Time Limit: 2 Seconds
Memory Limit: 65536 KB
In a knockout tournament there are 2^n players. One loss and a player is out
of the tournament. Winners then play each other with the new winners advancing
until there is only one winner left. If we number the players 1, 2, 3, ...,
2^n, with the first round pairings 2k - 1 vs 2k, for k = 1, 2, ..., 2^(n-1),
then we could give the results of the tournament in a complete binary tree.
The winners are indicated in the interior nodes of the tree. Below is an example
of a tournament with n = 3.
After the tournament, some reporters were arguing about the relative ranking
of the players, as determined by the tournament results. It's assumed that if
player A beats player B who in turn beats player C, that player A will also
beat player C; that is, winning is transitive. Now there is no doubt who the
best player is. The question is what is the highest ranking a player can reasonably
claim as a result of the tournament and what is the worst ranking a player can
have, as a result of the tournament? For example, in the above tournament player
2, having lost to the eventual winner, could claim to be the 2nd best player
in the field, but could well be the worst (ranked 8th). Player 5 could claim
to be as high as 3rd (having lost to someone who could be 2nd) but no worse
than 7th (having beaten one player in the 1st round).
You are to determine the highest and lowest possible rankings of a set of players
in the field, given the results of the tournament.
There will be multiple input instances. The input for each instance consists
of three lines. The first line will contain a positive integer n < 8, indicating
there are 2^n players in the tournament, numbered 1 through 2^n, paired in the
manner indicated above. A value of n = 0 indicates end of input. The next line
will contain the results of each round of the tournament (listed left-to-right)
starting with the 1st round. For example, the tournament above would be given
1 3 5 8 1 8 1
The final line of input for each instance will be a positive integer m followed
by integers k1, ..., km, where each ki is a player in the field.
For each ki, issue one line of output of the form:
Player ki can be ranked as high as h or as low as l.
where you supply the appropriate numbers. These lines should appear in the same
order as the ki did in the input. Output for problem instances should be separated
with a blank line.
1 3 5 8 1 8 1
2 2 5
2 3 6 7 9 11 14 15 3 6 9 15 6 9 6
4 1 15 7 6
Player 2 can be ranked as high as 2 or as low as 8.
Player 5 can be ranked as high as 3 or as low as 7.
Player 1 can be ranked as high as 4 or as low as 16.
Player 15 can be ranked as high as 3 or as low as 13.
Player 7 can be ranked as high as 2 or as low as 15.
Player 6 can be ranked as high as 1 or as low as 1.
Source: East Central North America 2002