Assignment 1: AVL & Splay Trees
COMP2003J: Data Structures and Algorithms 2
Weight: 10% of final grade
Due Date: 08:00 Monday May 7th 2018
Document Version: 1.0
Introduction
This assignment is intended to give you experience implementing, AVL and
Splay trees. It is also a good exercise to gain experience about how object
references work in Java.
Source code that you can start from has been posted to Moodle in the file
Assignment1-Source.zip. This also contains the Javadoc API documentation
for the classes that have been provided (in the “doc” folder). Import this
project into Eclipse in the usual way.
Tasks
The main tasks for this assignment are:
? Implement the key methods for an AVL Tree.
? Implement the key methods for a Splay Tree.
? Develop a strategy to test if your implementations are correct.
? Improve the efficiency of the AVL Tree implementation.
Implementation of AVL Tree Methods
The source code contains a partial implementation of an AVL Tree in a file
called AVLTree.java in the dsa.impl package. Your work in this section must
be in this class.
You must implement the following methods:
? private void restructure( INode<T> x ) – trinode restructuring (the
three nodes are x, its parent and its grandparent).
Hint: You can cast to an INode<T> to a BTNode in the same way as you
did in Worksheet 4.
? public void insert( T value ) – insert a value into the AVL tree.
? public void remove( T value ) – remove a value from the AVL tree.
? public boolean contains(T value) – check to see if a value is
contained in the AVL tree. Returns true if the value is in the tree, or
false if not.
If you wish, you may create other methods that help you to complete the task
(e.g. rightRotate(INode<T> n), leftRotate(INode<T> n), etc.).
Implementation of Splay Tree Methods
The source code contains a partial implementation of a Splay Tree in a file
called SplayTree.java in the dsa.impl package. Your work in this section
must be in this class.
You must implement the following methods:
? private void splay( INode<T> n ) – splay a node in the tree.
? public void insert( T value ) – insert a value into the splay tree.
? public void remove( T value ) – remove a value from the splay tree.
? public boolean contains(T value) – check to see if a value is
contained in the splay tree. Returns true if the value is in the tree, or
false if not.
Testing the Tree Implementations
It is important to check whether your implementations are correct. A good way
to do this is to use your tree to perform some operations, and then check if the
outcome is correct. This is best done using a program, rather than doing it
manually every time.
In the Main class, write code that will automatically perform some operations
on your tree implementations, to check if they are correct. Here are some
suggestions:
- A simple test: perform some operations on the trees, then print the
output using TreePrinter and manually compare it to what you expect
the output to be.
- A more complex test: A Binary Search Tree (BST) implementation has
been provided. Write a method to compare the structure and contents
of your AVL/Splay tree with a BST that represents the correct output.
- More complex again: Create some text files that represent operations
to be performed on different types of trees (e.g. I25 to insert 25 into the
tree, R13 to remove 13, etc.). Write code to read these files and
perform the operations on the trees, then compare the outputs.
In all of the above cases, you need to know what the correct output of your
implementation should be. The operations you perform should test all the
different types of restructuring that are possible (e.g. for a Splay Tree they
should cause zig, zig-zig and zig-zag splays to both sides, and at the root and
deeper in the tree).
Improving AVL Tree Efficiency
In this implementation, the height of each node must be recalculated every
time it is needed, which in practice makes both the insert(…) and remove(…)
methods O(n) operations, where n is the number of nodes in the tree.
Adjust the implementation of the AVL tree so that each node stores its own
height, and these are updated only when necessary (Hint: updating the
heights of nodes should be no worse than O(h) complexity following an
insert(…) or remove(…) operation, where h is the height of the tree).
For this task, you must not change the public API of the AVLTree class. All
your code must be inside the AVLTree.java file.
Submission
This is an individual assignment. Therefore all work submitted must
be your own. Refer to the UCD Plagiarism Policy for more
(http://www.ucd.ie/t4cms/RevisedPlagiarismProtocol.pdf).
? All code should be well-formatted and well-commented to describe
what it is trying to do.
? If you write code outside the Main.java, SplayTree.java and
AVLTree.java files, it will not be noticed when grading. Write code only
in these files.
? Submit a single .zip file to Moodle.
o This should Include only the ‘src’ folder from your project that
contains all your code (it should contain the Main, SplayTree and
AVLTree classes).
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