Binary tree complexities

问题

I would like to know some complexities of binary search tree.

I can't find complete information. I want to know complexities for the following operations on a binary search tree

1. to add/insert an element
2. to remove an element
3. to find an element (as I know this one is O(log(n)) )

回答1:

Insertion, deletion and searching in a binary search tree are:

• O(N) in the worst case;
• O(log(N)) in the average case.

回答2:

If you have balanced binary tree, all three complexities will be of O(log(N)). If you are not balancing the tree, it could be O(N).

回答3:

Search is effective. But unbalanced structure (which is often the case) can lead to O(N) for search/insert/remove operations. That is why binary heap or other kind of balanced trees are preferred with O(log n). .

来源：https://stackoverflow.com/questions/15586820/binary-tree-complexities