Math problem

[Ofnuts]

Looks like I made good score at nerd-sniping 

@Programmer_ceds: can't make you code to work. I have trouble relating your definition of the offset to mine (if they are the same, then there is a problem since we find different answers). For instance: 5px tiles, 2px lines, offset 6 in a 20px window should give 14 ([4,5,5]):

Code:

 123456 offset
TTTTTGGTTTTTGGTTTTTGGTTTTTGG
 [------------------]
 12345678901234567890

@ottiatuota: Nice one, not disappointed. Very interesting point of view. Can' t make you code to work exactly like mine,  possibly due to a different meaning:

This isn't an idle problem, I want to compute the width and height of this image after I have removed the red checkers lines:

   

From your PDF; the equivalent code is:

Code:

def otsize(span,tile,grid,offset):
    a=tile
    s=grid
    p=grid+tile
    w=span
    
    def k(x):
        return x-math.floor(float(x)/p)*p
    
    def h(x):
        return max(0,a-k(x))
    
    def g(x):
        return a*(1+math.floor(float(x)/p))
    
    def f(x):
        return g(x)-h(x)
    
    return f(offset+span)-f(offset)

But the result are different from mine (seem shifted by 1):

Code:

offset  0, total  15 (   [5, 5, 5]), ofn size  15, ot size  15
offset  1, total  15 (   [5, 5, 5]), ofn size  15, ot size  14
offset  2, total  14 (   [5, 5, 4]), ofn size  14, ot size  14
offset  3, total  14 ([1, 5, 5, 3]), ofn size  14, ot size  14
offset  4, total  14 ([2, 5, 5, 2]), ofn size  14, ot size  14
offset  5, total  14 ([3, 5, 5, 1]), ofn size  14, ot size  14
offset  6, total  14 (   [4, 5, 5]), ofn size  14, ot size  15

Otherwise, my code:

Code:

def ofnsize(span,tile,grid,offset):
    period=tile+grid
    whole,rest=divmod(span-offset,period)
    left=max(0,offset-grid)
    right=min(tile,span-offset-whole*period)
    return whole*tile+left+right