Lessons from Course Schedule II

What we learned:

$1.$ Prerequisite problems are graph problems. Each dependency $[a, b]$ ("$b$ before $a$") becomes a directed edge $b \to a$.

$2.$ Topological sort finds valid orderings. If we can process all nodes, we have a valid schedule.

$3.$ Cycle detection is built-in. If Kahn's algorithm can't process all nodes, there's a cycle. Return empty.

$4.$ In-degree tracks "remaining prerequisites." When in-degree hits $0$, the course is ready to take.

Pattern recognition: Any problem asking "can you order X given dependencies?" or "find a valid sequence respecting constraints" is likely a topological sort problem.