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GREEN PROBLEMS
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Four problems numbered 1 through 4
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PROBLEM 1: Cow Exhibition [Brian Jacokes, 2003]
"Fat and docile, big and dumb, they look so stupid, they aren’t much
fun…"
– Cows with Guns by Dana Lyons
The cows want to prove to the public that they are both smart and fun.
In order to do this, Bessie has organized an exhibition that will be put
on by the cows. She has given each of the N (1 <= N <= 100) cows a
thorough interview and determined two values for each cow: the smartness
Si (-1000 <= Si <= 1000) of the cow and the funness Fi (-1000 <= Fi <=
1000) of the cow.
Bessie must choose which cows she wants to bring to her exhibition. She
believes that the total smartness TS of the group is the sum of the Si’s
and, likewise, the total funness TF of the group is the sum of the Fi’s.
Bessie wants to maximize the sum of TS and TF, but she also wants both of
these values to be non-negative (since she must also show that the cows
are well-rounded; a negative TS or TF would ruin this). Help Bessie
maximize the sum of TS and TF without letting either of these values
become negative.
PROBLEM NAME: smrtfun
INPUT FORMAT:
* Line 1: A single integer N, the number of cows
* Lines 2..N+1: Two space-separated integers Si and Fi, respectively
the smartness and funness for each cow.
SAMPLE INPUT (file smrtfun.in):
5
-5 7
8 -6
6 -3
2 1
-8 -5
OUTPUT FORMAT:
* Line 1: One integer: the optimal sum of TS and TF such that both TS
and TF are non-negative. If no subset of the cows has
non-negative TS and non- negative TF, print 0.
SAMPLE OUTPUT (file smrtfun.out):
8
OUTPUT DETAILS:
Bessie chooses cows 1, 3, and 4, giving values of TS = -5+6+2 = 3 and TF
= 7-3+1 = 5, so 3+5 = 8. Note that adding cow 2 would improve the value
of TS+TF to 10, but the new value of TF would be negative, so it is not
allowed.
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PROBLEM 2: Milking Grid [Tom Widland, 2003]
Every morning when they are milked, the Farmer John’s cows form a
rectangular grid that is R (1 <= R <= 10,000) rows by C (1 <= C <=
75) columns. As we all know, Farmer John is quite the expert on cow
behavior, and is currently writing a book about feeding behavior in
cows. He notices that if each cow is labeled with an uppercase letter
indicating its breed, the two-dimensional pattern formed by his cows
during milking sometimes seems to be made from smaller repeating
rectangular patterns.
Help FJ find the rectangular unit of smallest area that can be
repetitively tiled to make up the entire milking grid. Note that the
dimensions of the small rectangular unit do not necessarily need to
divide evenly the dimensions of the entire milking grid, as indicated
in the sample input below.
PROBLEM NAME: mgrid
INPUT FORMAT:
* Line 1: Two space-separated integers: R and C
* Lines 2..R+1: The grid that the cows form, with an uppercase letter
denoting each cow’s breed. Each of the R input lines has C
characters with no space or other intervening character.
SAMPLE INPUT (file mgrid.in):
2 5
ABABA
ABABA
OUTPUT FORMAT:
* Line 1: The area of the smallest unit from which the grid is formed
SAMPLE OUTPUT (file mgrid.out):
2
OUTPUT DETAILS:
The entire milking grid can be constructed from repetitions of the
pattern ‘AB’.
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PROBLEM 3: Popular Cows [Brian Dean, 2003]
Every cow’s dream is to become the most popular cow in the herd. In a
herd of N (1 <= N <= 10,000) cows, you are given up to M (1 <= M <=
50,000) ordered pairs of the form (A, B) that tell you that cow A thinks
that cow B is popular. Since popularity is transitive, if A thinks B is
popular and B thinks C is popular, then A will also think that C is
popular, even if this is not explicitly specified by an ordered pair in
the input. Your task is to compute the number of cows that are
considered popular by every other cow.
PROBLEM NAME: popular
INPUT FORMAT:
* Line 1: Two space-separated integers, N and M
* Lines 2..1+M: Two space-separated numbers A and B, meaning that A
thinks B is popular.
SAMPLE INPUT (file popular.in):
3 3
1 2
2 1
2 3
OUTPUT FORMAT:
* Line 1: A single integer that is the number of cows who are
considered popular by every other cow.
SAMPLE OUTPUT (file popular.out):
1
OUTPUT DETAILS:
Cow 3 is the only cow of high popularity.
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PROBLEM 4: Beauty Contest [Quynh Tran, 2003]
Bessie, Farmer John’s prize cow, has just won first place in a bovine
beauty contest, earning the title ‘Miss Cow World’. As a result, Bessie
will make a tour of N (2 <= N <= 50,000) farms around the world in order
to spread goodwill between farmers and their cows. For simplicity, the
world will be represented as a two-dimensional plane, where each farm is
located at a pair of integer coordinates (x,y), each having a value in
the range -10,000 … 10,000. No two farms share the same pair of
coordinates.
Even though Bessie travels directly in a straight line between pairs of
farms, the distance between some farms can be quite large, so she wants to
bring a suitcase full of hay with her so she has enough food to eat on
each leg of her journey. Since Bessie refills her suitcase at every farm
she visits, she wants to determine the maximum possible distance she
might need to travel so she knows the size of suitcase she must bring.
Help Bessie by computing the maximum distance among all pairs of farms.
PROBLEM NAME: msworld
INPUT FORMAT:
* Line 1: A single integer, N
* Lines 2..N+1: Two space-separated integers x and y specifying
coordinate of each farm
SAMPLE INPUT (file msworld.in):
4
0 0
0 1
1 1
1 0
OUTPUT FORMAT:
* Line 1: A single integer that is the squared distance between the
pair of farms that are farthest apart from each other.
SAMPLE OUTPUT (file msworld.out):
2
OUTPUT DETAILS:
Farm 1 (0, 0) and farm 3 (1, 1) have the longest distance (square root of
2)
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