Rather than inserting your elements directly into the queue, wrap each element in a tuple, where the first element in the tuple is the desired sorting key. Tuples are sorted by in order of their elements (i.e., first element is compared first), hence why the sorting key needs to come first.
import heapq queue = [] my_list = [...] for element in my_list: heapq.heappush(queue, (my_func(element), element))
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