COP4530 Fall 2004: Assignment 5

Due: 15 Nov 2004

Educational objectives:

• Main objectives: Experience implementing a self-restructuring binary search tree and solving problems using the above class.
• Secondary objectives: Experience in writing makefiles, writing templated classes, using templated classes, and using the STL queue.

Statement of work: (i) Implement a self-restructuring BST based on single rotations, (ii) implement level-order traversal on such trees, and (iii) use that BST to write a program that will perform searches, and also simple range searches, as described below.

Deliverables: Turn in a makefile, LOG.txt file, and all header and cpp files that are needed to build your project, as described in www.cs.fsu.edu/~asriniva/courses/DS04/HWinstructions.html.

Background: Range searches retrieve data in a specified range of values. For example, a database may contain data about the salary and age of people. A range query may ask us to retrieve the records of all people with age between 20 and 30, having a salary between $100000 and $200000 a year. The dimension of the problem is, loosely speaking, the number of fields in the record. For example, in the above the problem, the dimension is two. Many interesting data structures have been proposed for the above problem. In this homework, we will perform only one dimensional range search, using a BST.

The one-dimensional range search is performed as follows. First, find the node v such that the search paths for x takes the left child of v, while the search path for y takes the right child of v. (If such a node does not exist, then there are no values in open interval (x,y).) Consider the portion of the search path for x after encountering v. If the search path takes a left child of a node w, then all the values in the right subtree of w are in the desired range. If the search path stops at an internal node, then its right subtree is in the range. Consider the portion of the search path for y after encountering v. If the search path takes a right child of a node w, then all the values in the left subtree of w are in the desired range. If the search path stops at an internal node, then its left subtree is in the range. Check all the values on the search paths too, and verify if they are in the range.

Requirements:

1. All your files should be under a directory called proj5.
2. You will create the following files:

- rBST.h: This file implements a simple generic self-restructuring BST based on single rotations. Apart from insert, Delete and search, your class should also implement a void RangeSearch(T &x, T &y) function which outputs the value of all nodes in the open interval (x, y). You should also overload the output operator so that it prints the BST using a level-order traversal, making use of the STL queue class.

- main.cpp: This is the main program, which will declare an object of the rBST type. It will then accept a series of commands from the user, with each command terminated by a newline. It takes an appropriate action on encountering each command, as described below.

- quit: causes the program to be terminated

- insert x: x is an integer. On reading this command, a node with key x will be inserted into the BST. The user will not attempt to insert duplicates.

- delete x: It causes the node with key x to be deleted from the BST.

- search x: This outputs Present or Absent, on a single line, terminated with a newline. This also causes a single-rotation of the node searched for, if it is present.

- range search x y: This outputs all the keys in the open interval (x y).

- print: This prints the BST using a level-order traversal..

- makefile

Notes:

1. Your program should not have any output other than those specified above.

2. You may use the STL string and queue classes. Please get my permission before using any other STL feature.

3. We will provide a sample input later.

4. It is a good idea to create sample test cases to test your program, early in the software development process.