結果

問題 No.1302 Random Tree Score
ユーザー sigma425sigma425
提出日時 2020-11-28 04:38:22
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 996 ms / 3,000 ms
コード長 11,894 bytes
コンパイル時間 2,553 ms
コンパイル使用メモリ 217,060 KB
実行使用メモリ 11,248 KB
最終ジャッジ日時 2024-09-12 21:59:32
合計ジャッジ時間 10,851 ms
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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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 4 ms
6,820 KB
testcase_01 AC 4 ms
6,940 KB
testcase_02 AC 175 ms
6,944 KB
testcase_03 AC 424 ms
7,644 KB
testcase_04 AC 166 ms
6,940 KB
testcase_05 AC 996 ms
10,340 KB
testcase_06 AC 796 ms
11,148 KB
testcase_07 AC 160 ms
6,940 KB
testcase_08 AC 471 ms
7,916 KB
testcase_09 AC 782 ms
11,160 KB
testcase_10 AC 837 ms
10,580 KB
testcase_11 AC 160 ms
6,944 KB
testcase_12 AC 953 ms
11,248 KB
testcase_13 AC 4 ms
6,940 KB
testcase_14 AC 784 ms
11,176 KB
testcase_15 AC 899 ms
10,544 KB
testcase_16 AC 4 ms
6,944 KB
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;
using ll = long long;
using uint = unsigned int;
#define rep(i,n) for(int i=0;i<int(n);i++)
#define rep1(i,n) for(int i=1;i<=int(n);i++)
#define per(i,n) for(int i=int(n)-1;i>=0;i--)
#define per1(i,n) for(int i=int(n);i>0;i--)
#define all(c) c.begin(),c.end()
#define si(x) int(x.size())
#define pb emplace_back
#define fs first
#define sc second
template<class T> using V = vector<T>;
template<class T> using VV = vector<vector<T>>;
template<class T,class U> void chmax(T& x, U y){if(x<y) x=y;}
template<class T,class U> void chmin(T& x, U y){if(y<x) x=y;}
template<class T> void mkuni(V<T>& v){sort(all(v));v.erase(unique(all(v)),v.end());}
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){
	return o<<"("<<p.fs<<","<<p.sc<<")";
}
template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){
	o<<"{";
	for(const T& v:vc) o<<v<<",";
	o<<"}";
	return o;
}
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n-1); }

#ifdef LOCAL
#define show(x) cerr << "LINE" << __LINE__ << " : " << #x << " = " << (x) << endl
void dmpr(ostream& os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ~ ";
	dmpr(os,args...);
}
#define shows(...) cerr << "LINE" << __LINE__ << " : ";dmpr(cerr,##__VA_ARGS__)
#define dump(x) cerr << "LINE" << __LINE__ << " : " << #x << " = {";  \
	for(auto v: x) cerr << v << ","; cerr << "}" << endl;
#else
#define show(x) void(0)
#define dump(x) void(0)
#define shows(...) void(0)
#endif

template<unsigned int mod_>
struct ModInt{
	using uint = unsigned int;
	using ll = long long;
	using ull = unsigned long long;

	constexpr static uint mod = mod_;

	uint v;
	ModInt():v(0){}
	ModInt(ll _v):v(normS(_v%mod+mod)){}
	explicit operator bool() const {return v!=0;}
	static uint normS(const uint &x){return (x<mod)?x:x-mod;}		// [0 , 2*mod-1] -> [0 , mod-1]
	static ModInt make(const uint &x){ModInt m; m.v=x; return m;}
	ModInt operator+(const ModInt& b) const { return make(normS(v+b.v));}
	ModInt operator-(const ModInt& b) const { return make(normS(v+mod-b.v));}
	ModInt operator-() const { return make(normS(mod-v)); }
	ModInt operator*(const ModInt& b) const { return make((ull)v*b.v%mod);}
	ModInt operator/(const ModInt& b) const { return *this*b.inv();}
	ModInt& operator+=(const ModInt& b){ return *this=*this+b;}
	ModInt& operator-=(const ModInt& b){ return *this=*this-b;}
	ModInt& operator*=(const ModInt& b){ return *this=*this*b;}
	ModInt& operator/=(const ModInt& b){ return *this=*this/b;}
	ModInt& operator++(int){ return *this=*this+1;}
	ModInt& operator--(int){ return *this=*this-1;}
	ll extgcd(ll a,ll b,ll &x,ll &y) const{
		ll p[]={a,1,0},q[]={b,0,1};
		while(*q){
			ll t=*p/ *q;
			rep(i,3) swap(p[i]-=t*q[i],q[i]);
		}
		if(p[0]<0) rep(i,3) p[i]=-p[i];
		x=p[1],y=p[2];
		return p[0];
	}
	ModInt inv() const {
		ll x,y;
		extgcd(v,mod,x,y);
		return make(normS(x+mod));
	}
	ModInt pow(ll p) const {
		if(p<0) return inv().pow(-p);
		ModInt a = 1;
		ModInt x = *this;
		while(p){
			if(p&1) a *= x;
			x *= x;
			p >>= 1;
		}
		return a;
	}
	bool operator==(const ModInt& b) const { return v==b.v;}
	bool operator!=(const ModInt& b) const { return v!=b.v;}
	friend istream& operator>>(istream &o,ModInt& x){
		ll tmp;
		o>>tmp;
		x=ModInt(tmp);
		return o;
	}
	friend ostream& operator<<(ostream &o,const ModInt& x){ return o<<x.v;}
};
using mint = ModInt<998244353>;

