HDU 2825-Wireless Password（AC自动机+状压DP）

Wireless Password

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 6710    Accepted Submission(s): 2227

Problem Description

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

 

Recommend

题意：给你m个字符串，设计一个长为n的密码，使得这个密码中至少含有k个所给的的字符串，问你能设计多少种。

题解：显然是DP了，定义dp[i][j][k]:表示前i位以结点j结尾（匹配到结点j）且当前所含的已知字符串状态为k的方案数。

（PS：题目不难，贵在熟练和加深理解）

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