1. Datacenter Cooling
We have some rooms in our datacenter, and we need to connect them all with a
single cooling duct.
Here are the rules:
- The datacenter is represented by a 2D grid.
- Rooms we own are represented by a 0.
- Rooms we do not own are represented by a 1.
- The duct has to start at the air intake valve, which is represented by
a 2.
- The duct has to end at the air conditioner, which is represented by a
3.
- The duct cannot go in multiple directions out of the intake or the AC -
they must be the two endpoints of the duct.
- The duct must pass through each room exactly once.
- The duct cannot pass through rooms we do not own.
- The duct can connect between rooms horizontally or vertically but not
diagonally.
Here is an example datacenter:
2 0 0 0
0 0 0 0
0 0 3 1
There are two possible ways to run the duct here:
2--0--0--0
|
0--0--0--0
|
0--0--3 1
or
2 0--0--0
| | |
0 0 0--0
| | |
0--0 3 1
Write a program to compute the number of possible ways to run the duct. For
the above example, the correct answer is 2.
Input format:
Your program should read from stdin. The input will be a series of integers
separated by whitespace.
The first two integers will be W and H, with width and height of the
datacenter. These will be followed by W*H more integers, specifying the 2D
grid representing the datacenter.
Output format:
Your program should write a single integer out to stdout: the number of
possible ways to run the duct.
See how fast you can make it.
Our best solution (written in C) can solve the following test case in under
5 seconds on a 2.4GHz Pentium 4, but it's pretty good if you can get to
within 1-2 orders of magnitude of that.
7 8
2 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
3 0 0 0 0 1 1
--
R@$!-!
"DoN'T LimIt Ur cHaLlEngeS, ChAlLenGe uR LImItS."
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