Input file COIN.INOutput file COIN.OUT
Time limit 10 seconds per test
1998-99 ACM Northeastern European Regional Programming Contest
Problem A
“False coin”
Input file COIN.IN
Output file COIN.OUT
Time limit 10 seconds per test
The “Gold Bar” bank received information from reliable sources that in their last group of N coins exactly one coin is false and differs in weight from other coins (while all other coins are equal in weight). After the economic crisis they have only a simple balance available (like one in the picture). Using this balance, one is able to determine if the weight of objects in the left pan is less than, greater than, or equal to the weight of objects in the right pan.
In order to detect the false coin the bank employees numbered all coins by the integers from 1 to N, thus assigning each coin a unique integer identifier. After that they began to weight various groups of coins by placing equal numbers of coins in the left pan and in the right pan. The identifiers of coins and the results of the weightings were carefully recorded.
You are to write a program that will help the bank employees to determine the identifier of the false coin using the results of these weightings.
Input
The first line of the input file contains two integers N
and K, separated by spaces, where N is the number
of coins (
) and K is the
number of weightings fulfilled (
).
The following 2K lines describe all weightings. Two
consecutive lines describe each weighting. The first of them
starts with a number Pi (![1<=P[i]<=N/2](Image213.gif){kind=small}
), representing the number of coins placed
in the left and in the right pans, followed by Pi
identifiers of coins placed in the left pan and Pi
identifiers of coins placed in the right pan. All numbers are
separated by spaces. The second line contains one of the
following characters: '<', '>', or '='. It represents the
result of the weighting:
Output
Write to the output file the identifier of the false coin or 0, if it cannot be found by the results of the given weightings.
Sample input #1
5 3
2 1 2 3 4
<
1 1 4
=
1 2 5
=
Output for the sample input #1
3
Sample input #2
6 4
3 1 2 3 4 5 6
<
1 1 2
=
2 1 3 4 5
<
2 4 5 2 6
>
Output for the sample input #2
0