Baltic Olympiad in Informatics 2018 Open - day 2

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2018-04-29 09:30 CEST

Baltic Olympiad in Informatics 2018 Open - day 2

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2018-04-29 14:30 CEST
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Problem B
Genetics

For villains that intend to take over the world, a common way to avoid getting caught is to clone themselves. You have managed to catch an evil villain and her $N-1$ clones, and you are now trying to figure out which one of them is the real villain.

To your aid you have each person’s DNA sequence, consisting of $M$ characters, each being either A, C, G or T. You also know that the clones are not perfectly made; rather, their sequences differ in exactly $K$ places compared to the real villain’s.

Can you identify the real villain?

Input

The first line contains the three integers $N$, $M$, and $K$, where $1 \le K \le M$. The following $N$ lines represent the DNA sequences. Each of these lines consists of $M$ characters, each of which is either A, C, G or T.

In the input, there is exactly one sequence that differs from all the other sequences in exactly $K$ places.

Warning: this problem has rather large amounts of input, and will require fast IO in Java.

Output

Output an integer – the index of the DNA sequence that belongs to the villain. The sequences are numbered starting from $1$.

Constraints

Your solution will be tested on a set of test groups, each worth a number of points. Each test group contains a set of test cases. To get the points for a test group you need to solve all test cases in the test group. Your final score will be the maximum score of a single submission.

Group

Points

Limits

Additional Constraints

1

27

$3 \le N, M \le 100$

 

2

19

$3 \le N, M \le 1800$

All characters are either A or C.

3

28

$3 \le N, M \le 4100$

All characters are either A or C.

4

26

$3 \le N, M \le 4100$

 
Sample Input 1 Sample Output 1
4 3 1
ACC
CCA
ACA
AAA
3
Sample Input 2 Sample Output 2
4 4 3
CATT
CAAA
ATGA
TCTA
4