bzoj5093: [Lydsy1711月赛]图的价值

不难想到考虑每个点的贡献，ans=n*sigema(1~n)i C(n-1,i)*(2^C(n-1,2))*i^k

直接套第二类斯特林拆柿子即可。提示:sigema(1~n)i C(n,i)*C(i,j) = C(n,j)*2^(n-j)

#include<cstdio>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<cmath>
using namespace std;
typedef long long LL;
const int _=1e2;
const int maxK=2e5+_;
const int fbiK=(<<)+_;
const int mod=;
inline int ad(int x,int y){return (x>=mod-y)?(x-mod+y):x+y;}
inline int re(int x,int y){return (x<y)?(x-y+mod):x-y;}
inline int mu(int x,int y){return (LL)x*y%mod;}
inline int qp(int x,int y){int r=;while(y>){if(y&)r=mu(r,x);x=mu(x,x);y/=;}return r;}

int fac[maxK],fac_inv[maxK],inv[maxK];
void yu(int K)
{
    fac[]=;for(int i=;i<=K;i++)fac[i]=mu(fac[i-],i);
    fac_inv[K]=qp(fac[K],mod-);
    for(int i=K-;i>=;i--)fac_inv[i]=mu(fac_inv[i+],i+);

    inv[]=;for(int i=;i<=K;i++)inv[i]=mu(inv[mod%i],mod-mod/i);
}

namespace GETS2
{
    int Re[*fbiK];
    void NTT(int *a,int n,int op)
    {
        for(int i=;i<n;i++)
            if(i<Re[i])swap(a[i],a[Re[i]]);
        for(int i=;i<n;i<<=)
        {
            int gn=qp(,(mod-)/(i<<));
            if(op==-)gn=qp(gn,mod-);
            for(int j=;j<n;j+=(i<<))
            {
                int g=;
                for(int k=;k<i;k++,g=mu(g,gn))
                {
                    int k1=a[j+k],k2=mu(a[j+k+i],g);
                    a[j+k]=ad(k1,k2);
                    a[j+k+i]=re(k1,k2);
                }
            }
        }
        if(op==-)
        {
            int inv=qp(n,mod-);
            for(int i=;i<n;i++)a[i]=mu(a[i],inv);
        }
    }
    int n,m,L,A[*fbiK],B[*fbiK],S2K[*fbiK];
    void main(int K)
    {
        m=*K-;for(n=;n<=m;n<<=)L++;
        for(int i=;i<n;i++)Re[i]=(Re[i>>]>>)|((i&)<<(L-));

        for(int i=;i<=K;i++)
        {
            A[i]=mu((i&)?mod-:,fac_inv[i]);
            B[i]=mu(qp(i,K),fac_inv[i]);
        }

        NTT(A,n,),NTT(B,n,);
        for(int i=;i<n;i++)S2K[i]=mu(A[i],B[i]);
        NTT(S2K,n,-);
    }
}
int S2[][];
void QWQ()
{
    S2[][]=;
    for(int i=;i<=;i++)
        for(int j=;j<=i;j++)
            S2[i][j]=ad(S2[i-][j-],mu(S2[i-][j],j));
}

int main()
{
    int n,K;
    scanf("%d%d",&n,&K);yu(K);
    GETS2::main(K);//QWQ();

    using namespace GETS2;
    int ans=,C=;
    for(int j=;j<=K;j++)
    {
        C=mu(mu(C,n-j),inv[j]);
        ans=ad(ans, mu( mu(S2K[j],fac[j]) , mu(C,qp(,n--j)) ) );
    }
    printf("%d\n", mu( mu(ans,n) , qp(,(LL)(n-)*(n-)/%(mod-)) ) );

    return ;
}