結果
| 問題 |
No.1356 Split Tile2
|
| コンテスト | |
| ユーザー |
 KoD
|
| 提出日時 | 2021-01-14 18:22:44 |
| 言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 83 ms / 2,000 ms |
| コード長 | 14,504 bytes |
| コンパイル時間 | 3,556 ms |
| コンパイル使用メモリ | 118,060 KB |
| 最終ジャッジ日時 | 2025-01-17 17:52:31 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 31 |
ソースコード
#include <iostream>
#include <algorithm>
#include <utility>
#include <numeric>
#include <vector>
#include <array>
#include <cassert>
template <uint32_t Modulus>
class modular {
public:
using value_type = uint32_t;
using max_type = uint64_t;
static constexpr value_type mod = Modulus;
static constexpr value_type get_mod() { return mod; }
static_assert(mod >= 2, "invalid mod :: smaller than 2");
static_assert(mod < (value_type(1) << 31), "invalid mod :: over 2^31");
template <class T>
static constexpr value_type normalize(T value_) {
if (value_ < 0) {
value_ = -value_;
value_ %= mod;
if (value_ == 0) return 0;
return mod - value_;
}
return value_ % mod;
}
private:
value_type value;
public:
constexpr modular(): value(0) { }
template <class T>
explicit constexpr modular(T value_): value(normalize(value_)) { }
template <class T>
explicit constexpr operator T() { return static_cast<T>(value); }
constexpr value_type get() const { return value; }
constexpr modular operator - () const { return modular(mod - value); }
constexpr modular operator ~ () const { return inverse(); }
constexpr value_type &extract() { return value; }
constexpr modular inverse() const { return power(mod - 2); }
constexpr modular power(max_type exp) const {
modular res(1), mult(*this);
while (exp > 0) {
if (exp & 1) res *= mult;
mult *= mult;
exp >>= 1;
}
return res;
}
constexpr modular operator + (const modular &rhs) const { return modular(*this) += rhs; }
constexpr modular& operator += (const modular &rhs) {
if ((value += rhs.value) >= mod) value -= mod;
return *this;
}
constexpr modular operator - (const modular &rhs) const { return modular(*this) -= rhs; }
constexpr modular& operator -= (const modular &rhs) {
if ((value += mod - rhs.value) >= mod) value -= mod;
return *this;
}
constexpr modular operator * (const modular &rhs) const { return modular(*this) *= rhs; }
constexpr modular& operator *= (const modular &rhs) {
value = (max_type) value * rhs.value % mod;
return *this;
}
constexpr modular operator / (const modular &rhs) const { return modular(*this) /= rhs; }
constexpr modular& operator /= (const modular &rhs) { return (*this) *= rhs.inverse(); }
constexpr bool zero() const { return value == 0; }
constexpr bool operator == (const modular &rhs) const { return value == rhs.value; }
constexpr bool operator != (const modular &rhs) const { return value != rhs.value; }
friend std::ostream& operator << (std::ostream &stream, const modular &rhs) {
return stream << rhs.value;
}
};
namespace ntt_detail {
constexpr uint32_t calc_primitive_root(uint32_t mod) {
uint32_t exp[32] = {};
uint32_t cur = mod - 1;
size_t size = 0;
for (uint32_t i = 2; i * i <= cur; ++i) {
if (cur % i == 0) {
exp[size++] = (mod - 1) / i;
while (cur % i == 0) cur /= i;
}
}
if (cur != 1) {
exp[size++] = (mod - 1) / cur;
}
uint32_t res = 2;
while (true) {
bool ok = true;
for (size_t i = 0; i < size; ++i) {
uint64_t a = res, e = exp[i], x = 1;
while (e > 0) {
if (e & 1) (x *= a) %= mod;
