結果

問題 No.1936 Rational Approximation
コンテスト
ユーザー cutmdo
提出日時 2022-05-16 05:04:28
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 36 ms / 2,000 ms
コード長 7,552 bytes
コンパイル時間 3,419 ms
コンパイル使用メモリ 329,168 KB
最終ジャッジ日時 2025-01-29 08:29:00
ジャッジサーバーID
（参考情報） 		judge4 / judge4
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 1
other AC * 14
権限があれば一括ダウンロードができます

ソースコード

diff # 

//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,avx512f")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <iostream>
#include <iomanip>
#include <string>
#include <cmath>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <list>
#include <stack>
#include <queue>
#include <bitset>
#include <numeric>
#include <cassert>
#include <memory>
#include <random>
#include <functional>
#include <complex>
#include <immintrin.h>
#include <stdexcept>
#ifdef DEBUG
#include "./CompetitiveProgrammingCpp/debug.hpp"
#include "./CompetitiveProgrammingCpp/Timer.hpp"
#include "./CompetitiveProgrammingCpp/sample.hpp"
#else
#define dump(...)
#endif

/* macro */
#define FOR(i, b, e) for(ll i = (ll)(b); i < (ll)(e); ++i)
#define RFOR(i, b, e) for(ll i = (ll)((e)-1); i >= (ll)(b); --i)
#define REP(i, n) FOR(i, 0, (n))
#define RREP(i, n) RFOR(i, 0, (n))
#define REPC(x,c) for(const auto& x:(c))
#define REPI2(it,b,e) for(auto it = (b); it != (e); ++it)
#define REPI(it,c) REPI2(it, (c).begin(), (c).end())
#define RREPI(it,c) REPI2(it, (c).rbegin(), (c).rend())
#define REPI_ERACE2(it, b, e) for(auto it = (b); it != (e);)
#define REPI_ERACE(it, c) REPI_ERACE2(it, (c).begin(), (c).end())
#define ALL(x) (x).begin(),(x).end()
#define cauto const auto&
/* macro func */
template<class T>
inline auto sort(T& t) { std::sort(ALL(t)); }
template<class T>
inline auto rsort(T& t) { std::sort((t).rbegin(), (t).rend()); }
template<class T>
inline auto unique(T& t) { (t).erase(unique((t).begin(), (t).end()), (t).end()); }
template<class T, class S>
inline auto chmax(T& t, const S& s) { if(s > t) { t = s; return true; } return false; }
template<class T, class S>
inline auto chmin(T& t, const S& s) { if(s < t) { t = s; return true; } return false; }
inline auto BR() { std::cout << "\n"; }

/* type define */
using ll = long long;
using VS = std::vector<std::string>;
using VL = std::vector<long long>;
using VVL = std::vector<VL>;
using VVVL = std::vector<VVL>;
using VVVVL = std::vector<VVVL>;
using VVVVVL = std::vector<VVVVL>;
using VD = std::vector<double>;
template<class T>
using V = std::vector<T>;
template<class T = ll, class U = T>
using P = std::pair<T, U>;
using PAIR = P<ll>;

/* using std */
using std::cout;
constexpr char endl = '\n';
using std::cin;
using std::pair;
using std::string;
using std::stack;
using std::queue;
using std::deque;
using std::vector;
using std::list;
using std::map;
using std::unordered_map;
using std::multimap;
using std::unordered_multimap;
using std::set;
using std::unordered_set;
using std::unordered_multiset;
using std::multiset;
using std::bitset;
using std::priority_queue;

/* Initial processing  */
struct Preprocessing { Preprocessing() { std::cin.tie(0); std::ios::sync_with_stdio(0); }; }_Preprocessing;

/* Remove the source of the bug */
auto pow(signed, signed) { assert(false); }

/* define hash */
namespace std {
template <>	class hash<std::pair<ll, ll>> { public:	size_t operator()(const std::pair<ll, ll>& x) const { return hash<ll>()(1000000000 * x.first + x.second); } };
}

/* input */
template<class T> std::istream& operator >> (std::istream& is, vector<T>& vec) { for(T& x : vec) is >> x; return is; }

/* constant value */
constexpr ll MOD = 1000000007;
// constexpr ll MOD = 998244353;

