## USACO 2011 November Contest, Silver Division

## Problem 3. Tile Exchanging

Contest has ended.

**Not submitted**

Problem 3: Tile Exchanging [Ray Li]
Farmer John wants to remodel the floor of his barn using a collection of
square tiles he recently purchased from the local square mart store (which
of course, only sells square objects). Unfortunately, he didn't measure
the size of the barn properly before making his purchase, so now he needs
to exchange some of his tiles for new square tiles of different sizes.
The N square tiles previously purchased by FJ have side lengths A_1...A_N.
He would like to exchange some of these with new square tiles so that the
total sum of the areas of the his tiles is exactly M. Square mart is
currently offering a special deal: a tile of side length A_i can be
exchanged for a new tile of side length B_i for a cost of
|A_i-B_i|*|A_i-B_i| units. However, this deal only applies to
previously-purchased tiles -- FJ is not allowed to exchange a tile that he
has already obtained via exchanging some other tile (i.e., a size-3 tile
cannot be exchanged for a size-2 tile, which is then exchanged for a size-1
tile).
Please determine the minimum amount of money required to exchange tiles so
that the sum of the areas of the tiles becomes M. Output -1 if it is
impossible to obtain an area of M.
PROBLEM NAME: tilechng
INPUT FORMAT:
* Line 1: Two space-separated integers, N (1<=N<=10) and M
(1<=M<=10,000).
* Lines 2..1+N: Each line contains one of the integers A_1 through
A_N, describing the side length of an input square
(1<=A_i<=100).
SAMPLE INPUT (file tilechng.in):
3 6
3
3
1
INPUT DETAILS:
There are 3 tiles. Two are squares of side length 3, and one is a square
with side length 1. We would like to exchange these to make a total area of 6.
OUTPUT FORMAT:
* Line 1: The minimum cost of exchanging tiles to obtain M units of
total area, or -1 if this is impossible.
SAMPLE OUTPUT (file tilechng.out):
5
OUTPUT DETAILS:
Exchange one of the side-3 squares for a side-2 square, and another side-3
square for a side-1 square. This gives the desired area of 4+1+1=6 and
costs 4+1=5 units.

Contest has ended. No further submissions allowed.