What to submit and when:
Continue working in groups from lab 2.
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 improve efficiency of
quicksort. The approaches include a randomized
pivot selection, a median-of-three pivot selection to equalize the
split of elements, 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). In case you are getting a Stack Overflow exception: numbers in increasing order may generate a stack overflow because there are 10000 calls (that's the worst case of quicksort when there is one call per element) which is more than the default stack size. You need to increase the stack size in the JVM (Java Virtual Machine) which you can do by setting a JVM flag in Eclipse: http://stackoverflow.com/questions/2127217/java-stack-overflow-error-how-to-increase-the-stack-size-in-eclipse
You may submit one final version of the lab for labs 2 and 3 or separate final submissions. In either case please make sure that all questions are answered and clearly indicate whether you are submitting the two labs separately or together.