The core problem is basically course schedule, so I had seen it before.
Model the dependency graph as a directed graph where edges point from a service to its dependencies. Use DFS with memoization to collect all transitive dependencies of the target, then topologically sort the subgraph to produce a valid build order. For cycles, detect them during DFS and either report an error or break cycles by ignoring back edges, depending on requirements.
Pro tip: Clarify upfront whether the build order should be deterministic (e.g., alphabetical for ties) and whether cycles are considered errors or should be handled gracefully. This shows you think about real-world build systems and edge cases.
Ask if the graph is directed, if cycles are possible, and what to do if cycles exist. Confirm whether the output should include only the target and its dependencies or also unrelated services.
Perform a DFS or BFS from the target service to find all reachable nodes (dependencies). Use a visited set to avoid infinite loops in cyclic graphs.
Apply Kahn's algorithm or DFS-based topological sort on the induced subgraph of collected nodes. Ensure dependencies appear before dependents in the order.
If a cycle is detected, decide whether to throw an error, break the cycle by removing an edge, or return a partial order. Explain the trade-offs of each approach.
State time and space complexity (O(V+E)). Discuss edge cases: target not in graph, self-loop, disconnected components, and multiple valid orders.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.