poj3691

DNA repair Time Limit: 2000MS Memory Limit: 65536K Total Submissions: 5743 Accepted: 2693

Description

Biologists finally invent techniques of repairing DNA that contains segments causing kinds of inherited diseases. For the sake of simplicity, a DNA is represented as a string containing characters 'A', 'G' , 'C' and 'T'. The repairing techniques are simply to change some characters to eliminate all segments causing diseases. For example, we can repair a DNA "AAGCAG" to "AGGCAC" to eliminate the initial causing disease segments "AAG", "AGC" and "CAG" by changing two characters. Note that the repaired DNA can still contain only characters 'A', 'G', 'C' and 'T'.

You are to help the biologists to repair a DNA by changing least number of characters.

Input

The input consists of multiple test cases. Each test case starts with a line containing one integers N (1 ≤ N ≤ 50), which is the number of DNA segments causing inherited diseases.
The following N lines gives N non-empty strings of length not greater than 20 containing only characters in "AGCT", which are the DNA segments causing inherited disease.
The last line of the test case is a non-empty string of length not greater than 1000 containing only characters in "AGCT", which is the DNA to be repaired.

The last test case is followed by a line containing one zeros.

Output

For each test case, print a line containing the test case number( beginning with 1) followed by the
number of characters which need to be changed. If it's impossible to repair the given DNA, print -1.

Sample Input

2
AAA
AAG
AAAG    
2
A
TG
TGAATG
4
A
G
C
T
AGT
0

Sample Output

Case 1: 1
Case 2: 4
Case 3: -1

對給出的得病的串進行自動機構造，dp[i][j]對應了走i步從根到達第j個節點的最小值。

#include 
#include 
#include 
#include 
using namespace std ;
#define INF 0x3f3f3f3f
struct node{
    int flag , id ;
    node *next[4] , *fail ;
} tree[2100] ;
queue  que ;
int num , dp[1100][2100] ;
char str[2100] ;
char c[5] = "ACGT" ;
node *newnode()
{
    node *p = &tree[num] ;
    p->flag = 0 ;
    p->id = num++ ;
    p->fail = NULL ;
    for(int i = 0 ; i < 4 ; i++)
        p->next[i] = NULL ;
    return p ;
}
void settree(char *s,node *rt)
{
    int i , k , l = strlen(s) ;
    node *p = rt ;
    for(i = 0 ; i < l ; i++)
    {
        for(k = 0 ; k < 4 ; k++)
            if( s[i] == c[k] )
                break ;
        if( p->next[k] == NULL )
            p->next[k] = newnode() ;
        p = p->next[k] ;
    }
    p->flag = 1 ;
    return ;
}
void setfail(node *rt)
{
    node *p = rt , *temp ;
    p->fail = NULL;
    while( !que.empty() ) que.pop() ;
    que.push(p) ;
    while( !que.empty() )
    {
        p = que.front() ;
        que.pop() ;
        for(int i = 0 ; i < 4 ; i++)
        {
            if( p->next[i] )
            {
                temp = p->fail ;
                while( temp && !temp->next[i] )
                    temp = temp->fail ;
                p->next[i]->fail = temp ? temp->next[i] : rt ;
                que.push(p->next[i]) ;
                if( temp && temp->flag )
                    p->flag = 1 ;
            }
            else
                p->next[i] = p == rt ? rt : p->fail->next[i] ;
        }
    }
    return ;
}
int query(char *s,node *rt)
{
    int i , j , k , l = strlen(s) , flag ;
    memset(dp,INF,sizeof(dp)) ;
    dp[0][0] = 0 ;
    for(i = 0 ; i < l ; i++)
    {
        for(j = 0 ; j < num ; j++)
        {
            for(k = 0 ; k < 4 ; k++)
            {
                if( tree[j].next[k]->flag ) continue ;
                if( s[i] == c[k] )
                    dp[i+1][ tree[j].next[k]->id ] = min( dp[i][j] , dp[i+1][ tree[j].next[k]->id ] ) ;
                else
                    dp[i+1][ tree[j].next[k]->id ] = min( dp[i][j]+1 , dp[i+1][ tree[j].next[k]->id ] ) ;
            }
        }
        /*for(j = 0 ; j < num ; j++)
            printf("%d ", dp[i+1][j]) ;
        printf("\n") ;*/
    }

    int ans = INF ;
    for(i = 0 ; i < num ; i++)
        ans = min(ans,dp[l][i]) ;
    if( ans == INF )
        ans = -1 ;
    return ans ;
}
int main()
{
    int i , n , temp = 1 ;
    node *rt ;
    while( scanf("%d", &n) && n )
    {
        num = 0 ;
        rt = newnode() ;
        for(i = 0 ; i < n ; i++)
        {
            scanf("%s", str) ;
            settree(str,rt) ;
        }
        setfail(rt) ;
        scanf("%s", str) ;
        printf("Case %d: %d\n", temp++ , query(str,rt) ) ;
    }
    return 0 ;
}