DFS Cycle Detection (Directed Graph)
As a Tech Lead engineer, explain DFS Cycle Detection (Directed Graph). What problem does it solve and how would you describe it in an interview?
Answers use simple, clear English.
Quick interview answer
At Tech Lead depth: start with the problem, then mechanism, then a short example. Three-color DFS: white=unvisited, gray=in current stack, black=done.
Detailed answer
At Tech Lead depth: start with the problem, then mechanism, then a short example. Three-color DFS: white=unvisited, gray=in current stack, black=done. Back edge to gray node ⇒ cycle. Works for dependency graphs and course prerequisites. Core: Three-color DFS: white=unvisited, gray=in current stack, black=done. Back edge to gray node ⇒ cycle. Works for dependency graphs and course prerequisites. Real-time example: Build pipeline: detect circular module imports before CI runs. Pros: O(V+E); distinguishes directed vs undirected cycle logic. Cons: Recursive DFS risks stack overflow on huge graphs; use iterative + explicit stack. Common mistakes: Using two-color visited only (misses cross edges in undirected); forgetting disconnected components. Best practices: Loop all nodes as DFS roots; explain gray = active recursion path. Audience level: Tech Lead.
Full explanation
Three-color DFS: white=unvisited, gray=in current stack, black=done. Back edge to gray node ⇒ cycle. Works for dependency graphs and course prerequisites.
Real example & use case
Build pipeline: detect circular module imports before CI runs.
Pros & cons
Pros: O(V+E); distinguishes directed vs undirected cycle logic. Cons: Recursive DFS risks stack overflow on huge graphs; use iterative + explicit stack.
Common mistakes
Using two-color visited only (misses cross edges in undirected); forgetting disconnected components.
Best practices
Loop all nodes as DFS roots; explain gray = active recursion path.
Follow-up questions
- How would you test DFS Cycle Detection (Directed Graph)?
- What metrics prove DFS Cycle Detection (Directed Graph) is healthy in prod?
- How does DFS Cycle Detection (Directed Graph) change at 10× traffic?