Number of line segment intersection ?

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You are given N points in a plane (numbered 1 through N); for each valid i, the i-th point is Pi=(i,Ai). There are N−1 line segments between them (numbered 1 through N−1); for each valid i, the i-th line segment is formed by connecting the points Pi and Pi+1.

You are given Q horizontal line segments . Each query horizontal line segment is denoted by two points, from a point (x1,y) to a point (x2,y) (where it stops and does not propagate further). For Every Horizontal line segment, you have to find the number of line segments from those (N-1 line segments) it collides with on the way.

So this is the problem where :
2<=N<= 100000
!<=Q<= 100000

Can anyone teach me what approach will be best and most effective in terms of time complexity?

What I have tried:

I dont know how to approach it .I thought kd tree may help.But I dont know how to use it for line segment.

Posted 14-Mar-20 22:41pm

Member 14773225

Updated 14-Mar-20 22:57pm

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Patrice T · Answer 1 · 2020-03-14T22:57:00

Quote:
Can anyone teach me what approach will be best and most effective in terms of time complexity?

The approach is brut force, test very single segment against every horizontal segment.
Apply the KISS method a list of N-1 segments, a list of Q horizontal segments, nothing fancy.
Complexity is (N-1)*Q

Quote:
I thought kd tree may help.

To use a method with this or with that, you need to have an idea of how it will help before.
When you search the correct algorithm to solve a problem:
- first choose brute force and evaluate the workload.
- Search an improves method and evaluate new workload, keep if workload reduction.
- try to improve further with another method or refinement.