How to implement Priority Queues in Python?

Question

Sorry for such a silly question but Python docs are confusing.. .

Link 1: Queue Implementation http://docs.python.org/library/queue.html

It says thats Queue has a contruct for priority queue. But I could not find how to implement it.

class Queue.PriorityQueue(maxsize=0)

Link 2: Heap Implementation http://docs.python.org/library/heapq.html

Here they says that we can implement priority queues indirectly using heapq

pq = []                         # list of entries arranged in a heap
entry_finder = {}               # mapping of tasks to entries
REMOVED = '<removed-task>'      # placeholder for a removed task
counter = itertools.count()     # unique sequence count

def add_task(task, priority=0):
    'Add a new task or update the priority of an existing task'
    if task in entry_finder:
        remove_task(task)
    count = next(counter)
    entry = [priority, count, task]
    entry_finder[task] = entry
    heappush(pq, entry)

def remove_task(task):
    'Mark an existing task as REMOVED.  Raise KeyError if not found.'
    entry = entry_finder.pop(task)
    entry[-1] = REMOVED

def pop_task():
    'Remove and return the lowest priority task. Raise KeyError if empty.'
    while pq:
        priority, count, task = heappop(pq)
        if task is not REMOVED:
            del entry_finder[task]
            return task
    raise KeyError('pop from an empty priority queue'

Which is the most efficient priority queue implementation in python? And how to implement it?

Answer 1

There is no such thing as a "most efficient priority queue implementation" in any language.

A priority queue is all about trade-offs. See http://en.wikipedia.org/wiki/Priority_queue

You should choose one of these two, based on how you plan to use it:

• O(log(N)) insertion time and O(1) findMin+deleteMin time, or
• O(1) insertion time and O(log(N)) findMin+deleteMin time

In the latter case, you can choose to implement a priority queue with a Fibonacci heap: http://en.wikipedia.org/wiki/Heap_(data_structure)#Comparison_of_theoretic_bounds_for_variants (as you can see, heapq which is basically a binary tree, must necessarily have O(log(N)) for both insertion and findMin+deleteMin)

If you are dealing with data with special properties (such as bounded data), then you can achieve O(1) insertion and O(1) findMin+deleteMin time. You can only do this with certain kinds of data because otherwise you could abuse your priority queue to violate the O(N log(N)) bound on sorting.

To implement any queue in any language, all you need is to define the insert(value) and extractMin() -> value operations. This generally just involves a minimal wrapping of the underlying heap; see http://en.wikipedia.org/wiki/Fibonacci_heap to implement your own, or use an off-the-shelf library of a similar heap like a Pairing Heap (a Google search revealed http://svn.python.org/projects/sandbox/trunk/collections/pairing_heap.py )

---

If you only care about which of the two you referenced are more efficient (the heapq-based code from http://docs.python.org/library/heapq.html#priority-queue-implementation-notes which you included above, versus Queue.PriorityQueue), then:

There doesn't seem to be any easily-findable discussion on the web as to what Queue.PriorityQueue is actually doing; you would have to source dive into the code, which is linked to from the help documentation: http://hg.python.org/cpython/file/2.7/Lib/Queue.py

   224     def _put(self, item, heappush=heapq.heappush):
   225         heappush(self.queue, item)
   226 
   227     def _get(self, heappop=heapq.heappop):
   228         return heappop(self.queue)

As we can see, Queue.PriorityQueue is also using heapq as an underlying mechanism. Therefore they are equally bad (asymptotically speaking). Queue.PriorityQueue may allow for parallel queries, so I would wager that it might have a very slightly constant-factor more of overhead. But because you know the underlying implementation (and asymptotic behavior) must be the same, the simplest way would simply be to run them on the same large dataset.

(Do note that Queue.PriorityQueue does not seem to have a way to remove entries, while heapq does. However this is a double-edged sword: Good priority queue implementations might possibly allow you to delete elements in O(1) or O(log(N)) time, but if you use the remove_task function you mention, and let those zombie tasks accumulate in your queue because you aren't extracting them off the min, then you will see asymptotic slowdown which you wouldn't otherwise see. Of course, you couldn't do this with Queue.PriorityQueue in the first place, so no comparison can be made here.)