感谢东南大学的 CoupDeGrace 同学提供本题题解。
As we know, DreamGrid is a master of planning algorithm. Recently, a new type of autonomous car appears in Gridland. With the shape of a circle, the car can move in any direction. Being interested in this car, DreamGrid decides to design a specific path planning algorithm for it. Here is the first case he wants to solve.
Consider two cars on the two-dimensional plane with the same radius of $r$. We now want to move the center of the first car from $(0, 0)$ to $(d, 0)$, where $d$ is positive. The second car, starting its move with its center located at $(2r, 0)$, can be considered as an obstacle moving towards the positive direction of the x-axis with a constant speed of $v$. Luckily, after installing a new engine, the first car can move twice as fast as the obstacle car, which means the maximum speed of the first car can be $2v$.
DreamGrid wants to know the shortest time needed to move the first car to the end point without colliding with the second car. That is to say, before arriving at the end point, the circle representing the first car can’t intersect with (but can be tangent to) the circle representing the second car.
As DreamGrid is too busy, you are asked to solve this simple problem for him. Of course, if you successfully solve this problem, you will get a brand-new autonomous car in the Gridland!