Deletion in binary heap

Question

I am just trying to learn binary heap and have a doubt regarding doing delete operation in binary heap. I have read that we can delete an element from binary heap and we need to reheapify it.

But at the following link, it says unavailable:

http://en.wikibooks.org/wiki/Data_Structures/Tradeoffs

                Binary Search  AVL Tree   Binary Heap (min)  Binomial Queue (min)

Find            O(log n)       O(log n)   unavailable         unavailable
Delete element  O(log n        O(log n)   unavailable         unavailable

I am little confused about it.

Thanks in advance for all of the clarifications.

Answer 1

Binary heaps and other priority queue structures don't usually support a general "delete element" operation; you need an additional data structure that keeps track of each element's index in the heap, e.g. a hash table. If you have that, you can implement a general delete operation as

• find-element, O(1) expected time with a hash table
• decrease key to less than the minimum, O(lg n) time
• delete-min and update the hash table, O(lg n) combined expected time.