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 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 71 ms / 1,000 ms |
| コード長 | 11,113 bytes |
| コンパイル時間 | 2,838 ms |
| コンパイル使用メモリ | 128,128 KB |
| 最終ジャッジ日時 | 2025-02-17 21:46:45 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 52 |
ソースコード
#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 suisennamespace 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 suisennamespace 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; // 2^24static constexpr long long MOD2 = 167772161; // 2^25static constexpr long long MOD3 = 469762049; // 2^26static 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; // 2^24static constexpr long long MOD2 = 167772161; // 2^25static constexpr long long MOD3 = 469762049; // 2^26static 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 suisennamespace 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 <= 15f[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 suisenint main() {using Factorial = suisen::FactorialLargePrimeMod<mint>;int n;std::cin >> n;std::cout << Factorial::fac(n).val() << '\n';}