Show that at most one node in an AVL tree becomes unbalanced after operation remove External is…
Show that at most one node in an AVL tree becomes unbalanced after operation removeExternal is performed within the execution of a remove dictionary operation.
Show that at most one trinode restructuring operation is needed to restore balance after any insertion in an AVL tree.
Let T and U be (2,4) trees storing n and m entries, respectively, such that all the entries in T have keys less than the keys of all the entries in U. Describe an O(logn + logm) time method for joining Tand U into a single tree that stores all the entries in T and U.
The Boolean indicator used to mark nodes in a red-black tree as being “red” or “black” is not strictly needed when we have distinct keys. Describe a scheme for implementing a red-black tree without adding any extra space to standard binary search tree nodes. How does your scheme affect the search and update times?