Model the courses and prerequisites as a directed graph where an edge from course A to course B means A is a prerequisite for B. Then determine if the graph contains a cycle; if it does, it's impossible to complete all courses, otherwise it's possible. Use either depth-first search (DFS) with cycle detection or Kahn's algorithm for topological sorting.
Pro tip: Clarify edge direction upfront (prerequisite -> dependent) to avoid confusion, and mention that Kahn's algorithm naturally detects cycles by checking if the topological order includes all courses. Also, discuss handling disconnected graphs and potential follow-up questions like returning a valid course order.
Confirm that prerequisites are given as pairs [a, b] meaning b must be taken before a. Ask about constraints: number of courses, possible duplicate edges, self-loops, and whether the graph is guaranteed to be connected.
Represent courses as nodes and prerequisites as directed edges. Choose an adjacency list representation for efficiency, especially for sparse graphs.
Select either DFS with recursion stack (or colors) or Kahn's algorithm (BFS-based topological sort). Explain why cycle detection is equivalent to checking if all courses can be completed.
Describe the steps: for DFS, mark nodes as unvisited, visiting, visited and detect back edges; for Kahn's, compute in-degrees, use a queue, and count processed nodes. Mention that if the count equals the number of courses, no cycle exists.
State time complexity O(V+E) and space complexity O(V+E). Compare DFS vs Kahn's: DFS may be simpler to implement recursively but can hit recursion limits; Kahn's is iterative and naturally gives a topological order.
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