how to avoid using _siftup or _siftdown in heapq

I have no idea how to solve following problem efficiently without using _siftup or _siftdown:

How to restore the heap invariant, when one element is out-of-order?

In other words, update old_value in heap to new_value, and keep heap working. you can assume there is only one old_value in heap. The fucntion definition is like:

def update_value_in_heap(heap, old_value, new_value):

Here is _siftup or _siftdown version:

>>> from heapq import _siftup, _siftdown, heapify, heappop

>>> data = [10, 5, 18, 2, 37, 3, 8, 7, 19, 1]
>>> heapify(data)
>>> old, new = 8, 22              # increase the 8 to 22
>>> i = data.index(old)
>>> data[i] = new
>>> _siftup(data, i)
>>> [heappop(data) for i in range(len(data))]
[1, 2, 3, 5, 7, 10, 18, 19, 22, 37]

>>> data = [10, 5, 18, 2, 37, 3, 8, 7, 19, 1]
>>> heapify(data)
>>> old, new = 8, 4              # decrease the 8 to 4
>>> i = data.index(old)
>>> data[i] = new
>>> _siftdown(data, 0, i)
>>> [heappop(data) for i in range(len(data))]
[1, 2, 3, 4, 5, 7, 10, 18, 19, 37]

it costs O(n) to index and O(logn) to update. heapify is another solution, but less efficient than _siftup or _siftdown.

But _siftup and _siftdown are protected member in heapq, so they are not recommended to access from outside.

So is there a better and more efficient way to solve this problem? Best practice for this situation?

Thanks for reading, I really appreciate it to help me out. : )

already refer to heapq python - how to modify values for which heap is sorted, but no answer to my problem.

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