Maximum possible number of rectangles that can be crossed with a single straight line

Question

I found this challenge problem which states the following :

Suppose that there are n rectangles on the XY plane. Write a program to calculate the maxi

Answer 1

How about the following algorithm:

RES = 0 // maximum number of intersections
CORNERS[] // all rectangles corners listed as (x, y) points

for A in CORNERS
    for B in CORNERS // optimization: starting from corner next to A
        RES = max(RES, CountIntersectionsWithLine(A.x, A.y, B.x, B.y))

return RES

In other words, start drawing lines from each rectangle corner to each other rectangle corner and find the maximum number of intersections. As suggested by @weston, we can avoid calculating same line twice by starting inner loop from the corner next to A.