Description:

In this lab you will implement the Set abstract data type using binary search trees. We will consider sets of integers where each integer will be stored in a tree node. Therefore, the number of nodes in the binary search tree must be equal to the size of the set.

You will have to write a Java class BSTSet for this purpose. To implement the tree nodes you must use the Java class TNode provided in this lab. Additionally, you may need to implement Java classes MyStack and/or MyQueue to perform non-recursive tree traversals of a BSTSet. You are not permitted to use any predened Java methods or classes from Java API, other than for input and output, unless specied otherwise. You must also write a test class TestBSTSet. Please compute the asymptotic run time and space complexity of all methods and be ready to present them to the TA with explanations at your demo.

Definitions:

A set is an unordered collection of elements with no repetition. Examples are the set of real numbers, the set of integer numbers or the set consisting of numbers 1, 2, 30.

For this lab we will only be considering representing nite sets consisting of elements which are integers. Examples: {0, 34, 78, 1000}, {4, 5, 890, 65535}, {0, 1, 2, , 65534, 65535}, {} are all valid sets.

The union of two sets, say A and B, is written as AB and is the set which contains all of the elements in either A or B or both. Example: If A = {3, 8, 14, 15} and B = {2, 8, 9, 15, 100}, then A B = {2, 3, 8, 9, 14, 15, 100} (notice that there are no repeated elements in a set).

The intersection of two sets A and B is written as AB and is the set which contains the elements that are common to A and B. Examples: If A = {3, 8, 14, 15} and B = {2, 8, 9, 15, 100}, then A B = {8, 15}. If A = {17, 20, 38} and B = {200}, then A B = {}, which is termed the empty set.

Specifications:

You must use the Java class TNode given below, to implement the tree nodes.

Classes TNode and BSTSet must be contained in the same package.

public class TNode{

int element; TNode left; TNode right; TNode(int i, TNode l, TNode r)

1 of 3 McMaster University Dept. Electrical and Comp. Engineering

COE 2SI4 - Term II (Winter) 2018

{ element =i; left = l; right = r; } }//end class

Class BSTSet must contain only one private eld named root, of type TNode, which is a reference to the root of the tree. No other elds are allowed. When the set is empty you should have root==null.

Class BSTSet must contain at least the following constructors:

- public BSTSet() - initializes the BSTSet object to represent the empty set (an empty tree).

- public BSTSet(int[] input) - initializes the BSTSet object to represent the set containing all elements in array input, without repetitions. For example, if the array is: 5, 7, 4, 5, then the corresponding set is {5, 7, 4}.

Class BSTSet must contain the following public methods:

1) public boolean isIn(int v): Returns true if integer v is an element of this BSTSet. It returns false otherwise.

2) public void add(int v): Adds v to this BSTSet if v was not already an element of this BSTSet. It does nothing otherwise.

3) public boolean remove(int v): Removes v from this BSTSet if v was an element of this BSTSet and returns true. Returns false if v was not an element of this BSTSet.

4) public BSTSet union(BSTSet s): Returns a new BSTSet which represents the union of this BSTSet and s. This method should not modify the input sets.

5) public BSTSet intersection(BSTSet s): Returns a new BSTSet which represents the intersection of this BSTSet and s. This method should not modify the input sets.

6) public int size(): Returns the number of elements in this set.

7) public int height(): Returns the height of this BSTSet. Height of empty set is -1.

8) public void printBSTSet(): Outputs the elements of this set to the console, in increasing order. private void printBSTSet(TNode t): Outputs to the console the elements stored in the subtree rooted in t, in increasing order. For the two printing methods specied above you must use the following code public void printBSTSet(){ if(root==null) System.out.println("The set is empty");

else{ System.out.print("The set elements are: ");

printBSTSet(root); System.out.print(" "); } }

private void printBSTSet(TNode t){

if(t!=null){ printBSTSet(t.left); System.out.print(" " + t.element + ", "); printBSTSet(t.right); }

}

9) public void printNonRec(): Prints the integers in this BSTSet in increasing order. This method is nonrecursive and uses a stack to implement the inorder traversal.

SORRY, there is no other code provided, including MyStack/MyQueue.