結果

問題 No.1302 Random Tree Score
ユーザー ytqm3
提出日時 2022-10-09 17:46:26
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 434 ms / 3,000 ms
コード長 17,378 bytes
コンパイル時間 5,351 ms
コンパイル使用メモリ 290,924 KB
最終ジャッジ日時 2025-02-08 00:48:04
ジャッジサーバーID
(参考情報)
judge5 / judge3
このコードへのチャレンジ
(要ログイン)
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>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif
namespace ttl{
using namespace std;
using f80=long double;
using i64=int64_t;
using u64=uint64_t;
template<int mod> struct mymodint{
i64 vl;
static constexpr i64 get_mod(){ return mod; }
i64 val(){ return vl; }
mymodint(i64 vl_=0):vl(vl_%mod){}
mymodint operator-(){ return (vl==0)?0:mod-vl; }
mymodint operator+(mymodint rhs){ return mymodint(*this)+=rhs; }
mymodint operator-(mymodint rhs){ return mymodint(*this)-=rhs; }
mymodint operator*(mymodint rhs){ return mymodint(*this)*=rhs; }
mymodint operator/(mymodint rhs){ return mymodint(*this)/=rhs; }
mymodint pow(i64 rhs){
mymodint res=1,now=(*this);
while(rhs){
res*=((rhs&1)?now:1),now*=now,rhs>>=1;
}
return res;
}
mymodint& operator+=(mymodint rhs){
vl+=rhs.vl,vl-=((vl>=mod)?mod:0);
return (*this);
}
mymodint& operator-=(mymodint rhs){
vl+=((vl<rhs.vl)?mod:0),vl-=rhs.vl;
return (*this);
}
mymodint& operator*=(mymodint rhs){
vl=vl*rhs.vl%mod;
return (*this);
}
mymodint& operator/=(mymodint rhs){ return (*this)*=rhs.pow(mod-2); }
bool operator==(mymodint rhs){ return vl==rhs.vl; }
bool operator!=(mymodint rhs){ return vl!=rhs.vl; }
};
template<u64 mod> using modint=
#if __has_include(<atcoder/all>)
atcoder::static_modint<mod>;
#else
mymodint<mod>;
#endif
template<int mod> std::ostream& operator<<(std::ostream& os,modint<mod> x){
return os<<(x.val());
}
template<int mod> std::istream& operator>>(std::istream& is,modint<mod>& x){
i64 t;
is>>t,x=t;
return is;
}
template<class T> void scn_(T& a){ cin>>a; }
template<class T,class U> void scn_(pair<T,U>& a){ scn_(a.first),scn_(a.second); }
template<class T> void scn_(vector<T>& a){
for(auto& v:a){
scn_(v);
}
}
template<class T> void scn_(vector<vector<T>>& a){
for(auto& v:a){
for(auto& u:v){
cin>>u;
}
}
}
void scn(){}
template<class T,class... Args> void scn(T& n,Args&... args){ scn_(n),scn(args...); }
template<class T> void prt_(T a){ cout<<a; }
template<class T,class U> void prt_(pair<T,U> a){ cout<<"{"<<a.first<<", "<<a.second<<"}"; }
void prt_(f80 a){ printf("%.15Lf",a); }
template<class T> void prt(vector<T> a){
for(size_t i=0;i<a.size();++i){
prt_(a[i]);
cout<<" \n"[i==a.size()-1];
}
}
template<class T> void prt(vector<vector<T>> a){
for(auto& v:a){
for(size_t i=0;i<v.size();++i){
cout<<v[i]<<" \n"[i==v.size()-1];
}
}
}
template<class T> void prt(T a){ prt_(a),cout<<"\n"; }
template<class T,class... Args> void prt(T a,Args... args){ prt_(a),cout<<" ",prt(args...); }
template<class Head,class... Tail> struct multi_dim_vector{ using type=vector<typename multi_dim_vector<Tail...>::type>; };
template<class T> struct multi_dim_vector<T>{ using type=T; };
template<class T,class Arg> vector<T> mvec(int n,Arg&& arg){ return vector<T>(n,arg); }
