Task Scheduler

You are given a collection of tasks represented as nodes in a directed acyclic graph (DAG). Each task has:

• A unique identifier
• A processing time (a positive integer representing how long it takes to complete)
• A list of prerequisite task identifiers (tasks that must be completed before this task can start)

In addition, you are provided with an integer k representing the number of available workers. Each worker can perform only one task at a time. Time advances in discrete units, and a task can only be started at the beginning of a time unit if all its prerequisites have been completed. Multiple tasks may be processed concurrently if enough workers are available.

Your goal is to determine the minimum total amount of time required to complete all tasks.

Input:

• An integer k (number of workers)
• A list of tasks where each task is defined by:
  • id: a unique identifier (string or integer)
  • time: a positive integer representing the processing time
  • prerequisites: a list (possibly empty) of task identifiers

Output:

• A single integer representing the minimum total time to complete all tasks.

Write a program or function that, given the above input, computes and returns the minimum time needed to finish all tasks.

Example (illustrative, not exhaustive):

Consider the following tasks and k = 2 workers:

• Task A: time = 3, prerequisites = []
• Task B: time = 2, prerequisites = [A]
• Task C: time = 4, prerequisites = [A]
• Task D: time = 1, prerequisites = [B, C]

The solution should determine the minimal time required to execute tasks A, B, C, and D under the constraints described.

Note: The input format and output format can be designed as needed (e.g., command-line input, function parameters, etc.).