hdu2296 AC自动机+DP

http://acm.hdu.edu.cn/showproblem.php?pid=2296

Problem Description

For the hope of a forever love, Steven is planning to send a ring to Jane with a romantic string engraved on. The string's length should not exceed N. The careful Steven knows Jane so deeply that he knows her favorite words, such as "love", "forever". Also, he knows the value of each word. The higher value a word has the more joy Jane will get when see it.
The weight of a word is defined as its appeared times in the romantic string multiply by its value, while the weight of the romantic string is defined as the sum of all words' weight. You should output the string making its weight maximal. 

 

Input

The input consists of several test cases. The first line of input consists of an integer T, indicating the number of test cases. Each test case starts with a line consisting of two integers: N, M, indicating the string's length and the number of Jane's favorite words. Each of the following M lines consists of a favorite word Si. The last line of each test case consists of M integers, while the i-th number indicates the value of Si.
Technical Specification

1. T ≤ 15
2. 0 < N ≤ 50, 0 < M ≤ 100.
3. The length of each word is less than 11 and bigger than 0.
4. 1 ≤ Hi ≤ 100. 
5. All the words in the input are different.
6. All the words just consist of 'a' - 'z'.

 

Output

For each test case, output the string to engrave on a single line.
If there's more than one possible answer, first output the shortest one. If there are still multiple solutions, output the smallest in lexicographically order.

The answer may be an empty string. 

 

Sample Input

  
  

   
   2
7 2
love
ever
5 5
5 1
ab
5
  
  

 

Sample Output

  
  

   
   lovever
abab


   
   

    
    

     
     Hint
    
    
Sample 1: weight(love) = 5, weight(ever) = 5, so weight(lovever) = 5 + 5 = 10
Sample 2: weight(ab) = 2 * 5 = 10, so weight(abab) = 10 

   
   
   
    
  
  

/**
hdu2296 AC自动机+DP
题目大意：给出m个模式串，每个串有一定的分值，构造一个长度不超过n的串，使得分值最大，输出长度最小，字典序最小的串
解题思路：dp[i][j]表示长度为i的时候，在Trie上的第j个结点时的最大分值，str[i][j]表示状态(i,j)时的字典序最小的串。
*/
#include <stdio.h>
#include <string.h>
#include <iostream>
#include <algorithm>
#include <queue>
using namespace std;
const int INF=0x3f3f3f3f;
int a[110];
int dp[55][1110];
char str[55][1110][55];
bool cmp(char *s1,char *s2)
{
    int len1=strlen(s1);
    int len2=strlen(s2);
    if(len1!=len2)
        return len1<len2;
    return strcmp(s1,s2)<0;
}
struct Trie
{
    int next[1110][26],fail[1110],end[1110];
    int root,L;
    int newnode()
    {
        for(int i=0; i<26; i++)
            next[L][i]=-1;
        end[L++]=-1;
        return L-1;
    }
    void init()
    {
        L=0;
        root=newnode();
    }
    void insert(char *buf,int id)
    {
        int len=strlen(buf);
        int now=root;
        for(int i=0; i<len; i++)
        {
            if(next[now][buf[i]-'a']==-1)
                next[now][buf[i]-'a']=newnode();
            now=next[now][buf[i]-'a'];
        }
        end[now]=id;
    }
    void build()
    {
        queue<int>Q;
        fail[root]=root;
        for(int i=0; i<26; i++)
        {
            if(next[root][i]==-1)
                next[root][i]=root;
            else
            {
                fail[next[root][i]]=root;
                Q.push(next[root][i]);
            }
        }
        while(!Q.empty())
        {
            int now=Q.front();
            Q.pop();
            for(int i=0; i<26; i++)
            {
                if(next[now][i]==-1)
                    next[now][i]=next[fail[now]][i];
                else
                {
                    fail[next[now][i]]=next[fail[now]][i];
                    Q.push(next[now][i]);
                }
            }
        }
    }
    void solve(int n)
    {
        for(int i=0; i<=n; i++)
        {
            for(int j=0; j<L; j++)
            {
                dp[i][j]=-INF;
            }
        }
        dp[0][0]=0;
        char ans[55];
        memset(str[0][0],0,sizeof(str[0][0]));
        memset(ans,0,sizeof(ans));
        int maxx=0;
        char tmp[55];
        for(int i=0; i<n; i++)
        {
            for(int j=0; j<L; j++)
            {
                if(dp[i][j]>=0)
                {
                    strcpy(tmp,str[i][j]);
                    int len=strlen(tmp);
                    for(int k=0; k<26; k++)
                    {
                        int nxt=next[j][k];
                        tmp[len]='a'+k;
                        tmp[len+1]=0;
                        int tt=dp[i][j];
                        if(end[nxt]!=-1)
                            tt+=a[end[nxt]];
                        if(dp[i+1][nxt]<tt||(dp[i+1][nxt]==tt&&cmp(tmp,str[i+1][nxt])))
                        {
                            dp[i+1][nxt]=tt;
                            strcpy(str[i+1][nxt],tmp);
                            if(tt>maxx||(tt==maxx&&cmp(tmp,ans)))
                            {
                                maxx=tt;
                                strcpy(ans,tmp);
                            }
                        }
                    }
                }
            }
        }
        printf("%s\n",ans);
    }
} ac;
char buf[60];
int main()
{
    int T;
    int n,m;
    scanf("%d",&T);
    while(T--)
    {
        scanf("%d%d",&n,&m);
        ac.init();
        for(int i=0; i<m; i++)
        {
            scanf("%s",buf);
            ac.insert(buf,i);
        }
        for(int i=0; i<m; i++)
        {
            scanf("%d",&a[i]);
        }
        ac.build();
        ac.solve(n);
    }
    return 0;
}