Program | |
Did you know that you can use domino bones for other things besides playing
Dominoes? Take a number of dominoes and build a row by standing them on end
with only a small distance in between. If you do it right, you can tip the first
domino and cause all others to fall down in succession (this is where the phrase
“domino effect”' comes from).
While this is somewhat pointless with only a few dominoes, some people went
to the opposite extreme in the early Eighties. Using millions of dominoes of
different colors and materials to fill whole halls with elaborate patterns of
falling dominoes, they created (shortlived) pieces of art. In these constructions,
usually not only one but several rows of dominoes were falling at the same time.
As you can imagine, timing is an essential factor here.
It is now your task to write a program that, given such a system of rows formed
by dominoes, computes when and where the last domino falls. The system consists
of several “key” dominoes connected by rows of simple dominoes.
When a key domino falls, all rows connected to the domino will also start falling
(except for the ones that have already fallen). When the falling rows reach
other key dominoes that have not fallen yet, these other key dominoes will fall
as well and set off the rows connected to them. Domino rows may start collapsing
at either end. It is even possible that a row is collapsing on both ends, in
which case the last domino falling in that row is somewhere between its key
dominoes. You can assume that rows fall at a uniform rate.
The input file contains descriptions of several domino systems. The first line
of each description contains two integers: the number n of key dominoes (1 <=
n <=500) and the number m of rows between them. The key dominoes are numbered
from 1 to n. There is at most one row between any pair of key dominoes and the
domino graph is connected, i.e. there is at least one way to get from a domino
to any other domino by following a series of domino rows.
The following m lines each contain three integers a, b, and l, stating that
there is a row between key dominoes a and b that takes l seconds to fall down
from end to end. Each system is started by tipping over key domino number 1.
The file ends with an empty system (with n = m = 0), which should not be processed.
For each case output a line stating the number of the case ('System #1', 'System #2', etc.). Then output a line containing the time when the last domino falls, exact to one digit to the right of the decimal point, and the location of the last domino falling, which is either at a key domino or between two key dominoes. Adhere to the format shown in the output sample. If you find several solutions, output only one of them. Output a blank line after each system.
Sample Input
2 1
1 2 27
3 3
1 2 5
1 3 5
2 3 5
0 0
Expected Output
System #1
The last domino falls after 27.0 seconds, at key domino 2.
System #2
The last domino falls after 7.5 seconds, between key dominoes 2 and 3.