A task queue

Build a priority queue of named tasks (lesson 4). A smaller priority number means more urgent.

• add(task, priority): add a task. If the task is already waiting, change its priority instead; this counts as a new arrival.
• remove(task): take a waiting task out. Return True, or False if it was not waiting.
• pop(): remove and return the waiting task with the smallest priority. If several tasks share that priority, return the one that arrived first. Return None if nothing is waiting.
• len(q): the number of waiting tasks.

q = TaskQueue()
q.add('write', 3); q.add('fix', 1); q.add('test', 3)
q.pop()            # 'fix'
q.remove('write')  # True
q.pop()            # 'test'
q.pop()            # None

Task names are strings; priorities are integers.

The heapq module is switched off for this problem: write the heap yourself. A heap is a plain list with sift up and sift down (lessons 1 and 2); you can copy your class from HEAP-P1.

Limits

• Up to 30,000 tasks and about 70,000 operations; each should take O(log n) time.