It is important in distributed computer systems to identify
those events (at identifiable points in time) that are concurrent, or
not related to each other in time. A group of concurrent events may
sometimes attempt to simultaneously use the same resource, and this
could cause problems.
Events that are not concurrent can be ordered in time. For example,
if event 1 can be shown to always precede event 2 in time, then event
1 and 2 are obviously not concurrent. Notationally we indicate that
event 1 precedes 2 by writing 1 ! 2. Note that the precedes relation
is transitive, as expected. Thus if 1 ! 2 and 2 ! 3, then we can also
note that 1 ! 3.
Sequential events in a single computation are not concurrent. For example,
if a particular computation performs the operations identified
by events 1, 2 and 3 in that order, then clearly and 1 ! 2 and 2 ! 3.
Computations in a distributed system communicate by sending messages.
If event 1 corresponds to the sending of a message by one computation,
and event 2 corresponds to the reception of that message by
a different computation, then we can always note that 1 ! 2, since a
message cannot be received before it is sent.
In this problem you will be supplied with lists of sequential events
for an arbitrary number of computations, and the identification of an
arbitrary number of messages sent between these computations. Let n
be the number of events. Your task is to write an O(n3) program to
find out how many pairs of events are concurrent.
Input
The input will include first an integer, nc, specifying the number of
computations in the test case. For each of these nc computations there
will be a single line containing an integer ne that specifies the number
of sequential events in the computation followed by ne event IDs.
Following the specification of the events in the last computation there
will be a line with a single integer, nm, that specifies the number of
messages that are sent between computations. Finally, on each of the
following nm lines there will be a pair of event IDs specifying the name of the event associated with the sending of a message, and the event
associated with the reception of the message. These IDs will have previously
appeared in the lists of events associated with computations.
e.g.:
2
2 1 2
2 3 4
1
3 1
Output Your output should be the number of pairs of concurrent
events. e.g., the output for the above input should be:
2
