Determine if chasing points will meet
Company: Disney
Role: Machine Learning Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Technical Screen
You are given **N points** in 2D, indexed `0..N-1`, forming a cycle.
- At time `t = 0`, point `i` is at coordinates `(xi, yi)`.
- All points move **simultaneously** and continuously.
- Each point moves with **constant speed** `v = 1`.
- At any time `t`, point `i` moves in the direction of the **current position** of point `(i+1) mod N` (i.e., it “chases” the next point).
### Task
Write a program that determines whether the points will **all meet at the same location at the same time**.
If they do meet, output:
1. The meeting time `T`.
2. The meeting position `(X, Y)`.
If they do **not** meet, output `NEVER`.
### Input
- Integer `N` (`2 ≤ N ≤ 200`)
- `N` lines of real numbers: `xi yi`
### Output
- Either `NEVER`, or three real numbers `T X Y`.
### Requirements / Notes
- Your numeric outputs should be within `1e-4` absolute error.
- You may use numerical simulation (time-stepping) as long as it meets the error requirement and runs efficiently.
Overview: This question evaluates understanding of pursuit curves, continuous dynamical systems, computational geometry, and numerical simulation, measuring the ability to reason about concurrent motion, convergence behavior, and numerical precision when multiple agents chase one another.