Task Scheduler

You're given a set of tasks. Each task has a string name, an integer duration, and a list of names it depends on. The Scheduler class already stores them, checks that dependency names are known and that no two tasks directly reference each other in a 2-cycle, and exposes two helpers worth remembering. One helper returns every task that's currently ready to run given a set of completed tasks; call this the ready-task helper. The other returns the earliest moment a given task could start, given a map of when each of its dependencies finished; call this the earliest-start helper. You implement two methods on the Optimizer.

The first method returns a valid linear order (a topological sort of the dependency graph). Every dependency must appear before every task that depends on it. The second method returns a parallel schedule across a fixed number of workers, giving you a total makespan plus a timeline that says when each task runs.

The test suite has three graphs. The first two are small and well-behaved. The third is a critical-path graph where five tasks form a long chain that dominates the minimum possible makespan, plus four long-running independent "scans" that look tempting to schedule early but have nothing to do with the chain.

The order question has a standard answer in topological sort. In a dependency graph, a topological order is any sequence where every task comes after all of its dependencies. There are typically many valid orders; you just need one.