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Universidad Cat´
olica Boliviana
Training Session 6, July 28, 2009
Problem A. Graph Connectivity
ID
459
Judge
UVa
Consider a graph
G
formed from a large number of nodes
connected
by edges.
G
is said to
be connected if a path can be found in
0
or more steps between any pair of nodes in
G
. For
example, the graph below is not connected because there is no path from
A
to
C
.
This graph contains, however, a number of subgraphs that are connected, one for each of the
following sets of nodes: {
A
}, {
B
}, {
C
}, {
D
}, {
E
}, {
A,B
}, {
B,D
}, {
C,E
}, {
A,B,D
}
A connected subgraph is maximal if there are no nodes and edges in the original graph that
could be added to the subgraph and still leave it connected. There are two maximal connected
subgraphs above, one associated with the nodes {
A,B,D
} and the other with the nodes {
C,E
}.
Write a program to determine the number of maximal connected subgraphs of a given graph.
Input
The input begins with a single positive integer on a line by itself indicating the number of the
cases following, each of them as described below. This line is followed by a blank line, and there
is also a blank line between two consecutive inputs.
The ﬁrst line of each input set contains a single uppercase alphabetic character. This character
represents the largest node name in the graph. Each successive line contains a pair of uppercase
alphabetic characters denoting an edge in the graph. The sample input section contains a
possible input set for the graph pictured above.
Input is terminated by a blank line.
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This note was uploaded on 03/06/2010 for the course FCEI ITPC taught by Professor Hernanpayrumani during the Fall '10 term at Universidad Católica Boliviana.
 Fall '10
 HERNANPAYRUMANI

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