//=============================================================================================

class EuclideanAlgorithm {
    using T = long long;

    const T m_a;
    const T m_b;
    const T m_mx; // 大きすぎるとオーバーフローしてしまう

    T m_gcd;
    T m_x;
    T m_y;

    auto excludedEuclidAlgorithm(T a, T b) -> std::tuple<T, T, T> {
        if(a < 0) {
            auto [g, x, y] = excludedEuclidAlgorithm(-a, -b);
            return {g,-x,-y};
        }
        if(b == 0) { return {a, 1, 0}; }
        auto [g, y, x] = excludedEuclidAlgorithm(b, a % b);
        y -= a / b * x;
        return {g, x, y};
    }

    auto kRange(T x, T b, T l) const -> std::tuple<T, T> {
        // x + b * k >= l を満たす k の範囲を求める
        T xd = (l - x);
        if(b == 0 && x >= l) { return {-m_mx,m_mx}; }
        if(b == 0 && x < l) { return {m_mx,-m_mx}; }
        if(b > 0 && xd < 0) { return {xd / b,m_mx}; }
        if(b > 0 && xd >= 0) { return {(xd + b - 1) / b,m_mx}; }
        if(b < 0 && xd < 0) { return {-m_mx,(-xd) / (-b)}; }
        if(b < 0 && xd >= 0) { return {-m_mx,-(xd - b - 1) / (-b)}; }
        return {m_mx,-m_mx};
    }

public:
    auto debug()const {
        std::cout << m_a << " * " << m_x
            << " + " << m_b << " * " << m_y
            << " = " << m_gcd << std::endl;
        std::cout << m_a * m_x + m_b * m_y
            << " = " << m_gcd << std::endl;
    }

    EuclideanAlgorithm(T a, T b, T mx = 1e9) :m_a(a), m_b(b), m_mx(mx) {
        if(a == 0 && b == 0) { throw std::runtime_error(""); }
        auto [g, x, y] = excludedEuclidAlgorithm(a, b);
        m_gcd = g; m_x = x; m_y = y;
    }

    auto gcd() const {
        return m_gcd;
    }
    auto get(T x, T y) const {
        return m_a * x + m_b * y;
    }
    auto get(T k) const ->std::tuple<T, T> {
        if(m_b == 0) { return {m_x,m_y - k}; }
        if(m_a == 0) { return {m_x + k,m_y}; }
        return {m_x + m_b * k, m_y - m_a * k};
    }
    auto getMinX(T x_l = 0)const -> std::tuple<T, T> {
        return kRange(m_x, m_b, x_l);
    }
    auto getMinY(T y_l = 0)const -> std::tuple<T, T> {
        return kRange(m_y, -1 * m_a, y_l);
    }
    auto getMin(T x_l = 0, T y_l = 0)const -> std::tuple<T, T> {
        auto [xl, xr] = getMinX(x_l);
        auto [yl, yr] = getMinY(y_l);
        return {std::max(xl,yl),std::min(xr,yr)};
    }
};



using D = PAIR;
auto operator<(const D& a, const D& b) {
    ll l = a.first * b.second;
    ll r = a.second * b.first;
    return l < r;
}
auto g(const D& d) {
    ll g = std::gcd(d.first, d.second);
    return D{d.first / g,d.second / g};
}

auto solve(ll p, ll q) {

    auto pq = EuclideanAlgorithm(-p, q);
    auto [rk, _] = pq.getMin(1, 1);
    auto [rx, ry] = pq.get(rk);
    auto rg = pq.gcd();

    auto qp = EuclideanAlgorithm(-q, p);
    auto [lk, __] = qp.getMin(1, 1);
    auto [lx, ly] = qp.get(lk);
    auto lg = qp.gcd();

    ll ans = rx / rg + ry / rg + lx / lg + ly / lg;
    return ans;

}
auto solve_c(ll p, ll q) {
    D mx = {0,1};
    D mn = {1,1};
    FOR(i, 1, q) REP(j, i) {
        if(D{j, i} < D{p,q}) {
            if(mx < D{j,i}) {
                mx = D{j,i};
            }
        }
    }
    FOR(i, 1, q) REP(j, i + 1) if(D{p,q} < D{j, i}) {
        chmin(mn, D{j,i});
    }
    mn = g(mn);
    mx = g(mx);
    dump(mn, mx);
    return mx.first + mx.second + mn.second + mn.first;
}

signed main() {
    /**/
    ll p, q;
    cin >> p >> q;

    auto ans = solve(p, q);
    cout << ans << endl;

    //cout << "-- cor --" << endl;
    //auto ans_c = solve_c(p, q);
    //cout << ans_c << endl;

    /*/
    auto tm = Timer::SimpleTimer();
    auto gen = Sample::SampleGenerator();
    REP(_, 100) {
        auto [p] = gen.generate(PAIR{1,9});
        auto [q] = gen.generate(PAIR{p + 1,10});
        auto g = std::gcd(p, q);
        p /= g;
        q /= g;

        auto ans = solve(p, q);
        auto ans_c = solve_c(p, q);
        if(ans != ans_c) {
            cout << p << " " << q << endl;
            dump(ans, ans_c);
            return 0;
        }

    }
    tm.print();
    /**/
}
0