rational(l / (*this).deno_ * (*this).nume_ + l / b.deno_ * b.nume_, l);
    }

    auto operator-(const rational &b) {
      int64_t l = std::lcm((*this).deno_, b.deno_);
      return rational(l / (*this).deno_ * (*this).nume_ - l / b.deno_ * b.nume_, l);
    }

    auto operator*(const rational &b) {
      return rational((*this).nume_ * b.nume_, (*this).deno_ * b.deno_);
    }

    auto operator/(const rational &b) {
      return rational((*this).nume_ * b.deno_, (*this).deno_ * b.nume_);
    }

    auto &operator+=(const rational &a) {
      *this = *this + a;
      return *this;
    }
    auto &operator-=(const rational &a) {
      *this = *this - a;
      return *this;
    }
    auto &operator*=(const rational &a) {
      *this = *this * a;
      return *this;
    }
    auto &operator/=(const rational &a) {
      *this = *this / a;
      return *this;
    }

    explicit operator double() const { return (double) nume_ / deno_; }
    explicit operator long double() const { return (long double) nume_ / deno_; }

    auto operator-() { return rational(-nume_, deno_); }

    friend std::ostream &operator<<(std::ostream &os, const rational &r) {
      if (r.deno_ == 1)
        os << r.nume_;
      else
        os << r.nume_ << "/" << r.deno_;
      return os;
    }

    friend bool operator==(const rational &a, const rational &b) { return a.nume_ == b.nume_ and a.deno_ == b.deno_; }
    friend bool operator!=(const rational &a, const rational &b) { return !(a == b); }
    friend bool operator<(const rational &a, const rational &b) { return a.nume_ * b.deno_ < b.nume_ * a.deno_; }
    friend bool operator<=(const rational &a, const rational &b) { return a.nume_ * b.deno_ <= b.nume_ * a.deno_; }
    friend bool operator>(const rational &a, const rational &b) { return !(a <= b); }
    friend bool operator>=(const rational &a, const rational &b) { return !(a < b); }

    friend auto abs(const rational &a) {
      return rational(std::abs(a.nume_), std::abs(a.deno_));
    }
  };
}  // namespace haar_lib

#line 2 "Mylib/Number/Rational/rational.cpp"
#include <cmath>
#include <iostream>
#include <numeric>

namespace haar_lib {
  class rational {
    int64_t nume_, deno_;

  public:
    rational() : nume_(0), deno_(1) {}
    rational(int64_t nume) : nume_(nume), deno_(1) {}
    rational(int64_t nume, int64_t deno) {
      const int64_t g = std::gcd(nume, deno);
      nume_           = nume / g;
      deno_           = deno / g;
      if (deno_ < 0) {
        nume_ = -nume_;
        deno_ = -deno_;
      }
    }

    int64_t numerator() const { return nume_; }
    int64_t denominator() const { return deno_; }

    auto operator+(const rational &b) {
      int64_t l = std::lcm((*this).deno_, b.deno_);
      return rational(l / (*this).deno_ * (*this).nume_ + l / b.deno_ * b.nume_, l);
    }

    auto operator-(const rational &b) {
      int64_t l = std::lcm((*this).deno_, b.deno_);
      return rational(l / (*this).deno_ * (*this).nume_ - l / b.deno_ * b.nume_, l);
    }

    auto operator*(const rational &b) {
      return rational((*this).nume_ * b.nume_, (*this).deno_ * b.deno_);
    }

    auto operator/(const rational &b) {
      return rational((*this).nume_ * b.deno_, (*this).deno_ * b.nume_);
    }

    auto &operator+=(const rational &a) {
      *this = *this + a;
      return *this;
    }
    auto &operator-=(const rational &a) {
      *this = *this - a;
      return *this;
    }
    auto &operator*=(const rational &a) {
      *this = *this * a;
      return *this;
    }
    auto &operator/=(const rational &a) {
      *this = *this / a;
      return *this;
    }

    explicit operator double() const { return (double) nume_ / deno_; }
    explicit operator long double() const { return (long double) nume_ / deno_; }

    auto operator-() { return rational(-nume_, deno_); }

    friend std::ostream &operator<<(std::ostream &os, const rational &r) {
      if (r.deno_ == 1)
        os << r.nume_;
      else
        os << r.nume_ << "/" << r.deno_;
      return os;
    }

    friend bool operator==(const rational &a, const rational &b) { return a.nume_ == b.nume_ and a.deno_ == b.deno_; }
    friend bool operator!=(const rational &a, const rational &b) { return !(a == b); }
    friend bool operator<(const rational &a, const rational &b) { return a.nume_ * b.deno_ < b.nume_ * a.deno_; }
    friend bool operator<=(const rational &a, const rational &b) { return a.nume_ * b.deno_ <= b.nume_ * a.deno_; }
    friend bool operator>(const rational &a, const rational &b) { return !(a <= b); }
    friend bool operator>=(const rational &a, const rational &b) { return !(a < b); }

    friend auto abs(const rational &a) {
      return rational(std::abs(a.nume_), std::abs(a.deno_));
    }
  };
}  // namespace haar_lib

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