# Homework 7: AVL Trees Solution

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## Description

AVLs

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 di ers 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 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. Use the successor, not predecessor.

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

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

1. The traversals and the isBST() method have been removed, and two other recursive practice problems have been added.

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: add 19pts remove 25pts get 5pts contains 5pts deepestBranches 7pts sortedInBetween 7pts clear 2pts height 2pts constructor 3pts Other: Checkstyle 10pts E ciency 15pts Total: 100pts

A note on JUnits

We have provided a very basic set of tests for your code, in AVLStudentTests.java. These tests do not guarantee the correctness of your code (by any measure), nor do they guarantee you any grade. You may additionally post your own set of tests for others to use on the Georgia Tech GitHub as a gist. Do NOT post your tests on the public GitHub. There will be a link to the Georgia Tech GitHub as well as a list of JUnits other students have posted on the class Piazza.

If you need help on running JUnits, there is a guide, available on Canvas under Files, to help you run JUnits on the command line or in IntelliJ.

Style and Formatting

It is important that your code is not only functional but is also written clearly and with good style. We will be checking your code against a style checker that we are providing. It is located on Canvas, under Files, along with instructions on how to use it. We will take o a point for every style error that occurs. If you feel like what you wrote is in accordance with good style but still sets o the style checker please email Tim Aveni (tja@gatech.edu) with the subject header of \[CS 1332] CheckStyle XML”.

Javadoc any helper methods you create in a style similar to the existing Javadocs. If a method is overridden or implemented from a superclass or an interface, you may use @Override instead of writing Javadocs. Any Javadocs you write must be useful and describe the contract, parameters, and return value of the method; random or useless javadocs added only to appease Checkstyle may lose points.

Vulgar/Obscene Language

Any submission that contains profanity, vulgar, or obscene language will receive an automatic zero on the assignment. This policy applies not only to comments/javadocs but also things like variable names.

Exceptions

When throwing exceptions, you must include a message by passing in a String as a parameter. The mes-sage must be useful and tell the user what went wrong. \Error”, \BAD THING HAPPENED”, and \fail” are not good messages. The name of the exception itself is not a good message.

For example:

Bad: throw new IndexOutOfBoundsException(“Index is out of bounds.”);

Good: throw new IllegalArgumentException(“Cannot insert null data into data structure.”);

Generics

If available, use the generic type of the class; do not use the raw type of the class. For example, use new LinkedNode<Integer>() instead of new LinkedNode(). Using the raw type of the class will result in a penalty.

Forbidden Statements

You may not use these in your code at any time in CS 1332.

package

System.arraycopy() clone()

assert()

Arrays class Array class Thread class

Collections class

Collection.toArray()

Re ection APIs

Inner or nested classes Lambda Expressions

Method References (using the :: operator to obtain a reference to a method)

If you’re not sure on whether you can use something, and it’s not mentioned here or anywhere else in the homework les, just ask.

Debug print statements are ne, but nothing should be printed when we run your code. We expect clean runs – printing to the console when we’re grading will result in a penalty. If you submit these, we will take o points.

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.

1. 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 le.

1. 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 le(s). Please make sure the lename matches the lename(s) below, and that only the following le(s) are present. If you make resubmit, make sure only one copy of the le is present in the submission.

After submitting, double check to make sure it has been submitted on Canvas and then download your uploaded les to a new folder, copy over the support les, recompile, and run. It is your responsibility to re-test your submission and discover editing oddities, upload issues, etc.

1. AVL.java

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