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 that Queue has a class for the 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 say 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

(* sidenote: the findMin time of most queues is almost always O(1), so here I mostly mean the deleteMin time can either be O(1) quick if the insertion time is O(log(N)) slow, or the deleteMin time must be O(log(N)) slow if the insertion time is O(1) fast. One should note that both may also be unnecessarily slow like with binary-tree based priority queues.)

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. vEB trees kind of fall under a similar category, since you have a maximum set size (O(log(log(M)) is not referring to the number of elements, but the maximum number of elements) and thus you cannot circumvent the theoretical O(N log(N)) general-purpose comparison-sorting bound.

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.)

Answer 2

The version in the Queue module is implemented using the heapq module, so they have equal efficiency for the underlying heap operations.

That said, the Queue version is slower because it adds locks, encapsulation, and a nice object oriented API.

The priority queue suggestions shown in the heapq docs are meant to show how to add additional capabilities to a priority queue (such as sort stability and the ability to change the priority of a previously enqueued task). If you don't need those capabilities, then the basic heappush and heappop functions will give you the fastest performance.

Answer 3

Although this question has been answered and marked accepted, still here is a simple custom implementation of Priority Queue without using any module to understand how it works.

# class for Node with data and priority
class Node:

  def __init__(self, info, priority):
    self.info = info
    self.priority = priority

# class for Priority queue 
class PriorityQueue:

  def __init__(self):
    self.queue = list()
    # if you want you can set a maximum size for the queue

  def insert(self, node):
    # if queue is empty
    if self.size() == 0:
      # add the new node
      self.queue.append(node)
    else:
      # traverse the queue to find the right place for new node
      for x in range(0, self.size()):
        # if the priority of new node is greater
        if node.priority >= self.queue[x].priority:
          # if we have traversed the complete queue
          if x == (self.size()-1):
            # add new node at the end
            self.queue.insert(x+1, node)
          else:
            continue
        else:
          self.queue.insert(x, node)
          return True

  def delete(self):
    # remove the first node from the queue
    return self.queue.pop(0)

  def show(self):
    for x in self.queue:
      print str(x.info)+" - "+str(x.priority)

  def size(self):
    return len(self.queue)

Find the complete code and explanation here: https://www.studytonight.com/post/implementing-priority-queue-in-python (Updated URL)