Find a Valid Task Execution Order with Dependencies

Problem Statement

You are building a task execution engine for a cloud workflow system. You are given an integer numTasks representing the total number of tasks to execute, labeled from 0 to numTasks - 1.

You are also given a 2D array prerequisites, where prerequisites[i] = [task_a, task_b] indicates that task_b must be completed before task_a can be started (i.e., task_b -> task_a).

Return a valid sequence of tasks that allows all tasks to be completed. If there are multiple valid execution orders, return any one of them. If it is impossible to finish all tasks due to cyclic dependencies, return an empty array [].

Function Signature

def findTaskOrder(numTasks: int, prerequisites: list[list[int]]) -> list[int]:
    pass

Examples

Example 1

Input: numTasks = 2, prerequisites = [[1, 0]]
Output: [0, 1]
Explanation: To run task 1, task 0 must be finished first. Therefore, the only valid order is [0, 1].

Example 2

Input: numTasks = 4, prerequisites = [[1, 0], [2, 0], [3, 1], [3, 2]]
Output: [0, 1, 2, 3]
Explanation: Task 0 must be run before tasks 1 and 2. Task 3 requires both tasks 1 and 2 to finish. Another valid order is [0, 2, 1, 3].

Example 3

Input: numTasks = 2, prerequisites = [[1, 0], [0, 1]]
Output: []
Explanation: Task 1 depends on task 0, and task 0 depends on task 1. This circular dependency makes it impossible to complete all tasks.

Constraints

• 1 <= numTasks <= 2000
• 0 <= len(prerequisites) <= 5000
• prerequisites[i].length == 2
• 0 <= task_a, task_b < numTasks
• task_a != task_b
• All prerequisite pairs [task_a, task_b] are distinct.

Edge Cases

• prerequisites is empty: any permutation of [0, ..., numTasks - 1] is valid.
• Disconnected components: tasks with no dependencies can appear anywhere as long as relative dependencies are satisfied.
• Graphs containing self-contained sub-cycles: the entire process should return [].