$(25$ points$)$ You are a city planner working for a metropolitan area with a complex road

network. The city has recently expanded, and there is a need to establish a centralized

emergency service station $($such as a fire station, hospital, or police station$)$ that can be

quickly accessed from any intersection in the city.

The city has a mix of one$-$way and two$-$way streets, all of equal length. To ensure that

emergency response times are minimized, you need to identify a strategic location for this

emergency service station. Write an algorithm to determine if there exists an intersection as

emergency service station in the city that can be reached from every other intersection, or to

conclude that no such intersection exists.