How is the search time for an element in a binary tree determined?

The time to search for an element in a binary tree depends on its structure. On average, for a balanced binary tree, the search is performed in O(log n), where n is the number of nodes, since at each step we discard half of the remaining elements. In the worst case, if the tree degenerates into a list (for example, all elements go in one direction), the search time becomes O(n).

Example: if the tree is balanced, to find an element, we compare it with the root, then go to the left or right subtree, reducing the number of considered nodes by half at each step.