The police department in the city of Computopia has made all streets one-way. The mayor contendsthat there is still a way to drive legally from any intersection in the city to any otherintersection, but the opposition is not convinced. A computer program is needed to determinewhether the mayor is right. However, the city elections are coming up soon, and there is justenough time to run a linear-time algorithm.(a) Formulate this problem graph-theoretically, and explain why it can indeed be solved inlinear time.(b) Suppose it now turns out that the mayors original claim is false. She next claims somethingweaker: if you start driving from town hall, navigating one-way streets, then no matterwhere you reach, there is always a way to drive legally back to the town hall. Formulatethis weaker property as a graph-theoretic problem, and carefully show how it too can bechecked in linear time.