USACO 2012 March Contest, Silver Division
Problem 3. Landscaping
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Problem 3: Landscaping [Brian Dean, 2012]
Farmer John is building a nicely-landscaped garden, and needs to move a
large amount of dirt in the process.
The garden consists of a sequence of N flowerbeds (1 <= N <= 100), where
flowerbed i initially contains A_i units of dirt. Farmer John would like
to re-landscape the garden so that each flowerbed i instead contains B_i
units of dirt. The A_i's and B_i's are all integers in the range 0..10.
To landscape the garden, Farmer John has several options: he can purchase
one unit of dirt and place it in a flowerbed of his choice for $X. He can
remove one unit of dirt from a flowerbed of his choice and have it shipped
away for $Y. He can also transport one unit of dirt from flowerbed i to
flowerbed j at a cost of $Z times |i-j|. Please compute the minimum total
cost for Farmer John to complete his landscaping project.
PROBLEM NAME: landscape
INPUT FORMAT:
* Line 1: Space-separated integers N, X, Y, and Z (0 <= X, Y, Z <=
1000).
* Lines 2..1+N: Line i+1 contains the space-separated integers A_i and
B_i.
SAMPLE INPUT (file landscape.in):
4 100 200 1
1 4
2 3
3 2
4 0
INPUT DETAILS:
There are 4 flowerbeds in a row, initially with 1, 2, 3, and 4 units of
dirt. Farmer John wishes to transform them so they have 4, 3, 2, and 0
units of dirt, respectively. The costs for adding, removing, and
transporting dirt are 100, 200, and 1.
OUTPUT FORMAT:
* Line 1: A single integer giving the minimum cost for Farmer John's
landscaping project.
SAMPLE OUTPUT (file landscape.out):
210
OUTPUT DETAILS:
One unit of dirt must be removed (from flowerbed #4), at a cost of 200. The
remaining dirt can be moved at a cost of 10 (3 units from flowerbed #4 to
flowerbed #1, 1 unit from flowerbed #3 to flowerbed #2).
Contest has ended. No further submissions allowed.