Comparing Leaf and Root Insertion

We consider two ways of inserting a key into a binary search tree: leaf insertion which is the standard method, Amplifiers and root insertion which involves additional rotations.Although the respective cost of constructing leaf and root insertion binary search trees trees, in terms of comparisons, are the same in the average case, we show that in the worst case the construction of a root insertion binary search tree needs approximately 50% of Fans the number of comparisons required by leaf insertion.