Time Limit: 2 Seconds
Memory Limit: 65536 KB
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
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.
The first line of the input contains two integers N and K, separated by spaces,
where N is the number of coins (2 <= N <= 100) and K is the number of
weightings fulfilled (1 <= K <= 100). The following 2K lines describe
all weightings. Two consecutive lines describe each weighting. The first of
them starts with a number Pi (1 <= Pi <= N / 2), 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
- '<' means that the weight of coins in the left pan is less than the weight
of coins in the right pan,
- '>' means that the weight of coins in the left pan is greater than the
weight of coins in the right pan,
- '=' means that the weight of coins in the left pan is equal to the weight
of coins in the right pan.
Write to the output the identifier of the false coin or 0, if it cannot be found
by the results of the given weightings.
This problem contains multiple test cases!
The first line of a multiple input is an integer N, then a blank line followed
by N input blocks. Each input block is in the format indicated in the problem
description. There is a blank line between input blocks.
The output format consists of N output blocks. There is a blank line between
2 1 2 3 4
1 1 4
1 2 5
3 1 2 3 4 5 6
1 1 2
2 1 3 4 5
2 4 5 2 6
Source: Northeastern Europe 1998