How do you tell whether you can finish all courses given prerequisite pairs?
PICTURE THIS: HOW TO EXPLAIN IT
Simple meaning
Build a directed graph and detect a cycle: Kahn's algorithm peels indegree-zero nodes, or DFS colors nodes gray/black.
WHY — Graphs instead of guessing?
Why interviewers care about Graphs:
question about Graphs.
trade-offs, and what you would actually do on a DSA project - not buzzwords.
Name the idea, why it exists, then one short example.
End with when you use it and one common pitfall.
STEPS — What happens step by step?
Before you speak the answer, walk the interviewer through these steps:
- 1Build a directed graph
and detect a cycle: Kahn's algorithm peels indegree-zero nodes, or DFS colors nodes gray/black.
- 2Time is O(V+E) and
space is O(V+E).
- 3If the processed count
is less than the number of courses, a cycle exists and it is impossible.
- 4Give an example
One tiny concrete case you can say aloud.
- 5Common mistake
What juniors usually get wrong.
- 6Close
When you pick this over the alternative.
EXAMPLE — See it in action
Here's a short line you can speak, broken into clear beats:
Note: Adapt this scaffold to your own project — keep it under 60–90 seconds.
Key takeaway
Build a directed graph and detect a cycle: Kahn's algorithm peels indegree-zero nodes, or DFS colors nodes gray/black. Time is O(V+E) and space is O(V+E).