結果
| 問題 | No.1302 Random Tree Score |
| ユーザー |
 Pachicobue
|
| 提出日時 | 2020-11-27 22:29:45 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 17 ms / 3,000 ms |
| コード長 | 17,252 bytes |
| コンパイル時間 | 2,636 ms |
| コンパイル使用メモリ | 203,192 KB |
| 最終ジャッジ日時 | 2025-01-16 07:52:49 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
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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
#include <bits/stdc++.h>using ll = long long;using uint = unsigned int;using ull = unsigned long long;using ld = long double;template<typename T> using max_heap = std::priority_queue<T>;template<typename T> using min_heap = std::priority_queue<T, std::vector<T>, std::greater<T>>;template<typename T>constexpr std::pair<T, T> extgcd(const T a, const T b){if (b == 0) { return std::pair<T, T>{1, 0}; }const auto g = std::gcd(a, b), da = std::abs(b) / g;const auto p = extgcd(b, a % b);const auto x = (da + p.second % da) % da, y = (g - a * x) / b;return {x, y};}template<typename T> constexpr T inverse(const T a, const T mod) { return extgcd(a, mod).first; }template<uint mod_value, bool dynamic = false>class modint_base{public:template<typename UInt = uint>static std::enable_if_t<dynamic, const UInt> mod() { return mod_ref(); }template<typename UInt = uint>static constexpr std::enable_if_t<not dynamic, const UInt> mod() { return mod_value; }template<typename UInt = uint>static void set_mod(const std::enable_if_t<dynamic, const UInt> mod) { mod_ref() = mod, inv_ref() = {1, 1}; }modint_base() : v{0} {}modint_base(const ll val) : v{norm(static_cast<uint>(val % static_cast<ll>(mod()) + static_cast<ll>(mod())))} {}modint_base(const modint_base& n) : v{n()} {}explicit operator bool() const { return v != 0; }explicit operator int() const { return v; }explicit operator uint() const { return v; }explicit operator ll() const { return v; }explicit operator ull() const { return v; }bool operator!() const { return not static_cast<bool>(*this); }modint_base& operator=(const modint_base& m) { return v = m(), (*this); }modint_base& operator=(const ll val) { return v = norm(uint(val % static_cast<ll>(mod()) + static_cast<ll>(mod()))), (*this); }friend modint_base operator+(const modint_base& m) { return m; }friend modint_base operator-(const modint_base& m) { return make(norm(mod() - m.v)); }friend modint_base operator+(const modint_base& m1, const modint_base& m2) { return make(norm(m1.v + m2.v)); }friend modint_base operator-(const modint_base& m1, const modint_base& m2) { return make(norm(m1.v + mod() - m2.v)); }friend modint_base operator*(const modint_base& m1, const modint_base& m2) { return make(static_cast<uint>(static_cast<ll>(m1.v) * static_cast<ll>(m2.v) % static_cast<ll>(mod()))); }friend modint_base operator/(const modint_base& m1, const modint_base& m2) { return m1 * inv(m2.v); }friend modint_base operator+(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) + val}; }friend modint_base operator-(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) - val}; }friend modint_base operator*(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) * (val % static_cast<ll>(mod()))}; }friend modint_base operator/(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) * inv(val)}; }friend modint_base operator+(const ll val, const modint_base& m) { return modint_base{static_cast<ll>(m.v) + val}; }friend modint_base operator-(const ll val, const modint_base& m) { return modint_base{-static_cast<ll>(m.v) + val}; }friend modint_base operator*(const ll val, const modint_base& m) { return modint_base{static_cast<ll>(m.v) * (val % static_cast<ll>(mod()))}; }friend modint_base operator/(const ll val, const modint_base& m) { return modint_base{val * inv(static_cast<ll>(m.v))}; }friend modint_base& operator+=(modint_base& m1, const modint_base& m2) { return m1 = m1 + m2; }friend modint_base& operator-=(modint_base& m1, const modint_base& m2) { return m1 = m1 - m2; }friend modint_base& operator*=(modint_base& m1, const