Is the search complexity in binary trees always logarithmic?

No, not always. The search complexity in a binary tree depends on its height.

• In a balanced binary tree (for example, an AVL tree or a red-black tree), the height is proportional to log(n), where n is the number of nodes. In this case, the search complexity is logarithmic, O(log n).

• In an unbalanced binary tree, the height can degenerate to linear, reaching up to n in the worst case (for example, if elements are inserted in strictly increasing or decreasing order, forming a list). In this case, the search complexity is linear, O(n).

Thus, logarithmic complexity is guaranteed for balanced binary trees.