Question

Suppose I am given number of lines segments in Cartesian coordinate system.Each line is given as [x0,y0] and [x1,y1].Algorithm should find a perpendicular that cross maximum number of lines.
In this example it crosses four lines:

What algorithm can do it with minimum complexity?(i would prefer c++ but some kind of pseudo code is OK too)

P.S The point to think about is when several lines start/end in the same x coordinate

Thank you.

Answer 1

1. Convert each line to a interval of [x_start,x_end] for each segment.
2. Create a datastructure that contains a flag for whether it is a start or end point, as well as the point value.
3. Sort all the points and then iterate through them incrementing a counter when you hit a start point and decrementing a counter when you hit an end point. Keep track of the maximum value.
4. Repeat with the Y values if desired.

O(n lg n) time complexity