Comparing Leaf and Root Insertion

Jaco Geldenhuys, Brink van der Merwe


We consider two ways of inserting a key into a binary search tree: leaf insertion which is the standard method,
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 the number of
comparisons required by leaf insertion.


Binary search trees, leaf insertion, root insertion

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