Instructions Quick Sort Optimizations through Hybridization Consider…


Quick Sort Optimizations through Hybridization

Consider the QuickSort algorithm (see attached source file) for sorting arrays and two algorithm optimization proposals QSopt1 and QSopt2, described below. 
QSopt1 executes QuickSort for the partitions of size larger than a given cutoff value (usually 10) and executes Insertion Sort (see attached source file) for sorting the partitions of size less than or equal to the cutoff value. 
QSopt2 executes QuickSort until all partitions’ size gets lower than a given cutoff value (usually 10) and then, executes the improved Bubble Sort algorithm (see attached source file) upon the whole “almost sorted” array. 
This project requires writing two Java programs detailed below in Part 1 (testing the functionality of the proposed algorithms) and Part 2 (measuring and comparing their execution time).

Part 1 (Testing algorithms functionality)

Design and implement a program to test the QSopt1 and QSopt2 algorithms. Define an array of size 100, populated with randomly generated Integer or int values in the range 1 .. 999 and sort the array in increasing order by using the algorithms QuickSort, QSopt1 and QSopt2. Display the array content before sorting and then after invoking each sorting algorithm.

Part 2 (Measuring execution time)

 Design, implement and test a program which uses System.nanoTime() method to (1) measure the execution time of the three sorting algorithms and (2) display the average execution time values for 105 runs. Do this for each of the array sizes specified in the table below. Consider the arrays as being randomly populated with Integer or int values in the range 1 .. MAX as specified for each SIZE in the table below. After executing the program, fill-in the table cells with the measured values and include the table in the solution description document.

Note that due to the behavior of the JIT compiler, the execution time of the algorithms is much slower the first times they are run and therefore make sure to discard the measured values for the initial 5 runs. 

The programs should compile without errors.

1. The array contents should not be displayed for Part 2.  
2. For Part 2, the three algorithms should be executed and their execution time should be displayed for the required array sizes within the same program execution and without any user input.

Submission Requirements

Submit the following before the due date listed in the Calendar:

1. including all .java files for Part 1 and including all .java files for Part 2.

2. The solution description document _P3 (.pdf or .doc / .docx) containing:
(2.1) assumptions, main design decisions, error handling, (2.2) test plan, test cases and two relevant screenshots, (2.3) the table of average execution time filled in with the measure values. (2.4) discussion of the results, (2.5) lessons learned and (2.6) possible improvements. The size of the document file (including the screenshots) should be of three pages, single spaced, font size 12.