标签:mat net mes while post swa cal air col
定义贝尔数$B_n=\sum _{k=1}{n}S(n,k)$,其中$S(n,k)$为第二类斯特林数,我们有$B_{n+1}=\sum_{i=0}^{n}B_i*\tbinom{n}{i}$,
//#pragma GCC optimize(3,"Ofast","inline") //#pragma GCC optimize("-Ofast","-funroll-all-loops") #include<bits/stdc++.h> //#define getchar nc #define sight(c) (‘0‘<=c&&c<=‘9‘) #define swap(a,b) a^=b,b^=a,a^=b #define LL long long #define debug(a) cout<<#a<<" is "<<a<<"\n" #define dput(a) puts("a") #define eho(x) for(int i=head[x];i;i=net[i]) #define fi first #define se second #define mo 998244353 inline char nc(){ static char buf[1000000],*p1=buf,*p2=buf; return p1==p2&&(p2=(p1=buf)+fread(buf,1,1000000,stdin),p1==p2)?EOF:*p1++; } template <class T> inline void read(T &x){// unsigned static char c; for (c=getchar();!sight(c);c=getchar()); for (x=0;sight(c);c=getchar())x=x*10+c-48; } template <class T> void write(T x){if (x<10) {putchar(‘0‘+x); return;} write(x/10); putchar(‘0‘+x%10);} template <class T> inline void writeln(T x){ if (x<0) putchar(‘-‘),x*=-1; write(x); putchar(‘\n‘); } template <class T> inline void writel(T x){ if (x<0) putchar(‘-‘),x*=-1; write(x); putchar(‘ ‘); } using namespace std; LL qsm(LL x,LL y=mo-2){ static LL anw; for (anw=1,x=x%mo;y;y>>=1,x=x*x%mo) if (y&1) anw=anw*x%mo; return anw; } #define N 1000005 #define G 3 int rev[N];LL a[N],b[N]; void NTT(LL *a,int ln,int op){ int lim=1<<ln; for (int i=0;i<lim;i++) rev[i]=(rev[i>>1]>>1)|((i&1)<<ln-1); for (int i=0;i<lim;i++) if (i<rev[i]) swap(a[i],a[rev[i]]); for (int i=1;i<lim;i<<=1) { LL wn=qsm(G,(mo-1)/(i<<1)); if (op==-1) wn=qsm(wn); for (int j=0;j<lim;j+=i<<1) { LL w=1,X,Y; for (int k=j;k<i+j;k++,w=w*wn%mo) { X=a[k]; Y=w*a[k+i]%mo; a[k]=(X+Y)%mo; a[k+i]=(X-Y+mo)%mo; } } } if (op==-1) { LL sn=qsm(lim); for (int i=0;i<lim;i++) a[i]=a[i]*sn%mo; } } void mul(LL* a,LL *b,LL *c,int ln){//input array of len 1<<ln, return 1<<ln static LL A[N],B[N]; int lim=(1<<ln); for (int i=0;i<lim;i++) A[i]=a[i],B[i]=b[i]; for (int i=lim;i<2*lim;i++) A[i]=B[i]=0; NTT(A,ln+1,1); NTT(B,ln+1,1); for (int i=0;i<2*lim;i++) c[i]=A[i]*B[i]%mo; NTT(c,ln+1,-1); } void inv(LL *a,LL *b,int LG){ static LL C[N]; b[0]=qsm(a[0]); for (int k=1;k<=LG;k++) { mul(b,a,C,k); for (int i=0;i<(1<<k);i++) C[i]=C[i]?mo-C[i]:0; C[0]=(C[0]+2)%mo; mul(C,b,b,k); } } void Dif(LL *a,LL *b,int lim){ //传lim而不是LG for (int i=0;i<lim;i++) b[i]=a[i+1]*(i+1)%mo; b[lim-1]=0; } void Int(LL *a,LL *b,int lim){ //复杂度O(nlogn) for (int i=lim-1;i;i--) b[i]=a[i-1]*qsm(i)%mo; b[0]=0; } void Ln(LL *a,LL *b,int LG){ static LL C[N]; inv(a,b,LG); Dif(a,C,1<<LG); mul(b,C,b,LG); Int(b,b,1<<LG); } void exp(LL *a,LL *b,int LG){ static LL D[N]; b[0]=1; for (int k=1;k<=LG;k++) { Ln(b,D,k); for (int i=0;i<(1<<(k));i++) D[i]=(a[i]-D[i]+mo)%mo; D[0]=(D[0]+1)%mo; mul(b,D,b,k); } } int n,T,X; LL fac[N]; signed main() { #ifdef LOCAL // freopen("test.in", "r", stdin); // freopen("test.out", "w", stdout); #endif a[1]=1; exp(a,b,17); b[0]=0; exp(b,a,17); fac[0]=1; for (int i=1;i<N;i++) fac[i]=fac[i-1]*i%mo; read(T); while(T--) { read(X); writeln(a[X]*fac[X]%mo); } return 0; } /* 3 1 3 3 1 1 3 3 1 */
标签:mat net mes while post swa cal air col
原文地址:https://www.cnblogs.com/rrsb/p/14823450.html