[BJWC2011]禁忌 AC 自动机 概率与期望

#include<cstdio>
#include<algorithm>
#include<cstring>
#include<string>
#include<queue>
#include<cstdlib>
#include<iostream>
using namespace std;
void setIO(string a){
    freopen((a+".in").c_str(),"r",stdin);
}
#define db long double
#define maxn 100000

char arr[maxn];

int sigma, nodes, n;
struct matrix{
    long double mat[150][150];
}unit;

void init(matrix &a){
    for(int i=0;i<=n;++i)
        for(int j=0;j<=n;++j) a.mat[i][j]=0;
}
void get(matrix &a){
    init(a);
    for(int i=0;i<=n;++i) a.mat[i][i]=1;
}
matrix operator*(matrix a,matrix b){
    matrix c;
    init(c);
    for(int i=0;i<=n;++i)
        for(int j=0;j<=n;++j)
            for(int k=0;k<=n;++k) c.mat[i][j]+=a.mat[i][k]*b.mat[k][j];
    return c;
}
matrix operator^(matrix a,int p){
    matrix ans;
    get(ans);
    while(p){
        if(p&1) ans=ans*a;
        a=a*a;
        p>>=1;
    }
    return ans;
}
struct Automaton{
    int ch[maxn][30], fail[maxn], tag[maxn];
    #define idx str[i]-‘a‘
    void insert(char str[]){
        int cnt=strlen(str),j=0;
        for(int i=0;i<cnt;++i) {
            if(!ch[j][idx]) ch[j][idx]=++nodes;
            j=ch[j][idx];
        }
        tag[j]=true, n=nodes+1;
    }

    queue<int>Q;
    bool vis[maxn];
    void build(){
        for(int i=0;i<sigma;++i) if(ch[0][i]) Q.push(ch[0][i]);
        while(!Q.empty()){
            int u=Q.front();Q.pop();
            for(int i=0;i<sigma;++i){
                int r=ch[u][i];
                if(!r){ ch[u][i]=ch[fail[u]][i]; continue;}
                Q.push(r), fail[r]=ch[fail[u]][i], tag[r]|=tag[fail[r]];
            }
        }
        init(unit);
        Q.push(0), vis[0]=true;
        long double tmp=(long double)1/sigma;
        while(!Q.empty()){
            int u=Q.front();Q.pop();
            for(int i=0;i<sigma;++i){
                if(!vis[ch[u][i]]) vis[ch[u][i]]=true, Q.push(ch[u][i]);
                if(tag[ch[u][i]])  unit.mat[u][0]+=tmp, unit.mat[u][n]+=tmp;
                else unit.mat[u][ch[u][i]]+=tmp;
            }
            unit.mat[n][n]=1;
        }
    }
}aho;
int main(){
    //setIO("input");
    int m,len;
    scanf("%d%d%d",&m,&len,&sigma);
    for(int i=1;i<=m;++i) scanf("%s",arr), aho.insert(arr);
    aho.build();
    matrix g=unit^len;
    printf("%.10f",(double)g.mat[0][n]);
    return 0;
}