modint_base& m2) { return m1 = m1 * m2; }friend modint_base& operator/=(modint_base& m1, const modint_base& m2) { return m1 = m1 / m2; }friend modint_base& operator+=(modint_base& m, const ll val) { return m = m + val; }friend modint_base& operator-=(modint_base& m, const ll val) { return m = m - val; }friend modint_base& operator*=(modint_base& m, const ll val) { return m = m * val; }friend modint_base& operator/=(modint_base& m, const ll val) { return m = m / val; }friend modint_base operator^(const modint_base& m, const ll n) { return power(m.v, n); }friend modint_base& operator^=(modint_base& m, const ll n) { return m = m ^ n; }friend bool operator==(const modint_base& m1, const modint_base& m2) { return m1.v == m2.v; }friend bool operator!=(const modint_base& m1, const modint_base& m2) { return not(m1 == m2); }friend bool operator==(const modint_base& m, const ll val) { return m.v == norm(static_cast<uint>(static_cast<ll>(mod()) + val % static_cast<ll>(mod()))); }friend bool operator!=(const modint_base& m, const ll val) { return not(m == val); }friend bool operator==(const ll val, const modint_base& m) { return m.v == norm(static_cast<uint>(static_cast<ll>(mod()) + val % static_cast<ll>(mod()))); }friend bool operator!=(const ll val, const modint_base& m) { return not(m == val); }friend std::istream& operator>>(std::istream& is, modint_base& m){ll v;return is >> v, m = v, is;}friend std::ostream& operator<<(std::ostream& os, const modint_base& m) { return os << m(); }uint operator()() const { return v; }static modint_base fact(const int n){auto& fact_ = fact_ref();if (n < (int)fact_.size()) { return fact_[n]; }for (int i = (int)fact_.size(); i <= n; i++) { fact_.push_back(fact_.back() * i); }return fact_.back();}static modint_base inv_fact(const int n){auto& inv_fact_ = inv_fact_ref();if (n < (int)inv_fact_.size()) { return inv_fact_[n]; }for (int i = inv_fact_.size(); i <= n; i++) { inv_fact_.push_back(inv_fact_.back() * modint_base::small_inv(i)); }return inv_fact_.back();}static modint_base perm(const int n, const int k) { return k > n ? modint_base{0} : fact(n) * inv_fact(n - k); }static modint_base comb(const int n, const int k) { return k > n ? modint_base{0} : fact(n) * inv_fact(n - k) * inv_fact(k); }std::pair<ll, ll> quad() const{const auto ans = quad_r(v, mod());ll x = std::get<0>(ans), y = std::get<1>(ans);if (y < 0) { x = -x, y = -y; }return {x, y};}private:static std::tuple<ll, ll, ll> quad_r(const ll r, const ll p){if (std::abs(r) <= 1000) { return {r, 1, 0}; }ll nr = p % r, q = p / r;if (nr * 2LL >= r) { nr -= r, q++; }if (nr * 2LL <= -r) { nr += r, q--; }const auto sub = quad_r(nr, r);const ll x = std::get<0>(sub), z = std::get<1>(sub), y = std::get<2>(sub);return {x, y - q * z, z};}template<typename UInt = uint>static std::enable_if_t<dynamic, UInt&> mod_ref(){static UInt mod = 0;return mod;}static uint norm(const uint x) { return x < mod() ? x : x - mod(); }static modint_base make(const uint x){modint_base m;return m.v = x, m;}static modint_base power(modint_base x, ull n){modint_base ans = 1;for (; n; n >>= 1, x *= x) {if (n & 1) { ans *= x; }}return ans;}static modint_base small_inv(const int n){auto& inv_ = inv_ref();if (n < (int)inv_.size()) { return inv_[n]; }for (int i = inv_.size(); i <= n; i++) { inv_.push_back(-inv_[modint_base::mod() % i] * (modint_base::mod() / i)); }return inv_.back();}static modint_base inv(const ll v) { return v <= 2000000 ? small_inv(static_cast<int>(v)) : modint_base{inverse(v, static_cast<ll>(mod()))}; }static std::vector<modint_base>& inv_ref(){static std::vector<modint_base> inv_{1, 1};return inv_;}static std::vector<modint_base>& fact_ref(){static std::vector<modint_base> fact_{1, 1};return fact_;}static std::vector<modint_base>& inv_fact_ref(){static std::vector<modint_base> inv_fact_{1, 1};return inv_fact_;}uint v;};template<uint mod>using modint = modint_base<mod, false>;template<uint id>using dynamic_modint = modint_base<id, true>;constexpr int popcount(const ull v) { return v ? __builtin_popcountll(v) : 0; }constexpr int log2p1(const ull v) { return v ? 