template<class T,class... Args> class multi_dim_vector<Args...,T>::type mvec(int n,Args&&... args){
return typename multi_dim_vector<Args...,T>::type(n,mvec<T>(args...));
}
template<class T> void rev(T& a){ reverse(a.begin(),a.end());}
template<class T> void srt(T& a){ sort(a.begin(),a.end()); }
template<class T> void rsrt(T& a){ sort(a.rbegin(),a.rend()); }
template<class T> T revd(T a){
reverse(a.begin(),a.end());
return a;
}
template<class T> T srtd(T a){
sort(a.begin(),a.end());
return a;
}
template<class T> T rsrtd(T a){
sort(a.rbegin(),a.rend());
return a;
}
template<class T> T summ(vector<T> a){ return accumulate(a.begin(),a.end(),T(0)); }
template<class T> T maxi(vector<T> a){ return *max_element(a.begin(),a.end()); }
template<class T> T mini(vector<T> a){ return *min_element(a.begin(),a.end()); }
template<class T> void chmx(T& a,T b){ a=max(a,b); }
template<class T> void chmn(T& a,T b){ a=min(a,b); }
i64 ppcnt(u64 k){ return __builtin_popcountll(k); }
template<class T> T powe(T a,i64 n){
T res=1;
while(n){
if(n&1){ res*=a; }
a*=a;
n/=2;
}
return res;
}
i64 powe(i64 a,i64 n,i64 m){
i64 res=1;
while(n){
if(n&1){ res=res*a%m; }
a=a*a%m;
n/=2;
}
return res;
}
template<class T> void zip(vector<T>& a){
auto b=srtd(a);
b.erase(unique(b.begin(),b.end()),b.end());
map<T,int> mp;
for(int i=0;i<b.size();++i){
mp[b[i]]=i;
}
for(auto& v:a){
v=mp[v];
}
}
i64 sqrf(i64 n){
i64 ok=0,ng=1e9+5;
while(std::abs(ok-ng)>1){
i64 mid=(ok+ng)/2;
(mid*mid<=n?ok:ng)=mid;
}
return ok;
}
i64 sqrc(i64 n){
i64 ok=1e9+5,ng=0;
while(std::abs(ok-ng)>1){
i64 mid=(ok+ng)/2;
(mid*mid>=n?ok:ng)=mid;
}
return ok;
}
i64 dvf(i64 a,i64 b){
if(b<0){ a*=-1,b*=-1; }
if(a<0){ return -(-a+b-1)/b; }
return a/b;
}
i64 dvc(i64 a,i64 b){
if(b<0){ a*=-1,b*=-1; }
if(a<0){ return -(-a)/b; }
return (a+b-1)/b;
}
vector<int> bfs(vector<vector<int>> G,int v){
int N=G.size();
vector<int> dst(N,-1);
queue<int> q;
dst[v]=0;
q.emplace(v);
while(q.size()){
int t=q.front();
q.pop();
for(auto u:G[t]){
if(dst[u]==-1){
dst[u]=dst[t]+1;
q.emplace(u);
}
}
}
return dst;
}
vector<i64> dijkstra(vector<vector<pair<int,i64>>>& G,int s){
int N=G.size();
vector<i64> dst(N,1e18);
dst[s]=0;
priority_queue<pair<i64,int>,vector<pair<i64,int>>,greater<pair<i64,int>>> pq;
pq.emplace(0,s);
vector<int> f(N);
while(pq.size()){
auto [t,u]=pq.top();
pq.pop();
if(f[u]){ continue; }
f[u]=1;
for(auto [v,w]:G[u]){
if(dst[v]>dst[u]+w){
dst[v]=dst[u]+w;
pq.emplace(dst[v],v);
}
}
}
return dst;
}
vector<pair<i64,i64>> pfct(i64 n){
vector<pair<i64,i64>> res;
for(i64 i=2;i*i<=n;++i){
if(n%i!=0){ continue; }
i64 ex=0;
while(n%i==0){ ex++,n/=i; }
res.emplace_back(i,ex);
}
if(n!=1){ res.emplace_back(n,1); }
return res;
}
vector<i64> ediv(i64 n){
vector<i64> res;
for(i64 i=1;i*i<=n;++i){
if(n%i!=0){ continue; }
res.emplace_back(i);
if(i*i!=n){ res.emplace_back(n/i); }
}
srt(res);
return res;
}
template<class T> struct csm2d{
int n,m;
vector<vector<T>> a,c;
csm2d(vector<vector<T>> a_):n(a_.size()),m(a_[0].size()),a(a_){
auto b=mvec<T>(n,m+1,0);
for(int i=0;i<n;++i){
for(int j=0;j<m;++j){
