結果

問題 No.502 階乗を計算するだけ
ユーザー suisen
提出日時 2024-01-30 21:07:10
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
TLE  
実行時間 -
コード長 12,848 bytes
コンパイル時間 2,850 ms
コンパイル使用メモリ 127,480 KB
最終ジャッジ日時 2025-02-19 00:48:20
ジャッジサーバーID
(参考情報)
judge4 / judge1
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
other AC * 42 TLE * 10
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ソースコード

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プレゼンテーションモードにする

#define PROBLEM "https://yukicoder.me/problems/no/502"
#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];
}
template <typename ...Ds, std::enable_if_t<std::conjunction_v<std::is_integral<Ds>...>, std::nullptr_t> = nullptr>
U polynom(const int n, const Ds& ...ds) {
if (n < 0) return 0;
ensure(n);
int sumd = 0;
U res = _fac[n];
for (int d : { ds... }) {
if (d < 0 or d > n) return 0;
sumd += d;
res *= _fac_inv[d];
}
if (sumd > n) return 0;
res *= _fac_inv[n - sumd];
return res;
}
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 {
// mod must be a prime number
template <typename mint,
std::enable_if_t<atcoder::internal::is_static_modint<mint>::value, std::nullptr_t> = nullptr>
struct factorial_large {
using value_type = mint;
static constexpr int LOG_BLOCK_SIZE = 9;
static constexpr int BLOCK_SIZE = 1 << LOG_BLOCK_SIZE;
static constexpr int BLOCK_NUM = value_type::mod() >> LOG_BLOCK_SIZE;
static inline int threshold = 2000000;
static_assert(atcoder::internal::is_prime_constexpr(mint::mod()));
static value_type fac(int n) {
return n <= threshold ? factorial<mint>{}.fac(n) : _large_fac(n);
}
static value_type fac_inv(int n) {
return n <= threshold ? factorial<mint>{}.fac_inv(n) : _large_fac(n).inv();
}
static value_type binom(int n, int r) {
if (r < 0 or r > n) return 0;
return fac(n) * fac_inv(r) * fac_inv(n - r);
}
template <typename ...Ds, std::enable_if_t<std::conjunction_v<std::is_integral<Ds>...>, std::nullptr_t> = nullptr>
static value_type polynom(const int n, const Ds& ...ds) {
if (n < 0) return 0;
long long sumd = 0;
value_type res = fac(n);
for (int d : { ds... }) {
if (d < 0 or d > n) return 0;
sumd += d;
res *= fac_inv(d);
}
if (sumd > n) return 0;
res *= fac_inv(n - sumd);
return res;
}
static value_type perm(int n, int r) {
if (r < 0 or r > n) return 0;
return fac(n) * fac_inv(n - r);
}
private:
static inline std::vector<value_type> _block_fac{};
static void _build() {
if (_block_fac.size()) {
return;
}
std::vector<value_type> f{ 1 };
f.reserve(BLOCK_SIZE);
for (int i = 0; i < LOG_BLOCK_SIZE; ++i) {
std::vector<value_type> g = shift_of_sampling_points<value_type>(f, 1 << i, 3 << i, arbitrary_mod_convolution<value_type>);
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) {
f[j] = get(2 * j) * get(2 * j + 1) * ((2 * j + 1) << i);
}
}
// f_B(x) = (x+1) * ... * (x+B-1)
if (BLOCK_NUM > BLOCK_SIZE) {
std::vector<value_type> g = shift_of_sampling_points<value_type>(f, BLOCK_SIZE, BLOCK_NUM - BLOCK_SIZE, arbitrary_mod_convolution
                    <value_type>);
std::move(g.begin(), g.end(), std::back_inserter(f));
} else {
f.resize(BLOCK_NUM);
}
for (int i = 0; i < BLOCK_NUM; ++i) {
f[i] *= value_type(i + 1) * BLOCK_SIZE;
}
// f[i] = (i*B + 1) * ... * (i*B + B)
f.insert(f.begin(), 1);
for (int i = 1; i <= BLOCK_NUM; ++i) {
f[i] *= f[i - 1];
}
_block_fac = std::move(f);
}
static value_type _large_fac(int n) {
_build();
value_type res;
int q = n / BLOCK_SIZE, r = n % BLOCK_SIZE;
if (2 * r <= BLOCK_SIZE) {
res = _block_fac[q];
for (int i = 0; i < r; ++i) {
res *= value_type::raw(n - i);
}
} else if (q != factorial_large::BLOCK_NUM) {
res = _block_fac[q + 1];
value_type den = 1;
for (int i = 1; i <= BLOCK_SIZE - r; ++i) {
den *= value_type::raw(n + i);
}
res /= den;
} else {
// Wilson's theorem
res = value_type::mod() - 1;
value_type den = 1;
for (int i = value_type::mod() - 1; i > n; --i) {
den *= value_type::raw(i);
}
res /= den;
}
return res;
}
};
} // namespace suisen
int main() {
int n;
std::cin >> n;
std::cout << suisen::factorial_large<mint>{}.fac(n).val() << '\n';
}
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