How is the efficiency of data search in a binary tree structure evaluated?

The efficiency of search in a binary tree depends on its structure. In a balanced binary search tree (BST), the search time on average is O(log n), where n is the number of nodes, since at each step we discard half of the remaining elements.

If the tree is unbalanced (for example, degenerates into a list), the search time can worsen to O(n).

Example of estimation:

• Best and average case: O(log n)
• Worst case: O(n)

To improve guaranteed efficiency, balanced trees such as AVL or red-black trees are used.