結果

問題 No.1936 Rational Approximation
ユーザー hitonanodehitonanode
提出日時 2022-05-22 09:30:48
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
TLE  
実行時間 -
コード長 8,375 bytes
コンパイル時間 1,545 ms
コンパイル使用メモリ 169,396 KB
実行使用メモリ 16,960 KB
最終ジャッジ日時 2024-09-20 12:24:52
合計ジャッジ時間 8,050 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 TLE -
testcase_01 -- -
testcase_02 -- -
testcase_03 -- -
testcase_04 -- -
testcase_05 -- -
testcase_06 -- -
testcase_07 -- -
testcase_08 -- -
testcase_09 -- -
testcase_10 -- -
testcase_11 -- -
testcase_12 -- -
testcase_13 -- -
testcase_14 -- -
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ソースコード

diff # 

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr)
#else
#define dbg(x) 0
#define dbgif(cond, x) 0
#endif

#include <iostream>

// Rational number + {infinity(1 / 0), -infiity(-1 / 0)} （有理数）
struct Rational {
    using Int = long long int; // __int128
    Int num, den;
    static Int my_gcd(Int a, Int b) {
        // return __gcd(a, b);
        if (a < 0) a = -a;
        if (b < 0) b = -b;
        while (a and b) {
            if (a > b)
                a %= b;
            else
                b %= a;
        }
        return a + b;
    }
    Rational(Int num = 0, Int den = 1) : num(num), den(den) { normalize(); }
    void normalize() { // reduction and making denominator nonnegative
        Int g = my_gcd(num, den);
        num /= g, den /= g;
        if (den < 0) num = -num, den = -den;
    }
    Rational operator+(const Rational &r) const {
        return Rational(num * r.den + den * r.num, den * r.den);
    }
    Rational operator-(const Rational &r) const {
        return Rational(num * r.den - den * r.num, den * r.den);
    }
    Rational operator*(const Rational &r) const { return Rational(num * r.num, den * r.den); }
    Rational operator/(const Rational &r) const { return Rational(num * r.den, den * r.num); }
    Rational &operator+=(const Rational &r) { return *this = *this + r; }
    Rational &operator-=(const Rational &r) { return *this = *this - r; }
    Rational &operator*=(const Rational &r) { return *this = *this * r; }
    Rational &operator/=(const Rational &r) { return *this = *this / r; }
    Rational operator-() const { return Rational(-num, den); }
    Rational abs() const { return Rational(num > 0 ? num : -num, den); }
    bool operator==(const Rational &r) const { return num == r.num and den == r.den; }
    bool operator!=(const Rational &r) const { return num != r.num or den != r.den; }
    bool operator<(const Rational &r) const {
        if (den == 0 and r.den == 0)
            return num < r.num;
        else if (den == 0)
            return num < 0;
        else if (r.den == 0)
            return r.num > 0;
        else
            return num * r.den < den * r.num;
    }
    bool operator<=(const Rational &r) const { return (*this == r) or (*this < r); }
    bool operator>(const Rational &r) const { return r < *this; }
    bool operator>=(const Rational &r) const { return (r == *this) or (r < *this); }
    explicit operator double() const { return (double)num / (double)den; }
    explicit operator long double() const { return (long double)num / (long double)den; }
    friend std::ostream &operator<<(std::ostream &os, const Rational &x) {
        return os << x.num << '/' << x.den;
    }
};

int main() {
    lint P, Q;
    cin >> P >> Q;

    lint num = 1, den = 1;

    lint lnum = P - 1, lden = Q - 1;

    auto test = [&](lint D) -> void {
        lint N = P * D / Q + 1;
        lint N1 = (P * D - 1) / Q;
        if (N * den < D * num) num = N, den = D;
        if (N1 * lden > D * lnum) lnum = N1, lden = D;
    };

    FOR(d, 2, 100) if (d < Q) test(d);

    for (int i = 2; i < Q; ++i) {
        test(i);
    }

    dbg(make_tuple(lnum, lden, num, den));

    lint gl = __gcd(lnum, lden);
    lint gr = __gcd(num, den);

    cout << lnum / gl + lden / gl + num / gr + den / gr << endl;
}
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