USACO 2012 January Contest, Gold Division

Problem 1. Video Game

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Problem 1: Video Game Combos [Neal Wu, 2012] 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? PROBLEM NAME: combos INPUT FORMAT: * 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. SAMPLE INPUT (file 3 7 ABA CB ABACB OUTPUT FORMAT: * Line 1: A single integer, the maximum number of points Bessie can obtain. SAMPLE OUTPUT (file combos.out): 4 OUTPUT DETAILS: The optimal sequence of buttons in this case is ABACBCB, which gives 4 points--1 from ABA, 1 from ABACB, and 2 from CB.
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