Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

In Code Fragments 10.7 and 10.8, we show a complete Java class, AVLTree,
implementing a dictionary using an AVL tree (assuming the parent class includes
an implementation of the restructure method). This class extends
BinarySearchTree (Code Fragments 10.3–10.5) and includes a nested class,
AVLNode, which extends the BTNode class used to represent the nodes of a binary
tree. The AVLNode class defines an additional instance variable height,
representing the height of the node. We get our binary tree to use this node class
instead of the BTNode class simply by overriding the createNode method,
which is used exclusively to create new binary tree nodes. Class AVLTree inherits
methods size, isEmpty, find, and findAll from its superclass,
BinarySearchTree, but overrides methods insert and remove to keep the
search tree balanced.
Method insert (Code Fragment 10.8) begins by calling the superclass's insert
method, which inserts the new entry and assigns the insertion position (for example,
the node storing key 54 in Figure 10.8) to the instance variable actionPos. The
auxiliary method rebalance is then used to traverse the path from the insertion
position to the root. This traversal updates the heights of all the nodes visited, and
performs a trinode restructuring if necessary. Similarly, method remove (Code
Fragment 10.8) begins by calling the superclass's remove method, which performs
the removal of the entry and assigns the position replacing the deleted one to
instance variable actionPos. The auxiliary method rebalance is then used to
traverse the path from the removed position to the root, performing any needed
restructurings.
Code Fragment 10.7: Constructor and auxiliary
methods of class AVLTree.
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