## Problem Implement a task scheduler with three operations: ```text addTask(taskId, timestamp) removeTask(taskId) popTasks(count) ``` `addTask` inserts one task. `removeTask` removes that task if it is currently scheduled. `popTasks(count)` removes and returns up to `count` scheduled task IDs in ascending order of start timestamp. When timestamps tie, smaller task IDs come first. Process a sequence of operations and return one array for every `pop` operation. ### Function Contract Implement `runTaskScheduler(operations)`, where an operation is: ```text ["add", taskId, timestamp] ["remove", taskId] ["pop", count] ``` Return an array of task-ID arrays, one per `pop`, in operation order. ### Constraints & Assumptions - `0 <= len(operations) <= 200,000`. - `taskId` and `timestamp` are signed 64-bit integers. - An `add` uses a task ID that is not currently scheduled. A previously removed or popped ID may be added again. - Removing an absent task is a no-op. - `count >= 0`; if fewer than `count` tasks remain, return and remove all of them. - A `pop` with `count = 0` returns an empty array and changes no state. ### Clarifying Questions to Ask - Does `pop` only inspect tasks or remove them? It removes every returned task. - How are equal timestamps ordered? By increasing task ID. - May removed task IDs be reused? Yes. - What happens when `remove` names an absent task? Nothing. ```hint Combine ordering with membership A min-heap gives the next timestamp, while a map or set records which task version is still active. ``` ```hint Make reused IDs safe If removal is lazy, attach a generation number to each heap entry so an old entry cannot remove a later task that reused the same ID. ``` ### Example ```text operations = [ ["add", 7, 30], ["add", 2, 10], ["add", 5, 10], ["remove", 2], ["pop", 2], ["pop", 1] ] ``` Return `[[5, 7], []]`. ### Evaluation Focus - Removes tasks returned by `pop` and never returns a removed task. - Applies the timestamp-and-ID ordering deterministically. - Handles stale heap entries and reuse of a task ID correctly. - Runs each add or remove in `O(log n)` or better and returns `m` popped tasks in `O(m log n)` or better. ### Extensions to Discuss 1. How would an operation that changes a scheduled timestamp be supported? 2. What cleanup policy bounds stale heap entries after many removals? 3. How would the scheduler block until the earliest wall-clock timestamp becomes due?