64 - __builtin_clzll(v) : 0; }constexpr int lsbp1(const ull v) { return __builtin_ffsll(v); }constexpr int clog(const ull v) { return v ? log2p1(v - 1) : 0; }constexpr ull ceil2(const ull v) { return 1ULL << clog(v); }constexpr ull floor2(const ull v) { return v ? (1ULL << (log2p1(v) - 1)) : 0ULL; }constexpr bool btest(const ull mask, const int ind) { return (mask >> ind) & 1ULL; }template<typename T> void bset(T& mask, const int ind) { mask |= ((T)1 << ind); }template<typename T> void breset(T& mask, const int ind) { mask &= ~((T)1 << ind); }template<typename T> void bflip(T& mask, const int ind) { mask ^= ((T)1 << ind); }template<typename T> void bset(T& mask, const int ind, const bool b) { (b ? bset(mask, ind) : breset(mask, ind)); }template<typename T> bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); }template<typename T> bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); }template<typename T> constexpr T inf_v = std::numeric_limits<T>::max() / 4;template<typename Real> constexpr Real pi_v = Real{3.141592653589793238462643383279502884};template<typename T> constexpr T TEN(const int n) { return n == 0 ? T{1} : TEN<T>(n - 1) * T{10}; }template<typename F> struct fix : F{fix(F&& f) : F{std::forward<F>(f)} {}template<typename... Args> auto operator()(Args&&... args) const { return F::operator()(*this, std::forward<Args>(args)...); }};template<typename T, int n, int i = 0>auto nd_array(int const (&szs)[n], const T x = T{}){if constexpr (i == n) {return x;} else {return std::vector(szs[i], nd_array<T, n, i + 1>(szs, x));}}template<typename T, std::size_t N>std::ostream& operator<<(std::ostream& os, const std::array<T, N>& v){os << "[";for (const auto& e : v) { os << e << ","; }return (os << "]" << std::endl);}template<typename T, typename A>std::ostream& operator<<(std::ostream& os, const std::deque<T, A>& v){os << "[";for (const auto& e : v) { os << e << ","; }return (os << "]" << std::endl);}template<typename K, typename T, typename C, typename A>std::ostream& operator<<(std::ostream& os, const std::map<K, T, C, A>& v){os << "[";for (const auto& e : v) { os << "<" << e.first << ": " << e.second << ">,"; }return (os << "]" << std::endl);}template<typename K, typename T, typename C, typename A>std::ostream& operator<<(std::ostream& os, const std::multimap<K, T, C, A>& v){os << "[";for (const auto& e : v) { os << "<" << e.first << ": " << e.second << ">,"; }return (os << "]" << std::endl);}template<typename T, typename C, typename A>std::ostream& operator<<(std::ostream& os, const std::multiset<T, C, A>& v){os << "[";for (const auto& e : v) { os << e << ","; }return (os << "]" << std::endl);}template<typename T1, typename T2>std::ostream& operator<<(std::ostream& os, const std::pair<T1, T2>& v) { return (os << "<" << v.first << "," << v.second << ">"); }template<typename T1, typename T2, typename T3>std::ostream& operator<<(std::ostream& os, const std::priority_queue<T1, T2, T3>& v){auto q = v;os << "[";while (not q.empty()) { os << q.top() << ",", q.pop(); }return os << "]\n";}template<typename T1, typename T2>std::ostream& operator<<(std::ostream& os, const std::queue<T1>& v){auto q = v;os << "[";while (not q.empty()) { os << q.front() << ",", q.pop(); }return os << "]\n";}template<typename T, typename C, typename A>std::ostream& operator<<(std::ostream& os, const std::set<T, C, A>& v){os << "[";for (const auto& e : v) { os << e << ","; }return (os << "]" << std::endl);}template<typename T1, typename T2>std::ostream& operator<<(std::ostream& os, const std::stack<T1>& v){auto q = v;os << "[";while (not q.empty()) { os << q.top() << ",", q.pop(); }return os << "]\n";}template<typename TupType, size_t... I>std::ostream& print(std::ostream& os, const TupType& _tup, std::index_sequence<I...>) { return os << "(", (..., (os << (I == 0 ? "" : ", ") << std::get<I>(_tup))), os << ")\n"; }template<typename... T>std::ostream& operator<<(std::ostream& os, const std::tuple<T...