A network is composed of N
computers connected by N - 1
communication links such that
any two computers can be communicated via a unique route. Two computers are said to be
adjacent if there is a communication link between them. The neighbors of a computer is the set
of computers which are adjacent to it. In order to quickly access and retrieve large amounts of
information, we need to select some computers acting as servers to provide resources to their
neighbors. Note that a server can serve all its neighbors. A set of servers in the network forms
a perfect service if every client (non-server) is served by exactly one server. The problem is
to find a minimum number of servers which forms a perfect service, and we call this number
perfect service number.
We assume that N
(
10000)
is a positive integer and these N
computers are numbered
from 1 to N
. For example, Figure 1 illustrates a network comprised of six computers, where
black nodes represent servers and white nodes represent clients. In Figure 1(a), servers 3
and 5 do not form a perfect service because client 4 is adjacent to both servers 3 and 5 and thus it
is served by two servers which contradicts the assumption. Conversely, servers 3 and 4 form a
perfect service as shown in Figure 1(b). This set also has the minimum cardinality. Therefore,
the perfect service number of this example equals two.
Your task is to write a program to compute the perfect service number.
The input consists of a number of test cases. The format of each test case is as follows: The first
line contains one positive integer, N
, which represents the number of computers in the network.
The next N - 1
lines contain all of the communication links and one line for each link. Each line
is represented by two positive integers separated by a single space. Finally, a `0' at the (N + 1)
-th
line indicates the end of the first test case.
The next test case starts after the previous ending symbol `0'. A `-1' indicates the end of the
whole inputs.
The output contains one line for each test case. Each line contains a positive integer, which is
the perfect service number.
6
1 3
2 3
3 4
4 5
4 6
0
2
1 2
-1
2
1
Kaohsiung 2006-2007
