結果

問題 No.1302 Random Tree Score
コンテスト
ユーザー sak
提出日時 2020-12-02 04:01:27
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
TLE  
実行時間 -
コード長 3,180 bytes
コンパイル時間 2,510 ms
コンパイル使用メモリ 204,856 KB
最終ジャッジ日時 2025-01-16 13:01:18
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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 * 5 TLE * 9
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>

using namespace std;
typedef long long ll;
typedef pair<ll, ll> p_ll;

template<class T>
void debug(T itr1, T itr2) { auto now = itr1; while(now<itr2) { cout << *now << " "; now++; } cout << endl; }
#define repr(i,from,to) for (ll i=(ll)from; i<(ll)to; i++)
#define all(vec) vec.begin(), vec.end()
#define rep(i,N) repr(i,0,N)
#define per(i,N) for (int i=(int)N-1; i>=0; i--)

const ll MOD = 998244353;
const ll LLINF = pow(2,61)-1;
const int INF = pow(2,30)-1;

vector<ll> fac;
void c_fac(int x=pow(10,6)+10) { fac.resize(x,true); rep(i,x) fac[i] = i ? (fac[i-1]*i)%MOD : 1; }
ll modpow(ll x, ll p) { ll result = 1, now = 1, pm = x; while (now<=p) { if (p&now) { result = result * pm % MOD; } now*=2; pm = pm*pm % MOD; } return result; }
ll inv(ll a, ll m=MOD) { ll b = m, x = 1, y = 0; while (b!=0) { int d = a/b; a -= b*d; swap(a,b); x -= y*d; swap(x,y); } return (x+m)%m; }
ll nck(ll n, ll k) { return fac[n]*inv(fac[k]*fac[n-k]%MOD)%MOD; }
ll gcd(ll a, ll b) { if (a<b) swap(a,b); return b==0 ? a : gcd(b, a%b); }
ll lcm(ll a, ll b) { return a/gcd(a,b)*b; }

// ----------------------------------------------------------------------
// ----------------------------------------------------------------------

struct FastNumberTheoreticTransform {

  ll size = 1, size_x12, root;
  vector<ll> x1, x2, theta;

  FastNumberTheoreticTransform(ll N) {
    size_x12 = 2*N-1;
    size = 1; while (size<=size_x12) size<<=1;
    root = modpow(3,MOD/size);
    x1.resize(size); x2.resize(size); theta.resize(size);
    rep(i,size) theta[i] = i==0 ? 1 : theta[i-1]*root % MOD;
  }
  void set(vector<ll> &v1, vector<ll> &v2) { 
    x1 = v1; x2 = v2;  }

  vector<ll> convolution(vector<ll> &x, bool rev, ll s, ll pos=0) {
    if (s==1) return {x[pos]};
    vector<ll> ex = convolution(x,rev,s/2,pos), ox = convolution(x,rev,s/2,pos+size/s);
    vector<ll> result(s);
    rep(i,s) result[i] = (ex[i%(s/2)] + theta[size/s*i] * ox[i%(s/2)]) % MOD;
    if (rev && s==size) {
      reverse(result.begin()+1, result.end());
      ll invs = inv(size);
      for (auto &x: result) x = x * invs % MOD;
    }
    return result;
  };

  vector<ll> mul(vector<ll> &v1, vector<ll> &v2) {
    set(v1,v2);
    vector<ll> cx1 = convolution(x1, false, size), cx2 = convolution(x2, false, size);
    vector<ll> cx12(size); rep(i,size) cx12[i] = cx1[i] * cx2[i] % MOD;
    vector<ll> x12 = convolution(cx12, true, size);
    vector<ll> result(v1.size()); copy(x12.begin(), x12.begin()+v1.size(), result.begin());
    return result;
  }

};

// ----------------------------------------------------------------------
// ----------------------------------------------------------------------

int main() {
  ll N; cin >> N;

  c_fac();
  vector<ll> kei(N); rep(i,N) kei[i] = (i+1)*inv(fac[i])%MOD;

  // debug(all(kei));
  FastNumberTheoreticTransform fntt(N);
  vector<ll> result(N,0); result[0] = 1;
  ll np = 1;
  while (np<=N) {
    if (np&N) result = fntt.mul(result,kei);
    kei = fntt.mul(kei,kei);
    np<<=1;
  }
  ll ho = fac[N-2] * inv(modpow(N,N-2)) % MOD;
  rep(i,N) result[i] = result[i] * ho % MOD;
  // debug(all(result));
  cout << result[N-2] << endl;
  return 0;
}
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