Suppose a CS program consists of $n$ courses. The prerequisite graph $G$ has a vertex for each

course, and an edge from course $v$ to course $w$ if and only if $v$ is a prerequisite for $w.$ Design

a linear$-$time algorithm that works directly with this graph representation and computes the

minimum number of semesters necessary to complete the program, assuming that a student

can take any number of courses in one semester.

Be sure to prove the correctness of your algorithm and its running time.