What to submit and when:
Continue working in pairs.
In this lab we will continue studying efficiency of quicksort (see http://en.wikipedia.org/wiki/Quicksort). The goal is to develop and study approaches to make the quicksort split data as evenly as possible. The approaches include a randomized pivot selection, a median-of-three pivot selection, and use of insertion sort when the array is nearly sorted. You will continue experimenting with quicksort on different types of data (completely random, ordered, partially ordered) and compare it to the pre-defined mergesort in the number of comparisons. The goal is to learn practical approaches to efficient algorithm implementation.
Note that other ways of speeding up quicksort may reduce the program's running time by cutting down on recursive calls or by providing more efficient memory usage. However, they do not reduce the number of element comparisons, and thus will not be included in this lab.
Use your implementation of quicksort and the testing code from the previous lab. You will be using the same kind of data as in the lab last week, i.e. arrays of 10,000 elements filled in as follows:
You need to implement the modifications of quicksort listed below. Please write a new copy of quicksort for each of the three modifications. Then compare the results to the original quicksort and to the mergesort (use the same data for all three sorting algorithms). Make sure to test (for each modification!) that the resulting array is sorted. Record the results (the number of comparisons).
compareTo
for comparison of the three elements since their comparison contributes to the total cost. Note that this approach becomes less efficient as the array size decreases. Use a threshold value k to switch to the usual pivot choice when the portion of the array passed to quicksort is less than k. Try different values of k and choose an optimal one (approximately). Please submit all your code with the results. Also, please write up detailed observations about each of the modifications: did it improve the efficiency? If yes, on which kind of data? How do the modifications compare to each other? Are any of them close to (or better than) mergesort?