Deterministic Task Execution Order

Problem Statement

You are given a list of tasks, where each task is identified by an integer label from 0 to n-1. You are also given a list of dependencies, where [u, v] means task u must be completed before task v can begin.

Your goal is to return a valid execution order for all tasks. If there are multiple valid orders, you must always choose the task with the smallest numerical label among all currently 'ready' tasks (tasks whose dependencies have all been met). If it is impossible to complete all tasks (due to a circular dependency), return an empty list.

Function Signature

def get_task_order(n, dependencies):
    # n: int (number of tasks)
    # dependencies: List[List[int]]
    # returns: List[int]

Examples

Example 1: Input: n = 3, dependencies = [[1, 0], [2, 0]] Output: [1, 2, 0] Explanation: Both 1 and 2 have no incoming edges and are ready. We pick the smaller label 1 first, then 2. Finally, 0 becomes ready.

Example 2: Input: n = 2, dependencies = [[0, 1], [1, 0]] Output: [] Explanation: A cycle exists (0 depends on 1 and 1 depends on 0), so no valid order is possible.

Constraints

• 1 <= n <= 10^5
• 0 <= len(dependencies) <= 2 * 10^5
• Task labels are in the range [0, n-1]

Edge Cases

• Disconnected graph components.
• No dependencies provided.
• Graphs containing cycles.