V<mint> fact,ifact,invs;
mint Choose(int a,int b){
	if(b<0 || a<b) return 0;
	return fact[a] * ifact[b] * ifact[a-b];
}
void InitFact(int N){	//[0,N]
	N++;
	fact.resize(N);
	ifact.resize(N);
	invs.resize(N);
	fact[0] = 1;
	rep1(i,N-1) fact[i] = fact[i-1] * i;
	ifact[N-1] = fact[N-1].inv();
	for(int i=N-2;i>=0;i--) ifact[i] = ifact[i+1] * (i+1);
	rep1(i,N-1) invs[i] = fact[i-1] * ifact[i];
}

int bsr(int x) { return 31 - __builtin_clz(x); }
void ntt(bool type, V<mint>& c) {
	const mint G = 3;	//primitive root

	int N = int(c.size());
	int s = bsr(N);
	assert(1 << s == N);

	V<mint> a = c, b(N);
	rep1(i,s){
		int W = 1 << (s - i);
		mint base = G.pow((mint::mod - 1)>>i);
		if(type) base = base.inv();
		mint now = 1;
		for(int y = 0; y < N / 2; y += W) {
			for (int x = 0; x < W; x++) {
				auto l = a[y << 1 | x];
				auto r = now * a[y << 1 | x | W];
				b[y | x] = l + r;
				b[y | x | N >> 1] = l - r;
			}
			now *= base;
		}
		swap(a, b);
	}
	c = a;
}

V<mint> multiply_ntt(const V<mint>& a, const V<mint>& b) {
	int A = int(a.size()), B = int(b.size());
	if (!A || !B) return {};
	int lg = 0;
	while ((1 << lg) < A + B - 1) lg++;
	int N = 1 << lg;
	V<mint> ac(N), bc(N);
	for (int i = 0; i < A; i++) ac[i] = a[i];
	for (int i = 0; i < B; i++) bc[i] = b[i];
	ntt(false, ac);
	ntt(false, bc);
	for (int i = 0; i < N; i++) {
		ac[i] *= bc[i];
	}
	ntt(true, ac);
	V<mint> c(A + B - 1);
	mint iN = mint(N).inv();
	for (int i = 0; i < A + B - 1; i++) {
		c[i] = ac[i] * iN;
	}
	return c;
}

template<class D>
struct Poly{
	vector<D> v;
	int size() const{ return v.size();}	//deg+1
	Poly(){}
	Poly(vector<D> _v) : v(_v){shrink();}

	Poly& shrink(){
		while(!v.empty()&&v.back()==D(0)) v.pop_back();
		return *this;
	}
	D& operator[](int i){return v[i];}
	const D& operator[](int i) const {return v[i];}
	D at(int i) const{
		return (i<size())?v[i]:D(0);
	}
	void set(int i,const D& x){		//v[i] := x
		if(i>=size() && !x) return;
		while(i>=size()) v.push_back(D(0));
		v[i]=x;
		shrink();
		return;
	}
	D operator()(D x) const {
		D res = 0;
		int n = size();
		D a = 1;
		rep(i,n){
			res += a*v[i];
			a *= x;
		}
		return res;
	}

