Question $3$:$20$ points

The Computer Science program at Drexel University has a very complex course structure. As

you already know, certain courses are prerequisites for others. For example, you cannot take

CS$260$ before you take CS$265$ as the latter is a prerequisite for the former. For some reason, the

department has called upon you to help them figure out certain intricacies about the structure

of the program they themselves designed.

$($a$)[10$ points$]$ Is there any sequence of course that is not possible to take due to its, possibly,

unreasonable prerequisite requirements? Specify a graph algorithm, in plain English bullet

points, to answer this question by considering the following questions.

What will be the input to your algorithm? What will be the nodes and edges of your

graph?

How do you determine whether such an forbidden sequence exists?

What is the time complexity of your algorithm?

$($b$)[10$ points$]$ Assuming that a forbidden sequence of the form mentioned in part $($a$)$ doesn't

exist, specify an algorithm, in plain English bullet points, that will output a permissible

sequence of courses for a student to follow. Also, analyse your algorithm's time complexity.