线性代数（矩阵乘法）：NOI 2007 生成树计数

　　这道题就是深搜矩阵，再快速幂。

 #include <iostream>
 #include <cstring>
 #include <cstdio>
 #include <map>
 using namespace std;
 const int maxn=;
 const int mod=;
 struct Matrix{
     long long mat[maxn][maxn];
     int r,c;
     Matrix(int r_=,int c_=,int on=){
         memset(mat,,sizeof(mat));
         r=r_;c=c_;
         if(on)for(int i=;i<=r;i++)mat[i][i]=;
     }
     Matrix operator *(Matrix a){
         Matrix ret(r,a.c);
         long long l;
         for(int i=;i<=r;i++)
             for(int k=;k<=c;k++){
                 l=mat[i][k];
                 for(int j=;j<=a.c;j++)
                     (ret.mat[i][j]+=(l*a.mat[k][j])%mod)%=mod;
             }
         return ret;
     }
     Matrix operator ^(long long k){
         Matrix ret(r,c,),x(r,c);
         for(int i=;i<=r;i++)
             for(int j=;j<=c;j++)
                 x.mat[i][j]=mat[i][j];
         while(k){
             if(k&)
                 ret=ret*x;
             k>>=;
             x=x*x;
         }
         return ret;
     }
 }A,B;

 long long n;
 map<int,int>ID;
 map<int,bool>used;
 int k,e,e1,E[maxn][];
 int cnt,st[<<],mem[<<];
 int fa[maxn],sz[maxn],vis[maxn];
 int Find(int x){
     return x==fa[x]?x:fa[x]=Find(fa[x]);
 }
 bool Check(int s){
     for(int i=;i<maxn;i++)
         fa[i]=i,sz[i]=;
     for(int i=;i<e+e1;i++)
         if(s&(<<i)){
             int u=Find(E[i][]),v=Find(E[i][]);
             if(u!=v){fa[u]=v;sz[v]+=sz[u];}
             else return false;
         }
     return true;
 }

 void Solve(int x){
     for(int i=;i<=x;i++)
         for(int j=i+;j<=x;j++)
             E[e][]=i,E[e][]=j,e++;
     for(int i=;i<=x;i++)
         E[e+e1][]=i,E[e+e1][]=x+,e1++;

     for(int s=(<<e)-,num;s>=;s--)
         if(Check(s)){
             memset(vis,,sizeof(vis));num=;
             for(int i=;i<=x;i++){
                 if(vis[Find(i)])continue;
                 vis[Find(i)]=++num;
             }
             num=;
             for(int i=;i<=x;i++)
                 num=num*+vis[Find(i)];
             if(ID[num])B.mat[ID[num]][]+=;
             else{
                 A.r+=;A.c+=;B.r+=;
                 B.mat[ID[num]=B.r][]=;
                 st[++cnt]=s;mem[cnt]=num;
             }
         }

     for(int t=,s;t<=cnt;t++){
         for(int p=(<<e1)-,num;p>=;p--){
             s=st[t]^(p<<e);
             if(Check(s)&&sz[Find()]!=){
                 memset(vis,,sizeof(vis));num=;
                 for(int i=;i<=x+;i++){
                     if(vis[Find(i)])continue;
                     vis[Find(i)]=++num;
                 }
                 num=;
                 for(int i=;i<=x+;i++)
                     num=num*+vis[Find(i)];
                 A.mat[ID[num]][ID[mem[t]]]+=;
             }
         }
     }
     return;
 }

 int main(){
 #ifndef ONLINE_JUDGE
     freopen("count.in","r",stdin);
     freopen("count.out","w",stdout);
 #endif
     scanf("%d%lld",&k,&n);
     k=min(1ll*k,n);Solve(k);B.c=;
     A=A^((n-k)%(1ll*(mod+)*(mod-)));B=A*B;
     printf("%lld\n",B.mat[][]);
     return ;
 }