Homework 7: AVL Solution

You are to code an AVL, which is a special type of binary search tree. It must follow the same rules as binary search trees: each node has 0-2 children, all data in the node’s left subtree is less than the parent node’s data, and all data in the node’s right subtree is greater than the parent node’s data. However, an AVL di ers from a BST with its self-balancing rotations, which you must implement.

All methods in the AVL that are not O(1) must be implemented completely recursively. This includes all helper methods. For methods that change the structure of the tree in some way, we highly recommend you use a technique taught in class called pointer reinforcement.

The AVL will have two constructors: a no-argument constructor (which should initialize an empty tree), and a constructor that takes in a collection of data to be added to the tree, and initializes the tree with this collection of 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(left node’s height, right node’s height) + 1 where the height of a null 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, you no longer need to recursively compute it.

The tree should rotate appropriately to make sure it’s always balanced. 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:

    1. For two child remove, use the predecessor, not successor.

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

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





















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Homework 7: AVL    Due: See Canvas



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.

Methods:



constructor
4pts


add
19pts


remove
24pts


get
5pts


contains
5pts


height
2pts


clear
2pts


elementsWithinDistance
14pts


Other:



Checkstyle
10pts


E  ciency
15pts


Total:
100pts



Provided

The following    le(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 tree. It encapsulates the data, the left and right references, the height, and the balanceFactor. Do not alter this le.

    3. AVLStudentTest.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 le(s). Make sure all le(s) listed below are in each submission, as only the last submission will be graded. Make sure the lename(s) matches the lename(s) below, and that only the following le(s) are present. The only exception is that Canvas will automatically append a -n depending on the submission number to the le name(s). This is expected and will be handled by the TAs when grading as long as the le name(s) before this add-on matches what is shown below. If you resubmit, be sure only one copy of each le is present in the submission. If there are multiple les, do not zip up the les before submitting; submit them all as separate les.

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


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Homework 7: AVL    Due: See Canvas



    1. AVL.java

































































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