A Practical Introduction to Data Structures and Algorithm Analysis

13Advanced Tree StructuresThis chapter introduces several tree structures designed for use in specialized applications.The trie of Section 13.1 is commonly used to store strings and is suitablefor storing and searching collections of strings. It also serves to illustrate the conceptof a key space decomposition. The AVL tree and splay tree of Section 13.2are variants on the BST. They are examples of self-balancing search trees and haveguaranteed good performance regardless of the insertion order for records. Anintroduction to several spatial data structures used to organize point data by xycoordinatesis presented in Section 13.3.Descriptions of the fundamental operations are given for each data structure.Because an important goal for this chapter is to provide material for class programmingprojects, detailed implementations are left for the reader.13.1 TriesRecall that the shape of a BST is determined by the order in which its data recordsare inserted. One permutation of the records might yield a balanced tree whileanother might yield an unbalanced tree in the shape of a linked list. The reason isthat the value of the key stored in the root node splits the key range into two parts:those key values less than the root’s key value, and those key values greater thanthe root’s key value. Depending on the relationship between the root node’s keyvalue and the distribution of the key values for the other records in the the tree, theresulting BST might be balanced or unbalanced. Thus, the BST is an example of adata structure whose organization is based on an object space decomposition, socalled because the decomposition of the key range is driven by the objects (i.e., thekey values of the data records) stored in the tree.The alternative to object space decomposition is to predefine the splitting positionwithin the key range for each node in the tree. In other words, the root could be447