Find Affected Services After Shutdown

You are given a set of services and their dependency relationships. The input is a hash map where each key is a service name, and the value is a list of services that directly depend on it. For example, if `dependencies["Auth"] = ["Checkout", "Profile"]`, then shutting down `Auth` will directly affect `Checkout` and `Profile`. Given: - `dependencies: Map<String, List<String>>` - `stopped: Set<String>` representing the services that are intentionally taken offline Return the set of all services that will be affected by the shutdowns, either directly or transitively. Include the initially stopped services in the result. Assumptions: - The dependency graph is valid. - There are no cycles. - You may choose any reasonable function signature. - The goal is to design an efficient algorithm. Example: ```text dependencies = { "A": ["B", "C"], "B": ["D"], "C": ["E"], "D": [], "E": [] } stopped = {"A"} ``` Expected output: ```text {"A", "B", "C", "D", "E"} ```