b[i][j+1]=b[i][j]+a[i][j];
}
}
c=mvec<T>(n+1,m+1,0);
for(int j=0;j<m+1;++j){
for(int i=0;i<n;++i){
c[i+1][j]=c[i][j]+b[i][j];
}
}
}
T operator()(int p,int q,int r,int s){
return c[p][r]-c[p][s]-c[q][r]+c[q][s];
}
};
template<class T> auto runlng(T a) -> vector<pair<typename decltype(a)::value_type,i64>>{
int n=a.size();
vector<pair<typename decltype(a)::value_type,i64>> res;
typename decltype(a)::value_type now=a[0];
i64 l=1;
for(int i=1;i<n;++i){
if(a[i-1]==a[i]){ l++; }
else{
res.emplace_back(now,l);
now=a[i],l=1;
}
}
res.emplace_back(now,l);
return res;
}
template<class T> struct cmb{
vector<T> fac,ifac;
cmb(int mx=3000000):fac(mx+1,1),ifac(mx+1,1){
for(int i=1;i<=mx;++i){ fac[i]=fac[i-1]*i; }
ifac[mx]/=fac[mx];
for(int i=mx;i>0;--i){ ifac[i-1]=ifac[i]*i; }
}
T operator()(i64 n,i64 k){
if(n<0||k<0||n<k){ return 0; }
return fac[n]*ifac[k]*ifac[n-k];
}
T f(i64 n){
return n<0?T(0):fac[n];
}
T fi(i64 n){
return n<0?T(0):ifac[n];
}
};
}
using namespace ttl;
template<class mint> struct Poly{
vector<mint> val;
Poly():val({0}){}
Poly(mint t):val({t}){}
Poly(int siz):val(max(1,siz)){}
Poly(initializer_list<mint> init):val(init){}
Poly(vector<mint> init):val(init){}
mint &operator[](int i){
return val[i];
}
int size(){
return val.size();
}
void resize(int siz){
val.resize(siz);
}
void shrink(){
for(int i=val.size()-1;i>0;--i){
if(val[i]==0){
val.pop_back();
}
else{
return;
}
}
}
Poly operator+(Poly rhs){
return Poly(*this)+=rhs;
}
Poly operator-(Poly rhs){
return Poly(*this)-=rhs;
}
Poly operator*(Poly rhs){
return Poly(*this)*=rhs;
}
Poly operator/(Poly rhs){
return Poly(*this)/=rhs;
}
Poly operator%(Poly rhs){
return Poly(*this)%=rhs;
}
Poly operator-(){
for(mint& v:val){
v=mint(0)-v;
}
return (*this);
}
Poly operator+=(Poly rhs){
resize(max(this->size(),rhs.size()));
for(int i=0;i<int(rhs.size());++i){
(*this)[i]+=rhs[i];
}
shrink();
return (*this);
}
Poly operator-=(Poly rhs){
resize(max(this->size(),rhs.size()));
for(int i=0;i<int(rhs.size());++i){
(*this)[i]-=rhs[i];
}
shrink();
return (*this);
}
Poly operator*=(Poly rhs){
val=atcoder::convolution(val,rhs.val);
return (*this);
}
Poly operator/=(Poly rhs){
if(val.size()<rhs.size()){
val.resize(0);
return (*this);
}
int rsiz=val.size()-rhs.size()+1;
reverse(val.begin(),val.end());
reverse(rhs.val.begin(),rhs.val.end());
val.resize(rsiz),rhs.inv(rsiz);
(*this)*=rhs;
val.resize(rsiz);
reverse(val.begin(),val.end());
return (*this);
}
Poly operator%=(Poly rhs){
if(val.size()<rhs.size()){
return (*this);
}
(*this)-=(*this)/rhs*rhs;
val.resize(rhs.size()-1);
shrink();
return (*this);
}
mint eval(mint a){
mint t=1,res=0;
int n=(*this).size();
for(int i=0;i<n;++i){
res+=val[i]*t;
t*=a;
}
return res;
}
void diffrent(){
Poly f(val.size()-1);
for(int i=1;i<val.size();++i){
f[i-1]=val[i]*i;
}
(*this)=f;
}
void integral(){
Poly f(val.size()+1);
for(int i=0;i<val.size();++i){
f[i+1]=val[i]/(i+1);
}
(*this)=f;
}
void inv(int mx){
Poly g({mint(1)/val[0]});
int now=1;
while(now<mx){
now<<=1;
Poly t=(*this);
t.resize(now);
t*=g,t=-t;
t[0]+=2,g*=t;
g.resize(now);
}
