Can we use binary search tree to simulate heap operation?

Question

I was wondering if we can use a binary search tree to simulate heap operations (insert, find minimum, delete minimum), i.e., use a BST for doing the same job?

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Answer 1

Yes, but you lose the O(1) average insert of the heap

As others mentioned, you can use a BST to simulate a heap.

However this has one major downside: you lose the O(1) insert average time, which is basically the only reason to use the heap in the first place: https://stackoverflow.com/a/29548834/895245

If you want to track both min and max on a heap, I recommend that you do it with two heaps instead of a BST to keep the O(1) insert advantage.