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#include "utility/rational.hpp"
#pragma once #include "../template/template.hpp" namespace lib { struct rational { rational() : p(0), q(1) {} rational(ll n) : p(n), q(1) {} rational(ll n, ll m) { assert(m != 0); if (m < 0) n = -n, m = -m; ll g = gcd(n, m); p = n / g; q = m / g; } explicit operator const ld () const { return ld(p) / ld(q); } rational& operator+=(const rational& rhs){ ll g = gcd(q, rhs.q); ll np = rhs.q / g * p + q / g * rhs.p; ll nq = q / g * rhs.q; ll ng = gcd(np, nq); p = np / ng, q = nq / ng; return *this; } rational& operator-=(const rational& rhs) { (*this) += rational(-rhs.p, rhs.q); return *this; } rational& operator*=(const rational& rhs) { ll g1 = gcd(q, rhs.p), g2 = gcd(p, rhs.q); ll np = p / g2 * rhs.p / g1; ll nq = q / g1 * rhs.q / g2; p = np, q = nq; return *this; } rational& operator/=(const rational& rhs) { (*this) *= rational(rhs.q, rhs.p); return *this; } rational operator+() const { return *this; } rational operator-() const { return rational() - *this; } friend rational operator+(const rational& lhs, const rational& rhs) { return rational(lhs) += rhs; } friend rational operator-(const rational& lhs, const rational& rhs) { return rational(lhs) -= rhs; } friend rational operator*(const rational& lhs, const rational& rhs) { return rational(lhs) *= rhs; } friend rational operator/(const rational& lhs, const rational& rhs) { return rational(lhs) /= rhs; } friend bool operator==(const rational& lhs, const rational& rhs) { return lhs.p == rhs.p && lhs.q == rhs.q; } friend bool operator!=(const rational& lhs, const rational& rhs) { return lhs.p != rhs.p || lhs.q != rhs.q; } friend bool operator<(const rational lhs, const rational rhs) { return less_than(lhs, rhs); } friend bool operator>(const rational lhs, const rational rhs) { return less_than(rhs, lhs); } friend bool operator<=(const rational lhs, const rational rhs) { return lhs == rhs || lhs < rhs; } friend bool operator>=(const rational lhs, const rational rhs) { return lhs == rhs || lhs > rhs; } friend std::ostream& operator<<(std::ostream& os, const rational& r) { return os << r.p << " / " << r.q; } std::pair<ll,ll> val() const { return {p, q}; } private: ll p, q; static bool less_than(rational lhs, rational rhs) { __int128_t lv = __int128_t(lhs.p) * __int128_t(rhs.q); __int128_t rv = __int128_t(lhs.q) * __int128_t(rhs.p); return lv < rv; } }; } // namespace lib
#line 2 "utility/rational.hpp" #line 2 "template/template.hpp" #include <bits/stdc++.h> #define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++) #define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--) #define all(v) v.begin(), v.end() using ll = long long; using ld = long double; using ull = unsigned long long; template <typename T> bool chmin(T &a, const T &b) { if (a <= b) return false; a = b; return true; } template <typename T> bool chmax(T &a, const T &b) { if (a >= b) return false; a = b; return true; } namespace lib { using namespace std; } // namespace lib // using namespace lib; #line 4 "utility/rational.hpp" namespace lib { struct rational { rational() : p(0), q(1) {} rational(ll n) : p(n), q(1) {} rational(ll n, ll m) { assert(m != 0); if (m < 0) n = -n, m = -m; ll g = gcd(n, m); p = n / g; q = m / g; } explicit operator const ld () const { return ld(p) / ld(q); } rational& operator+=(const rational& rhs){ ll g = gcd(q, rhs.q); ll np = rhs.q / g * p + q / g * rhs.p; ll nq = q / g * rhs.q; ll ng = gcd(np, nq); p = np / ng, q = nq / ng; return *this; } rational& operator-=(const rational& rhs) { (*this) += rational(-rhs.p, rhs.q); return *this; } rational& operator*=(const rational& rhs) { ll g1 = gcd(q, rhs.p), g2 = gcd(p, rhs.q); ll np = p / g2 * rhs.p / g1; ll nq = q / g1 * rhs.q / g2; p = np, q = nq; return *this; } rational& operator/=(const rational& rhs) { (*this) *= rational(rhs.q, rhs.p); return *this; } rational operator+() const { return *this; } rational operator-() const { return rational() - *this; } friend rational operator+(const rational& lhs, const rational& rhs) { return rational(lhs) += rhs; } friend rational operator-(const rational& lhs, const rational& rhs) { return rational(lhs) -= rhs; } friend rational operator*(const rational& lhs, const rational& rhs) { return rational(lhs) *= rhs; } friend rational operator/(const rational& lhs, const rational& rhs) { return rational(lhs) /= rhs; } friend bool operator==(const rational& lhs, const rational& rhs) { return lhs.p == rhs.p && lhs.q == rhs.q; } friend bool operator!=(const rational& lhs, const rational& rhs) { return lhs.p != rhs.p || lhs.q != rhs.q; } friend bool operator<(const rational lhs, const rational rhs) { return less_than(lhs, rhs); } friend bool operator>(const rational lhs, const rational rhs) { return less_than(rhs, lhs); } friend bool operator<=(const rational lhs, const rational rhs) { return lhs == rhs || lhs < rhs; } friend bool operator>=(const rational lhs, const rational rhs) { return lhs == rhs || lhs > rhs; } friend std::ostream& operator<<(std::ostream& os, const rational& r) { return os << r.p << " / " << r.q; } std::pair<ll,ll> val() const { return {p, q}; } private: ll p, q; static bool less_than(rational lhs, rational rhs) { __int128_t lv = __int128_t(lhs.p) * __int128_t(rhs.q); __int128_t rv = __int128_t(lhs.q) * __int128_t(rhs.p); return lv < rv; } }; } // namespace lib