結果
| 問題 | No.1302 Random Tree Score |
| ユーザー |
 ebi_fly
|
| 提出日時 | 2023-07-28 23:32:11 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 880 ms / 3,000 ms |
| コード長 | 20,596 bytes |
| コンパイル時間 | 2,010 ms |
| コンパイル使用メモリ | 161,172 KB |
| 実行使用メモリ | 11,300 KB |
| 最終ジャッジ日時 | 2024-10-06 21:52:31 |
| 合計ジャッジ時間 | 10,428 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
（要ログイン）
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
5,248 KB |
| testcase_01 | AC | 2 ms
5,248 KB |
| testcase_02 | AC | 185 ms
5,248 KB |
| testcase_03 | AC | 393 ms
7,640 KB |
| testcase_04 | AC | 190 ms
5,248 KB |
| testcase_05 | AC | 861 ms
11,104 KB |
| testcase_06 | AC | 874 ms
11,132 KB |
| testcase_07 | AC | 194 ms
5,340 KB |
| testcase_08 | AC | 400 ms
7,776 KB |
| testcase_09 | AC | 869 ms
11,164 KB |
| testcase_10 | AC | 861 ms
10,340 KB |
| testcase_11 | AC | 188 ms
5,248 KB |
| testcase_12 | AC | 880 ms
10,724 KB |
| testcase_13 | AC | 2 ms
5,248 KB |
| testcase_14 | AC | 865 ms
11,300 KB |
| testcase_15 | AC | 847 ms
11,172 KB |
| testcase_16 | AC | 2 ms
5,248 KB |
ソースコード
#line 1 "a.cpp"
#include <algorithm>
#include <bitset>
#include <cassert>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <cstddef>
#include <cstdint>
#include <cstdlib>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
/* macro */
#define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++)
#define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--)
#define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++)
#define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
/* macro end */
/* template */
namespace ebi {
#ifdef LOCAL
#define debug(...) \
std::cerr << "LINE: " << __LINE__ << " [" << #__VA_ARGS__ << "]:", \
debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif
void debug_out() {
std::cerr << std::endl;
}
template <typename Head, typename... Tail> void debug_out(Head h, Tail... t) {
std::cerr << " " << h;
if (sizeof...(t) > 0) std::cerr << " :";
debug_out(t...);
}
template <typename T1, typename T2>
std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &pa) {
return os << pa.first << " " << pa.second;
}
template <typename T1, typename T2>
std::istream &operator>>(std::istream &os, std::pair<T1, T2> &pa) {
return os >> pa.first >> pa.second;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &vec) {
for (std::size_t i = 0; i < vec.size(); i++)
os << vec[i] << (i + 1 == vec.size() ? "" : " ");
return os;
}
template <typename T>
std::istream &operator>>(std::istream &os, std::vector<T> &vec) {
for (T &e : vec) std::cin >> e;
return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::optional<T> &opt) {
if (opt) {
os << opt.value();
} else {
os << "invalid value";
}
return os;
}
using std::size_t;
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
template <class T> inline bool chmin(T &a, T b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T> inline bool chmax(T &a, T b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <class T> T pow(T x, i64 n) {
T res = 1;
while (n > 0) {
if (n & 1) res = res * x;
x = x * x;
n >>= 1;
}
return res;
}
template <class T> struct Edge {
int to;
T cost;
Edge(int _to, T _cost = 1) : to(_to), cost(_cost) {}
};
template <class T> struct Graph : std::vector<std::vector<Edge<T>>> {
using std::vector<std::vector<Edge<T>>>::vector;