g.resize(mx);
(*this)=g;
}
vector<mint> MultiEval(vector<mint> a){
int siz=1;
while(siz<int(a.size())){
siz<<=1;
}
vector<Poly> t(siz*2-1,{1});
for(int i=0;i<int(a.size());++i){
t[i+siz-1]={-a[i],1};
}
for(int i=siz-2;i>=0;--i){
t[i]=t[2*i+1]*t[2*i+2];
}
vector<Poly> g(siz*2-1);
g[0]=(*this)%t[0];
for(int i=1;i<siz*2-1;++i){
g[i]=g[(i-1)/2]%t[i];
}
vector<mint> res(a.size());
for(int i=0;i<int(a.size());++i){
res[i]=g[i+siz-1][0];
}
return res;
}
void TaylorShift(mint c){
cmb<mint> C(val.size());
vector<mint> g(val.size());
mint now=1;
for(size_t i=0;i<val.size();++i){
val[i]*=C.dat[i];
g[i]=now*C.idat[i];
now*=c;
}
reverse(val.begin(),val.end());
g=atcoder::convolution(val,g);
g.resize(val.size());
reverse(g.begin(),g.end());
for(size_t i=0;i<val.size();++i){
g[i]*=C.idat[i];
}
val=g;
}
void LagrangeInterpolation(vector<mint> x,vector<mint> y){
int N=x.size();
vector<Poly> h(N);
for(int i=0;i<N;++i){
h[i]={-x[i],1};
}
auto g=Product(h);
auto g_=g;
g_.diffrent();
vector<mint> t=g_.MultiEval(x);
for(int i=0;i<N;++i){
t[i]=y[i]/t[i];
}
vector<Poly> den(2*N-1),num(2*N-1,{1});
for(int i=0;i<N;++i){
den[i+N-1]={-x[i],1};
num[i+N-1]={t[i]};
}
for(int i=N-2;i>=0;--i){
den[i]=den[2*i+1]*den[2*i+2];
num[i]=num[2*i+1]*den[2*i+2]+num[2*i+2]*den[2*i+1];
}
(*this)=num[0];
}
};
template<class mint> struct FPS{
vector<mint> val;
FPS():val({0}){}
FPS(mint t):val({t}){}
FPS(int siz):val(max(1,siz)){}
FPS(initializer_list<mint> init):val(init){}
FPS(vector<mint> init):val(init){}
mint &operator[](int i){
return val[i];
}
int size(){
return val.size();
}
void resize(int siz){
val.resize(siz);
}
FPS& resize_(int siz){
auto tmp=val;
tmp.resize(siz);
return (*this)=tmp;
}
FPS operator-(){
for(mint& v:val){
v=mint(0)-v;
}
return (*this);
}
FPS& operator+=(mint rhs){
val[0]+=rhs;
return (*this);
}
FPS& operator-=(mint rhs){
val[0]-=rhs;
return (*this);
}
FPS& operator*=(mint rhs){
for(auto& v:val){
v*=rhs;
}
return (*this);
}
FPS& operator/=(mint rhs){
for(auto& v:val){
v/=rhs;
}
return (*this);
}
FPS operator+(mint rhs){
return FPS(*this)+=rhs;
}
FPS operator-(mint rhs){
return FPS(*this)-=rhs;
}
FPS operator*(mint rhs){
return FPS(*this)*=rhs;
}
FPS operator/(mint rhs){
return FPS(*this)/=rhs;
}
FPS& operator+=(FPS rhs){
resize(max(this->size(),rhs.size()));
for(size_t i=0;i<rhs.size();++i){
(*this)[i]+=rhs[i];
}
return (*this);
}
FPS& operator-=(FPS rhs){
resize(max(this->size(),rhs.size()));
for(size_t i=0;i<rhs.size();++i){
(*this)[i]-=rhs[i];
}
return (*this);
}
FPS& operator*=(FPS rhs){
val=atcoder::convolution(val,rhs.val);
return (*this);
}
FPS& operator/=(FPS rhs){
return (*this)*=rhs.inv();
}
FPS& operator>>=(int k){
if(int(val.size())<=k){
return (*this)={0};
}
FPS res=val;
res.val.erase(res.val.begin(),res.val.begin()+k);
return (*this)=res;
}
FPS& operator<<=(int k){
FPS res=val;
res.val.insert(res.val.begin(),k,mint(0));
return (*this)=res;
}
FPS operator+(FPS rhs){
return FPS(*this)+=rhs;
}
FPS operator-(FPS rhs){
return FPS(*this)-=rhs;
}
FPS operator*(FPS rhs){
return FPS(*this)*=rhs;
}
FPS operator/(FPS rhs){
