結果

問題 No.1302 Random Tree Score
コンテスト
ユーザー carrot46
提出日時 2020-12-03 00:55:48
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 480 ms / 3,000 ms
コード長 8,246 bytes
コンパイル時間 2,375 ms
コンパイル使用メモリ 183,280 KB
実行使用メモリ 28,072 KB
最終ジャッジ日時 2024-09-13 10:56:29
合計ジャッジ時間 7,066 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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 # 

#include <bits/stdc++.h>
//#include <chrono>
//#pragma GCC optimize("O2")
using namespace std;
#define reps(i,s,n) for(int i = s; i < n; i++)
#define rep(i,n) reps(i,0,n)
#define Rreps(i,n,e) for(int i = n - 1; i >= e; --i)
#define Rrep(i,n) Rreps(i,n,0)
#define ALL(a) a.begin(), a.end()

using ll = long long;
using vec = vector<ll>;
using mat = vector<vec>;

ll N,M,H,W,Q,K,A,B;
string S;
using P = pair<ll, ll>;
const ll INF = (1LL<<60);

template<class T> bool chmin(T &a, const T &b){
    if(a > b) {a = b; return true;}
    else return false;
}
template<class T> bool chmax(T &a, const T &b){
    if(a < b) {a = b; return true;}
    else return false;
}
template <class T> ostream& operator<<(ostream& os, const vector<T>& a){
    int _n = a.size();
    for(int _i = 0; _i < _n; ++_i) os << a[_i] << " \n"[_i == _n - 1];
    return os;
}

template <unsigned long long mod > class modint{
public:
    ll x;
    constexpr modint(){x = 0;}
    constexpr modint(ll _x) : x((_x < 0 ? ((_x += (LLONG_MAX / mod) * mod) < 0 ? _x + (LLONG_MAX / mod) * mod : _x) : _x)%mod){}
    constexpr modint set_raw(ll _x){
        //_x in [0, mod)
        x = _x;
        return *this;
    }
    constexpr modint operator-(){
        return x == 0 ? 0 : mod - x;
    }
    constexpr modint& operator+=(const modint& a){
        if((x += a.x) >= mod) x -= mod;
        return *this;
    }
    constexpr modint operator+(const modint& a) const{
        return modint(*this) += a;
    }
    constexpr modint& operator-=(const modint& a){
        if((x -= a.x) < 0) x += mod;
        return *this;
    }
    constexpr modint operator-(const modint& a) const{
        return modint(*this) -= a;
    }
    constexpr modint& operator*=(const modint& a){
        (x *= a.x)%=mod;
        return *this;
    }
    constexpr modint operator*(const modint& a) const{
        return modint(*this) *= a;
    }
    constexpr modint pow(unsigned long long pw) const{
        modint res(1), comp(*this);
        while(pw){
            if(pw&1) res *= comp;
            comp *= comp;
            pw >>= 1;
        }
        return res;
    }
    //以下、modが素数のときのみ
    constexpr modint inv() const{
        if(x == 2) return (mod + 1) >> 1;
        return modint(*this).pow(mod - 2);
    }
    constexpr modint& operator/=(const modint &a){
        (x *= a.inv().x)%=mod;
        return *this;
    }
    constexpr modint operator/(const modint &a) const{
        return modint(*this) /= a;
    }
};
#define mod1 998244353
using mint = modint<mod1>;

ostream& operator<<(ostream& os, const mint& a){
    os << a.x;
    return os;
}
using vm = vector<mint>;

class NTT{
    static int root;
    static vector<int> id;

