Classic DFS with a recursion stack to track back edges.
Clarify the problem constraints (e.g., graph size, whether the graph is mutable) and then propose a cycle detection algorithm such as DFS with recursion stack or Kahn's topological sort. Explain the algorithm step-by-step, analyze time and space complexity, and discuss edge cases like self-loops and disconnected components.
Pro tip: Mention that Kahn's algorithm can also provide a topological order if no cycle exists, which is useful for dependency resolution. Also, note that early termination upon finding a back edge can save time in practice.
Ask about graph size, whether it's mutable, and if additional information (like topological order) is needed. This shows you consider practical aspects before coding.
Select either DFS with recursion stack or Kahn's algorithm based on constraints. Explain why your choice is suitable (e.g., DFS is simpler for sparse graphs, Kahn's avoids recursion depth issues).
Describe the steps: for DFS, track visited and recursion stack; for Kahn's, compute in-degrees and process nodes with zero in-degree. Highlight how cycles are detected.
State time and space complexity (O(V+E) for both). Discuss edge cases: empty graph, self-loops, disconnected components, and large graphs.
Mention iterative DFS to avoid stack overflow, early termination, and that Kahn's can return a topological order if no cycle. Compare trade-offs between approaches.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Treat the union of all dependency arrays as a single directed graph and detect cycles using DFS with a recursion stack or Kahn's topological sort. Clarify that duplicate edges are harmless and can be ignored, then analyze complexity in terms of total vertices and total edges across all arrays.
Pro tip: Mention that you would deduplicate edges or use a visited set to avoid redundant work, and note that Kahn's algorithm can also produce a valid build order if no cycle exists—showing you think beyond just detection.
Confirm that each dependency array represents directed edges (e.g., A depends on B means B -> A or A -> B, depending on convention). Define V as the set of unique services and E as the union of all edges across arrays.
Select either DFS with three colors (white/gray/black) or Kahn's topological sort. Explain why both work: DFS detects back edges, while Kahn's detects cycles if not all nodes are processed.
Iterate through all arrays, adding edges to an adjacency list. Use a set per node or a global set to deduplicate edges, ensuring O(V + E) space where E is the number of unique edges.
Execute the chosen algorithm. State time complexity O(V + E) and space O(V + E), where E is the total unique edges across all arrays. Mention that if arrays are large with many duplicates, deduplication keeps E bounded by V^2.
Compare DFS vs Kahn's: DFS is simpler for pure detection, Kahn's gives topological order and can be more intuitive for dependency resolution. Address edge cases: empty arrays, self-loops, disconnected components.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.