Lab 6: Smaller/Bigger Sort
- Use the
compareTo()method from the
Comparableinterface to determine which of two objects is bigger
- Understand and apply recusion in algorithm development
In this assignment you will implement a recursive algorithm to sort elements
of a list. The basic idea is to look at the first element in the
list - let's call it
first - and rearrange the list such that all
of the elements smaller than
first appear before
first and all elements
first appear after
first. For example,
We now have a sublist of elements from index 0 to (but not including) index 4 with elements no bigger than 8 and a sublist of elements no smaller than 8 from index 5 to index 9. The elements in the sublists can be in any order.
- A significant portion of this assignment is related to your analysis (see end of assignment). Make sure you complete the coding part of this assignment well in advance so that you have time to give appropriate attention to the analysis.
- Writing your tests before or as you implement your solution may help you understand the requirements of the code and design better solutions.
You will create a class,
SmallerBiggerSort with three class methods:
public static <T extends Comparable<T>> int smallerBigger(List<T> list, int start, int end)— used to get a feel for how the non-recursive portion of the next method works.
public static <T extends Comparable<T>> void sort(List<T> list, int start, int end)— a recursive sort method that works by creating sublists of all the elements smaller than a particular value and larger than the value (details below).
public static <T extends Comparable<T>> void sort(List<T> list)— calls the recursive
sort()method with the bounds of the list.
Implement a \( O(n) \) method,
smallerBigger(List<T> list, int start, int end), that
places all of the elements smaller than
first = list.get(start) between position
first and all elements larger than
first between the location of
end. For example, using
start = 2 and
end = 6
sort(List<T>, int start, int end) which sorts the
list by recursively creating sublists of smaller and larger elements. For example,
We now have two sublists that need to be sorted, so we need to call
sort(list, 0, 4)
sort(list, 5, 9).
sort(list, 0, 4) looks like:
We now have just one sublist that needs to be processed:
sort(list, 1, 4)
which leads to
sort(list, 2, 4) and this result:
sort(list, 0, 4) call is complete and we can progress
sort(list, 5, 9) call:
resulting in no changes, but a recursive call to
sort(list, 6, 9)
which, likewise causes no changes. The next recursive call is
sort(list, 7, 9) which swaps the 18 and 13 producing a sort list:
Write thorough JUnit tests for your implementation.
You must create a Word document that describes your approach, results of your benchmarking, and your analysis to answer the following question:
Does the algorithm change based on the starting order of the elements? For example, if the elements are sorted or nearly sorted, is it faster to sort than if the elements are in random order?
This assignment was originally developed by Dr. Chris Taylor.