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As I understand, binary heap does not support removing random elements. What if I need to remove random elements from a binary heap?
Obviously, I can remove an element and re-arrange the entire heap in O(N). Can I do better?
Yes and no.
The problem is a binary heap does not support search for an arbitrary element. Finding it is itself
O(n).However, if you have a pointer to the element (and not only its value) – you can swap the element with the rightest leaf, remove this leaf, and than re-heapify the relevant sub-heap (by sifting down the newly placed element as much as needed). This results in
O(logn)removal, but requires a pointer to the actual element you are looking for.