#928462 (C++17) No.502 階乗を計算するだけ

提出ソース

結果

問題	No.502 階乗を計算するだけ
ユーザー	suisen
提出日時	2023-11-12 23:23:49
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	74 ms / 1,000 ms
コード長	11,113 bytes
コンパイル時間	2,743 ms
コンパイル使用メモリ	130,624 KB
実行使用メモリ	6,676 KB
最終ジャッジ日時	2023-11-12 23:23:58
合計ジャッジ時間	8,109 ms
ジャッジサーバーID （参考情報）	judge11 / judge15

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	71 ms 6,676 KB
testcase_01	AC	71 ms 6,676 KB
testcase_02	AC	72 ms 6,676 KB
testcase_03	AC	72 ms 6,676 KB
testcase_04	AC	72 ms 6,676 KB
testcase_05	AC	72 ms 6,676 KB
testcase_06	AC	72 ms 6,676 KB
testcase_07	AC	72 ms 6,676 KB
testcase_08	AC	72 ms 6,676 KB
testcase_09	AC	72 ms 6,676 KB
testcase_10	AC	73 ms 6,676 KB
testcase_11	AC	72 ms 6,676 KB
testcase_12	AC	72 ms 6,676 KB
testcase_13	AC	72 ms 6,676 KB
testcase_14	AC	72 ms 6,676 KB
testcase_15	AC	73 ms 6,676 KB
testcase_16	AC	72 ms 6,676 KB
testcase_17	AC	72 ms 6,676 KB
testcase_18	AC	73 ms 6,676 KB
testcase_19	AC	72 ms 6,676 KB
testcase_20	AC	72 ms 6,676 KB
testcase_21	AC	72 ms 6,676 KB
testcase_22	AC	73 ms 6,676 KB
testcase_23	AC	72 ms 6,676 KB
testcase_24	AC	72 ms 6,676 KB
testcase_25	AC	73 ms 6,676 KB
testcase_26	AC	72 ms 6,676 KB
testcase_27	AC	72 ms 6,676 KB
testcase_28	AC	72 ms 6,676 KB
testcase_29	AC	73 ms 6,676 KB
testcase_30	AC	74 ms 6,676 KB
testcase_31	AC	72 ms 6,676 KB
testcase_32	AC	71 ms 6,676 KB
testcase_33	AC	72 ms 6,676 KB
testcase_34	AC	71 ms 6,676 KB
testcase_35	AC	72 ms 6,676 KB
testcase_36	AC	72 ms 6,676 KB
testcase_37	AC	72 ms 6,676 KB
testcase_38	AC	72 ms 6,676 KB
testcase_39	AC	71 ms 6,676 KB
testcase_40	AC	72 ms 6,676 KB
testcase_41	AC	73 ms 6,676 KB
testcase_42	AC	2 ms 6,676 KB
testcase_43	AC	1 ms 6,676 KB
testcase_44	AC	2 ms 6,676 KB
testcase_45	AC	2 ms 6,676 KB
testcase_46	AC	2 ms 6,676 KB
testcase_47	AC	2 ms 6,676 KB
testcase_48	AC	1 ms 6,676 KB
testcase_49	AC	5 ms 6,676 KB
testcase_50	AC	2 ms 6,676 KB
testcase_51	AC	2 ms 6,676 KB

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ソースコード

raw source code

#define PROBLEM "https://judge.yosupo.jp/problem/factorial"

#include <iostream>

#include <atcoder/modint>

using mint = atcoder::modint1000000007;

#include <utility>

#include <vector>
#include <atcoder/convolution>

#include <cassert>

namespace suisen {
    template <typename T, typename U = T>
    struct factorial {
        factorial() = default;
        factorial(int n) { ensure(n); }

        static void ensure(const int n) {
            int sz = _fac.size();
            if (n + 1 <= sz) return;
            int new_size = std::max(n + 1, sz * 2);
            _fac.resize(new_size), _fac_inv.resize(new_size);
            for (int i = sz; i < new_size; ++i) _fac[i] = _fac[i - 1] * i;
            _fac_inv[new_size - 1] = U(1) / _fac[new_size - 1];
            for (int i = new_size - 1; i > sz; --i) _fac_inv[i - 1] = _fac_inv[i] * i;
        }

