Fully cover a rectangle with minimum amount of fixed radius circles

Question

I\'ve had this problem for a few years. It was on an informatics contest in my town a while back. I failed to solve it, and my teacher failed to solve it. I haven\'t met anyone

Answer 1

According my calculations the right answer is:

D=2*R; X >= 2*D, Y >= 2*D,
N = ceil(X/D) + ceil(Y/D) + 2*ceil(X/D)*ceil(Y/D)

In particular case if the remainder for X/D and Y/D equal to 0, then

N = (X + Y + X*Y/R)/D

Case 1: R = 1, X = 2, Y = 2, then  N = 4

Case 2: R = 1, X = 4, Y = 6, then  N = 17

Case 3: R = 1, X = 5, Y = 7, then  N = 31

Hope it helps.