結果
問題 | No.963 門松列列(2) |
ユーザー | noshi91 |
提出日時 | 2019-12-14 22:53:40 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 468 ms / 3,000 ms |
コード長 | 7,217 bytes |
コンパイル時間 | 1,337 ms |
コンパイル使用メモリ | 126,956 KB |
実行使用メモリ | 29,980 KB |
最終ジャッジ日時 | 2024-06-28 03:27:02 |
合計ジャッジ時間 | 3,755 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge3 |
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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
6,816 KB |
testcase_01 | AC | 2 ms
6,944 KB |
testcase_02 | AC | 2 ms
6,940 KB |
testcase_03 | AC | 2 ms
6,940 KB |
testcase_04 | AC | 2 ms
6,940 KB |
testcase_05 | AC | 226 ms
17,104 KB |
testcase_06 | AC | 25 ms
6,940 KB |
testcase_07 | AC | 228 ms
16,820 KB |
testcase_08 | AC | 462 ms
28,300 KB |
testcase_09 | AC | 465 ms
29,360 KB |
testcase_10 | AC | 468 ms
29,980 KB |
ソースコード
#include <cstdint> namespace n91 { template <std::uint_fast64_t Modulus> class modint { using u64 = std::uint_fast64_t; public: using value_type = u64; static constexpr u64 mod = Modulus; private: static_assert(mod < static_cast<u64>(1) << 32, "Modulus must be less than 2**32"); u64 v; constexpr modint &negate() noexcept { if (v != 0) v = mod - v; return *this; } public: constexpr modint(const u64 x = 0) noexcept : v(x % mod) {} constexpr u64 &value() noexcept { return v; } constexpr const u64 &value() const noexcept { return v; } constexpr modint operator+() const noexcept { return modint(*this); } constexpr modint operator-() const noexcept { return modint(*this).negate(); } constexpr modint operator+(const modint rhs) const noexcept { return modint(*this) += rhs; } constexpr modint operator-(const modint rhs) const noexcept { return modint(*this) -= rhs; } constexpr modint operator*(const modint rhs) const noexcept { return modint(*this) *= rhs; } constexpr modint operator/(const modint rhs) const noexcept { return modint(*this) /= rhs; } constexpr modint &operator+=(const modint rhs) noexcept { v += rhs.v; if (v >= mod) v -= mod; return *this; } constexpr modint &operator-=(const modint rhs) noexcept { if (v < rhs.v) v += mod; v -= rhs.v; return *this; } constexpr modint &operator*=(const modint rhs) noexcept { v = v * rhs.v % mod; return *this; } constexpr modint &operator/=(modint rhs) noexcept { u64 exp = mod - 2; while (exp) { if (exp % 2 != 0) *this *= rhs; rhs *= rhs; exp /= 2; } return *this; } constexpr bool operator==(const modint rhs) const noexcept { return v == rhs.v; } constexpr bool operator!=(const modint rhs) const noexcept { return v != rhs.v; } }; template <std::uint_fast64_t Modulus> constexpr typename modint<Modulus>::u64 modint<Modulus>::mod; } // namespace n91 #include <cstddef> #include <utility> #include <vector> #include <algorithm> #include <cassert> #include <cstddef> #include <cstdint> #include <utility> #include <vector> #include <functional> #include <utility> namespace n91 { template <class T, class U, class Operate = std::multiplies<T>> constexpr T power(T base, U exp, const Operate &oper = Operate(), T iden = 1) { while (exp != 0) { if (exp % 2 != 0) { iden = oper(iden, base); } exp /= 2; base = oper(base, base); } return iden; } } // namespace n91 namespace n91 { template <class T, class PrimitiveRoot> std::vector<T> number_theoretic_transform(std::vector<T> a) { using usize = std::size_t; const usize size = a.size(); const usize m = size - 1; std::vector<T> b(size); const T root = power(PrimitiveRoot::value, (T::mod - 1) / size); for (usize i = size; i != 1;) { i /= 2; std::swap(a, b); T c = 1; T d = root; for (usize j = 1; j != i; j *= 2) d *= d; for (usize j = 0; j != size; j += i) { const usize l = j * 2 & m; const usize r = l + i; for (usize k = 0; k != i; k += 1) a[j + k] = b[l + k] + b[r + k] * c; c *= d; } } return a; } template <class T, class PrimitiveRoot> std::vector<T> inverse_number_theoretic_transform(std::vector<T> a) { a = number_theoretic_transform<T, PrimitiveRoot>(std::move(a)); std::reverse(a.begin() + 1, a.end()); const T inv = T::mod - (T::mod - 1) / a.size(); for (T &e : a) e *= inv; return a; } } // namespace n91 namespace n91 { template <class T, class PrimitiveRoot> class ntt_polynomial : public std::vector<T> { using Self = ntt_polynomial; using size_t = std::size_t; public: template <class... Args> ntt_polynomial(Args &&... args) : std::vector<T>(std::forward<Args>(args)...) {} friend Self operator+(const Self &l, const Self &r) { const size_t n = std::min(l.size(), r.size()); Self ret(n); for (size_t i = 0; i != n; ++i) ret[i] = l[i] + r[i]; return ret; } friend Self operator-(const Self &l, const Self &r) { const size_t n = std::min(l.size(), r.size()); Self ret(n); for (size_t i = 0; i != n; ++i) ret[i] = l[i] - r[i]; return ret; } friend Self operator*(Self l, Self r) { if (l.size() > r.size()) std::swap(l, r); const size_t n = l.size(); size_t s = 1; while (s < 2 * n - 1) s *= 2; l.resize(s); l = number_theoretic_transform<T, PrimitiveRoot>(std::move(l)); r.resize(n); r.resize(s); r = number_theoretic_transform<T, PrimitiveRoot>(std::move(r)); for (size_t i = 0; i != s; ++i) l[i] *= r[i]; l = inverse_number_theoretic_transform<T, PrimitiveRoot>(std::move(l)); l.resize(n); l.shrink_to_fit(); return l; } friend Self operator*(const T l, Self r) { for (T &e : r) e *= l; return r; } Self inverse() const { Self ret(1); ret[0] = static_cast<T>(1) / this->front(); while (ret.size() < this->size()) { ret.resize(ret.size() * 2); ret = T(2) * ret - ret * ret * (*this); } ret.shrink_to_fit(); return ret; } }; } // namespace n91 #include <chrono> #include <cstddef> #include <cstdint> #include <random> namespace n91 { template <class T, class U, U v> class constant_type { public: using value_type = T; static constexpr T value = v; }; template <class T, class U, U v> constexpr T constant_type<T, U, v>::value; } // namespace n91 namespace n91 { template <class T> constexpr T primitive_root() { using size_t = std::size_t; using V = typename T::value_type; size_t c = 0; V exp_list[9] = {}; { V q = T::mod - 1; for (V i = 2; i * i <= q; i += 1) { if (q % i == 0) { exp_list[c++] = i; do q /= i; while (q % i == 0); } } if (q != 1) exp_list[c++] = q; } for (size_t i = 0; i != c; ++i) exp_list[i] = (T::mod - 1) / exp_list[i]; T cand = 1; while (true) { bool f = true; for (size_t i = 0; i != c; ++i) if (power(cand, exp_list[i]) == 1) f = false; if (f) return cand; cand += 1; } } template <class T> using primitive_root_constant = constant_type<T, typename T::value_type, primitive_root<T>().value()>; } // namespace n91 #include <cstdio> #include <iostream> int main() { using usize = std::size_t; using mint = n91::modint<1012924417>; using pr = n91::primitive_root_constant<mint>; using poly = n91::ntt_polynomial<mint, pr>; usize n; std::cin >> n; poly sin(n + 1); { mint temp = 1; for (usize i = 0; i <= n; ++i) { if (i % 2 == 1) { sin[i] = static_cast<mint>(1) / temp; temp = -temp; } temp *= i + 1; } sin[0] += 1; } poly cos(n + 1); { mint temp = 1; for (usize i = 0; i <= n; ++i) { if (i % 2 == 0) { cos[i] = static_cast<mint>(1) / temp; temp = -temp; } temp *= i + 1; } } const auto ans = sin * cos.inverse(); mint temp = 2; for (usize i = 1; i <= n; ++i) temp *= i; std::cout << (ans[n] * temp).value() << std::endl; }