## USACO 2012 March Contest, Gold Division

## Problem 3. Cows in a Skyscraper

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Problem 3: Cows in a Skyscraper [Mark Gordon, Neal Wu, Fatih Gelgi, 2012]
A little known fact about Bessie and friends is that they love stair
climbing races. A better known fact is that cows really don't like going
down stairs. So after the cows finish racing to the top of their favorite
skyscraper, they had a problem. Refusing to climb back down using
the stairs, the cows are forced to use the elevator in order to get back to
the ground floor.
The elevator has a maximum weight capacity of W (1 <= W <= 100,000,000)
pounds and cow i weighs C_i (1 <= C_i <= W) pounds. Please help Bessie
figure out how to get all the N (1 <= N <= 18) of the cows to the ground
floor using the least number of elevator rides. The sum of the weights of
the cows on each elevator ride must be no larger than W.
PROBLEM NAME: skyscraper
INPUT FORMAT:
* Line 1: N and W separated by a space.
* Lines 2..1+N: Line i+1 contains the integer C_i, giving the weight
of one of the cows.
SAMPLE INPUT (file skyscraper.in):
4 10
5
6
3
7
INPUT DETAILS:
There are four cows weighing 5, 6, 3, and 7 pounds. The elevator has a
maximum weight capacity of 10 pounds.
OUTPUT FORMAT:
* Line 1: A single integer, R, indicating the minimum number of
elevator rides needed.
* Lines 2..1+R: Each line describes the set of cows taking
one of the R trips down the elevator. Each line starts with
an integer giving the number of cows in the set, followed by
the indices of the individual cows in the set.
SAMPLE OUTPUT (file skyscraper.out):
3
2 1 3
1 2
1 4
OUTPUT DETAILS:
We can put the cow weighing 3 on the same elevator as any other cow but the
other three cows are too heavy to be combined. For the solution above,
elevator ride 1 involves cow #1 and #3, elevator ride 2 involves cow #2,
and elevator ride 3 involves cow #4. Several other solutions are possible
for this input.

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