1. Write a program to read a list of grade point averages (0.0 - 4.0) from a text file and sort them in descending order. Select the most efficient sorting algorithm for your program.
2. Some algorithms are too complex to analyze using simple big-O notation or a representative data set may not be easily identifiable. In these cases, we must actually execute and test the algorithms on different sized data sets and compare the results. Special care must be taken to be fair in the actual implementation and execution of the different algorithms. This is known as an empirical analysis. We can also use an empirical analysis to verify and compare the time-complexities of a family of algorithms such as those for searching or sorting.
Design and implement a program to evaluate the efficiency of the comparison sorts used with sequences by performing an empirical analysis using random numbers. Your program should:
* Prompt the user for the size of the sequence: n.
* Generate a random list of n values (integers) from the range [0 . . . 4n].
* Sort the original list using each of the sorting algorithms, keeping track of the number of comparisons performed by each algorithm.
* Compute the average number of comparisons for each algorithm and then report the results.
When performing the empirical analysis on a family of algorithms, it is important that you use the same original sequence for each algorithm. Thus, instead of sorting the original sequence, you must make a duplicate copy of the original and sort that sequence in order to preserve the original for use with each algorithm.