CS 261 — Data Structures
Homework #6: Trees and Heaps (50 pts)
Due date: Monday, May 19, 2003 (5:00 PM)
Treat this paper as a specification for your assignment. Your code will be graded on correctness, read-
ability, and style. Study problems and exercises must be legible and will be graded on correctness.
What to do:
Programming:
1. Finding the largest value in a Binary Search Tree is no more difficult than finding the smallest value.
Create a new interface called FindMax that is similar to FindMin (with the exception that the
FindMax methods are called getLast and removeLast). Create a new class called AVLMax-
Tree that extends the AVLTree in the JDS library and implements the FindMax interface. (5 pts).
2. Create a class, BSTSet that extends the BinarySearchTree class in the JDS library and that
adds the following methods (15 pts).
(a) Sorted subSet(Object start, Object stop) — returns a sorted collection that
contains all the elements larger than or equal to start and smaller than stop.
(b) Sorted headSet(Object stop) — returns a sorted collection that contains all the ele-
ments smaller than stop.
(c) Sorted tailSet(Object start) — returns a sorted collection that contains all the ele-
ments larger than or equal to start.
Written homework:
• Add the Integers 7, 4, 2, 5, 6, 8, 1, 3, 0 to an initially empty AVL tree in order. Examine the
toString() methods in jds/collection/AVLTree.java and write the output of the tree
after each insertion as it would be output by toString(). You can, if you want, write a small pro-
gram to create an AVL tree, insert the above values in the order indicated, and then invoke the
toString() method to generated the results (10 pts).
• Chapter 14 Exercises 2 (5 pts) and 6 (5 pts).
E 14.2) Show the result after inserting the values 1, 3, 1, 4, 1, 5, 9 into an initially empty binary
search tree. Then show the result after deleting the root node.
E 14.6) Show all the AVL trees that could result after inserting the values 1, 2, 3, and 4 in various
permutations. How many different trees are there?
• Chapter 15 Exercise 3 (10 pts).
E 15.3) The following tasks are intended to help you get a better feel for the implementation of the
operations in the Heap data type.
d. Create an initially empty heap, and verify that the method isEmpty will return
true.
e. Add the element 4 to the heap. Verify that isEmpty will now return false.
