AVL Trees/AVLs

Description

You are required to implement an AVL tree. An AVL is a special type of binary search tree that follows all the same rules: each node has 0-2 children, all data in the left subtree is less than the node’s data, and all data in the right subtree is greater than the node’s data. The AVL differs from the BST with its own self-balancing rotations, which you must implement.

All methods in the AVL tree that are not O(1) must be implemented recursively. Good recur-sion with simple, focused states is strongly encouraged for this assignment in particular.

It will have two constructors: a no-argument constructor (which should initialize an empty tree), and a constructor that takes in data to be added to the tree, and initializes the tree with this data.

Balancing

Each node has two additional instance variables, height and balanceFactor. The height variable should represent the height of the node. If you recall, a node’s height is max(child nodes’ heights)

• 1 where the height of a null node is -1. The balance factor of a node should be equal to its left child’s height minus its right child’s height. Since we’ve stored this information in each node, we no longer need to recursively compute them.

The tree should rotate appropriately to make sure it’s always balanced. For an AVL tree, a tree is balanced if every node’s balance factor is either -1, 0, or 1. Keep in mind that you will have to update the balancing information stored in the nodes on the way back up the tree after modifying the tree; the variables are not updated automatically.

Important Notes

Here are a few notes to keep in mind when switching from BST to AVL trees:

1. You must still use the predecessor, not successor in remove().

2. After every change to the tree, make sure to update height and balance factor fields of all nodes whose subtrees have been modified.

3. Make sure the height method is O(1).

4. The traversals and the pruneGreaterThan() method have been removed, and one other recursive practice problem – findMedian() – has been added.

Grading

Here is the grading breakdown for the assignment. There are various deductions not listed that are incurred when breaking the rules listed in this PDF, and in other various circumstances.

Provided

The following file(s) have been provided to you. There are several, but we’ve noted the ones to edit.

1. AVL.java

This is the class in which you will implement the AVL. Feel free to add private helper methods but do not add any new public methods, inner/nested classes, instance variables, or static variables.

2. AVLNode.java

This class represents a single node in the AVL. It encapsulates the data, height, balanceFactor, and left and right references. Do not alter this file.

3. AVLStudentTests.java

This is the test class that contains a set of tests covering the basic operations on the AVL class. It is not intended to be exhaustive and does not guarantee any type of grade. Write your own tests to ensure you cover all edge cases.

Deliverables

You must submit all of the following file(s) to the course Gradescope. Make sure all file(s) listed below are in each submission, as only the last submission will be graded. Make sure the filename(s) matches the filename(s) below, and thatonly the following file(s) are present. If you resubmit, be sure only one copy of each file is present in the submission. If there are multiple files, do not zip up the files before submitting; submit them all as separate files.

Once submitted, double check that it has uploaded properly on Gradescope. To do this, download your uploaded file(s) to a new folder, copy over the support file(s), recompile, and run. It is your sole responsibility to re-test your submission and discover editing oddities, upload issues, etc.

1. AVL.java

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