(a *= a) %= mod;
e >>= 1;
}
if (x == 1) {
ok = false;
break;
}
}
if (ok) break;
++res;
}
return res;
};
template <size_t N, class T>
constexpr std::array<T, N> calculate_roots(T omega) {
std::array<T, N> res;
res[N - 1] = omega;
for (size_t i = N - 1; i > 0; --i) {
res[i - 1] = res[i] * res[i];
}
return res;
}
template <class OtherModular, class Modular>
constexpr OtherModular convert_mod(Modular x) {
return OtherModular(x.get());
}
template <class OtherModular, class Modular>
std::vector<OtherModular> convert_mod_vec(const std::vector<Modular> &vec) {
std::vector<OtherModular> res(vec.size());
std::transform(vec.cbegin(), vec.cend(), res.begin(), convert_mod<OtherModular, Modular>);
return res;
}
namespace bit_operation {
constexpr uint32_t b16 = 0b00000000000000001111111111111111;
constexpr uint32_t b8 = 0b00000000111111110000000011111111;
constexpr uint32_t b4 = 0b00001111000011110000111100001111;
constexpr uint32_t b2 = 0b00110011001100110011001100110011;
constexpr uint32_t b1 = 0b01010101010101010101010101010101;
constexpr size_t reverse(size_t x) {
x = ((x >> 16) & b16) | ((x & b16) << 16);
x = ((x >> 8) & b8) | ((x & b8) << 8);
x = ((x >> 4) & b4) | ((x & b4) << 4);
x = ((x >> 2) & b2) | ((x & b2) << 2);
x = ((x >> 1) & b1) | ((x & b1) << 1);
return x;
}
};
namespace garner_mod {
constexpr uint32_t m0 = 754974721;
constexpr uint32_t m1 = 167772161;
constexpr uint32_t m2 = 469762049;
constexpr uint64_t m0m1 = (uint64_t) m0 * m1;
constexpr auto im0_m1 = modular<m1>(m0).inverse();
constexpr auto im0m1_m2 = modular<m2>(m0m1).inverse();
};
/*
prime numbers for ntt
[ 1051721729 ] [ 2^20 ]
[ 1045430273 ] [ 2^20 ]
[ 1007681537 ] [ 2^20 ]
[ 962592769 ] [ 2^21 ]
[ 924844033 ] [ 2^21 ]
[ 985661441 ] [ 2^22 ]
[ 943718401 ] [ 2^22 ]
[ 935329793 ] [ 2^22 ]
[ 998244353 ] [ 2^23 ]
[ 754974721 ] [ 2^24 ]
[ 167772161 ] [ 2^25 ]
[ 469762049 ] [ 2^26 ]
*/
}
template <uint32_t Modulus, class Modular = modular<Modulus>>
class number_theoretic_transform {
public:
using value_type = Modular;
static constexpr uint32_t mod = Modulus;
static constexpr uint32_t prim = ntt_detail::calc_primitive_root(mod);
private:
static constexpr size_t level = __builtin_ctz(mod - 1);
static constexpr value_type unit = value_type(1);
static constexpr value_type omega = value_type(prim).power((mod - 1) >> level);
static constexpr auto roots = ntt_detail::calculate_roots<level>(omega);
static constexpr auto inv_roots = ntt_detail::calculate_roots<level>(omega.inverse());
protected:
void M_transform(std::vector<value_type> &F) const {
size_t size = F.size();
size_t logn = __builtin_ctz(size);
for (size_t i = 0; i < size; ++i) {
size_t j = ntt_detail::bit_operation::reverse(i) >> (32 - logn);
if (i < j) {
std::swap(F[i], F[j]);
}
}
value_type coeff = unit;
for (size_t s = 0; s < logn; ++s) {
size_t mh = 1 << s;
size_t m = mh << 1;
for (size_t i = 0; i < size; i += m) {
coeff = unit;
for (size_t j = i; j < i + mh; ++j) {
auto a = F[j];
auto b = F[j + mh] * coeff;
F[j] = a + b;
F[j + mh] = a - b;
coeff *= roots[s];
}
}
}
}
void M_inv_transform(std::vector<value_type> &F) const {
size_t size = F.size();
size_t logn = __builtin_ctz(size);
for (size_t i = 0; i < size; ++i) {
size_t j = ntt_detail::bit_operation::reverse(i) >> (32 - logn);
if (i < j) {
std::swap(F[i], F[j]);
}
}