void add_edge(int u, int v, T w, bool directed = false) {
(*this)[u].emplace_back(v, w);
if (directed) return;
(*this)[v].emplace_back(u, w);
}
};
struct graph : std::vector<std::vector<int>> {
using std::vector<std::vector<int>>::vector;
void add_edge(int u, int v, bool directed = false) {
(*this)[u].emplace_back(v);
if (directed) return;
(*this)[v].emplace_back(u);
}
};
constexpr i64 LNF = std::numeric_limits<i64>::max() / 4;
constexpr int INF = std::numeric_limits<int>::max() / 2;
const std::vector<int> dy = {1, 0, -1, 0, 1, 1, -1, -1};
const std::vector<int> dx = {0, 1, 0, -1, 1, -1, 1, -1};
} // namespace ebi
#line 2 "convolution/ntt.hpp"
#line 4 "convolution/ntt.hpp"
#include <array>
#line 8 "convolution/ntt.hpp"
#line 2 "math/internal_math.hpp"
#line 4 "math/internal_math.hpp"
namespace ebi {
namespace internal {
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
if (m == 880803841) return 26;
assert(0);
return -1;
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
} // namespace ebi
#line 2 "utility/bit_operator.hpp"
namespace ebi {
constexpr int bsf_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
int bit_reverse(int n, int bit_size) {
int rev_n = 0;
for (int i = 0; i < bit_size; i++) {
rev_n |= ((n >> i) & 1) << (bit_size - i - 1);
}
return rev_n;
}
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
int popcnt(int x) {
return __builtin_popcount(x);
}
int msb(int x) {
return (x == 0) ? -1 : 31 - __builtin_clz(x);
}
int bsf(int x) {
return (x == 0) ? -1 : __builtin_ctz(x);
}
} // namespace ebi
#line 2 "utility/modint_base.hpp"
#line 4 "utility/modint_base.hpp"
namespace ebi {
namespace internal {
struct modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
struct static_modint_base : modint_base {};
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
} // namespace internal
} // namespace ebi
#line 12 "convolution/ntt.hpp"
namespace ebi {
namespace internal {
template <class mint, int g = internal::primitive_root<mint::mod()>,
internal::is_static_modint_t<mint>* = nullptr>
struct ntt_info {
static constexpr int rank2 = bsf_constexpr(mint::mod() - 1);
std::array<mint, rank2 + 1> root, inv_root;
ntt_info() {
root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
inv_root[rank2] = root[rank2].inv();
for (int i = rank2 - 1; i >= 0; i--) {
root[i] = root[i + 1] * root[i + 1];
inv_root[i] = inv_root[i + 1] * inv_root[i + 1];
}
}
};
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
static const ntt_info<mint> info;
int n = int(a.size());
int bit_size = bsf(n);
assert(n == 1 << ceil_pow2(n));
// bit reverse
for (int i = 0; i < n; i++) {
int rev = bit_reverse(i, bit_size);
if (i < rev) {
std::swap(a[i], a[rev]);
}
}
for (int bit = 0; bit < bit_size; bit++) {
for (int i = 0; i < n / (1 << (bit + 1)); i++) {
mint zeta1 = 1;
mint zeta2 = info.root[1];
for (int j = 0; j < (1 << bit); j++) {
int idx = i * (1 << (bit + 1)) + j;
int jdx = idx + (1 << bit);
mint p1 = a[idx];
mint p2 = a[jdx];
a[idx] = p1 + zeta1 * p2;
a[jdx] = p1 + zeta2 * p2;
zeta1 *= info.root[bit + 1];
zeta2 *= info.root[bit + 1];
}
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
static const ntt_info<mint> info;
int n = int(a.size());
int bit_size = bsf(n);
assert(n == 1 << ceil_pow2(n));
// bit reverse
for (int i = 0; i < n; i++) {
