Suppose a CS curriculum consists of n courses, all of them mandatory. The prerequisite graph G has a node for each course, and an edge from course v to course w if and only if v is a prerequisite for w. Find an algorithm that works directly with this graph representation, and computes the minimum number of semesters necessary to complete the curriculum (assume that a student can take any number of courses in one semester). The running time of your algorithm should be linear; make sure to state (and briefly explain) the running time of your algorithm.

(a) Describe an algorithm to determine the minimum number of semesters to complete the curriculum.

(b) You want to finish each course as early as possible. What is the number of courses to take in the first semester to do that, i.e., what is the maximum number of courses you can take in the first semester?