## USACO 2014 January Contest, Gold

## Problem 3. Ski Course Rating

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Problem 3: Ski Course Rating [William Hu and Brian Dean, 2014]
The cross-country skiing course at the winter Moolympics is described by an
M x N grid of elevations (1 <= M,N <= 500), each elevation being in the
range 0 .. 1,000,000,000.
Some of the cells in this grid are designated as starting points for the
course. The organizers of the Moolympics want to assign a difficulty
rating to each starting point. The difficulty level of a starting point P
should be the minimum possible value of D such that a cow can successfully
reach at least T total cells of the grid (1 <= T <= MN), if she starts at P
and can only move from cell to adjacent cell if the absolute difference in
elevation between the cells is at most D. Two cells are adjacent if one is
directly north, south, east, or west of the other.
Please help the organizers compute the difficulty rating for each starting
point.
PROBLEM NAME: skilevel
INPUT FORMAT:
* Line 1: The integers M, N, and T.
* Lines 2..1+M: Each of these M lines contains N integer elevations.
* Lines 2+M..1+2M: Each of these M lines contains N values that are
either 0 or 1, with 1 indicating a cell that is a starting
point.
SAMPLE INPUT (file skilevel.in):
3 5 10
20 21 18 99 5
19 22 20 16 17
18 17 40 60 80
1 0 0 0 0
0 0 0 0 0
0 0 0 0 1
INPUT DETAILS:
The ski course is described by a 3 x 5 grid of elevations. The upper-left
and lower-right cells are designated as starting points. From each
starting point, we must be able to reach at least 10 cells.
OUTPUT FORMAT:
* Line 1: The sum of difficulty ratings of all starting points (note
that this may not fit into a 32-bit integer, even though
individual difficulty ratings will).
SAMPLE OUTPUT (file skilevel.out):
24
OUTPUT DETAILS:
The difficulty rating of the upper-left starting point is 4, and for the
lower-right it is 20.

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