#938791 (C++23) No.2589 Prepare Integers

提出ソース
結果

問題	No.2589 Prepare Integers
ユーザー	hitonanode
提出日時	2023-12-17 02:24:04
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	TLE
実行時間	-
コード長	19,639 bytes
コンパイル時間	2,269 ms
コンパイル使用メモリ	198,720 KB
実行使用メモリ	10,624 KB
最終ジャッジ日時	2024-09-27 07:54:41
合計ジャッジ時間	5,812 ms
ジャッジサーバーID （参考情報）	judge5 / judge4
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 10,624 KB
testcase_01	AC	2 ms 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	TLE	-
testcase_05	--	-
testcase_06	--	-
testcase_07	--	-
testcase_08	--	-
testcase_09	--	-
testcase_10	--	-
testcase_11	--	-
testcase_12	--	-
testcase_13	--	-
testcase_14	--	-
testcase_15	--	-
testcase_16	--	-
testcase_17	--	-
testcase_18	--	-
testcase_19	--	-
testcase_20	--	-
testcase_21	--	-
testcase_22	--	-
testcase_23	--	-
testcase_24	--	-
testcase_25	--	-
testcase_26	--	-
testcase_27	--	-
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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 <memory>
#include <numeric>
#include <optional>
#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> 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; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
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; }
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 << ')'; }
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

#include <iostream>
#include <set>
#include <vector>

struct ModIntRuntime {
private:
    static int md;

public:
    using lint = long long;
    static int mod() { return md; }
    int val_;
    static std::vector<ModIntRuntime> &facs() {
        static std::vector<ModIntRuntime> facs_;
        return facs_;
    }
    static int &get_primitive_root() {
        static int primitive_root_ = 0;
        if (!primitive_root_) {
            primitive_root_ = [&]() {
                std::set<int> fac;
                int v = md - 1;
                for (lint i = 2; i * i <= v; i++)
                    while (v % i == 0) fac.insert(i), v /= i;
                if (v > 1) fac.insert(v);
                for (int g = 1; g < md; g++) {
                    bool ok = true;
                    for (auto i : fac)
                        if (ModIntRuntime(g).power((md - 1) / i) == 1) {
                            ok = false;
                            break;
                        }
                    if (ok) return g;
                }
                return -1;
            }();
        }
        return primitive_root_;
    }
    static void set_mod(const int &m) {
        if (md != m) facs().clear();
        md = m;
        get_primitive_root() = 0;
    }
    ModIntRuntime &_setval(lint v) {
        val_ = (v >= md ? v - md : v);
        return *this;
    }
    int val() const noexcept { return val_; }
    ModIntRuntime() : val_(0) {}
    ModIntRuntime(lint v) { _setval(v % md + md); }
    explicit operator bool() const { return val_ != 0; }
    ModIntRuntime operator+(const ModIntRuntime &x) const {
        return ModIntRuntime()._setval((lint)val_ + x.val_);
    }
    ModIntRuntime operator-(const ModIntRuntime &x) const {
        return ModIntRuntime()._setval((lint)val_ - x.val_ + md);
    }
    ModIntRuntime operator*(const ModIntRuntime &x) const {
        return ModIntRuntime()._setval((lint)val_ * x.val_ % md);
    }
    // ModIntRuntime operator/(const ModIntRuntime &x) const {
    //     return ModIntRuntime()._setval((lint)val_ * x.inv().val() % md);
    // }
    ModIntRuntime operator-() const { return ModIntRuntime()._setval(md - val_); }
    ModIntRuntime &operator+=(const ModIntRuntime &x) { return *this = *this + x; }
    ModIntRuntime &operator-=(const ModIntRuntime &x) { return *this = *this - x; }
    ModIntRuntime &operator*=(const ModIntRuntime &x) { return *this = *this * x; }
    // ModIntRuntime &operator/=(const ModIntRuntime &x) { return *this = *this / x; }
    friend ModIntRuntime operator+(lint a, const ModIntRuntime &x) {
        return ModIntRuntime()._setval(a % md + x.val_);
    }
    friend ModIntRuntime operator-(lint a, const ModIntRuntime &x) {
        return ModIntRuntime()._setval(a % md - x.val_ + md);
    }
    friend ModIntRuntime operator*(lint a, const ModIntRuntime &x) {
        return ModIntRuntime()._setval(a % md * x.val_ % md);
    }
    // friend ModIntRuntime operator/(lint a, const ModIntRuntime &x) {
    //     return ModIntRuntime()._setval(a % md * x.inv().val() % md);
    // }
    bool operator==(const ModIntRuntime &x) const { return val_ == x.val_; }
    bool operator!=(const ModIntRuntime &x) const { return val_ != x.val_; }
    bool operator<(const ModIntRuntime &x) const {
        return val_ < x.val_;
    } // To use std::map<ModIntRuntime, T>
    friend std::istream &operator>>(std::istream &is, ModIntRuntime &x) {
        lint t;
        return is >> t, x = ModIntRuntime(t), is;
    }
    friend std::ostream &operator<<(std::ostream &os, const ModIntRuntime &x) {
        return os << x.val_;
    }

