Lab 10: AVL Trees

Objectives:

The main goals for this lab are:

Getting practice with AVL Trees and Rotations

Paired Programming rules

This lab is a paired programming assignment. What exactly does that mean? You will be working in pairs on the CS lab computers. Each pair will be working on one computer. One person will be the driver and the other person will be the navigator. Here is the rule: the driver controlls the lab computer, but the driver can only type what the navigator tells them to type. For this to work well, each pair should be constantly talking among themselves. After each problem, you will switch roles, the navigator will become the driver and the driver will become the navigator.

Exercise

In this assignment you will write a AVLTree (AVLTree.java) that extends your LinkedBinaryTree from HW05. Your AVLTree should be generic over type E. First, copy over your LinkedBinaryTree.java and the BinaryTree.java interface from HW05. Then, modify the Node class in LinkedBinaryTree to have public access.

1

Add a parent reference and a height instance variable to the Node class of LinkedBinaryTree. Also add public methods Node<E> getParent(), int getHeight(), E getData(), Node<E> getLeft(), and Node<E> getRight() for testing. Inheritance of inner/nested classes of Java could be weird so it’s easier to just make changes to the Node in LinkedBinaryTree instead.

getHeight() should return the height of the subtree rooted at that node. A leaf node should have a height of 1.

2

Modify/override LinkedBinaryTree and/or AVLTree so that parent and height are set correctly on insertion and deletion. You might need additional helper methods (to compute height, for example).

3

Add the following methods / constructors to AVLTree.java
public Node getRoot()
public AVLTree()
public AVLTree(E data)

4

Override toString of the Node class to print the element followed by its height in parenthesis.

5

Modify/Override toStringInOrder so that it uses the above toString of Node and returns a traversal string listing the elements with height attached.

6

Implement public Node rebalance() with associated helpers (public Node rotateLeft(Node n), public Node rotateRight(Node n), public Node rotateLeftRight(Node n), public Node rotateRightLeft(Node n)) and call appropriately on insertion. rotateLeftRight and rotateRightLeft should take the root that we want to perform the second rotation over.

7 - Testing

Create an AVLTree<String> and insert the exercise example given in class, i.e. “M”, “N”, “O”, “L”, “K”, “Q”, “P”, “H”, “I”, “A”. Draw the expected tree by hand and assert that your code does indeed create the expected tree.

8

Override toString of AVLTree to print out the in-order traversal, with the height of each node attached. For example, the tree above should return the following string:

A(1) H(2) I(3) K(1) L(2) M(1) N(4) O(1) P(2) Q(1)

Summary

In this lab we covered AVL Trees.

Signing out

This lab will be autograded. Submit the following files to gradescope:

LinkedBinaryTree.java
AVLTree.java