CMSC 132 Quiz 3 Worksheet
The third quiz for the course will be on Wed, Apr 8, during your lab session. The following list provides more
information about the quiz:
The quiz will be a written quiz (no computer).
Closed book, closed notes quiz.
Answers must be neat and legible. We recommend that you use pencil and eraser.
The following exercises cover the material to be included in this quiz. Solutions to these exercises will not be
provided, but you are welcome to discuss your solutions with the TA or instructor during office hours. We strongly
recommend you do not use Eclipse to write the code associated with these exercises. Try to answer the
exercises in a piece of paper and then use Eclipse to verify your solutions. This approach will better prepare you for
the quiz.
Some recursion problems require an auxiliary method. For example, a recursive implementation for the tree size()
method may use an auxiliary method that takes as parameter a reference to a Node. Keep this in mind while solving
the problems below.
The following Java class definition for a binary search tree will be used to answer the questions that follow. Unlike
project #3, the following tree is not polymorphic and we use null to represent an empty tree. For example, an empty
BinarySearchTree has a null root, and a leaf node has null left and right fields. For this problem you may not add any
variables (instance or static) to the class in order to answer the questions below.
public class BinarySearchTree <K extends Comparable<K>, V> {
private class Node {
private K key;
private V data;
private Node left, right;
public Node(K key, V data) {
this.key = key;
this.data = data;
}
}
private Node root;
}
1. Define a constructor that creates an empty tree.
2. Define a recursive method add(K key, V data) that adds a key,value pair to the proper location in the tree.
3. Define a recursive method size() that returns the number of entries in the tree.
4. Define a non-recursive method max() that returns the data associated with the maximum key value in the tree.
5. Define a recursive method max() that returns the data associated with maximum key value in the tree.
6. Define a recursive method min() that returns the data associated with minimum key value in the tree.
7. Define a recursive method named postOrderTraversal() which returns a string representing a post-order
traversal of the tree.
8. Define a recursive method getNumInteriorNodes() that returns the number of non-leaf nodes in the tree.
9. Define a recursive method getHeight() that returns the height of the tree.
10. Define a recursive method leaves(ArrayList<K> L) that adds to the ArrayList L the key value of leaf nodes.
11. Define a recursive method isDegenerate() that returns true if a binary search tree is a degenerate tree and false
otherwise. A degenerate tree is one where every node has only one child.
12. Define a recursive method getDecreasingOrderList() that returns an ArrayList with the data elements of the
tree inserted into the list based on decreasing key order.