	Poly operator+(const Poly &r) const{
		int N=max(size(),r.size());
		vector<D> ret(N);
		rep(i,N) ret[i]=at(i)+r.at(i);
		return Poly(ret);
	}
	Poly operator-(const Poly &r) const{
		int N=max(size(),r.size());
		vector<D> ret(N);
		rep(i,N) ret[i]=at(i)-r.at(i);
		return Poly(ret);
	}
	Poly operator-() const{
		int N=size();
		vector<D> ret(N);
		rep(i,N) ret[i] = -at(i);
		return Poly(ret);
	}
	Poly operator*(const Poly &r) const{
		if(size()==0||r.size()==0) return Poly();
		return mul_ntt(r);									// FFT or NTT ?
	}
	Poly operator*(const D &r) const{
		int N=size();
		vector<D> ret(N);
		rep(i,N) ret[i]=v[i]*r;
		return Poly(ret);
	}
	Poly operator/(const D &r) const{
		return *this * r.inv();
	}
	Poly operator/(const Poly &y) const{
		return div_fast(y);
	}
	Poly operator%(const Poly &y) const{
		return rem_fast(y);
//		return rem_naive(y);
	}
	Poly operator<<(const int &n) const{	// *=x^n
		assert(n>=0);
		int N=size();
		vector<D> ret(N+n);
		rep(i,N) ret[i+n]=v[i];
		return Poly(ret);
	}
	Poly operator>>(const int &n) const{	// /=x^n
		assert(n>=0);
		int N=size();
		if(N<=n) return Poly();
		vector<D> ret(N-n);
		rep(i,N-n) ret[i]=v[i+n];
		return Poly(ret);
	}
	bool operator==(const Poly &y) const{
		return v==y.v;
	}
	bool operator!=(const Poly &y) const{
		return v!=y.v;
	}

	Poly& operator+=(const Poly &r) {return *this = *this+r;}
	Poly& operator-=(const Poly &r) {return *this = *this-r;}
	Poly& operator*=(const Poly &r) {return *this = *this*r;}
	Poly& operator*=(const D &r) {return *this = *this*r;}
	Poly& operator/=(const Poly &r) {return *this = *this/r;}
	Poly& operator/=(const D &r) {return *this = *this/r;}
	Poly& operator%=(const Poly &y) {return *this = *this%y;}
	Poly& operator<<=(const int &n) {return *this = *this<<n;}
	Poly& operator>>=(const int &n) {return *this = *this>>n;}

	Poly diff() const {
		int n = size();
		if(n == 0) return Poly();
		V<D> u(n-1);
		rep(i,n-1) u[i] = at(i+1) * (i+1);
		return Poly(u);
	}
	Poly intg() const {
		int n = size();
		V<D> u(n+1);
		rep(i,n) u[i+1] = at(i) / (i+1);
		return Poly(u);
	}

	Poly pow(long long n, int L) const {		// f^n, ignoring x^L,x^{L+1},..
		Poly a({1});
		Poly x = *this;
		while(n){
			if(n&1){
				a *= x;
				a = a.strip(L);
			}
			x *= x;
			x = x.strip(L);
			n /= 2;
		}
		return a;
	}

	/*
		[x^0~n] exp(f) = 1 + f + f^2 / 2 + f^3 / 6 + ..
		f(0) should be 0

		O((N+n) log n)	(N = size())
		NTT, -O3
		- N = n = 100000 : 200 [ms]
		- N = n = 200000 : 400 [ms]
		- N = n = 500000 : 1000 [ms]
	*/
	Poly exp(int n) const {
		assert(at(0) == 0);
		Poly f({1}), g({1});
		for(int i=1;i<=n;i*=2){
			g = (g*2 - f*g*g).strip(i);
			Poly q = (this->diff()).strip(i-1);
			Poly w = (q + g * (f.diff() - f*q)) .strip(2*i-1);
			f = (f + f * (*this - w.intg()).strip(2*i)) .strip(2*i);
		}
		return f.strip(n+1);
	}

	/*
		[x^0~n] log(f) = log(1-(1-f)) = - (1-f) - (1-f)^2 / 2 - (1-f)^3 / 3 - ...
		f(0) should be 1
		O(n log n)

		NTT, -O3
		1e5 : 140 [ms]
		2e5 : 296 [ms]
		5e5 : 640 [ms]
		1e6 : 1343 [ms]
	*/
	Poly log(int n) const {
		assert(at(0) == 1);
		auto f = strip(n+1);
		return (f.diff() * f.inv(n)).strip(n).intg();
	}

	/*
		[x^0~n] sqrt(f)
		f(0) should be 1
		いや平方剰余なら何でもいいと思うけど探すのがめんどくさいので
		+- 2通りだけど 定数項が 1 の方
		O(n log n)

