#940419 (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	2023-12-25 22:13:45
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	1,369 ms / 2,000 ms
コード長	20,413 bytes
コンパイル時間	2,475 ms
コンパイル使用メモリ	203,344 KB
実行使用メモリ	6,548 KB
最終ジャッジ日時	2023-12-25 22:13:55
合計ジャッジ時間	10,379 ms
ジャッジサーバーID （参考情報）	judge11 / judge14
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 6,548 KB
testcase_01	AC	2 ms 6,548 KB
testcase_02	AC	2 ms 6,548 KB
testcase_03	AC	2 ms 6,548 KB
testcase_04	AC	53 ms 6,548 KB
testcase_05	AC	1,369 ms 6,548 KB
testcase_06	AC	698 ms 6,548 KB
testcase_07	AC	577 ms 6,548 KB
testcase_08	AC	122 ms 6,548 KB
testcase_09	AC	55 ms 6,548 KB
testcase_10	AC	55 ms 6,548 KB
testcase_11	AC	62 ms 6,548 KB
testcase_12	AC	894 ms 6,548 KB
testcase_13	AC	603 ms 6,548 KB
testcase_14	AC	480 ms 6,548 KB
testcase_15	AC	449 ms 6,548 KB
testcase_16	AC	397 ms 6,548 KB
testcase_17	AC	156 ms 6,548 KB
testcase_18	AC	113 ms 6,548 KB
testcase_19	AC	83 ms 6,548 KB
testcase_20	AC	55 ms 6,548 KB
testcase_21	AC	56 ms 6,548 KB
testcase_22	AC	55 ms 6,548 KB
testcase_23	AC	60 ms 6,548 KB
testcase_24	AC	63 ms 6,548 KB
testcase_25	AC	64 ms 6,548 KB
testcase_26	AC	63 ms 6,548 KB
testcase_27	AC	34 ms 6,548 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 <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); }
};
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;
}

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

// https://codeforces.com/blog/entry/98376
class LinearBasis {
    using Int = int;
    using Long = long long;

    static 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;
    }

    Int m; // mod
    int d; // dimension

    std::vector<std::vector<Int>> A;

public:
    LinearBasis(Int m_, int d_) : m(m_), d(d_), A(d_, std::vector<Int>(d_)) {}

    auto getA() const {
        vector<vector<Int>> ret;
        for (const auto &v : A) if (v != vector<Int>(v.size())) ret.push_back(v);
        return ret;
    }

    void add_vector(std::vector<Int> V) {
        assert((int)V.size() == d);

        for (int i = 0; i < d; ++i) {
            if (V.at(i) == Int(0)) continue;

            if (A.at(i).at(i) == Int(0)) {
                Int s, t;
                _extgcd(V.at(i), m, s, t);
                s = (s % m + m) % m;

                for (int j = 0; j < d; ++j) {
                    A.at(i).at(j) = (Long)V.at(j) * s % m;
                }

                assert(m % A.at(i).at(i) == Int(0));
                const Int c = m / A.at(i).at(i);

                for (int j = 0; j < d; ++j) V.at(j) = (Long)V.at(j) * c % m;

            } else if (V.at(i) % A.at(i).at(i) == Int(0)) {
                const Long c = V.at(i) / A.at(i).at(i);
                for (int j = 0; j < d; ++j) {
                    V.at(j) = (V.at(j) - A.at(i).at(j) * c % m + m) % m;
                }
            } else {
                vector<Int> W = A.at(i);
                Int s, t;
                _extgcd(V.at(i), W.at(i), s, t);
                s = (s % m + m) % m;
                t = (t % m + m) % m;
                for (int j = 0; j < d; ++j) {
                    A.at(i).at(j) = ((Long)V.at(j) * s + (Long)W.at(j) * t) % m;
                }

                assert(V.at(i) % A.at(i).at(i) == Int(0));
                const Long c = V.at(i) / A.at(i).at(i);
                for (int j = 0; j < d; ++j) {
                    V.at(j) = (V.at(j) - A.at(i).at(j) * c % m + m) % m;
                }

                assert(W.at(i) % A.at(i).at(i) == Int(0));
                const Long c2 = W.at(i) / A.at(i).at(i);
                for (int j = 0; j < d; ++j) {
                    W.at(j) = (W.at(j) - A.at(i).at(j) * c2 % m + m) % m;
                }

                vector<Int> U = A.at(i);
                const Long c3 = m / A.at(i).at(i);
                for (int j = 0; j < d; ++j) U.at(j) = (Long)U.at(j) * c3 % m;

                add_vector(W);
                add_vector(U);
            }
        }
    }

    bool contains(std::vector<Int> V) {
        assert((int)V.size() == d);

        for (int i = 0; i < d; ++i) {
            if (A.at(i).at(i) != Int(0) and V.at(i) % A.at(i).at(i) == Int(0)) {
                const Long c = V.at(i) / A.at(i).at(i);
                for (int j = 0; j < d; ++j) {
                    V.at(j) = (V.at(j) - A.at(i).at(j) * c % m + m) % m;
                }
            }
            if (V.at(i) != Int(0)) return false;
        }

        return true;
    }

    long long count_less_or_eq(const std::vector<Int> &V) {  // V 以下を数える
        assert((int)V.size() == d);

        vector<Int> same(d);

        long long ret_less = 0;
        bool has_same = true;

