#940427 (C++23) No.2589 Prepare Integers

提出ソース
結果

問題	No.2589 Prepare Integers
コンテスト
ユーザー	hitonanode
提出日時	2023-12-25 22:49:03
言語	C++23 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	123 ms / 2,000 ms
コード長	15,698 bytes
コンパイル時間	2,506 ms
コンパイル使用メモリ	195,680 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-09-27 14:46:20
合計ジャッジ時間	4,110 ms
ジャッジサーバーID （参考情報）	judge2 / judge3
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 * 4
other	AC * 24
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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


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;  // for Int * Int multiplication

    // solve ax + by = gcd(a, b)
    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_)) {}

    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 = i; 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 = i; 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 = i; 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 = i; 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 = i; 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 = i; j < d; ++j) {
                    W.at(j) = (W.at(j) - A.at(i).at(j) * c2 % m + m) % m;
                }

                add_vector(W);
            }
        }
    }

    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;
                    }
                }
            }
        }

        return ret_less + has_same;
    }

    // 辞書順 k 番目 (0-indexed) の要素
    std::vector<Int> kth_element(long long k) {
        long long nall = 1;
        for (int i = 0; i < d; ++i) {
            if (A.at(i).at(i) != Int(0)) nall *= m / A.at(i).at(i);
        }
        dbg(make_tuple(nall, k));

        if (k >= nall) return {};

        std::vector<Int> ret(d);        
        for (int i = 0; i < d; ++i) {
            if (A.at(i).at(i) == Int(0)) continue;

            nall /= m / A.at(i).at(i);

            const Int v = k / nall;
            k -= nall * v;

            const Long e = -(ret.at(i) / A.at(i).at(i)) + v;
            for (int j = 0; j < d; ++j) {
                ret.at(j) = (ret.at(j) + A.at(i).at(j) * e % m + m) % m;
            }
        }
        dbg(ret);

        assert(k == 0);
        return ret;
    }
};


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;
        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);

    while (Q--) {
        int t;
        lint x;
        cin >> 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) {
                if (K == 2) {
                    // 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));
                        }
                        (y < x ? lo : hi) = c;
                    }

                    if (hi == inf) cout << -1 << '\n';
                    else cout << hi << '\n';
                } else {
                    auto vec = lb.kth_element(x - 1);
                    if (vec.empty()) {
                        cout << "-1\n";
                    } else {
                        lint res = 0;
                        REP(i, D) {
                            res *= K;
                            res += vec.at(i);
                        }
                        cout << res << '\n';
                    }
                }
            }
        }
    }
}
yukicoder

結果

ソースコード
