The following binary search tree (BST) operations can be implemented efficiently on splay trees. For simplicity, assume that all elements are distinct.
Join (T₁,T₂): Assume every element in BST T₁ is less than or equal to every element in BST T₂, and returns the BST formed by combining the trees T₁ and T₂ SpLit (T, a): Split BST T, containing element a, into two BSTs: T₁ containing all elements in T with key less or equal to a; and T₂, con- taining all elements in T with key greater than a.
Show how to correctly implement those operations on splay trees so that the amortized running time of your operations is O(log n). Justify your procedures and their corresponding running times.
Would you be able to also implement the JoIN and SPLIT operations on a Red-Black tree in O(log n) worst-case running time? Briefly justify your answer.