Classic cycle detection in a directed graph.
Model the jobs and dependencies as a directed graph where an edge from A to B means job A must be completed before job B. Then, determine if the graph is a Directed Acyclic Graph (DAG) by attempting a topological sort using Kahn's algorithm (BFS) or DFS cycle detection. If a topological ordering exists, all jobs can be completed; otherwise, a cycle prevents completion.
Pro tip: Clarify edge direction upfront (e.g., 'dependency → dependent') to avoid confusion, and mention that this problem is equivalent to cycle detection in a directed graph. Also, discuss how you would handle large inputs by using iterative BFS instead of recursive DFS to avoid stack overflow.
Confirm the input format and define the graph: each job is a node, and a dependency is a directed edge from the prerequisite job to the dependent job. Ask if there can be multiple dependencies or if the graph is connected.
Select either Kahn's algorithm (BFS-based topological sort) or DFS-based cycle detection. Explain that both run in O(V+E) time and O(V+E) space.
For Kahn's: compute in-degrees, enqueue nodes with in-degree 0, process until queue empty, and count processed nodes. For DFS: track visited and recursion stack to detect back edges.
If all nodes are processed (Kahn's) or no back edge is found (DFS), return true; otherwise, return false. Explain that a cycle indicates a circular dependency, making completion impossible.
State time and space complexity, and discuss edge cases: empty list, single job, self-loop, disconnected components, and duplicate edges.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.