Implement task queue with insert, delete, execute

Problem: Task manager with insert/delete/execute-next

Design a data structure to manage executable tasks.

Each task has:

• taskId (unique)
• priority (higher means executed earlier)
• createdAt (or seq ) to break ties among equal priority (earlier first)

Support operations:

1. add(taskId, priority)
2. remove(taskId) (task may or may not exist; removing a task prevents future execution)
3. executeNext() -> taskId | null
   • Returns and removes the highest-priority remaining task.
   • Tie-breaker: smaller createdAt/seq first.

Requirements

• Aim for O(log n) per operation.
• You may not linearly scan all tasks on executeNext() .

Notes

• Explain how you handle remove() efficiently even if the task is not at the top of the heap when removed.