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AA-tree A balanced search tree that is the tree of choice when an O(1og N) worst case is needed, a casual implementation is acceptable, and deletions are needed (p 685) AVL tree A binary search tree with the additional balance property that, for any node in the tree, the height of the left and right subtrees can differ by at most 1 As the first balanced search tree, it has historical significance It also illustrates most of the ideas that are used in other search tree schemes (p 661) balanced binary search tree A tree that has an added structure property to guarantee logarithmic depth in the worst case Updates are slower than with the binary search tree, but accesses are faster (P 66 1 1
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binary search tree A data structure that supports insertion, searching, and deletion in O(1og N) average time For any node in the binary search tree, all smaller keyed nodes are in the left subtree and all larger keyed nodes are in the right subtree Duplicates are not allowed (p 641) B-tree The most popular data structure for disk-bound searching There are many variations of the same idea (p 7 10) double rotation Equivalent to two single rotations (p 667) external path length The sum of the cost of accessing all external tree nodes in a binary tree, which measures the cost of an unsuccessful search (p 660) external tree node The NULL node (p 660) horizontal link In an AA-tree, a connection between a node and a child of equal levels A horizontal link should go only to the right, and there should not be two consecutive horizontal links (p 685) internal path length The sum of the depths of the nodes in a binary tree, which measures the cost of a successful search (p 659) lazy deletion A method that marks items as deleted but does not actually delete them (p 685) level of a node In an AA-tree, the number of left links on the path to the nullNode sentinel (p 685) M-ary tree A tree that allows M-way branching, and as branching increases, the depth decreases (p 709) red-black tree A balanced search tree that is a good alternative to the AVL tree because a single top-down pass can be used during the insertion and deletion routines Nodes are colored red and black in a restricted way that guarantees logarithmic depth The coding details tend to give a faster implementation (p 670) single rotation Switches the roles of the parent and child while maintaining search order Balance is restored by tree rotations (p 664) skew Removal of left horizontal links by performing a rotation between a node and its left child (p 686) s p l i t Fixing consecutive right horizontal links by performing a rotation between a node and its right child (p 686)
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1 Using an unbalanced search tree when the input sequence is not random will give poor performance 2 The remove operation is very tricky to code correctly, especially for a balanced search tree 3 Lazy deletion is a good alternative to the standard remove,but you must then change other routines, such as findMin 4 Code for balanced search trees is almost always error-prone 5 Passing a pointer to a tree by value is wrong for insert and removeThe pointer must be passed by reference 6 Using sentinels and then writing code that forgets about the sentinels can lead to infinite loops A common case is testing against NULL when a nullNode sentinel is used
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All of the code in this chapter is available online Contains the class interface for both the ~inar~~earch~ree~ith~ankand BinarySearchTree classes Contains the implementation of both the ~inary~earch~ree~ith~ankand BinarySearchTree classes Contains a test program for both the
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