結果
問題 | No.1302 Random Tree Score |
ユーザー |
|
提出日時 | 2023-07-28 23:32:11 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 822 ms / 3,000 ms |
コード長 | 20,596 bytes |
コンパイル時間 | 2,013 ms |
コンパイル使用メモリ | 157,312 KB |
最終ジャッジ日時 | 2025-02-15 20:44:09 |
ジャッジサーバーID (参考情報) |
judge2 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 14 |
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(...)#endifvoid 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 reversefor (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 reversefor (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 internaltemplate <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 ebiint 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;}