        T fac(const int i) {
            ensure(i);
            return _fac[i];
        }
        T operator()(int i) {
            return fac(i);
        }
        U fac_inv(const int i) {
            ensure(i);
            return _fac_inv[i];
        }
        U binom(const int n, const int r) {
            if (n < 0 or r < 0 or n < r) return 0;
            ensure(n);
            return _fac[n] * _fac_inv[r] * _fac_inv[n - r];
        }
        U perm(const int n, const int r) {
            if (n < 0 or r < 0 or n < r) return 0;
            ensure(n);
            return _fac[n] * _fac_inv[n - r];
        }
    private:
        static std::vector<T> _fac;
        static std::vector<U> _fac_inv;
    };
    template <typename T, typename U>
    std::vector<T> factorial<T, U>::_fac{ 1 };
    template <typename T, typename U>
    std::vector<U> factorial<T, U>::_fac_inv{ 1 };
} // namespace suisen

namespace suisen {
    template <typename mint, typename Convolve,
        std::enable_if_t<std::is_invocable_r_v<std::vector<mint>, Convolve, std::vector<mint>, std::vector<mint>>, std::nullptr_t> = nullptr>
    std::vector<mint> shift_of_sampling_points(const std::vector<mint>& ys, mint t, int m, const Convolve &convolve) {
        const int n = ys.size();
        factorial<mint> fac(std::max(n, m));

        std::vector<mint> b = [&] {
            std::vector<mint> f(n), g(n);
            for (int i = 0; i < n; ++i) {
                f[i] = ys[i] * fac.fac_inv(i);
                g[i] = (i & 1 ? -1 : 1) * fac.fac_inv(i);
            }
            std::vector<mint> b = convolve(f, g);
            b.resize(n);
            return b;
        }();
        std::vector<mint> e = [&] {
            std::vector<mint> c(n);
            mint prd = 1;
            std::reverse(b.begin(), b.end());
            for (int i = 0; i < n; ++i) {
                b[i] *= fac.fac(n - i - 1);
                c[i] = prd * fac.fac_inv(i);
                prd *= t - i;
            }
            std::vector<mint> e = convolve(b, c);
            e.resize(n);
            return e;
        }();
        std::reverse(e.begin(), e.end());
        for (int i = 0; i < n; ++i) {
            e[i] *= fac.fac_inv(i);
        }

        std::vector<mint> f(m);
        for (int i = 0; i < m; ++i) f[i] = fac.fac_inv(i);
        std::vector<mint> res = convolve(e, f);
        res.resize(m);
        for (int i = 0; i < m; ++i) res[i] *= fac.fac(i);
        return res;
    }

    template <typename mint>
    std::vector<mint> shift_of_sampling_points(const std::vector<mint>& ys, mint t, int m) {
        auto convolve = [&](const std::vector<mint> &f, const std::vector<mint> &g) { return atcoder::convolution(f, g); };
        return shift_of_sampling_points(ys, t, m, convolve);
    }
} // namespace suisen

#include <atcoder/convolution>
#include <iostream>

namespace suisen::internal {
    template <typename T, typename R = T>
    std::vector<R> convolution_naive(const std::vector<T>& a, const std::vector<T>& b) {
        const int n = a.size(), m = b.size();
        std::vector<R> c(n + m - 1);
        if (n < m) {
            for (int j = 0; j < m; j++) for (int i = 0; i < n; i++) c[i + j] += R(a[i]) * b[j];
        } else {
            for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) c[i + j] += R(a[i]) * b[j];
        }
        return c;
    }
} // namespace suisen

