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The problem is:

Tommy has a square house with size N divided into cell and he want to place sensor detection devices around the house for security. Each sensor can detect up to K step count from the position it is placed. There are M positions inside the house which is pole and sensor can not detect through it. He plans to place at max 5 devices and wondering how to use a minimum number of devices to cover the whole house.

Let visualize the sample like below (= is empty cell and o is pole cell)

=====

ooo==

=====

=ooo=

=====

If he place the device (D) at position (3, 4) the device coverage will be visualized as below (the number inside each cell indicate the instance from the device)

==323

ooo12

321D1

=ooo2

====3

My question is:

Is there any optimal solution to solve this problem?

I have searched and read some article about Set Cover, Exact Cover problem but could not find out the way to implement it to solve the problem above.

Nguyễn Việt Anh
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  • Xin chiao Viet, did you try anything apart from searching for solution directly? It's better if you also mention what all you already tried. :) – www.hybriscx.com Oct 30 '19 at 08:42
  • Like I said, I have searched and read about Set cover problem. Of course, you can use brute force when N is small, but I don't think it's optimal – Nguyễn Việt Anh Oct 30 '19 at 08:47

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