You are given a problem of class scheduling for the computer science department. The class timings are Tuesdays, Thursdays, and Fridays. There are 5 different classes on these given days and 3 professors who are qualified for teaching these classes.

Problem constraint: Each professor can teach only one class at a time.

Classes: C1 Introduction to Artificial Intelligence: Time: 1:00 - 2:15pm C2 Operating Systems: Time: 9:00 10:15am C3 Software Engineering: Time: 10:30-11:45am C4 Database Systems: Time: 10:30 - 11:45am C5 Machine Learning: Time: 2:30 - 3:45pm Professors: Professor A: Qualified to teach Classes 1, 2, and 5. Professor B: Qualified to teach Classes 3, 4, and 5. Professor C: Qualified to teach Classes 1, 3, and 4.

Please answer these questions. a) Formulate this problem as a CSP where there is one variable per class, reporting the domains and constraints (e.g., for each class, the entry in the table should be ). Also, list binary constraints on the classes. Your constraints should be specified formally which can be implicit rather than explicit.

b) Draw the constraint graph for your problem in item 1.

c) Make sure your CSP looks nearly tree-structure. Provide a one-paragraph description of why the solution to CSP via tree-structured CSPs is preferred. Review lecture slides and videos for help.