namespace suisen {
    template <typename mint, atcoder::internal::is_modint_t<mint>* = nullptr>
    std::vector<mint> arbitrary_mod_convolution(const std::vector<mint>& a, const std::vector<mint>& b) {
        int n = int(a.size()), m = int(b.size());

        if constexpr (atcoder::internal::is_static_modint<mint>::value) {
            int maxz = 1;
            while (not ((mint::mod() - 1) & maxz)) maxz <<= 1;
            int z = 1;
            while (z < n + m - 1) z <<= 1;
            if (z <= maxz) return atcoder::convolution<mint>(a, b);
        }

        if (n == 0 or m == 0) return {};
        if (std::min(n, m) <= 120) return internal::convolution_naive(a, b);

        static constexpr long long MOD1 = 754974721;  // 2^24
        static constexpr long long MOD2 = 167772161;  // 2^25
        static constexpr long long MOD3 = 469762049;  // 2^26
        static constexpr long long M1M2 = MOD1 * MOD2;
        static constexpr long long INV_M1_MOD2 = atcoder::internal::inv_gcd(MOD1, MOD2).second;
        static constexpr long long INV_M1M2_MOD3 = atcoder::internal::inv_gcd(M1M2, MOD3).second;

        std::vector<int> a2(n), b2(m);
        for (int i = 0; i < n; ++i) a2[i] = a[i].val();
        for (int i = 0; i < m; ++i) b2[i] = b[i].val();

        auto c1 = atcoder::convolution<MOD1>(a2, b2);
        auto c2 = atcoder::convolution<MOD2>(a2, b2);
        auto c3 = atcoder::convolution<MOD3>(a2, b2);

        const long long m1m2 = mint(M1M2).val();
        std::vector<mint> c(n + m - 1);
        for (int i = 0; i < n + m - 1; ++i) {
            // Garner's Algorithm
            // X = x1 + x2 * m1 + x3 * m1 * m2
            // x1 = c1[i], x2 = (c2[i] - x1) / m1 (mod m2), x3 = (c3[i] - x1 - x2 * m1) / m2 (mod m3)
            long long x1 = c1[i];
            long long x2 = (atcoder::static_modint<MOD2>(c2[i] - x1) * INV_M1_MOD2).val();
            long long x3 = (atcoder::static_modint<MOD3>(c3[i] - x1 - x2 * MOD1) * INV_M1M2_MOD3).val();
            c[i] = x1 + x2 * MOD1 + x3 * m1m2;
        }
        return c;
    }

    std::vector<__uint128_t> convolution_int(const std::vector<int> &a, const std::vector<int> &b) {
        int n = int(a.size()), m = int(b.size());

        auto check_nonnegative = [](int e) { return e >= 0; };
        assert(std::all_of(a.begin(), a.end(), check_nonnegative));
        assert(std::all_of(b.begin(), b.end(), check_nonnegative));

        if (n == 0 or m == 0) return {};
        if (std::min(n, m) <= 120) return internal::convolution_naive<int, __uint128_t>(a, b);

        static constexpr long long MOD1 = 754974721;  // 2^24
        static constexpr long long MOD2 = 167772161;  // 2^25
        static constexpr long long MOD3 = 469762049;  // 2^26
        static constexpr long long M1M2 = MOD1 * MOD2;
        static constexpr long long INV_M1_MOD2 = atcoder::internal::inv_gcd(MOD1, MOD2).second;
        static constexpr long long INV_M1M2_MOD3 = atcoder::internal::inv_gcd(M1M2, MOD3).second;

        auto c1 = atcoder::convolution<MOD1>(a, b);
        auto c2 = atcoder::convolution<MOD2>(a, b);
        auto c3 = atcoder::convolution<MOD3>(a, b);
        std::vector<__uint128_t> c(n + m - 1);
        for (int i = 0; i < n + m - 1; ++i) {
            // Garner's Algorithm
            // X = x1 + x2 * m1 + x3 * m1 * m2
            // x1 = c1[i], x2 = (c2[i] - x1) / m1 (mod m2), x3 = (c3[i] - x1 - x2 * m1) / m2 (mod m3)
            int x1 = c1[i];
            int x2 = (atcoder::static_modint<MOD2>(c2[i] - x1) * INV_M1_MOD2).val();
            int x3 = (atcoder::static_modint<MOD3>(c3[i] - x1 - x2 * MOD1) * INV_M1M2_MOD3).val();
            c[i] = x1 + x2 * MOD1 + __uint128_t(x3) * M1M2;
        }
        return c;
    }
} // namespace suisen