int rev = bit_reverse(i, bit_size);
if (i < rev) std::swap(a[i], a[rev]);
}
for (int bit = 0; bit < bit_size; bit++) {
for (int i = 0; i < n / (1 << (bit + 1)); i++) {
mint zeta1 = 1;
mint zeta2 = info.inv_root[1];
for (int j = 0; j < (1 << bit); j++) {
int idx = i * (1 << (bit + 1)) + j;
int jdx = idx + (1 << bit);
mint p1 = a[idx];
mint p2 = a[jdx];
a[idx] = p1 + zeta1 * p2;
a[jdx] = p1 + zeta2 * p2;
zeta1 *= info.inv_root[bit + 1];
zeta2 *= info.inv_root[bit + 1];
}
}
}
mint inv_n = mint(n).inv();
for (int i = 0; i < n; i++) {
a[i] *= inv_n;
}
}
} // namespace internal
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_naive(const std::vector<mint>& f,
const std::vector<mint>& g) {
if (f.empty() || g.empty()) return {};
int n = int(f.size()), m = int(g.size());
std::vector<mint> c(n + m - 1);
if (n < m) {
for (int j = 0; j < m; j++) {
for (int i = 0; i < n; i++) {
c[i + j] += f[i] * g[j];
}
}
} else {
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
c[i + j] += f[i] * g[j];
}
}
}
return c;
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(const std::vector<mint>& f,
const std::vector<mint>& g) {
if (f.empty() || g.empty()) return {};
if (std::min(f.size(), g.size()) < 60) return convolution_naive(f, g);
int n = 1 << ceil_pow2(f.size() + g.size() - 1);
std::vector<mint> a(n), b(n);
std::copy(f.begin(), f.end(), a.begin());
std::copy(g.begin(), g.end(), b.begin());
internal::butterfly(a);
internal::butterfly(b);
for (int i = 0; i < n; i++) {
a[i] *= b[i];
}
internal::butterfly_inv(a);
a.resize(f.size() + g.size() - 1);
return a;
}
} // namespace ebi
#line 2 "fps/fps.hpp"
#line 7 "fps/fps.hpp"
namespace ebi {
template <class mint, std::vector<mint> (*convolution)(
const std::vector<mint> &, const std::vector<mint> &)>
struct FormalPowerSeries : std::vector<mint> {
private:
using std::vector<mint>::vector;
using std::vector<mint>::vector::operator=;
using FPS = FormalPowerSeries;
public:
FPS operator+(const FPS &rhs) const noexcept {
return FPS(*this) += rhs;
}
FPS operator-(const FPS &rhs) const noexcept {
return FPS(*this) -= rhs;
}
FPS operator*(const FPS &rhs) const noexcept {
return FPS(*this) *= rhs;
}
FPS operator/(const FPS &rhs) const noexcept {
return FPS(*this) /= rhs;
}
FPS operator%(const FPS &rhs) const noexcept {
return FPS(*this) %= rhs;
}
FPS operator+(const mint &rhs) const noexcept {
return FPS(*this) += rhs;
}
FPS operator-(const mint &rhs) const noexcept {
return FPS(*this) -= rhs;
}
FPS operator*(const mint &rhs) const noexcept {
return FPS(*this) *= rhs;
}
FPS operator/(const mint &rhs) const noexcept {
return FPS(*this) /= rhs;
}
FPS &operator+=(const FPS &rhs) noexcept {
if (this->size() < rhs.size()) this->resize(rhs.size());
for (int i = 0; i < (int)rhs.size(); ++i) {
(*this)[i] += rhs[i];
}
return *this;
}
FPS &operator-=(const FPS &rhs) noexcept {
if (this->size() < rhs.size()) this->resize(rhs.size());
for (int i = 0; i < (int)rhs.size(); ++i) {
(*this)[i] -= rhs[i];
}
return *this;
}
FPS &operator*=(const FPS &rhs) noexcept {
*this = convolution(*this, rhs);
return *this;
}
FPS &operator/=(const FPS &rhs) noexcept {
int n = deg() - 1;
int m = rhs.deg() - 1;
if (n < m) {
*this = {};
return *this;
}
*this = (*this).rev() * rhs.rev().inv(n - m + 1);
(*this).resize(n - m + 1);
