Problem H
Fire! Fire!! Fire!!!
Input:
standard input
Output: standard output
Time Limit: 15
seconds
Memory Limit: 32 MB
The ACM
(
However, in order to reduce installation cost, it has been decided that not every gallery will have a fire exit. Fire exits will be installed in such a way that if any gallery does not have a fire exit then at least one of its adjacent galleries must have one and for each corridor at least one of the two galleries it connects must have a fire exit.. You are hired to determine where to put the fire exits under this constraint.
However, as a first step, you are expected to determine the minimum number of fire exits required.
Input
The input file may contain multiple test cases. The first line of each test case contains an integer N (1 £ N £ 1,000) indicating the number of galleries in this test case. Then follow N lines where the i-th (1 £ i £ N) line is the adjacency list of the i-th gallery (Each gallery is given a unique identification number from 1 to N for convenience). The adjacency list for gallery i starts with an integer ni (0 £ ni £ N - 1) indicating the number of galleries adjacent to this gallery, followed by ni integers giving the identification numbers of those galleries.
A test case containing a zero for
N terminates the input.
Output
For each test case in the input file print a line containing the minimum number of fire exits required to meet the given constraint.
Sample
Input
4
3 2 3 4
1 1
1
1
1 1
16
4 6 12 15 16
3 3 8 10
4 2 4 6 9
1 3
1 6
3 1 3
5
1 15
1 2
1 3
1 2
1 16
1 1
1 15
1 15
4 1 7 13
14
2 1 11
0
Sample
Output
1
6
(World Finals Warm-up Contest,
Problem setter: Rezaul Alam Chowdhury)
“I would rather make fire escapes in all galleries than solve this problem :-)”