Question

I have a situation where I want to delete a random node from the heap, what choices do I have? I know we can easily delete the last node and the first node of the heap. However if we say delete the last node, then I am not sure if the behavior is correctly defined for deleting a random node from the heap.

e.g.

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|X|12|13|14|18|20|21|22|
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So in this case I can delete the node 12 and 22, this is defined, but can I for example delete a random node, e.g. say 13, and still somehow maintain the complete tree property of the heap (along with other properties)?

Answer 1

I’m assuming that you’re describing a binary heap maintained in an array, with the invariant that A[N] <= A[N*2] and A[N] <= A[N*2 + 1] (a min-heap).

If yes, then the approach to deletion is straightforward: replace the deleted element with the last element, and perform a sift-down to ensure that it ends up in the proper place. And, of course, decrement the variable that holds the total number of entries in the heap.

Incidentally, if you’re working through heap examples, I find it better to use examples that do not have a total ordering. There’s nothing in the definition of a heap that requires (eg) A[3] <= A[5], and it’s easy to get misled if your examples have such an ordering.