SOLVED: AVL Trees

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Homework 7: AVL Trees    Due: See Canvas



    • Collections class

    • Collection.toArray()

    • Reflection 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 files, just ask.

Debug print statements are fine, 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 off points.

JUnits

We have provided a very basic set of tests for your code. 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.

































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Homework 7: AVL Trees



AVLs

Due: See Canvas

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 successor, not predecessor 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 findPathBetween() method have been removed, and two other recursive practice problems - predecessor() and kSmallest() - have 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.














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Homework 7: AVL Trees
Due: See Canvas




Methods:







add
19pts






remove
24pts






get
5pts






contains
5pts






predecessor
8pts






kSmallest
6pts






clear
2pts






height
2pts






constructor
4pts






Other:







Checkstyle
10pts






Efficiency
15pts






Total:
100pts








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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