    static void make_bit_reverse(int n){
        if(n == (int)id.size()) return;
        if(n == (int)id.size() * 2){
            int n2 = (int)id.size();
            id.resize(n);
            rep(i, n2) {
                id[i] <<= 1;
                id[i | n2] = id[i] | 1;
            }
        }else {
            id.resize(n);
            iota(ALL(id), 0);
            for (int i = 1; (1 << i) <= n; ++i) {
                int l = 1 << (i - 1), r = 1 << i;
                int plus = n >> i;
                for (int j = l; j < r; ++j) {
                    int temp = id[j - l] + plus;
                    if (j < temp) swap(id[j], id[temp]);
                }
            }
        }
    }
    static void dft(int n, vm &f, bool inv){
        make_bit_reverse(n);
        rep(i, n) if (i > id[i]) swap(f[i], f[id[i]]);
        int l{1};
        for (int len = 1; len < n; ++l, len <<= 1) {
            mint root_diff = mint(root).pow(inv ? (mod1 - 1) - ((mod1 - 1)>>l) : ((mod1 - 1)>>l));
            int len2 = len << 1;
            for (int i = 0; i < n; i += len2) {
                mint z = 1;
                reps(j, i, i + len) {
                    mint z_f = z * f[j + len];
                    f[j + len] = f[j] - z_f;
                    f[j] += z_f;
                    z *= root_diff;
                }
            }
        }
        if(inv) {
            mint n_inv = mint(n).inv();
            rep(i, n) f[i] *= n_inv;
        }
    }
public:
    static void dft_2D(int n, int m, vector<vm> &a, bool inv){
        //簡単に、書き換える形で
        //aがn×mサイズであることや、n,mが2冪であることは仮定
        rep(i, n) dft(m, a[i], inv);
        rep(j, m){
            vm temp(n);
            rep(i, n) temp[i] = a[i][j];
            dft(n, temp, inv);
            rep(i, n) a[i][j] = temp[i];
        }
    }
    static vm convolution(vm g, vm h){
        int sz = g.size() + h.size() - 1, n = 1;
        while(sz > n) n *= 2;
        g.resize(n); h.resize(n);
        dft(n, g, false);
        dft(n, h, false);
        rep(i, n) g[i] *= h[i];
        dft(n, g, true);
        g.resize(sz);
        return g;
    }
    static vm simple_pow(vm &a, ll pw){
        int sz = a.size(), n = 1;
        while(sz > n) n <<= 1;
        n <<= 1;
        vm res(n, 0), cpy(n, 0);
        res[0] = 1;
        copy(ALL(a), cpy.begin());
        while(pw){
            dft(n, cpy, false);
            if(pw&1){
                dft(n, res, false);
                rep(i, n) res[i] *= cpy[i];
                dft(n, res, true);
                reps(i, n / 2, n) res[i] = 0;
            }
            rep(i, n) cpy[i] *= cpy[i];
            dft(n, cpy, true);
            reps(i, n / 2, n) cpy[i] = 0;
            pw >>= 1;
        }
        res.resize(sz);
        return res;
    }
    static vm inversion(vm f){
        assert(f[0].x != 0);
        int n = 1, sz = 1, first_sz = f.size();
        while(first_sz > n) n <<= 1;
        f.resize(n);
        vm g(n), cpy_f(n<<1), cpy_g(n<<1);
        g[0] = f[0].inv();
        while(sz < n){
            sz <<= 1;
            copy(f.begin(), f.begin() + sz, cpy_f.begin());
            copy(g.begin(), g.begin() + sz, cpy_g.begin());

            dft(sz<<1, cpy_f, false);
            dft(sz<<1, cpy_g, false);
            rep(i, sz<<1) cpy_f[i] *= cpy_g[i] * cpy_g[i];
            dft(sz<<1, cpy_f, true);

            rep(i, sz) (g[i] += g[i])-= cpy_f[i];
        }
        g.resize(first_sz);
        return g;
    }
    static vm differential(vm f){
        int n = f.size();
        rep(i, n) f[i] = (i == n - 1 ? 0 : f[i + 1] * (i + 1));
        return f;
    }
    static vm integral(vm f){
        int n = f.size();
        Rrep(i, n) f[i] = (i ? f[i - 1] : 0);
        mint fct(1);
        reps(i, 1, n){f[i] *= fct; fct*=i;}
        fct = fct.inv();
        Rreps(i, n, 1){f[i] *= fct; fct*=i;}
        return f;
    }
    static vm log(vm f){
        //if(f[0].x == 0) f[0].x = 1;
        assert(f[0].x == 1);
        vm res = convolution(differential(f), inversion(f));
        res.resize((int)f.size());
        return integral(res);
    }
    static vm exp(vm f){
        assert(f[0].x == 0);
        int n = 1, sz = 1, first_sz = f.size();
        while(first_sz > n) n <<= 1;
        f.resize(n);
        vm g(1, 1), log_g;
        while(sz < n){
            sz <<= 1;
            g.resize(sz);
            reps(i, sz>>1, sz) g[i] = 0;
            log_g = log(g);
            rep(i, sz) log_g[i] = f[i] - log_g[i];
            log_g[0] += 1;
            g = convolution(g, log_g);
        }
        g.resize(first_sz);
        return g;
    }
    static vm pow(vm f, ll pw){
        f = log(f);
        for(auto &e : f) e *= pw;
        return exp(f);
    }
};
int NTT::root = 3;
vector<int> NTT::id;

const ll MAX_N = ll(4e+5) + 10;
vm fact(MAX_N, mint(1)), fact_inv(MAX_N, mint(1)), n_inv(MAX_N, mint(1));
void makefact(){
    mint tmp;
    reps(i,2,MAX_N) fact[i] = fact[i-1] * tmp.set_raw(i);
    fact_inv[MAX_N - 1] = fact[MAX_N - 1].inv();
    Rreps(i, MAX_N - 1, 1){
        fact_inv[i] = fact_inv[i + 1] * tmp.set_raw(i + 1);
        n_inv[i + 1] = fact[i] * fact_inv[i + 1];
    }
}
mint nCm(ll n, ll m){
    return fact[n] * fact_inv[n-m] * fact_inv[m];
}
mint nCm_inv(ll n, ll m){
    return fact[n-m] * fact[m] * fact_inv[n];
}

int main(){
    makefact();
    cin>>N;
    vm pol(N - 1);
    rep(i, N - 1) pol[i] = fact_inv[i] * (i + 1);
    cout<<fact[N - 2] * mint(N).pow(N - 2).inv() * NTT::pow(pol, N)[N - 2]<<endl;
}
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