std::reverse((*this).begin(), (*this).end());
return *this;
}
FPS &operator%=(const FPS &rhs) noexcept {
*this -= *this / rhs * rhs;
shrink();
return *this;
}
FPS &operator+=(const mint &rhs) noexcept {
if (this->empty()) this->resize(1);
(*this)[0] += rhs;
return *this;
}
FPS &operator-=(const mint &rhs) noexcept {
if (this->empty()) this->resize(1);
(*this)[0] -= rhs;
return *this;
}
FPS &operator*=(const mint &rhs) noexcept {
for (int i = 0; i < deg(); ++i) {
(*this)[i] *= rhs;
}
return *this;
}
FPS &operator/=(const mint &rhs) noexcept {
mint inv_rhs = rhs.inv();
for (int i = 0; i < deg(); ++i) {
(*this)[i] *= inv_rhs;
}
return *this;
}
FPS operator>>(int d) const {
if (deg() <= d) return {};
FPS f = *this;
f.erase(f.begin(), f.begin() + d);
return f;
}
FPS operator<<(int d) const {
FPS f = *this;
f.insert(f.begin(), d, 0);
return f;
}
FPS operator-() const {
FPS g(this->size());
for (int i = 0; i < (int)this->size(); i++) g[i] = -(*this)[i];
return g;
}
FPS pre(int sz) const {
return FPS(this->begin(), this->begin() + std::min(deg(), sz));
}
FPS rev() const {
auto f = *this;
std::reverse(f.begin(), f.end());
return f;
}
FPS differential() const {
int n = deg();
FPS g(std::max(0, n - 1));
for (int i = 0; i < n - 1; i++) {
g[i] = (*this)[i + 1] * (i + 1);
}
return g;
}
FPS integral() const {
int n = deg();
FPS g(n + 1);
g[0] = 0;
if (n > 0) g[1] = 1;
auto mod = mint::mod();
for (int i = 2; i <= n; i++) g[i] = (-g[mod % i]) * (mod / i);
for (int i = 0; i < n; i++) g[i + 1] *= (*this)[i];
return g;
}
FPS inv(int d = -1) const {
int n = 1;
if (d < 0) d = deg();
FPS g(n);
g[0] = (*this)[0].inv();
while (n < d) {
n <<= 1;
g = (g * 2 - g * g * this->pre(n)).pre(n);
}
g.resize(d);
return g;
}
FPS log(int d = -1) const {
assert((*this)[0].val() == 1);
if (d < 0) d = deg();
return ((*this).differential() * (*this).inv(d)).pre(d - 1).integral();
}
FPS exp(int d = -1) const {
assert((*this)[0].val() == 0);
int n = 1;
if (d < 0) d = deg();
FPS g(n);
g[0] = 1;
while (n < d) {
n <<= 1;
g = (g * (this->pre(n) - g.log(n) + 1)).pre(n);
}
g.resize(d);
return g;
}
FPS pow(int64_t k, int d = -1) const {
const int n = deg();
if (d < 0) d = n;
if (k == 0) {
FPS f(d);
if (d > 0) f[0] = 1;
return f;
}
for (int i = 0; i < n; i++) {
if ((*this)[i] != 0) {
mint rev = (*this)[i].inv();
FPS f = (((*this * rev) >> i).log(d) * k).exp(d);
f *= (*this)[i].pow(k);
f = (f << (i * k)).pre(d);
if (f.deg() < d) f.resize(d);
return f;
}
if (i + 1 >= (d + k - 1) / k) break;
}
return FPS(d);
}
int deg() const {
return (*this).size();
}
void shrink() {
while ((!this->empty()) && this->back() == 0) this->pop_back();
}
int count_terms() const {
int c = 0;
for (int i = 0; i < deg(); i++) {
if ((*this)[i] != 0) c++;
}
return c;
}
std::optional<FPS> sqrt(int d = -1) const;
};
} // namespace ebi
#line 2 "math/combination.hpp"
#line 5 "math/combination.hpp"
namespace ebi {
template <class mint>
struct combination {
combination(int n) : m(n), fact(n + 1), inv_fact(n + 1) {
fact[0] = 1;
for (int i = 1; i <= n; i++) {
fact[i] = fact[i - 1] * i;
}
inv_fact[n] = fact[n].inv();
for (int i = n; i > 0; i--) {
inv_fact[i - 1] = inv_fact[i] * i;
}
}
mint operator()(int n, int k) const {
assert(n <= m);
if (k < 0 || n < k) return 0;
return fact[n] * inv_fact[k] * inv_fact[n - k];
}
mint f(int n) const {
assert(n <= m);
