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 combos.in):
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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