Find the Critical Path

You are given a project represented as a directed acyclic graph of tasks. Each task has:

• a unique task name
• a list of prerequisite task names
• a positive duration

The input format is:

TASK(name, dependencies, duration)

A task may start only after all of its dependencies have finished.

Write a function that, given a list of tasks, returns:

1. the critical path value: the maximum total duration needed along any valid dependency chain
2. one corresponding critical path: the ordered list of task names on that longest path

If multiple critical paths have the same total duration, returning any one of them is acceptable.

Example inputs:

graph1 = [
 TASK("A", [], 3),
 TASK("B", [], 5),
 TASK("C", ["A"], 5),
]

graph2 = [
 TASK("A", [], 2),
 TASK("B", ["A"], 4),
 TASK("C", ["B"], 3),
 TASK("D", ["C"], 6),
]

graph3 = [
 TASK("A", [], 3),
 TASK("B", ["A"], 2),
 TASK("C", ["A"], 7),
 TASK("D", ["B", "C"], 4),
 TASK("E", ["D"], 2),
]

graph4 = [
 TASK("A", [], 3),
 TASK("B", [], 8),
 TASK("C", ["A"], 2),
 TASK("D", ["C"], 5),
 TASK("E", ["B"], 1),
 TASK("F", ["D", "E"], 4),
]

graph5 = [
 TASK("A", [], 1),
 TASK("B", ["A"], 2),
 TASK("C", ["A"], 5),
 TASK("D", ["B"], 4),
 TASK("E", ["C"], 3),
 TASK("F", ["D", "E"], 3),
 TASK("G", ["F"], 6),
 TASK("H", ["C"], 2),
 TASK("I", ["H"], 7),
 TASK("J", ["G", "I"], 2),
]

graph6 = [
 TASK("M", [], 4),
 TASK("N", ["M"], 3),
 TASK("O", ["N"], 2),
 TASK("P", ["M"], 6),
 TASK("Q", ["O", "P"], 5),
 TASK("R", ["Q"], 4),
 TASK("S", ["N"], 1),
 TASK("T", ["S", "R"], 2),
]

Assume the dependency graph is valid and acyclic.