Job Scheduling with Dependencies

You are given a set of jobs, where each job is represented by a unique identifier, a positive integer duration, and a list of dependencies. Each dependency of a job specifies another job that must complete before the current job can start. Assume that there are unlimited processing resources so that any jobs whose dependencies have been satisfied can run concurrently.

Your task is to design and implement an algorithm that computes a schedule for these jobs that minimizes the overall completion time. The schedule should assign a start time and finish time to each job, ensuring that:

• A job does not start until all jobs it depends on have finished.
• Jobs that are independent (or whose dependencies have been met) can run in parallel.

If it is impossible to schedule the jobs (for example, due to cyclic dependencies), your solution should detect this and report that scheduling is impossible.

Input:

• A list of jobs, where each job includes:
  • A unique identifier (e.g., a string or an integer).
  • A positive integer representing its duration.
  • A list of zero or more identifiers representing the jobs it depends on.

Output:

• If scheduling is possible: a mapping (or list) that for each job provides its computed start time and finish time such that the overall completion time (i.e., the maximum finish time among all jobs) is minimized.
• If scheduling is not possible: an indication that the input contains cycles and the schedule cannot be computed.

Implement your solution in the programming language of your choice. The focus is on correctness and efficiency in computing the optimal schedule given the dependency constraints.

Remember, you are not required to handle resource limitations besides dependency management.