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                           GOLD PROBLEMS
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                  Three problems numbered 1 through 3
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Problem 1: Jersey Politics [Coaches, 2004]

In the newest census of Jersey Cows and Holstein Cows, Wisconsin
cows have earned three stalls in the Barn of Representatives. The
Jersey Cows currently control the state's redistricting committee.
They want to partition the state into three equally sized voting
districts such that the Jersey Cows are guaranteed to win elections
in at least two of the districts.

Wisconsin has 3*K (1 <= K <= 60) cities of 1,000 cows, numbered
1..3*K, each with a known number (range: 0..1,000) of Jersey Cows.
Find a way to partition the state into three districts, each with
K cities, such that the Jersey Cows have the majority percentage
in at least two of districts.

All supplied input datasets are solvable.

PROBLEM NAME: jpol

INPUT FORMAT:

* Line 1: A single integer, K

* Lines 2..3*K+1: One integer per line, the number of cows in each
        city that are Jersey Cows.  Line i+1 contains city i's cow
        census.

SAMPLE INPUT (file jpol.in):

2
510
500
500
670
400
310

OUTPUT FORMAT:

* Lines 1..K: K lines that are the city numbers in district one, one
        per line

* Lines K+1..2K: K lines that are the city numbers in district two,
        one per line

* Lines 2K+1..3K: K lines that are the city numbers in district three,
        one per line

SAMPLE OUTPUT (file jpol.out):

1
2
3
6
5
4

OUTPUT DETAILS:

Other solutions might be possible.  Note that "2 3" would NOT be a
district won by the Jerseys, as they would be exactly half of the
cows.

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Problem 2: Secret Milking Machine [Vladimir Novakovski, 2003]

Farmer John is constructing a new milking machine and wishes to
keep it secret as long as possible. He has hidden in it deep within
his farm and needs to be able to get to the machine without being
detected.  He must make a total of T (1 <= T <= 200) trips to the
machine during its construction. He has a secret tunnel that he
uses only for the return trips.

The farm comprises N (2 <= N <= 200) landmarks (numbered 1..N)
connected by P (1 <= P <= 40,000) bidirectional trails (numbered
1..P) and with a positive length that does not exceed 1,000,000.
Multiple trails might join a pair of landmarks.

To minimize his chances of detection, FJ knows he cannot use any
trail on the farm more than once and that he should try to use the
shortest trails.

Help FJ get from the barn (landmark 1) to the secret milking machine
(landmark N) a total of T times.  Find the minimum possible length
of the longest single trail that he will have to use, subject to the
constraint that he use no trail more than once. (Note well: The goal
is to minimize the length of the longest trail, not the sum of the
trail lengths.)

It is guaranteed that FJ can make all T trips without reusing a trail.

PROBLEM NAME: secret

INPUT FORMAT:

* Line 1: Three space-separated integers: N, P, and T

* Lines 2..P+1: Line i+1 contains three space-separated integers, A_i,
        B_i, and L_i, indicating that a trail connects landmark A_i to
        landmark B_i with length L_i.

SAMPLE INPUT (file secret.in):

7 9 2
1 2 2
2 3 5
3 7 5
1 4 1
4 3 1
4 5 7
5 7 1
1 6 3
6 7 3

OUTPUT FORMAT:

* Line 1: A single integer that is the minimum possible length of the
        longest segment of Farmer John's route.

SAMPLE OUTPUT (file secret.out):

5

OUTPUT DETAILS:

Farmer John can travel trails 1 - 2 - 3 - 7 and 1 - 6 - 7.  None of
the trails travelled exceeds 5 units in length.  It is impossible
for Farmer John to travel from 1 to 7 twice without using at least
one trail of length 5.

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Problem 3: Aggressive cows [Dutch Championships, via Jan Kuipers, 2004]

Farmer John has built a new long barn, with N (2 <= N <= 100,000)
stalls. The stalls are located along a straight line at positions
x1,...,xN (0 <= xi <= 1,000,000,000).

His C (2 <= C <= N) cows don't like this barn layout and become
aggressive towards each other once put into a stall. To prevent the
cows from hurting each other, FJ want to assign the cows to the
stalls, such that the minimum distance between any two of them is
as large as possible.  What is the largest minimum distance?

PROBLEM NAME: aggr

INPUT FORMAT:

* Line 1: Two space-separated integers: N and C

* Lines 2..N+1: Line i+1 contains an integer stall location, xi

SAMPLE INPUT (file aggr.in):

5 3
1
2
8
4
9

OUTPUT FORMAT:

* Line 1: One integer: the largest minimum distance

SAMPLE OUTPUT (file aggr.out):

3

OUTPUT DETAILS:

FJ can put his 3 cows in the stalls at positions 1, 4 and 8, resulting in 
a minimum distance of 3.

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