if (n < 0) return 0;
return fact[n];
}
mint inv_f(int n) const {
assert(n <= m);
if (n < 0) return 0;
return inv_fact[n];
}
mint inv(int n) const {
assert(n <= m);
return inv_fact[n] * fact[n-1];
}
private:
int m;
std::vector<mint> fact, inv_fact;
};
} // namespace ebi
#line 2 "utility/modint.hpp"
#line 6 "utility/modint.hpp"
#line 8 "utility/modint.hpp"
namespace ebi {
template <int m> struct static_modint : internal::static_modint_base {
private:
using modint = static_modint;
public:
static constexpr int mod() {
return m;
}
static constexpr modint raw(int v) {
modint x;
x._v = v;
return x;
}
constexpr static_modint() : _v(0) {}
constexpr static_modint(long long v) {
v %= (long long)umod();
if (v < 0) v += (long long)umod();
_v = (unsigned int)v;
}
constexpr unsigned int val() const {
return _v;
}
constexpr unsigned int value() const {
return val();
}
constexpr modint &operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
constexpr modint &operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
constexpr modint &operator+=(const modint &rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
constexpr modint &operator-=(const modint &rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
constexpr modint &operator*=(const modint &rhs) {
unsigned long long x = _v;
x *= rhs._v;
_v = (unsigned int)(x % (unsigned long long)umod());
return *this;
}
constexpr modint &operator/=(const modint &rhs) {
return *this = *this * rhs.inv();
}
constexpr modint operator+() const {
return *this;
}
constexpr modint operator-() const {
return modint() - *this;
}
constexpr modint pow(long long n) const {
assert(0 <= n);
modint x = *this, res = 1;
while (n) {
if (n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
constexpr modint inv() const {
assert(_v);
return pow(umod() - 2);
}
friend modint operator+(const modint &lhs, const modint &rhs) {
return modint(lhs) += rhs;
}
friend modint operator-(const modint &lhs, const modint &rhs) {
return modint(lhs) -= rhs;
}
friend modint operator*(const modint &lhs, const modint &rhs) {
return modint(lhs) *= rhs;
}
friend modint operator/(const modint &lhs, const modint &rhs) {
return modint(lhs) /= rhs;
}
friend bool operator==(const modint &lhs, const modint &rhs) {
return lhs.val() == rhs.val();
}
friend bool operator!=(const modint &lhs, const modint &rhs) {
return !(lhs == rhs);
}
private:
unsigned int _v = 0;
static constexpr unsigned int umod() {
return m;
}
};
template <int m>
std::istream &operator>>(std::istream &os, static_modint<m> &a) {
long long x;
os >> x;
a = x;
return os;
}
template <int m>
std::ostream &operator<<(std::ostream &os, const static_modint<m> &a) {
return os << a.val();
}
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
} // namespace ebi
#line 169 "a.cpp"
namespace ebi {
using mint = modint998244353;
using FPS = FormalPowerSeries<mint, convolution>;
void main_() {
int n;
std::cin >> n;
FPS f(n+1);
combination<mint> comb(n);
rep(i,0,n+1) {
f[i] = (i + 1) * comb.inv_f(i);
}
mint ans = f.pow(n)[n-2] * comb.f(n-2) / mint(n).pow(n-2);
std::cout << ans.val() << '\n';
}
} // namespace ebi
int main() {
std::cout << std::fixed << std::setprecision(15);
std::cin.tie(nullptr);
std::ios::sync_with_stdio(false);
int t = 1;
// std::cin >> t;
while (t--) {
ebi::main_();
}
return 0;
}