BZOJ 2580: [Usaco2012 Jan]Video Game

2580: [Usaco2012 Jan]Video Game

Time Limit: 10 Sec  Memory Limit: 128 MB
Submit: 142  Solved: 96
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Description

Bessie is playing a video game! In the game, the three letters 'A', 'B', and 'C' are the only valid buttons. Bessie may press the buttons in any order she likes; however, there are only N distinct combos possible (1 <= N <= 20). Combo i is represented as a string S_i which has a length between 1 and 15 and contains only the letters 'A', 'B', and 'C'. Whenever Bessie presses a combination of letters that matches with a combo, she gets one point for the combo. Combos may overlap with each other or even finish at the same time! For example if N = 3 and the three possible combos are "ABA", "CB", and "ABACB", and Bessie presses "ABACB", she will end with 3 points. Bessie may score points for a single combo more than once. Bessie of course wants to earn points as quickly as possible. If she presses exactly K buttons (1 <= K <= 1,000), what is the maximum number of points she can earn? 

 

给出n个ABC串combo[1..n]和k，现要求生成一个长k的字符串S，问S与word[1..n]的最大匹配数

Input

Line 1: Two space-separated integers: N and K. * Lines 2..N+1: Line i+1 contains only the string S_i, representing combo i.

Output

Line 1: A single integer, the maximum number of points Bessie can obtain.

Sample Input

3 7 ABA CB ABACB

Sample Output

4

HINT

The optimal sequence of buttons in this case is ABACBCB, which gives 4 points--1 from ABA, 1 from ABACB, and 2 from CB.

Source

 

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总串长只有300，即Trie树大小<=300，那建个AC自动机，拎出Fail树，在上面给每个EndPos的子树+1，此时每个结点的权值就是到达这个结点会新增的匹配数。在一张有向有环图上走1000步，使得经过点的权值和最大，而且点数<=300，那就DP好了,f[i][j]表示当前在i点，已经走了j步，得到的最大权值，向i的每个出边做转移就好。

@Author: YouSiki