#794678 (C++23) No.2066 Simple Math !

提出ソース

結果

問題	No.2066 Simple Math !
ユーザー	hitonanode
提出日時	2022-09-02 21:43:08
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	194 ms / 2,000 ms
コード長	8,856 bytes
コンパイル時間	2,099 ms
コンパイル使用メモリ	171,016 KB
実行使用メモリ	6,820 KB
最終ジャッジ日時	2024-11-16 02:53:43
合計ジャッジ時間	8,232 ms
ジャッジサーバーID （参考情報）	judge4 / judge3

このコードへのチャレンジ
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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	AC	2 ms 6,816 KB
testcase_01	AC	42 ms 6,816 KB
testcase_02	AC	47 ms 6,816 KB
testcase_03	AC	6 ms 6,820 KB
testcase_04	AC	193 ms 6,820 KB
testcase_05	AC	189 ms 6,816 KB
testcase_06	AC	192 ms 6,820 KB
testcase_07	AC	194 ms 6,816 KB
testcase_08	AC	191 ms 6,816 KB
testcase_09	AC	192 ms 6,816 KB
testcase_10	AC	191 ms 6,816 KB
testcase_11	AC	192 ms 6,816 KB
testcase_12	AC	193 ms 6,816 KB
testcase_13	AC	191 ms 6,820 KB
testcase_14	AC	171 ms 6,816 KB
testcase_15	AC	175 ms 6,820 KB
testcase_16	AC	171 ms 6,820 KB
testcase_17	AC	166 ms 6,816 KB
testcase_18	AC	166 ms 6,816 KB
testcase_19	AC	97 ms 6,820 KB
testcase_20	AC	97 ms 6,816 KB
testcase_21	AC	96 ms 6,816 KB
testcase_22	AC	98 ms 6,816 KB
testcase_23	AC	102 ms 6,816 KB
testcase_24	AC	157 ms 6,820 KB
testcase_25	AC	153 ms 6,816 KB
testcase_26	AC	154 ms 6,816 KB
testcase_27	AC	156 ms 6,820 KB
testcase_28	AC	156 ms 6,816 KB
testcase_29	AC	38 ms 6,820 KB
testcase_30	AC	6 ms 6,820 KB
testcase_31	AC	26 ms 6,820 KB

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ソースコード

raw source code

#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 <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class 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 <class 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 <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::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) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif

// \sum_{i=0}^{n-1} floor((ai + b) / m)
// 0 <= n < 2e32
// 1 <= m < 2e32
// 0 <= a, b < m
// Complexity: O(lg(m))
long long floor_sum(long long n, long long m, long long a, long long b) {
    auto safe_mod = [](long long x, long long m) -> long long {
        x %= m;
        if (x < 0) x += m;
        return x;
    };
    auto floor_sum_unsigned = [](unsigned long long n, unsigned long long m, unsigned long long a,
                                 unsigned long long b) -> unsigned long long {
        unsigned long long ans = 0;
        while (true) {
            if (a >= m) {
                ans += n * (n - 1) / 2 * (a / m);
                a %= m;
            }
            if (b >= m) {
                ans += n * (b / m);
                b %= m;
            }

            unsigned long long y_max = a * n + b;
            if (y_max < m) break;
            // y_max < m * (n + 1)
            // floor(y_max / m) <= n
            n = (unsigned long long)(y_max / m);
            b = (unsigned long long)(y_max % m);
            std::swap(m, a);
        }
        return ans;
    };

    unsigned long long ans = 0;
    if (a < 0) {
        unsigned long long a2 = safe_mod(a, m);
        ans -= 1ULL * n * (n - 1) / 2 * ((a2 - a) / m);
        a = a2;
    }
    if (b < 0) {
        unsigned long long b2 = safe_mod(b, m);
        ans -= 1ULL * n * ((b2 - b) / m);
        b = b2;
    }
    return ans + floor_sum_unsigned(n, m, a, b);
}


lint solve(lint P, lint Q, int K) {
    if (P == Q) return P * K;

    dbg(make_pair(P, Q));

    const lint up = (P - 1) * (Q - 1);
    lint hi = 1LL << 60, lo = 0;
    dbg(up);

    while (hi - lo > 1) {
        lint t = (hi + lo) / 2;

        lint no = min(t, up);

        lint tmp = 0;
        lint limi = no / P;
        tmp += floor_sum(limi + 1, Q, P, no - P * limi + Q);
        tmp -= 1;

        if (t > up) tmp += t - up;

        (tmp < K ? lo : hi) = t;
    }

    return hi;
}

int main() {
    int T;
    cin >> T;
    while (T--) {
        int P, Q, K;
        cin >> P >> Q >> K;
        lint g = __gcd(P, Q);
        cout << solve(P / g, Q / g, K) * g << '\n';
    }
}

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結果

テストケース

ソースコード