>& _tup) { return print(os, _tup, std::make_index_sequence<sizeof...(T)>()); }template<typename K, typename T, typename H, typename P, typename A>std::ostream& operator<<(std::ostream& os, const std::unordered_map<K, T, H, P, A>& v){os << "[";for (const auto& e : v) { os << "<" << e.first << ": " << e.second << ">,"; }return (os << "]" << std::endl);}template<typename K, typename T, typename H, typename P, typename A>std::ostream& operator<<(std::ostream& os, const std::unordered_multimap<K, T, H, P, A>& v){os << "[";for (const auto& e : v) { os << "<" << e.first << ": " << e.second << ">,"; }return (os << "]" << std::endl);}template<typename T, typename H, typename P, typename A>std::ostream& operator<<(std::ostream& os, const std::unordered_multiset<T, H, P, A>& v){os << "[";for (const auto& e : v) { os << e << ","; }return (os << "]" << std::endl);}template<typename T, typename H, typename P, typename A>std::ostream& operator<<(std::ostream& os, const std::unordered_set<T, H, P, A>& v){os << "[";for (const auto& e : v) { os << e << ","; }return (os << "]" << std::endl);}template<typename T, typename A>std::ostream& operator<<(std::ostream& os, const std::vector<T, A>& v){os << "[";for (const auto& e : v) { os << e << ","; }return (os << "]" << std::endl);}class printer{public:printer(std::ostream& os_ = std::cout) : m_os{os_} { m_os << std::fixed << std::setprecision(15); }template<typename... Args> int ln(const Args&... args) { return dump(args...), m_os << '\n', 0; }template<typename... Args> int el(const Args&... args) { return dump(args...), m_os << std::endl, 0; }private:template<typename T> void dump(const T& v) { m_os << v; }template<typename T> void dump(const std::vector<T>& vs){for (int i = 0; i < (int)vs.size(); i++) { m_os << (i ? " " : ""), dump(vs[i]); }}template<typename T> void dump(const std::vector<std::vector<T>>& vss){for (int i = 0; i < (int)vss.size(); i++) { m_os << (0 <= i or i + 1 < (int)vss.size() ? "\n" : ""), dump(vss[i]); }}template<typename T, typename... Args> int dump(const T& v, const Args&... args) { return dump(v), m_os << ' ', dump(args...), 0; }std::ostream& m_os;};printer out;class scanner{public:scanner(std::istream& is_ = std::cin) : m_is{is_} { m_is.tie(nullptr), std::ios::sync_with_stdio(false); }template<typename T> T val(){T v;return m_is >> v, v;}template<typename T> T val(const T offset) { return val<T>() - offset; }template<typename T> std::vector<T> vec(const int n){return make_v<T>(n, [this]() { return val<T>(); });}template<typename T> std::vector<T> vec(const int n, const T offset){return make_v<T>(n, [this, offset]() { return val<T>(offset); });}template<typename T> std::vector<std::vector<T>> vvec(const int n0, const int n1){return make_v<std::vector<T>>(n0, [this, n1]() { return vec<T>(n1); });}template<typename T> std::vector<std::vector<T>> vvec(const int n0, const int n1, const T offset){return make_v<std::vector<T>>(n0, [this, n1, offset]() { return vec<T>(n1, offset); });}template<typename... Args> auto tup() { return std::tuple<std::decay_t<Args>...>{val<Args>()...}; }template<typename... Args> auto tup(const Args&... offsets) { return std::tuple<std::decay_t<Args>...>{val<Args>(offsets)...}; }private:template<typename T, typename F>std::vector<T> make_v(const int n, F f){std::vector<T> ans;for (int i = 0; i < n; i++) { ans.push_back(f()); }return ans;}std::istream& m_is;};scanner in;template<typename T>void HogeHogeSansuu(T x) { std::cerr << x; }template<typename T, typename... Args>void HogeHogeSansuu(T x, Args... args) { std::cerr << x << ",", HogeHogeSansuu(args...); }int main(){using mint = modint<998244353>;const auto N = in.val<int>();mint ans = 0;for (int i = 0; i < N - 1; i++) {const mint exn = mint::inv_fact(i) * (mint(N) ^ i);const int res = N - 2 - i;const mint bin = mint::comb(N, res);ans += exn * bin;}ans *= mint::fact(N - 2);const mint total = mint(N) ^ (N - 2);out.ln(ans / total);return 0;}