value_type coeff = unit;
for (size_t s = 0; s < logn; ++s) {
size_t mh = 1 << s;
size_t m = mh << 1;
for (size_t i = 0; i < size; i += m) {
coeff = unit;
for (size_t j = i; j < i + mh; ++j) {
auto a = F[j];
auto b = F[j + mh] * coeff;
F[j] = a + b;
F[j + mh] = a - b;
coeff *= inv_roots[s];
}
}
}
coeff = value_type(size).inverse();
for (auto &x: F) {
x *= coeff;
}
}
public:
std::vector<value_type> convolve(
std::vector<value_type> A,
std::vector<value_type> B,
bool same = false
) const {
if (A.empty() || B.empty()) return { };
size_t res_size = A.size() + B.size() - 1;
size_t fix_size = 1 << (31 - __builtin_clz(2 * res_size - 1));
if (same) {
A.resize(fix_size);
M_transform(A);
for (size_t i = 0; i < fix_size; ++i) {
A[i] *= A[i];
}
}
else {
A.resize(fix_size);
B.resize(fix_size);
M_transform(A);
M_transform(B);
for (size_t i = 0; i < fix_size; ++i) {
A[i] *= B[i];
}
}
M_inv_transform(A);
A.resize(res_size);
return A;
}
template <class OtherModular>
std::vector<value_type> convolve_convert(
const std::vector<OtherModular> &A,
const std::vector<OtherModular> &B,
bool same = false
) const {
return convolve(
ntt_detail::convert_mod_vec<value_type>(A),
ntt_detail::convert_mod_vec<value_type>(B),
same
);
}
};
template <class Modular>
std::vector<Modular> convolve_arbitrary_mod(
const std::vector<Modular> &A,
const std::vector<Modular> &B,
bool same = false
) {
using namespace ntt_detail::garner_mod;
number_theoretic_transform<m0> ntt0;
number_theoretic_transform<m1> ntt1;
number_theoretic_transform<m2> ntt2;
auto X = ntt0.convolve_convert(A, B, same);
auto Y = ntt1.convolve_convert(A, B, same);
auto Z = ntt2.convolve_convert(A, B, same);
size_t size = X.size();
std::vector<Modular> res(size);
for (size_t i = 0; i < size; ++i) {
uint32_t s = (uint32_t) X[i];
uint64_t t = (uint64_t) ((Y[i] - modular<m1>(s)) * im0_m1) * m0 + s;
res[i] = Modular((__uint128_t) ((Z[i] - modular<m2>(t)) * im0m1_m2) * m0m1 + t);
}
return res;
}
template <uint32_t Modulus, class Modular = modular<Modulus>>
class formal_power_series: public number_theoretic_transform<Modulus, Modular> {
public:
using value_type = Modular;
using size_type = size_t;
private:
std::vector<value_type> M_data;
public:
template <class... Args>
formal_power_series(Args... args): M_data(args...) { }
formal_power_series(std::initializer_list<value_type> data_): M_data(data_.begin(), data_.end()) { }
formal_power_series operator + (const formal_power_series &rhs) const { return formal_power_series(*this) += rhs; }
formal_power_series& operator += (const formal_power_series &rhs) {
if (M_data.size() < rhs.M_data.size()) M_data.resize(rhs.M_data.size());
for (size_type i = 0; i < rhs.M_data.size(); ++i) M_data[i] += rhs.M_data[i];
return *this;
}
formal_power_series operator - (const formal_power_series &rhs) const { return formal_power_series(*this) -= rhs; }
formal_power_series& operator -= (const formal_power_series &rhs) {
if (M_data.size() < rhs.M_data.size()) M_data.resize(rhs.M_data.size());
for (size_type i = 0; i < rhs.M_data.size(); ++i) M_data[i] -= rhs.M_data[i];
return *this;
}
formal_power_series operator * (const formal_power_series &rhs) const { return formal_power_series(*this) *= rhs; }
formal_power_series& operator *= (const formal_power_series &rhs) {
M_data = this -> convolve(M_data, rhs.M_data);