return FPS(*this)/=rhs;
}
FPS operator%(FPS rhs){
return FPS(*this)%=rhs;
}
FPS operator<<(int k){
return FPS(*this)<<=k;
}
FPS operator>>(int k){
return FPS(*this)>>=k;
}
FPS shrink(){
for(int i=val.size()-1;i>0;--i){
if(val[i]==0){
val.pop_back();
}
else{
break;
}
}
return (*this);
}
FPS diff_(){
if(val.size()==1){
return (*this)={0};
}
FPS f(val.size()-1);
for(size_t i=1;i<val.size();++i){
f[i-1]=val[i]*i;
}
return f;
}
FPS integral_(){
FPS f(val.size()+1);
for(size_t i=0;i<val.size();++i){
f[i+1]=val[i]/(i+1);
}
return f;
}
FPS inv_(int mx=-1){
if(mx==-1){
mx=val.size();
}
if(val[0]==0){
assert(0);
}
FPS g({mint(1)/val[0]});
int now=1;
while(now<mx){
now<<=1;
FPS t=(*this);
t.resize(now);
t*=g;
t=-t+mint(2);
g*=t;
g.resize(now);
}
g.resize(mx);
return g;
}
FPS exp_(int mx=-1){
if(mx==-1){
mx=val.size();
}
if(val[0]!=0){
assert(0);
}
FPS g(mint(1));
int now=1;
while(now<mx){
now<<=1;
FPS t=(*this);
t.resize(now);
g*=t-g.log_(now)+mint(1);
g.resize(now);
}
g.resize(mx);
return g;
}
FPS log_(int mx=-1){
if(mx==-1){
mx=val.size();
}
if(val[0]!=1){
assert(0);
}
auto f=(*this);
f.resize(mx);
return (f.diff_()/f).integral_().resize_(mx);
}
FPS pow_(i64 k,int mx=-1){
if(mx==-1){
mx=val.size();
}
i64 t=0;
for(auto v:val){
if(v==0){
t++;
}
else{
break;
}
}
auto f=(*this)>>t;
if(f[0]==0){
f={0},f.resize(mx);
return f;
}
mint c=f[0];
f/=c;
(f.log(mx)*=mint(k)).exp(mx)*=(c.pow(k));
if(t*k<=mx){
f<<=t*k;
f.resize(mx);
return f;
}
else{
f={0},f.resize(mx);
return f;
}
}
FPS& diff(){
return (*this)=diff_();
}
FPS& integral(){
return (*this)=integral_();
}
FPS& inv(int mx=-1){
return (*this)=inv_(mx);
}
FPS& exp(int mx=-1){
return (*this)=exp_(mx);
}
FPS& log(int mx=-1){
return (*this)=log_(mx);
}
FPS& pow(i64 k,int mx=-1){
return (*this)=pow_(k,mx);
}
};
template<typename T> T Product(vector<T> a){
int siz=1;
while(siz<int(a.size())){
siz<<=1;
}
vector<T> res(siz*2-1,{1});
for(size_t i=0;i<a.size();++i){
res[i+siz-1]=a[i];
}
for(int i=siz-2;i>=0;--i){
res[i]=res[2*i+1]*res[2*i+2];
}
return res[0];
}
template<class mint> vector<mint> StirlingNumber2(int N){
FPS<mint> f(N+1),g(N+1);
mint fact=1;
for(int i=0;i<=N;++i){
f[i]=(mint(i).pow(N))/fact;
g[i]=(mint(-1).pow(i))/fact;
fact*=i+1;
}
f*=g;
vector<mint> res(N+1);
for(int i=0;i<=N;++i){
res[i]=f[i];
}
return res;
}
template<class T> T Even(T f){
T g((f.size()+1)/2);
for(size_t i=0;i<(f.size()+1)/2;++i){
g[i]=f[i*2];
}
return g;
}
template<class T> T Odd(T f){
T g(f.size()/2);
for(size_t i=0;i<f.size()/2;++i){
g[i]=f[i*2+1];
}
return g;
}
template<class T> T Minus(T f){
for(size_t i=1;i<f.size();i+=2){
f[i]*=-1;
}
return f;
}
template<class mint> mint BostanMori(FPS<mint> f,FPS<mint> g,i64 k){
while(k>0){
if(k%2==0){
f=Even(f*Minus(g));
}
else{
f=Odd(f*Minus(g));
}
g=Even(g*Minus(g));
k/=2;
}
return f[0]/g[0];
}
int main(){
constexpr int mod=998244353;
using mint=modint<mod>;
cmb<mint> Cb;
int N;
scn(N);
FPS<mint> f(N-1);
for(int i=0;i<N-1;++i){
f[i]=Cb.fi(i)*(i+1);
}
prt(Cb.f(N-2)*f.pow(N)[N-2]/mint(N).pow(N-2));
}
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