Task Execution Order

You are given a set of numTasks tasks that need to be executed, labeled from 0 to numTasks - 1. Some tasks have prerequisite dependencies, meaning certain tasks must be completed before others can begin.

You are provided with an array dependencies where each element dependencies[i] = [taskA, taskB] indicates that task taskB must be completed before task taskA can be started.

Your goal is to determine a valid execution order that allows all tasks to be completed while respecting all dependencies. If multiple valid orderings exist, return any one of them. If it is impossible to complete all tasks due to circular dependencies, return an empty array.

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Understanding the Dependency Relationship

For a dependency pair [taskA, taskB]:

• taskB is the prerequisite for taskA
• You must finish taskB before you can start taskA
• Think of it as: "To do taskA, I first need to complete taskB"

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Key Observations

1. Dependency Graph: The tasks and their dependencies form a directed graph where an edge from taskB to taskA means "taskB must come before taskA"

2. Valid Ordering: A valid task execution order is one where every task appears after all of its prerequisites in the sequence

3. Cycle Detection: If the dependency graph contains a cycle (e.g., Task A depends on B, B depends on C, C depends on A), then no valid ordering exists

4. Multiple Solutions: When there's no dependency between two tasks, they can appear in any relative order, leading to multiple valid solutions