Compute Earliest Completion Times

You are given n tasks numbered from 0 to n - 1. Each task i has a positive duration duration[i].

You are also given a list of prerequisite relationships prerequisites, where [a, b] means task a must be fully completed before task b can start.

Assume there are unlimited workers, so any number of tasks may run in parallel as long as their prerequisites are satisfied.

Implement a function that returns:

• the earliest completion time for every task, and
• the minimum total time required to complete all tasks.

If the prerequisite graph contains a cycle, return an error or a special value indicating that the schedule is impossible.

Example:

n = 4
duration = [3, 2, 4, 1]
prerequisites = [[0, 2], [1, 2], [2, 3]]

Task 0 finishes at time 3.
Task 1 finishes at time 2.
Task 2 can start after both 0 and 1 finish, so it starts at time 3 and finishes at time 7.
Task 3 starts at time 7 and finishes at time 8.

Return earliestFinish = [3, 2, 7, 8], totalTime = 8.

Compute Earliest Completion Times

Constraints

• 0 <= n <= 200000
• len(duration) == n
• 1 <= duration[i] <= 10^9 for each valid i
• 0 <= len(prerequisites) <= 200000
• Each prerequisite is a pair [a, b] with 0 <= a, b < n

Hints

1. A valid schedule exists only if the prerequisite graph is a DAG. Think about using topological sorting to process tasks in dependency order.
2. For each task, track the maximum completion time among all of its prerequisites. Its own earliest finish is that value plus its duration.