Reference no: EM133028693

Algorithm Development and Data Structures

Part 1 - INDIVIDUAL WORK : BST, BBST and Sorting Understanding and Applying

a. Show in the style given in the class, how the last 5 digits of your student number (e.g. 123456789) will be inserted in the following ADT-Please make sure to change these digits to be unique digits:

- Binary Search Tree
- Red-Black Tree

Show your Tree after you insert a number to the tree.

b.Show in the style given in the class, how the last 5 digits of your student number(e.g. 123456789) will be sorted using the following sorting algorithms-Please make sure to change these digits to be unique digits:
a. Selection sort-
b. Quick sort
c. Merge sort
c. You need to design TWO algorithms in Pseudo code that takes N numbers (size of input) in array A and counts the number of distinct values in A.
a. First algorithm will do the count without using any sorting algorithms
b. Second algorithm counts the number of distinct values in the array with using any sorting algorithms.
c. What is the complexity of the designed algorithm? Explain your answer.

Part 2- Binary Search Tree Empirical and Theoretical Results

Part 1: You need to define a binary search tree data structure . Also, you need to implement the following functions:
1. Insert Sorted
• BSTREE insert(BSTREE root, intnum): root points to a node in a binary search tree; num is a number to be inserted in the tree rooted at "root". This function returns the root of the modified tree.

2. Print Elements
• void inorderTraversal(BSTREE root, FILE *fp): root points to a node in a binary search tree. This function does not return anything, but prints out, to the file specified, the nodes in the tree rooted at "root" by performing an inorder traversal.

Part 2: Test the performance of the designed data structure using theoretical and experimental approaches as follows:
1. Dataset 1-Dataset is sorted- Add code to insert the numbers 1...n in that order in an initially empty doubly linked list and a binary search tree.
a. Run it on different values of n where :
i. n = 20,000
ii. n = 50,000
iii. n = 100,000
b. Do an in-order traversal of the tree, printing out the contents to a file (named "sorted") to verify that you indeed built the data structure correctly.
c. Note the time for each program executions to just build the data structure (i.e., don't include printing in the time) and include the timings in your report. For each n, you must run it 3 times and then take the average time. Don't forget to submit all your data though.
d. Report the results of the analyzed algorithms for each data structure using the Big-O and the timings.
2. Dataset 2-Dataset is random - Add code to read in values from "dataToBuildDS.txt" and properly insert them in an initially empty doubly linked list and binary search tree.
1. Run your program on different values of n by doing the following:
• Read in the first 20,000 entries only found in "dataToBuildDS.txt"
• Read in the first 50,000 entries only found in "dataToBuildDS.txt"
• Read in the first 100,000 entries only found in "dataToBuildDS.txt"
2. Do an in-order traversal of the tree, printing out the contents to a file (named "unsorted") to verify that you indeed built the data structure correctly.
3. Note the time to build the data structure. For each n, you must run it at least 3 times and then take the average. Include all timings as well as the average in your report.
4. Report the results of the analyzed algorithms for each data structure using the Big-O and the timings.

Your Answer should include the following parts :
Implementation of the data structures that shows the experimental study in timings for the datasets for insertion and print algorithms for each data set.

Report:
o Describe the data structure [BST] and algorithms [insert, find and print] in pseudocode.
o Comparison in terms of:
- Big-O and datasets for insert and print
- Timings and datasets for insert and print

Attachment:- Algorithm Development.rar