結果
問題 | No.1302 Random Tree Score |
ユーザー |
|
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 14 |
ソースコード
#include <bits/stdc++.h>#if __has_include(<atcoder/all>)#include <atcoder/all>#endifnamespace 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>;#elsemymodint<mod>;#endiftemplate<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));}