Tie breaking in a priority queue using python

Question

I'm using a heap queue to implement an algorithm, when i add new nodes to my queue, they're sorted by a heuristic function: eg heappush(queue, (score(node), node)), which is fantastic, apart from the fact that when I come to pop the next node out of the queue, i want the most recently added node, as opposed to the first added node, which is what heappop returns. how can I get the most recent nodes added to the queue without breaking it?

I guess I could just begin iteration at the first element, and while the next element has the same score, continue. Then when I find the final element with that score, I select it and remove it from the list. This obviously isn't very efficient though and breaks the time complexity of a priority queue?

I'm stuck on this and I can't figure out a way to do it.

Thanks.

edit; Using a counter, as suggested will not work (perhaps I've misunderstood)

>>> queue = []
>>> heappush(queue, (2, 0, 'a'))
>>> heappush(queue, (3, -1, 'b'))
>>> queue
[(2, 0, 'a'), (3, -1, 'b')]
>>> heappush(queue, (2, -2, 'c'))
>>> queue
[(2, -2, 'c'), (3, -1, 'b'), (2, 0, 'a')]

Now the queue is ordered incorrectly, and 'b' which is a worse option than 'a' is placed before it.

EDIT 2:

What the hell?

>>> heappop(queue)
(2, -2, 'c')
>>> queue
[(2, 0, 'a'), (3, -1, 'b')]
>>> 

Answer 1

One very simple way is to add a middle term containing a timestamp or a counter value. So for example:

>>> heap = []
>>> counter = itertools.count()
>>> for i in range(10):
...     heapq.heappush(heap, (i, -next(counter), str(i) + ' oldest'))
...     heapq.heappush(heap, (i, -next(counter), str(i) + ' newest'))
... 
>>> heapq.heappop(heap)
(0, -1, '0 newest')
>>> heapq.heappop(heap)
(0, 0, '0 oldest')
>>> heapq.heappop(heap)
(1, -3, '1 newest')
>>> heapq.heappop(heap)
(1, -2, '1 oldest')

As agf mentions, this is the approach used by the heapq docs, only using negative indices. (The implementation there also includes a nice task-removal and priority-change routine.)