HDU 2825 Wireless Password

Wireless Password

Time Limit: 1000ms

Memory Limit: 32768KB

This problem will be judged on HDU. Original ID: 2825
64-bit integer IO format: %I64d      Java class name: Main

Liyuan lives in a old apartment. One day, he suddenly found that there was a wireless network in the building. Liyuan did not know the password of the network, but he got some important information from his neighbor. He knew the password consists only of lowercase letters 'a'-'z', and he knew the length of the password. Furthermore, he got a magic word set, and his neighbor told him that the password included at least k words of the magic word set (the k words in the password possibly overlapping).

For instance, say that you know that the password is 3 characters long, and the magic word set includes 'she' and 'he'. Then the possible password is only 'she'.

Liyuan wants to know whether the information is enough to reduce the number of possible passwords. To answer this, please help him write a program that determines the number of possible passwords.

 

Input

There will be several data sets. Each data set will begin with a line with three integers n m k. n is the length of the password (1<=n<=25), m is the number of the words in the magic word set(0<=m<=10), and the number k denotes that the password included at least k words of the magic set. This is followed by m lines, each containing a word of the magic set, each word consists of between 1 and 10 lowercase letters 'a'-'z'. End of input will be marked by a line with n=0 m=0 k=0, which should not be processed.

 

Output

For each test case, please output the number of possible passwords MOD 20090717.

 

Sample Input

10 2 2
hello 
world 
4 1 1
icpc 
10 0 0
0 0 0

Sample Output

2
1
14195065

Source

2009 Multi-University Training Contest 1 - Host by TJU

 

解题：Trie图+状压dp

#include <bits/stdc++.h>
using namespace std;
const int maxn = 105;
const int mod = 20090717;
int dp[2][maxn][1<<10];
struct Trie {
    int ch[maxn][26],fail[maxn],cnt[maxn],tot;
    int newnode() {
        memset(ch[tot],0,sizeof ch[tot]);
        fail[tot] = cnt[tot] = 0;
        return tot++;
    }
    void init() {
        tot = 0;
        newnode();
    }
    void insert(char *str,int pos,int rt = 0) {
        for(int i = 0; str[i]; ++i) {
            int &x = ch[rt][str[i]-'a'];
            if(!x) x = newnode();
            rt = x;
        }
        cnt[rt] |= (1<<pos);
    }
    void build(int rt = 0) {
        queue<int>q;
        for(int i = 0; i < 26; ++i)
            if(ch[rt][i]) q.push(ch[rt][i]);
        while(!q.empty()) {
            rt = q.front();
            q.pop();
            cnt[rt] |= cnt[fail[rt]];
            for(int i = 0; i < 26; ++i) {
                int &x = ch[rt][i],y = ch[fail[rt]][i];
                if(x) {
                    q.push(x);
                    fail[x] = y;
                } else x = y;
            }
        }
    }
    void solve(int n,int m,int z) {
        memset(dp,0,sizeof dp);
        dp[0][0][0] = 1;
        int cur = 0;
        for(int i = 1; i <= n; ++i) {
            for(int j = 0; j < tot; ++j) {
                for(int k = 0; k < (1<<m); ++k) {
                    if(!dp[cur][j][k] || (k&cnt[j] != cnt[j])) continue;
                    for(int t = 0; t < 26; ++t) {
                        int x = ch[j][t];
                        dp[cur^1][x][k|cnt[x]] += dp[cur][j][k];
                        dp[cur^1][x][k|cnt[x]] %= mod;
                    }
                }
            }
            memset(dp[cur],0,sizeof dp[cur]);
            cur ^= 1;
        }
        int ret = 0;
        for(int i = 0; i < tot; ++i)
            for(int j = 0; j < (1<<m); ++j) {
                int nd = 0;
                for(int k = j; k; k >>= 1) if(k&1) ++nd;
                if(nd >= z) ret = (ret + dp[cur][i][j])%mod;
            }
        cout<<ret<<endl;
    }
}ac;
int main() {
    int n,m,k;
    char str[maxn];
    while(scanf("%d%d%d",&n,&m,&k),n||m||k){
        ac.init();
        for(int i = 0; i < m; ++i){
            scanf("%s",str);
            ac.insert(str,i);
        }
        ac.build();
        ac.solve(n,m,k);
    }
    return 0;
}