Detect cycle in directed dependency graph

You are given a directed dependency graph representing services in a system. - There are `n` services, labeled from `0` to `n - 1`. - You are given a list of directed edges `dependencies`, where each element is a pair `[a, b]` meaning **service `a` depends on service `b`** (i.e., there is a directed edge `a -> b`). Assume: - `1 <= n <= 10^5` - `0 <= a, b < n` - There may be zero or more edges. **Task:** 1. Implement a function that determines whether there is at least one cycle in this directed graph. - Return `true` if there is a cycle. - Return `false` otherwise. 2. Follow-up: Now you are given **multiple dependency arrays** instead of just one. Each array represents an additional list of edges on the same set of services. For example: - `dependencies1`, `dependencies2`, ..., `dependenciesk` Each `dependenciesi` is a list of `[a, b]` pairs as defined above. Treat the union of all these edges as a single directed graph and determine whether this combined graph contains any cycle. Describe the approach, data structures, and algorithm you would use, and analyze the time and space complexity.