How do you solve the course schedule (prerequisites) problem?

Question presented to candidate: "There are numCourses courses labelled 0 to numCourses - 1, and a list of pairs [a, b] meaning you must take course b before course a. Can you finish all the courses? If so, give me one valid order. Please code it in Python."

What a strong answer should cover:

• Model it as a directed graph with an edge b -> a for each pair, and recognise that "can finish" means "the graph has no cycle".
• Kahn's algorithm: in-degree counts, a queue of courses with no remaining prerequisites, and len(order) == numCourses as the cycle test; the same function answers both Course Schedule I and II.
• O(V + E) time and space, compared with the O(V * (V + E)) rescan brute force.
• The DFS three-colour alternative, and the follow-up of minimum semesters via level-by-level Kahn.
• Python specifics: collections.deque for the queue, [[] for _ in range(n)] (not [[]] * n) for adjacency, all(...) in the brute force, and the 1000-frame default recursion limit if you choose DFS.

Clarifying questions expected:

• "Does [a, b] mean b comes before a?"
• "Do you want just true/false, or an order — and is any valid order acceptable?"
• "Can pairs repeat, or can a course list itself?"

Code / implementation expected: Yes — findOrder (and canFinish on top of it) in Python, using Kahn's algorithm.