I know this would be an O(k log n) operation on a traditional heap, and I know there are ways to maintain Kth-smallest over a stream of inserts/deletes for constant-time access...
My question though is, when we have an implicit array representation of a min-heap, e.g.:
min_heap = [1, 2, 4, 3, 6, 5, 54, 12, 12, 34]
In this case, is it possible to infer the Kth-smallest value's index from the value of K, so you can use the array index to get the value in O(1) time?