		NTT, -O3
		1e5 : 234 [ms]
		2e5 : 484 [ms]
		5e5 : 1000 [ms]
		1e6 : 2109 [ms]
	*/
	Poly sqrt(int n) const {
		assert(at(0) == 1);
		Poly f = strip(n+1);
		Poly g({1});
		for(int i=1; i<=n; i*=2){
			g = (g + f.strip(2*i)*g.inv(2*i-1)) / 2;
		}
		return g.strip(n+1);
	}

	/*
		[x^0~n] f^-1 = (1-(1-f))^-1 = (1-f) + (1-f)^2 + ...
		f * f.inv(n) = 1 + x^n * poly
		f(0) should be non0
		O(n log n)
	*/
	Poly inv(int n) const {
		assert(at(0) != 0);
		Poly f = strip(n+1);
		Poly g({at(0).inv()});
		for(int i=1; i<=n; i*=2){		//need to strip!!
			g *= (Poly({2}) - f.strip(2*i)*g).strip(2*i);
		}
		return g.strip(n+1);
	}	

	Poly exp_naive(int n) const {
		assert(at(0) == 0);
		Poly res;
		Poly fk({1});
		rep(k,n+1){
			res += fk;
			fk *= *this;
			fk = fk.strip(n+1) / (k+1);
		}
		return res;
	}
	Poly log_naive(int n) const {
		assert(at(0) == 1);
		Poly res;
		Poly g({1});
		rep1(k,n){
			g *= (Poly({1}) - *this);
			g = g.strip(n+1);
			res -= g / k;
		}
		return res;
	}


	Poly mul_naive(const Poly &r) const{
		int N=size(),M=r.size();
		vector<D> ret(N+M-1);
		rep(i,N) rep(j,M) ret[i+j]+=at(i)*r.at(j);
		return Poly(ret);
	}
	Poly mul_ntt(const Poly &r) const{
		return Poly(multiply_ntt(v,r.v));
	}
	Poly mul_fft(const Poly &r) const{
		return Poly(multiply_fft(v,r.v));
	}

	Poly div_fast_with_inv(const Poly &inv, int B) const {
		return (*this * inv)>>(B-1);
	}
	Poly div_fast(const Poly &y) const{
		if(size()<y.size()) return Poly();
		int n = size();
		return div_fast_with_inv(y.inv_div(n-1),n);
	}
	Poly rem_naive(const Poly &y) const{
		Poly x = *this;
		while(y.size()<=x.size()){
			int N=x.size(),M=y.size();
			D coef = x.v[N-1]/y.v[M-1];
			x -= (y<<(N-M))*coef;
		}
		return x;
	}
	Poly rem_fast(const Poly &y) const{
		return *this - y * div_fast(y);
	}
	Poly strip(int n) const {	//ignore x^n , x^n+1,...
		vector<D> res = v;
		res.resize(min(n,size()));
		return Poly(res);
	}
	Poly rev(int n = -1) const {	//ignore x^n ~  ->  return x^(n-1) * f(1/x)
		vector<D> res = v;
		if(n!=-1) res.resize(n);
		reverse(all(res));
		return Poly(res);
	}

	/*
		f.inv_div(n) = x^n / f
		f should be non0
		O((N+n) log n)

		for division
	*/
	Poly inv_div(int n) const {
		n++;
		int d = size() - 1;
		assert(d != -1);
		if(n < d) return Poly();
		Poly a = rev();
		Poly g({at(d).inv()});
		for(int i=1; i+d<=n; i*=2){		//need to strip!!
			g *= (Poly({2})-a.strip(2*i)*g).strip(2*i);
		}
		return g.rev(n-d);
	}


	friend ostream& operator<<(ostream &o,const Poly& x){
		if(x.size()==0) return o<<0;
		rep(i,x.size()) if(x.v[i]!=D(0)){
			o<<x.v[i]<<"x^"<<i;
			if(i!=x.size()-1) o<<" + ";
		}
		return o;
	}
};

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);		//DON'T USE scanf/printf/puts !!
	cout << fixed << setprecision(20);
	InitFact(100010);

	int N; cin >> N;
//	int N = 100000;
	Poly<mint> f;
	rep(i,N-1) f.set(i,ifact[i]*(i+1));
	f = f.pow(N,N-1);
	cout << f[N-2]*fact[N-2] / mint(N).pow(N-2) << endl;
}
0