return *this;
}
formal_power_series operator + (const value_type &rhs) const { return formal_power_series(*this) += rhs; }
formal_power_series& operator += (const value_type &rhs) { M_data[0] += rhs; return *this; }
formal_power_series operator - (const value_type &rhs) const { return formal_power_series(*this) -= rhs; }
formal_power_series& operator -= (const value_type &rhs) { M_data[0] -= rhs; return *this; }
formal_power_series operator * (const value_type &rhs) const { return formal_power_series(*this) *= rhs; }
formal_power_series& operator *= (const value_type &rhs) { for (auto &x: M_data) x *= rhs; return *this; }
formal_power_series operator / (const value_type &rhs) const { return formal_power_series(*this) /= rhs; }
formal_power_series& operator /= (const value_type &rhs) { return (*this) *= rhs.inverse(); }
formal_power_series lower(size_type size) const {
return formal_power_series(M_data.begin(), M_data.begin() + std::min(M_data.size(), size));
}
formal_power_series square() const {
return formal_power_series(this -> convolve(M_data, M_data, true));
}
formal_power_series diff() const {
if (M_data.size() < 1) return formal_power_series();
formal_power_series res(M_data.size() - 1);
for (size_type i = 0; i + 1 < M_data.size(); ++i) {
res.M_data[i] = M_data[i + 1] * value_type(i + 1);
}
return res;
}
formal_power_series inte() const {
formal_power_series res(M_data.size() + 1);
value_type cur(1);
for (size_type i = 0; i < M_data.size(); ++i) {
res.M_data[i + 1] = M_data[i] * cur;
cur *= value_type(i + 1);
}
cur = cur.inverse();
for (size_type i = M_data.size(); i > 0; --i) {
res.M_data[i] *= cur;
cur *= value_type(i);
}
return res;
}
formal_power_series inverse(size_type m) const {
formal_power_series res(m);
res.M_data[0] = M_data[0].inverse();
for (size_type d = 1; d < m; d <<= 1) {
formal_power_series f = lower(d + d);
if (f.M_data.size() < d + d) f.M_data.resize(d + d);
this -> M_transform(f.M_data);
formal_power_series g = res.lower(d + d);
if (g.M_data.size() < d + d) g.M_data.resize(d + d);
this -> M_transform(g.M_data);
for (size_type i = 0; i < d + d; ++i) f.M_data[i] *= g.M_data[i];
this -> M_inv_transform(f.M_data);
for (size_type i = 0; i < d; ++i) f.M_data[i] = value_type();
this -> M_transform(f.M_data);
for (size_type i = 0; i < d + d; ++i) f.M_data[i] *= g.M_data[i];
this -> M_inv_transform(f.M_data);
size_type right = std::min(d + d, m);
for (size_type i = d; i < right; ++i) res.M_data[i] = -f.M_data[i];
}
return res;
}
formal_power_series log(size_type m) const {
return (lower(m).diff() * inverse(m - 1)).low(m - 1).inte();
}
value_type get(size_type i) const { return i >= M_data.size() ? value_type() : M_data[i]; }
value_type& extract(size_type i) { return M_data[i]; }
size_type size() const { return M_data.size(); }
bool empty() const { return M_data.empty(); }
};
int main() {
using m32 = modular<998244353>;
using fps = formal_power_series<m32::mod>;
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
size_t N;
std::cin >> N;
assert(2 <= N && N <= 100000);
std::vector<m32> vec(N + 1);
{
m32 cur(1);
for (size_t i = 0; i < N; ++i) {
cur *= m32(i + 1);
vec[i] = cur;
}
}
auto ans = fps(vec).inverse(N + 1);
m32 sum;
for (size_t i = 1; i < N; ++i) {
sum += ans.get(i);
}
std::cout << -sum << '\n';
return 0;
}