結果

問題 No.1302 Random Tree Score
ユーザー tokusakurai
提出日時 2020-11-27 22:58:55
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 330 ms / 3,000 ms
コード長 11,275 bytes
コンパイル時間 2,583 ms
コンパイル使用メモリ 213,396 KB
最終ジャッジ日時 2025-01-16 08:18:23
ジャッジサーバーID
（参考情報） 		judge5 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 14
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0; i < n; i++)
#define rep2(i, x, n) for(int i = x; i <= n; i++)
#define rep3(i, x, n) for(int i = x; i >= n; i--)
#define each(e, v) for(auto &e: v)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
const int MOD = 1000000007;
//const int MOD = 998244353;
const int inf = (1<<30)-1;
const ll INF = (1LL<<60)-1;
template<typename T> bool chmax(T &x, const T &y) {return (x < y)? (x = y, true) : false;};
template<typename T> bool chmin(T &x, const T &y) {return (x > y)? (x = y, true) : false;};
struct io_setup{
    io_setup(){
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;
template<int mod>
struct Mod_Int{
    int x;
    Mod_Int() : x(0) {}
    Mod_Int(ll y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
    Mod_Int &operator += (const Mod_Int &p){
        if((x += p.x) >= mod) x -= mod;
        return *this;
    }
    Mod_Int &operator -= (const Mod_Int &p){
        if((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }
    Mod_Int &operator *= (const Mod_Int &p){
        x = (int) (1LL * x * p.x % mod);
        return *this;
    }
    Mod_Int &operator /= (const Mod_Int &p){
        *this *= p.inverse();
        return *this;
    }
    Mod_Int &operator ++ () {return *this += Mod_Int(1);}
    Mod_Int operator ++ (int){
        Mod_Int tmp = *this;
        ++*this;
        return tmp;
    }
    Mod_Int &operator -- () {return *this -= Mod_Int(1);}
    Mod_Int operator -- (int){
        Mod_Int tmp = *this;
        --*this;
        return tmp;
    }
    Mod_Int operator - () const {return Mod_Int(-x);}
    Mod_Int operator + (const Mod_Int &p) const {return Mod_Int(*this) += p;}
    Mod_Int operator - (const Mod_Int &p) const {return Mod_Int(*this) -= p;}
    Mod_Int operator * (const Mod_Int &p) const {return Mod_Int(*this) *= p;}
    Mod_Int operator / (const Mod_Int &p) const {return Mod_Int(*this) /= p;}
    bool operator == (const Mod_Int &p) const {return x == p.x;}
    bool operator != (const Mod_Int &p) const {return x != p.x;}
    Mod_Int inverse() const {
        assert(*this != Mod_Int(0));
        return pow(mod-2);
    }
    Mod_Int pow(ll k) const{
        Mod_Int now = *this, ret = 1;
        for(; k; k >>= 1, now *= now){
            if(k&1) ret *= now;
        }
        return ret;
    }
    friend ostream &operator << (ostream &os, const Mod_Int &p){
        return os << p.x;
    }
    friend istream &operator >> (istream &is, Mod_Int &p){
        ll a;
        is >> a;
        p = Mod_Int<mod>(a);
        return is;
    }
};
using mint = Mod_Int<998244353>;
template<int mod, int primitive_root>
struct Number_Theorem_Transform{
    using T = Mod_Int<mod>;
    vector<T> r, ir;
    Number_Theorem_Transform(){
        r.resize(30), ir.resize(30);
        rep(i, 30){
            r[i] = -T(primitive_root).pow((mod-1)>>(i+2));
            ir[i] = r[i].inverse();
        }
    }
    void ntt(vector<T> &a, int n) const{
        assert((n&(n-1)) == 0);
        a.resize(n);
        for(int k = n; k >>= 1;){
            T w = 1;
            for(int s = 0, t = 0; s < n; s += 2*k){
                for(int i = s, j = s+k; i < s+k; i++, j++){
                    T x = a[i], y = w*a[j];
                    a[i] = x+y, a[j] = x-y;
                }
                w *= r[__builtin_ctz(++t)];
            }
        }
    }
    void intt(vector<T> &a, int n) const{
        assert((n&(n-1)) == 0);