namespace suisen {
    template <typename mint, atcoder::internal::is_static_modint_t<mint>* = nullptr>
    struct FactorialLargePrimeMod {
    private:
        static constexpr int _p = mint::mod();
        static constexpr int _log_b = 15;
        static constexpr int _b = 1 << _log_b;
        static constexpr int _q = _p >> _log_b;
    public:
        static constexpr int block_size = _b;
        static constexpr int log_block_size = _log_b;
        static constexpr int block_num = _q;

        FactorialLargePrimeMod() = delete;

        static mint fac(long long n) {
            if (_p <= n) return 0;
            build();
            const int q = n >> _log_b, r = n & (_b - 1);
            // n! = (qb)! * (n-r+1)(n-r+2)...(n)
            mint ans = _block_fact[q];
            for (int j = 0; j < r; ++j) {
                ans *= mint::raw(n - j);
            }
            return ans;
        }
    private:
        static inline std::vector<mint> _block_fact{};
        static inline bool _built = false;

        static void build() {
            if (std::exchange(_built, true)) return;

            const auto convolve = [&](const std::vector<mint> &f, const std::vector<mint> &g) {
                return arbitrary_mod_convolution(f, g);
            };

            // f_d(x) := (dx+1)*...*(dx+d-1)

            // Suppose that we have f_d(0),...,f_d(d-1). (Note that (deg f_d)+1=d)
            // f_{2d}(x) = ((2dx+1)*...*(2dx+d-1)) * (2dx+d) * (((2dx+d)+1)* ...*((2dx+d)+d-1))
            //           = f_d(2x) * f_d(2x+1) * (2dx+d)
            // We can calculate f_{2d}(0), ..., f_{2d}(2d-1) from f_d(0), f_d(1), ..., f_d(4d-2), f_d(4d-1)

            std::vector<mint> f{ 1 };
            f.reserve(_b);
            for (int i = 0; i < _log_b; ++i) {
                std::vector<mint> g = shift_of_sampling_points<mint>(f, 1 << i, 3 << i, convolve);
                const auto get = [&](int j) { return j < (1 << i) ? f[j] : g[j - (1 << i)]; };
                f.resize(2 << i);
                for (int j = 0; j < 2 << i; ++j) {
                    // (2*j+1)*2^i <= 2^(2*_log_b) + 2^(_log_b-1) < 2^31 holds if _log_b <= 15
                    f[j] = get(2 * j) * get(2 * j + 1) * ((2 * j + 1) << i);
                }
            }
            // f_B(x) = (x+1) * ... * (x+B-1)
            if (_q > _b) {
                std::vector<mint> g = shift_of_sampling_points<mint>(f, _b, _q - _b, convolve);
                std::move(g.begin(), g.end(), std::back_inserter(f));
            } else {
                f.resize(_q);
            }
            for (int i = 0; i < _q; ++i) {
                f[i] *= mint(i + 1) * _b;
            }
            // f[i] = (i*B + 1) * ... * (i*B + B)
            _block_fact = std::move(f);

            _block_fact.insert(_block_fact.begin(), 1);
            for (int i = 1; i <= _q; ++i) {
                _block_fact[i] *= _block_fact[i - 1];
            }
        }
    };
} // namespace suisen

int main() {
    using Factorial = suisen::FactorialLargePrimeMod<mint>;

    int n;
    std::cin >> n;
    std::cout << Factorial::fac(n).val() << '\n';
}

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結果

テストケース

ソースコード