Minimum Time to Produce a Goal Dataset in a Data Pipeline (Parallel Tasks)

Problem: Minimum Time to Produce a Goal Dataset in a Parallel Data Pipeline You are given a set of data processing tasks that form a data pipeline. Each task: Consumes one or more input datasets Produces a single output dataset Takes a fixed amount of time to execute Rules: A task can start only after all its input datasets are available. Multiple tasks can run in parallel (unlimited parallelism). Any dataset that is not produced by any task is considered available at time 0 (a source dataset). Given goal_dataset, compute the minimum time required to produce it. Input tasks: a list of tasks, each defined as: ([input_datasets], output_dataset, time_cost) goal_dataset: a string dataset id Output Return an integer: the minimum time to produce goal_dataset. Example tasks = [ (["d0", "d1", "d2"], "d3", 30), (["d1", "d2"], "d4", 15), (["d2", "d3"], "d5", 100), (["d0", "d3", "d4"], "d6", 60) ] goal_dataset = "d6" Expected output: 90 Constraints (assume for interview) 1 <= len(tasks) <= 2e5 Total number of input edges <= 2e5 time_cost is a positive integer Dataset ids are strings Assume each output dataset is produced by at most one task; if cycles exist, you may define behavior (e.g., unreachable/error). Example Input 4 d0 d1 d2 -> d3 30 d1 d2 -> d4 15 d2 d3 -> d5 100 d0 d3 d4 -> d6 60 d6 Output 90