Advanced Data Structures

The BST model: For concreteness, we choose the following model for BSTs, among many choices that are constant-factor equivalent. A search is conducted with a pointer starting at the root, which is free to move about the tree and perform rotations; however, the pointer must at some point in the operation visit the item being searched. The cost of a search is simply the total number of distinct nodes in the tree that have been visited by the pointer during the operation. The letters n and m always refer to the size of a BST, and the total number of search operations performed on it, respectively. For simplicity, we denote the ordered values in the BST by the integers 1, 2, . . . , n. The letters n and m always refer to the size of a BST, and the total number of search operations performed on it, respectively.