    lint power(lint n) const {
        lint ans = 1, tmp = this->val_;
        while (n) {
            if (n & 1) ans = ans * tmp % md;
            tmp = tmp * tmp % md;
            n /= 2;
        }
        return ans;
    }
    ModIntRuntime pow(lint n) const { return power(n); }
    // ModIntRuntime inv() const { return this->pow(md - 2); }

    // ModIntRuntime fac() const {
    //     int l0 = facs().size();
    //     if (l0 > this->val_) return facs()[this->val_];

    //     facs().resize(this->val_ + 1);
    //     for (int i = l0; i <= this->val_; i++)
    //         facs()[i] = (i == 0 ? ModIntRuntime(1) : facs()[i - 1] * ModIntRuntime(i));
    //     return facs()[this->val_];
    // }

    // ModIntRuntime doublefac() const {
    //     lint k = (this->val_ + 1) / 2;
    //     return (this->val_ & 1)
    //                ? ModIntRuntime(k * 2).fac() / (ModIntRuntime(2).pow(k) * ModIntRuntime(k).fac())
    //                : ModIntRuntime(k).fac() * ModIntRuntime(2).pow(k);
    // }

    // ModIntRuntime nCr(int r) const {
    //     if (r < 0 or this->val_ < r) return ModIntRuntime(0);
    //     return this->fac() / ((*this - r).fac() * ModIntRuntime(r).fac());
    // }

    // ModIntRuntime sqrt() const {
    //     if (val_ == 0) return 0;
    //     if (md == 2) return val_;
    //     if (power((md - 1) / 2) != 1) return 0;
    //     ModIntRuntime b = 1;
    //     while (b.power((md - 1) / 2) == 1) b += 1;
    //     int e = 0, m = md - 1;
    //     while (m % 2 == 0) m >>= 1, e++;
    //     ModIntRuntime x = power((m - 1) / 2), y = (*this) * x * x;
    //     x *= (*this);
    //     ModIntRuntime z = b.power(m);
    //     while (y != 1) {
    //         int j = 0;
    //         ModIntRuntime t = y;
    //         while (t != 1) j++, t *= t;
    //         z = z.power(1LL << (e - j - 1));
    //         x *= z, z *= z, y *= z;
    //         e = j;
    //     }
    //     return ModIntRuntime(std::min(x.val_, md - x.val_));
    // }
};
int ModIntRuntime::md = 1;
using mint = ModIntRuntime;