        for (int i = 0; i < d; ++i) {
            if (A.at(i).at(i) == Int(0)) {
                if (same.at(i) < V.at(i)) {
                    ret_less += has_same;
                    has_same = false;
                } else if (same.at(i) > V.at(i)) {
                    has_same = false;
                }
            } else {
                assert(m % A.at(i).at(i) == Int(0));

                const Int u = m / A.at(i).at(i);
                ret_less *= u;

                if (has_same) {
                    if (same.at(i) < V.at(i)) {
                        ret_less += (V.at(i) - same.at(i) + A.at(i).at(i) - 1) / A.at(i).at(i);
                    }

                    const Int hi = min(u, (V.at(i) + m - same.at(i) + A.at(i).at(i) - 1) / A.at(i).at(i));
                    const Int lo = (m - same.at(i) + A.at(i).at(i) - 1) / A.at(i).at(i);

                    if (hi > lo) ret_less += hi - lo;

                    if ((V.at(i) + m - same.at(i)) % A.at(i).at(i) == Int(0)) {
                        const Int diff = (V.at(i) + m - same.at(i)) % m;
                        assert(diff % A.at(i).at(i) == 0);
                        const Long c = diff / A.at(i).at(i);
                        for (int j = 0; j < d; ++j) { same.at(j) = (same.at(j) + A.at(i).at(j) * c) % m; }
                    } else {
                        has_same = false;
                    }
                }
            }
        }
        // dbg(make_tuple(V, ret_less, has_same));

        return ret_less + has_same;
    }
};


class LinearBasisMod2 {
    int d;
    std::vector<long long> A;

public:
    LinearBasisMod2(int d_) : d(d_), A(d_) {}


    void add_vector(long long V) {
        for (int i = 0; i < d; ++i) {
            V = std::min(V, V ^ A.at(i));
            if (!V) break;
            if ((V >> (d - 1 - i)) & 1) {
                A.at(i) = V;
                break;
            }
        }
    }

    bool contains(long long V) {
        for (int i = 0; i < d; ++i) {
            V = std::min(V, V ^ A.at(i));
            if (!V) break;
            if ((V >> (d - 1 - i)) & 1) return false;
        }
        return true;
    }

    long long count_less_or_eq(long long V) {  // V 以下を数える
        long long ret_less = 0;
        bool has_same = true;

        long long same = 0;

        for (int i = 0; i < d; ++i) {
            if (A.at(i)) {
                ret_less *= 2;
                if ((V >> (d - 1 - i)) & 1) ret_less += has_same;
                if (((V ^ same) >> (d - 1 - i)) & 1) same ^= A.at(i);
            } else {
                if ((same >> (d - 1 - i)) & (~V >> (d - 1 - i)) & 1) {
                    has_same = false;
                } else if ((~same >> (d - 1 - i)) & (V >> (d - 1 - i)) & 1) {
                    ret_less += has_same;
                    has_same = false;
                }
            }
        }

        return ret_less + has_same;
    }
};

// https://codeforces.com/blog/entry/98376
int main() {
    int Q;

    {
        cin >> K >> Q;
        mint::set_mod(K);
        D = 1;
        __int128 ub = K;
        while (ub < 1LL << 62) {
            ub *= K;
            D++;
            assert(D <= 100);
        }
    }
    dbg(D);

    LinearBasis lb(K, D);
    LinearBasisMod2 lb2(D);

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

    vector<lint> base2(D);

    auto count_less_or_eq_k2 = [&](lint x) -> lint {
        if (x < 0) return 0;
        if (x == 0) return 1;

        lint nall = 1;
        REP(d, D) {
            if (base2.at(d)) nall *= 2;
        }

        lint ret = 0;
        lint cur = 0;

        REP(d, D) {
            const bool curd = (cur >> (D - 1 - d)) & 1;
            const bool curx = (x >> (D - 1 - d)) & 1;

            if (!base2.at(d)) {
                if (curd > curx) {
                    nall = 0;
                    break;
                } else if (curd == curx) {

                } else {
                    ret += nall;
                    nall = 0;
                    break;
                }
            } else {
                nall /= 2;
                if (curd > curx) {
                    cur ^= base2.at(d);
                } else if (curd == curx) {
                    if (curd) ret += nall;
                } else {
                    cur ^= base2.at(d);
                    ret += nall;
                }
            }
        }
        assert(nall == 0 or nall == 1);
        return ret + nall;
    };

    while (Q--) {
        int t;
        lint x;
        cin >> t >> x;
        dbg(make_tuple(t, x));

        if (t == 1) {
            if (K == 2) {
                lb2.add_vector(x);
            } else {
                auto v = to_basek(x);
                lb.add_vector(v);
            }
        } else {
            if (t == 3) {
                if (K == 2) {
                    cout << lb2.count_less_or_eq(x) << '\n';
                } else {
                    cout << lb.count_less_or_eq(to_basek(x)) << '\n';
                }
            } else if (t == 2) {
                dbg(lb.getA());
                // lo 以下は x 個未満、 hi 以下は x 個以上
                constexpr lint inf = (1LL << 62) - 1;
                lint lo = x - 2, hi = inf;
                while (hi - lo > 1) {
                    const lint c = (lo + hi) / 2;

                    long long y;
                    if (K == 2) {
                        y = lb2.count_less_or_eq(c);
                    } else {
                        y = lb.count_less_or_eq(to_basek(c));
                    }
                    if (y < 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
