I coded for 10 minutes brute force which got TL on test 4.. any ideas about the "good" algo ?

Surely! std::set 4ever!

Haha :) Some more hints ;)

You can implement stuff, described in Cormen, easily, using set. That's what I was trying to say.
Ilya Razenshteyn.

There is obvious "slide line" algo, that can be applied in O(NlogN). But there is a little problem here: perpendicular to ox line segments...

It's not problem! I don't exam this case and got AC.

Can you explain a little more about this algo ?

This isn't problem too. Just rotate all points by the constant angle.

const
  angle=pi/60;
var
  x,y,buf1,buf2:real;
begin
...
  Buf1:=x;
  Buf2:=y;
  x:=Buf1*cos(angle)-Buf2*sin(angle);
  y:=Buf1*sin(angle)+Buf2*cos(angle);

Edited by author 01.04.2007 16:14

I solved for me the little problem of vertical segments by
applying affine matrix
[2 3]
[5 -7]
or any other to given coordinates.
As result algo from Cormen can be taken without any changes.

Edited by author 13.07.2007 17:09

As far as me, I used some my heuristics with vertical segments:
First, when reading points i makred point with lesser x cordinate as enter point.
I sorted points by X, and if X are eual then sorted by enter mark.
This assumes then enterpoint will be before exitpoint of segment in set.

Vertical segments are easy to treat. Just sort X ascendingly and for equal X sort Y ascendingly. When you add vertical segment, consider its topmost Y coordinate during comparisons, and when you add some other segment, assume equality when its scan-line ordinate is compared to that one of vertical segment in the set.

Such behavior is identical to the one we'd apply to the segments set after rotating it for small enough angle. Another way to see that - apply skew affine transform

x2 = x+y*1e-6
y2 = y

and see how formerly vertical segments are handled in this case.

Edited by author 30.08.2008 04:52