Bomb dropping algorithm

Question

I have an n x m matrix consisting of non-negative integers. For example:

2 3 4 7 1
1 5 2 6 2
4 3 4 2 1
2 1 2 4 1
3 1 3 4 1
2 1 4 3 2
6 9 1 6 4
         


        

Answer 1

To minimize the number of bombs, we have to maximize effect of every bomb. To achive this, on every step we have to select the best target. For each point summing it and it's eight neighbours - could be used as an efficiency quantity of bombing this point. This will provide close to optimal sequence of bombs.

UPD: We should also take number of zeros into account, becouse bombin them is inefficiently. In fact the problem is to minimize number of hitted zeros. But we can not know how any step gets us closer to this aim. I agree with idea that the problem is NP-complete. I sugest a greedy approach, which will give an answer close to real.