        a.resize(n);
        for(int k = 1; k < n; k <<= 1){
            T w = 1;
            for(int s = 0, t = 0; s < n; s += 2*k){
                for(int i = s, j = s+k; i < s+k; i++, j++){
                    T x = a[i], y = a[j];
                    a[i] = x+y, a[j] = w*(x-y);
                }
                w *= ir[__builtin_ctz(++t)];
            }
        }
        T inv = T(n).inverse();
        for(auto &e: a) e *= inv;
    }
    vector<T> convolve(vector<T> a, vector<T> b) const{
        int k = sz(a)+sz(b)-1, n = 1;
        while(n < k) n <<= 1;
        ntt(a, n), ntt(b, n);
        rep(i, n) a[i] *= b[i];
        intt(a, n), a.resize(k);
        return a;
    }
};
Number_Theorem_Transform<998244353, 3> NTT;
template<typename T>
struct Formal_Power_Series : vector<T>{
    using vector<T> :: vector;
    Formal_Power_Series(const vector<T> &v) : vector<T>(v) {}
    Formal_Power_Series pre(int n) const{
        return Formal_Power_Series(begin(*this), begin(*this)+min((int)this->size(), n));
    }
    Formal_Power_Series rev() const{
        Formal_Power_Series ret = *this;
        reverse(all(ret));
        return ret;
    }
    Formal_Power_Series &normalize(){
        while(!this->empty() && this->back() == 0) this->pop_back();
        return *this;
    }
    Formal_Power_Series operator - () const noexcept{
        Formal_Power_Series ret = *this;
        rep(i, sz(ret)) ret[i] = -ret[i];
        return ret; 
    }
    Formal_Power_Series &operator += (const T &x){
        if(this->empty()) this->resize(1);
        (*this)[0] += x;
        return *this;
    }
    Formal_Power_Series &operator += (const Formal_Power_Series &v){
        if(v.size() > this->size()) this->resize(sz(v));
        rep(i, sz(v)) (*this)[i] += v[i];
        return this->normalize();
    }
    Formal_Power_Series &operator -= (const T &x){
        if(this->empty()) this->resize(1);
        *this[0] -= x;
        return *this;
    }
    Formal_Power_Series &operator -= (const Formal_Power_Series &v){
        if(v.size() > this->size()) this->resize(sz(v));
        rep(i, sz(v)) (*this)[i] -= v[i];
        return this->normalize();
    }
    Formal_Power_Series &operator *= (const T &x){
        rep(i, this->size()) (*this)[i] *= x;
        return *this;
    }
    Formal_Power_Series &operator *= (const Formal_Power_Series &v){
        return *this = NTT.convolve(*this, v);
    }
    Formal_Power_Series &operator /= (const T &x){
        assert(x != 0);
        T inv = x.inverse();
        rep(i, this->size()) (*this)[i] *= inv;
        return *this;
    }
    Formal_Power_Series &operator /= (const Formal_Power_Series &v){
        if(v.size() > this->size()){
            this->clear();
            return *this;
        }
        int n = this->size()-sz(v)+1;
        return *this = (rev().pre(n)*v.rev().inv(n)).pre(n).rev(n);
    }
    Formal_Power_Series &operator %= (const Formal_Power_Series &v){
        return *this -= (*this/v)*v;
    }
    Formal_Power_Series &operator <<= (int x){
        Formal_Power_Series ret(x, 0);
        ret.insert(end(ret), begin(*this), end(*this));
        return *this = ret;
    }
    Formal_Power_Series &operator >>= (int x){
        Formal_Power_Series ret;
        ret.insert(end(ret), begin(*this)+x, end(*this));
        return *this = ret;
    }
    Formal_Power_Series operator + (const T &x) const {return Formal_Power_Series(*this) += x;}
    Formal_Power_Series operator + (const Formal_Power_Series &v) const {return Formal_Power_Series(*this) += v;}
    Formal_Power_Series operator - (const T &x) const {return Formal_Power_Series(*this) -= x;}
    Formal_Power_Series operator - (const Formal_Power_Series &v) const {return Formal_Power_Series(*this) -= v;}
