結果

問題 No.1936 Rational Approximation
コンテスト
ユーザー cutmdo
提出日時 2022-05-13 23:06:36
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 18 ms / 2,000 ms
コード長 5,763 bytes
コンパイル時間 3,124 ms
コンパイル使用メモリ 320,140 KB
最終ジャッジ日時 2025-01-29 07:29:01
ジャッジサーバーID
（参考情報） 		judge2 / judge4
このコードへのチャレンジ
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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;

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

long long extGCD(long long a, long long b, long long& x, long long& y) {
    if(b == 0) {
        x = 1;
        y = 0;
        return a;
    }
    long long d = extGCD(b, a % b, y, x);
    y -= a / b * x;
    return d;
}


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) {

    D mn, mx;
    {
        ll x, y;
        extGCD(q, p, x, y);
        y = -y;
        ll n1 = (x > 0) ? 0 : (std::abs(x) + p) / p;
        ll n2 = (y > 0) ? 0 : (std::abs(y) + q) / q;
        ll need = std::max(n1, n2);
        y += q * need;
        mn.first = p * y + 1;
        mn.second = q * y;
        mn = g(mn);

    }
    {
        ll x, y;
        extGCD(p, q, x, y);
        y = -y;
        ll d = (q - x) / q;
        x += q * d;
        mx.first = p * x - 1;
        mx.second = q * x;
        mx = g(mx);
    }
    dump(mn, mx);

    ll ans = mn.first + mn.second + mx.first + mx.second;
    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();
    /**/
}
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