【AC自动机】【矩阵乘法】【等比数列】hdu2243 考研路茫茫——单词情结

题解：http://blog.csdn.net/xingyeyongheng/article/details/10005923

这里采用了二分法求等比数列前n项和。

等比数列前n项和也可以用矩乘快速幂来求[a 1] [Sn] = [Sn+1]

　　　　　　　　　　　　　　　　　　 [0 1] [a ] [ a ]

#include<cstdio>
#include<cstring>
#include<vector>
#include<queue>
#include<iostream>
using namespace std;
typedef unsigned long long ull;
typedef vector<ull> vec;
typedef vector<vec> mat;
typedef pair<mat,mat> Point2;
typedef pair<ull,ull> Point;
int N;
mat I;
mat operator * (const mat &a,const mat &b)
{
mat c(N,vec(N));
for(int i=0;i<N;++i)
for(int j=0;j<N;++j)
for(int k=0;k<N;++k)
c[i][j]=c[i][j]+a[i][k]*b[k][j];
return c;
}
mat operator - (const mat &a,const mat &b)
{
mat c(N,vec(N));
for(int i=0;i<N;++i)
for(int j=0;j<N;++j)
c[i][j]=a[i][j]-b[i][j];
return c;
}
mat operator + (const mat &a,const mat &b)
{
mat c(N,vec(N));
for(int i=0;i<N;++i)
for(int j=0;j<N;++j)
c[i][j]=a[i][j]+b[i][j];
return c;
}
Point sum_a_n(ull a,ull n)
{
if(n==0)
return Point(1,1);
Point t=sum_a_n(a,n>>1);
if(n&1)
return Point(t.first*t.first*a,t.second*(t.first*a+1));
else
return Point(t.first*t.first,(t.second-t.first)*(t.first*a+1)+t.first);
}
Point2 sum_A_n(mat a,ull n)
{
if(n==0)
return Point2(I,I);
Point2 t=sum_A_n(a,n>>1);
if(n&1)
return Point2(t.first*t.first*a,t.second*(t.first*a+I));
else
return Point2(t.first*t.first,(t.second-t.first)*(t.first*a+I)+t.first);
}
queue<int>q;
int child[40][26],fail[40],size=1;
bool word[40];
void Insert(char S[])
{
int len=strlen(S);
int now=0;
for(int i=0;i<len;++i)
{
if(!child[now][S[i]-'a'])
child[now][S[i]-'a']=size++;
now=child[now][S[i]-'a'];
}
word[now]=1;
}
void build()
{
fail[0]=-1;
q.push(0);
while(!q.empty())
{
int U=q.front(); q.pop();
for(int i=0;i<26;++i)
if(child[U][i])
{
int V=fail[U];
while(V!=-1)
{
if(child[V][i])
{
fail[child[U][i]]=child[V][i];
break;
}
V=fail[V];
}
if(V==-1)
fail[child[U][i]]=0;
if(word[fail[child[U][i]]])
word[child[U][i]]=1;
q.push(child[U][i]);
}
else if(U)
child[U][i]=child[fail[U]][i];
}
}
int n,ma2[40];
ull m;
void Init()
{
memset(child,0,sizeof(child));
memset(fail,0,sizeof(fail));
memset(word,0,sizeof(word));
N=0;
size=1;
}
int main()
{
//freopen("hdu2243.in","r",stdin);
char s[8];
while(cin>>n>>m){
Init();
for(int i=1;i<=n;++i)
{
scanf("%s",s);
Insert(s);
}
build();
for(int i=0;i<size;++i)
if(!word[i])
ma2[i]=N++;
I.assign(N,vec(N));
for(int i=0;i<N;++i)
I[i][i]=1;
mat A(N,vec(N));
for(int i=0;i<size;++i)
for(int j=0;j<26;++j) if((!word[i]) && (!word[child[i][j]]))
++A[ma2[i]][ma2[child[i][j]]];
A=sum_A_n(A,m).second-I;
ull ans=sum_a_n(26,m).second-1;
for(int i=0;i<N;++i)
ans=ans-A[0][i];
cout<<ans<<endl;
}
return 0;
}