I started with BFS which felt right, but I kept second-guessing the direction of the edges.
Model the services as a directed graph where an edge from A to B means B depends on A. Then perform a traversal (BFS/DFS) starting from the set of shut-down services to find all reachable nodes, which are the transitively affected services.
Pro tip: Clarify the direction of dependencies early: the input maps a service to its dependents, so traversal should follow those edges. Also mention that since the graph is acyclic, you don't need to handle cycles, but you could still use a visited set to avoid redundant work.
Confirm the input format: a hashmap where key is a service and value is a list of services that depend on it. Also confirm that the set of shut-down services is given, and we need to find all services that are transitively affected (i.e., depend on any shut-down service).
Treat each service as a node. For each key-value pair, add directed edges from the key to each service in its value list, indicating that the value service depends on the key service.
Use BFS or DFS to traverse the graph starting from all shut-down services. Since the graph is acyclic, either works; BFS might be more intuitive for level-by-level propagation.
Initialize a queue with the shut-down services and a visited set. While traversing, for each service, add its dependents (from the hashmap) to the queue if not visited, and mark them as affected. Exclude the initially shut-down services from the final affected set if they are not to be counted.
Discuss time complexity O(V+E) where V is number of services and E is number of dependency edges. Mention edge cases: shut-down service not in map, empty input, multiple shut-down services, and services with no dependents.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.