Algernon's Noxious Emissions
Time Limit: 2 Seconds
Memory Limit: 65536 KB
One of the greatest alchemists of the lower Middle Renaissance, Algernon da
Vinci (one of Leonardo's lesserknown cousins), had the foresight to construct
his chemical works directly over a fast-running stream. Through a series of
clever pipes and sluices, he routed portions of the stream past each of the
tables where his alchemists prepared their secret brews, allowing them to dispose
of their chemical byproducts into the waters flowing by the table.
As Algernon's business grew, he even added additional floors to his factory,
with water lifted to the higher floors by treadmill-powered pumps (much to the
dismay of the apprentices who found themselves assigned to pump duty). The pipework
for the entire disposal system became quite complex. It was even rumored by
some that the pipes actually circled back in some places, so that a particularly
odorous compound flushed away from one table might return to that very same
spot a few minutes later.
All was not well, however. Algernon's factory suffered from a series of mishaps,
minor explosions, gas clouds, etc. It became obvious that chemicals dumped at
one table might react violently with other chemicals dumped from another table
downstream. Algernon realized that he needed to trace the possible chemical
flows through his factory.
Write a program to aid Algernon in this task. To preserve the secrecy of the
chemical processes that are Algernon's stock in trade, all chemicals will be
identified by a single upper-case letter. All tables are identified by positive
numbers in the range 1��N, where N is the number of tables.
# of work tables, integer (henceforth referred to as N). N < 50
For each table:
- a list of chemicals dumped into the stream at that table, followed by
- a list of chemicals that, if they appeared at that table, would be harmlessly
neutralized by the reactions at that table, allowing no further trace of that
chemical to flow downstream (we will assume that the rate of work at each table
can be adjusted as necessary to guarantee total neutralization of whatever amount
of these chemicals arrive from upstream).
Each of these lists is given as a series of upper-case alphabetic characters.
The only exception is that a special list, consisting of a single '.' character,
will be used to denote an empty list. The two lists are separated from one other
by one or more blanks. The same chemical will never appear in both lists.
These lines provide a description of the pipeworks. Each line contains a pair
of integers in the range 1��N, separated by one or more blanks:
meaning that the table number I is upstream of table number J - anything dumped
into the stream at table I or that arrives in the stream at table I and is not
neutralized can then be counted on to arrive at table J.
No (I,J) pair will be listed more than once, but the pairs may occur in any
order. I and J will never be the same number.
The end of input is signaled by a pair of zeros:
Note that if a table only receives water directly from the stream entering the
building, that table will never occur in the second position of a pair. Similarly,
any table that discharges only into the stream leaving the building will never
occur in the first position of a pair.
There will be N lines of output, one for each table, in the same order as they
appeared in the program input. Each line will contain the list of chemicals
that can be expected at that table's output. This list will be printed as a
(possibly empty) list of upper-case alphabetic characters between two colons
(:). No empty spaces should be printed on the line. The characters in the list
should be sorted in alphabetic order.
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
For the figure at the right, an input would be:
Source: Mid-Atlantic USA 2001