    Formal_Power_Series operator * (const T &x) const {return Formal_Power_Series(*this) *= x;}
    Formal_Power_Series operator * (const Formal_Power_Series &v) const {return Formal_Power_Series(*this) *= v;}
    Formal_Power_Series operator / (const T &x) const {return Formal_Power_Series(*this) /= x;}
    Formal_Power_Series operator / (const Formal_Power_Series &v) const {return Formal_Power_Series(*this) /= v;}
    Formal_Power_Series operator % (const Formal_Power_Series &v) const {return Formal_Power_Series(*this) %= v;}
    Formal_Power_Series operator << (int x) const {return Formal_Power_Series(*this) <<= x;}
    Formal_Power_Series operator >> (int x) const {return Formal_Power_Series(*this) >>= x;}
    T val(const T &x) const{
        T ret = 0;
        rep3(i, this->size()-1, 0) ret *= x, ret += (*this)[i];
        return ret;
    }
    Formal_Power_Series diff() const{ // df/dx
        int n = this->size();
        Formal_Power_Series ret(n-1);
        rep2(i, 1, n-1) ret[i-1] = (*this)[i]*i;
        return ret;
    }
    Formal_Power_Series integral() const{ // ∫fdx
        int n = this->size();
        Formal_Power_Series ret(n+1);
        rep(i, n) ret[i+1] = (*this)[i]/(i+1);
        return ret;
    }
    Formal_Power_Series inv(int deg) const{ // 1/f (f[0] != 0)
        assert((*this)[0] != T(0));
        Formal_Power_Series ret(1, (*this)[0].inverse());
        for(int i = 1; i < deg; i <<= 1){
            Formal_Power_Series f = pre(i<<1), g = ret;
            NTT.ntt(f, 2*i), NTT.ntt(g, 2*i);
            Formal_Power_Series h(2*i);
            rep(j, 2*i) h[j] = f[j]*g[j];
            NTT.intt(h, 2*i);
            rep(j, i) h[j] = 0;
            NTT.ntt(h, 2*i);
            rep(j, 2*i) h[j] *= g[j];
            NTT.intt(h, 2*i);
            rep(j, i) h[j] = 0;
            ret -= h;
            //ret = (ret+ret-ret*ret*pre(i<<1)).pre(i<<1);
        }
        ret.resize(deg);
        return ret;
    }
    Formal_Power_Series inv() const {return inv(this->size());}
    Formal_Power_Series log(int deg) const{ // log(f) (f[0] = 1)
        assert((*this)[0] == 1);
        Formal_Power_Series ret = (diff()*inv(deg)).pre(deg-1).integral();
        ret.resize(deg);
        return ret;
    }
    Formal_Power_Series log() const {return log(this->size());}
    Formal_Power_Series exp(int deg) const{ // exp(f) (f[0] = 0)
        assert((*this)[0] == 0);
        Formal_Power_Series ret(1, 1);
        for(int i = 1; i < deg; i <<= 1){
            ret = (ret*(pre(i<<1)+1-ret.log(i<<1))).pre(i<<1);
        }
        ret.resize(deg);
        return ret;
    }
    Formal_Power_Series exp() const {return exp(this->size());}
    Formal_Power_Series pow(ll k, int deg) const{ // f^k
        int n = this->size();
        rep(i, n){
            if((*this)[i] == 0) continue;
            T rev = (*this)[i].inverse();
            Formal_Power_Series C(*this*rev), D(n-i, 0);
            rep2(j, i, n-1) D[j-i] = C[j];
            D = (D.log()*k).exp()*((*this)[i].pow(k));
            Formal_Power_Series E(deg, 0);
            if(i > 0 && k > deg/i) return E;
            ll S = i*k;
            for(int j = 0; j+S < deg && j < D.size(); j++) E[j+S] = D[j];
            E.resize(deg);
            return E;
        }
        return Formal_Power_Series(deg, 0);
    }
    Formal_Power_Series pow(ll k) const {return pow(k, this->size());}
};
using fps = Formal_Power_Series<mint>;
int main(){
    int N; cin >> N;
    fps f(N-1);
    mint fac = 1;
    rep(i, N-1){
        f[i] = mint(i+1)/fac;
        if(i+1 < N-1) fac *= mint(i+1);
    }
    auto res = f.pow(N);
    mint ans = res[N-2];
    ans *= fac, ans /= mint(N).pow(N-2);
    cout << ans << '\n';
}
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