Count People Reaching the Boundary

You are given a 1-dimensional line segment with a right boundary at position `L`. There are `N` people with initial positions `p1, p2, ..., pN`, and there is a stationary watcher at position `W`. Each person wants to move to the right. Time is first considered in discrete unit steps for a total of `T` steps. The watcher has an initial facing direction, either left or right. The watcher does not move, but it reverses direction at specified times `t1, t2, ..., tC`. During each time step: - Every person attempts to move `1` unit to the right. - If a person is currently visible to the watcher, that person cannot move during that step. - If the watcher is facing right, then any person strictly to the right of `W` is visible. - If the watcher is facing left, then any person strictly to the left of `W` is visible. - If a person is exactly at position `W`, that person is allowed to move. A person who reaches `L` is considered to have arrived at the destination. Return how many people have reached position `L` after `T` time steps. Follow-up: How would you handle the continuous-time version of the problem, where movement is continuous instead of step-based, and the watcher still changes direction only at the given switch times?