// Solve ax+by=gcd(a, b)
template <class Int> Int extgcd(Int a, Int b, Int &x, Int &y) {
    Int d = a;
    if (b != 0) {
        d = extgcd(b, a % b, y, x), y -= (a / b) * x;
    } else {
        x = 1, y = 0;
    }
    return d;
}
// Calculate a^(-1) (MOD m) s if gcd(a, m) == 1
// Calculate x s.t. ax == gcd(a, m) MOD m
template <class Int> Int mod_inverse(Int a, Int m) {
    Int x, y;
    extgcd<Int>(a, m, x, y);
    x %= m;
    return x + (x < 0) * m;
}

// Require: 1 <= b
// return: (g, x) s.t. g = gcd(a, b), xa = g MOD b, 0 <= x < b/g
template <class Int> /* constexpr */ std::pair<Int, Int> inv_gcd(Int a, Int b) {
    a %= b;
    if (a < 0) a += b;
    if (a == 0) return {b, 0};
    Int s = b, t = a, m0 = 0, m1 = 1;
    while (t) {
        Int u = s / t;
        s -= t * u, m0 -= m1 * u;
        auto tmp = s;
        s = t, t = tmp, tmp = m0, m0 = m1, m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

template <class Int>
/* constexpr */ std::pair<Int, Int> crt(const std::vector<Int> &r, const std::vector<Int> &m) {
    assert(r.size() == m.size());
    int n = int(r.size());
    // Contracts: 0 <= r0 < m0
    Int r0 = 0, m0 = 1;
    for (int i = 0; i < n; i++) {
        assert(1 <= m[i]);
        Int r1 = r[i] % m[i], m1 = m[i];
        if (r1 < 0) r1 += m1;
        if (m0 < m1) {
            std::swap(r0, r1);
            std::swap(m0, m1);
        }
        if (m0 % m1 == 0) {
            if (r0 % m1 != r1) return {0, 0};
            continue;
        }
        Int g, im;
        std::tie(g, im) = inv_gcd<Int>(m0, m1);

        Int u1 = m1 / g;
        if ((r1 - r0) % g) return {0, 0};

        Int x = (r1 - r0) / g % u1 * im % u1;
        r0 += x * m0;
        m0 *= u1;
        if (r0 < 0) r0 += m0;
    }
    return {r0, m0};
}

// 蟻本 P.262
// 中国剰余定理を利用して，色々な素数で割った余りから元の値を復元
// 連立線形合同式 A * x = B mod M の解
// Requirement: M[i] > 0
// Output: x = first MOD second (if solution exists), (0, 0) (otherwise)
template <class Int>
std::pair<Int, Int>
linear_congruence(const std::vector<Int> &A, const std::vector<Int> &B, const std::vector<Int> &M) {
    Int r = 0, m = 1;
    assert(A.size() == M.size());
    assert(B.size() == M.size());
    for (int i = 0; i < (int)A.size(); i++) {
        assert(M[i] > 0);
        const Int ai = A[i] % M[i];
        Int a = ai * m, b = B[i] - ai * r, d = std::__gcd(M[i], a);
        if (b % d != 0) {
            return std::make_pair(0, 0); // 解なし
        }
        Int t = b / d * mod_inverse<Int>(a / d, M[i] / d) % (M[i] / d);
        r += m * t;
        m *= M[i] / d;
    }
    return std::make_pair((r < 0 ? r + m : r), m);
}

int K;
int D = 1;
vector<mint> to_basek(lint x) {
    vector<mint> res(D);
    REP(d, D) {
        res.at(D - 1 - d) = x % K;
        x /= K;
        if (!x) break;
    }
    return res;
}

int main() {
    int Q;

    {
        cin >> K >> Q;
        mint::set_mod(K);
        D = 1;
        __int128 ub = K;
        while (ub <= 1LL << 60) {
            ub *= K;
            D++;
        }
    }

    dbg(D);
    assert(pow(K, D) > 1e18);

    vector<vector<mint>> base(D);

    auto count_less_or_eq = [&](lint x) -> lint {
        assert(x >= 0);
        if (x == 0) return 1;

        const auto ub = to_basek(x);

        lint nall = 1;
        REP(d, D) {
            if (base.at(d).empty()) continue;
            nall *= K / base.at(d).at(d).val();
        }
        // dbg(nall);

        vector<mint> current(D);

        lint ret = 0;

