hdu 3992 Crazy Typewriter AC自动机+高斯消元求期望

Problem Description

There was a crazy typewriter before. When the writer is not very sober, it would type characters randomly, one per second, the possiblities of characters may differ.
The protagonist in this problem wants to tell acmers some secrets, of course, by the typewriter.

There had been several opportunities, but the protagonist let them sliped. Now, another opportunity came, the writer started a new paragraph. The protagonist found 
that he could set the possiblities of each character in happy astonishment. After the possiblities had been set, he wanted to know the exception of time at least the writer need to be mind-absent if any secret was typed out.

fewovigwnierfbiwfioeifaorfwarobahbgssjqmdowj

 

Input

There are several cases, no more than 15.
The first line of each case contains an integer n, no more than 15, indicating the number of secrets.
The second line contains 26 real numbers, indicating the set possibilities of 'a'-'z', respectively, the sum would be 1.0 .
Then n lines, each contains a secret, no longer than 15, which is made up by lowercase letters 'a'-'z'.

 

Output

A single line contains the expectation of time for each case， in seconds with six decimal, if the exception doesn't exist, output "Infinity"

 

Sample Input

2
0.5000 0.5000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
ab
aa

 

Sample Output

3.000000

//

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
const int maxn=100000;
struct Node
{
    int flag;
    int id;
    Node* next[26];
    Node* fail;
};
Node* root;
Node temp[maxn];
int tp;
void reset(Node* p)
{
    p->flag=0;p->id=tp-1;
    for(int i=0;i<26;i++) p->next[i]=NULL;
    p->fail=root;
    if(p==root) p->fail=NULL;
}
void init()
{
    tp=0;
    root=&temp[tp++];
    reset(root);
}
void insert(char* str)
{
    Node* p=root;
    for(int i=0;str[i];i++)
    {
        int x=str[i]-'a';
        if(p->next[x]==NULL)
        {
            p->next[x]=&temp[tp++];
            reset(p->next[x]);
        }
        p=p->next[x];
    }
    p->flag=1;
}
Node* que[maxn];
int front,rear;
void DFA()
{
    front=rear=0;
    que[rear++]=root;
    while(front<rear)
    {
        Node* t=que[front++];
        for(int i=0;i<26;i++)
        {
            Node* cnt=t->next[i];
            if(cnt!=NULL)
            {
                Node* fath=t->fail;
                while(fath!=NULL&&fath->next[i]==NULL)
                {
                    fath=fath->fail;
                }
                if(fath==NULL)
                {
                    cnt->fail=root;
                }
                else cnt->fail=fath->next[i];
                cnt->flag|=cnt->fail->flag;//important
                que[rear++]=cnt;
            }
        }
    }
}
double pet[26];
int n;
char str[maxn];
double a[1000][1000];
int equ,var;//从0开始
void toMatrix()
{
    var=rear;
    equ=0;
    memset(a,0,sizeof(a));
    for(int i=0;i<rear;i++)
    {
        Node* p=&temp[i];
        if(p->flag)
        {
            a[equ][p->id]=1;
            a[equ++][var]=0;
            continue;
        }
        a[equ][p->id]=-1;
        a[equ][var]=-1;
        for(int j=0;j<26;j++)
        {
            Node* cnt=p->next[j];
            int k;
            if(cnt!=NULL)
            {
                k=cnt->id;
                a[equ][k]+=pet[j];
            }
            else
            {
                Node* fath=p->fail;
                while(fath!=NULL&&fath->next[j]==NULL)
                {
                    fath=fath->fail;
                }
                if(fath!=NULL)
                {
                    k=fath->next[j]->id;
                    a[equ][k]+=pet[j];
                }
                else
                {
                    k=0;
                    a[equ][0]+=pet[j];
                }
            }
        }
        equ++;
    }
}
const double eps=1e-10;
double x[1000];
void Gauss()
{
    for(int i=0;i<equ;i++)
    {
        int j;
        for(j=i;j<equ;j++)
        {
            if(fabs(a[j][i])>eps) break;
        }
        for(int k=i;k<=var;k++) swap(a[i][k],a[j][k]);
        for(j=i+1;j<equ;j++)
        {
            double p=-a[j][i]/a[i][i];
            for(int k=i;k<=var;k++) a[j][k]+=a[i][k]*p;
        }
    }
    for(int i=equ-1;i>=0;i--)
    {
        x[i]=a[i][var]/a[i][i];
        a[i][var]/=a[i][i];a[i][i]=1;
        for(int j=i-1;j>=0;j--)
        {
            a[j][var]+=-a[j][i]*a[i][var];
            a[j][i]=0;
        }
    }
}
void debug()
{
    for(int i=0;i<equ;i++)
    {
        for(int j=0;j<=var;j++) cout<<a[i][j]<<"  ";cout<<endl;
    }cout<<"........................"<<endl;
}
int main()
{
    while(scanf("%d",&n)==1)
    {
        init();
        for(int i=0;i<26;i++) scanf("%lf",&pet[i]);
        int flag=0;
        for(int i=0;i<n;i++)
        {
            scanf("%s",str);
            insert(str);
            int f=1;
            for(int j=0;str[j];j++)
            {
                int x=str[j]-'a';
                if(fabs(pet[x])<eps)
                {
                    f=0;break;
                }
            }
            if(f) flag=1;


        }
        if(!flag)
        {
            printf("Infinity\n");
            continue;
        }
        DFA();
        toMatrix();
        //debug();
        Gauss();
        //debug();
        printf("%.6lf\n",x[0]);
    }
    return 0;
}