How do you detect a cycle in a directed graph?
PICTURE THIS: STACK VS QUEUE
StackLIFOlast in, first out
QueueFIFOfirst in, first out
Simple meaning
DFS colors or recursion stack tracking.
WHY — Graphs instead of guessing?
Why interviewers care about Graphs:
This is a process
question about Graphs.
Panels listen for order,
trade-offs, and what you would actually do on a DSA project - not buzzwords.
Stay structured
Name the idea, why it exists, then one short example.
Close cleanly
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:
- 1DFS colors or recursion
stack tracking.
- 2Kahn’s algorithm also fails
to finish if a cycle exists.
- 3Undirected graphs use parent-aware
DFS or Union-Find.
- 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:
Say this line
“Kahn’s algorithm also fails to finish if a cycle exists.”
Break into beats
Kahnsalgorithmalsofailsto
Speaking order
2987408337471632900
Note: Adapt this scaffold to your own project — keep it under 60–90 seconds.
Key takeaway
DFS colors or recursion stack tracking. Kahn’s algorithm also fails to finish if a cycle exists.