        REP(d, D) {
            // const int lo = (mint(K) - current.at(d)).val();
            // const int hi = (ub.at(d) - current.at(d)).val();

            if (base.at(d).empty()) {
                if (ub.at(d) < current.at(d)) {
                    nall = 0;
                    break;
                } else if (ub.at(d) == current.at(d)) {

                } else {
                    ret += nall;
                    nall = 0;
                    break;
                }
            } else {
                const int m = base.at(d).at(d).val();
                nall /= K / m;

                auto calc_width = [&](int lo, int hi) -> int {
                    int now = current.at(d).val();
                    chmax(lo, now);
                    if (lo >= hi) return 0;
                    assert(now <= lo and lo < hi);
                    lo -= now;
                    hi -= now;
                    int ilo = (lo + m - 1) / m;
                    int ihi = min(K / m, (hi + m - 1) / m);
                    return ihi - ilo;
                };

                const int width = calc_width(0, ub.at(d).val()) + calc_width(K, K + ub.at(d).val());
                ret += lint(width) * nall;

                if ((ub.at(d) - current.at(d)).val() % m == 0) {
                    const mint c = (ub.at(d) - current.at(d)).val() / m;
                    REP(i, D) current.at(i) += (c * base.at(d).at(i)).val();
                    assert(current.at(d) == ub.at(d));
                } else {
                    nall = 0;
                    break;
                }
            }
        }

        assert(nall == 0 or nall == 1);
        return nall + ret;

        // if (!break_used) ++ret;

        // return ret;
    };

    while (Q--) {
        int t;
        cin >> t;
        if (t == 1) {
            int x;
            cin >> x;

            auto v = to_basek(x);

            REP(d, D) {
                if (!v.at(d)) continue;

                if (base.at(d).empty()) {
                    int g = std::gcd(K, v.at(d).val());
                    mint c = mod_inverse<lint>(v.at(d).val() / g, K / g);
                    for (auto &x : v) x *= c;
                    base.at(d) = v;
                    break;
                }

                {
                    lint p, q;
                    const lint g = extgcd<lint>(v.at(d).val(), base.at(d).at(d).val(), p, q);
                    dbg(make_tuple(d, p, q));
                    if (q == 0) {
                        swap(p, q);
                        swap(base.at(d), v);
                    }
                    vector<mint> new_b(v.size());
                    REP(i, v.size()) new_b.at(i) = (mint(v.at(i)) * p + mint(base.at(d).at(i)) * q).val();
                    assert(new_b.at(d) == g);
                    base.at(d) = new_b;

                    mint w = v.at(d).val() / g;
                    REP(i, v.size()) v.at(i) = (mint(v.at(i)) - w * base.at(d).at(i)).val();

                    assert(v.at(d) == 0);
                }
            }
            dbg(make_tuple("Added", x, to_basek(x), v));
            for (auto b : base) if (b.size()) dbg(b);

        } else {
            lint x;
            cin >> x;
            if (t == 3) {
                cout << count_less_or_eq(x) << '\n';
            } else if (t == 2) {
                // lo 以下は x 個未満、 hi 以下は x 個以上
                constexpr lint inf = 1LL << 60;
                lint lo = x - 2, hi = inf;
                while (hi - lo > 1) {
                    const lint c = (lo + hi) / 2;
                    if (count_less_or_eq(c) < x) lo = c;
                    else hi = c;
                }

                if (hi == inf) cout << -1 << '\n';
                else cout << hi << '\n';
            }
        }
    }
}
yukicoder

結果

テストケース

ソースコード
