Schedule Seller Tasks with Tier-Weighted Round Robin

Implement scheduleSellerTasks(operations). Tasks arrive over time and belong to sellers. Each task has a unique taskId, a sellerId, a seller tier, and a priority. Process operations in order and return the selected seller and task for every process request.

Each operation is an array of strings:

• ["receive", taskId, sellerId, tier, priority] adds a task. tier is VIP or STANDARD; priority is 1, 2, or 3, where 1 is highest.
• ["process"] selects the next task and returns [sellerId, taskId], or null if no task is pending.

Scheduling Rules

• Within one seller, process lower numeric priority first. Tasks with the same priority use their receive order.
• Active sellers take turns in the order they first became nonempty.
• A STANDARD seller may process one task in its turn. A VIP seller may process up to two consecutive tasks in its turn.
• If a seller becomes empty before using its quota, its turn ends immediately.
• After using its quota, a still-nonempty seller moves to the back of the active-seller order.
• A seller that becomes nonempty while absent from the active order joins its back.
• A seller's tier is consistent across all of its tasks.

Constraints

• 1 <= operations.length <= 200,000
• Task and seller IDs contain 1 to 50 English letters or digits.
• Task IDs are globally unique.
• Return results in process-operation order.

Example 1

Input: operations = [["receive", "a1", "A", "VIP", "2"], ["receive", "b1", "B", "STANDARD", "1"], ["receive", "a2", "A", "VIP", "1"], ["process"], ["process"], ["process"]]
Output: [["A", "a2"], ["A", "a1"], ["B", "b1"]]

Seller A uses both VIP slots, while its priority-1 task precedes its earlier priority-2 task.

Example 2

Input: operations = [["receive", "a1", "A", "VIP", "1"], ["receive", "b1", "B", "STANDARD", "2"], ["process"], ["receive", "a2", "A", "VIP", "1"], ["process"], ["receive", "b2", "B", "STANDARD", "1"], ["process"], ["process"]]
Output: [["A", "a1"], ["B", "b1"], ["A", "a2"], ["B", "b2"]]

When A becomes empty, its first turn ends. Its new task later rejoins behind already-active seller B.

Schedule Seller Tasks with Tier-Weighted Round Robin

Hints

1. Separate the order among sellers from the priority order within one seller.
2. A fixed set of three FIFO queues can preserve both task priority and receive-order ties.
3. Remember how much of the seller at the front's current tier quota has been used.

Approach

Keep three FIFO queues per seller, one for each priority, and a global deque of active seller IDs. The front seller owns the current turn. Select from its first nonempty priority queue and count how many slots of the current tier quota have been used. Remove an empty seller immediately; otherwise rotate it to the back when its quota is consumed. On receive, append the seller to the active deque only when it was absent. This separates seller fairness from priority order inside each seller.

• Time complexity: O(m) expected time for m operations, because there are only three priority queues and every receive, process, activation, and rotation uses constant expected time.
• Space complexity: O(t + s + p), where t is the number of received tasks retained in queues, s is the number of known sellers, and p is the number of process results.