Sorting Algorithms Solution

Sorting

For this assignment you will be coding 6 different sorts: selection sort, cocktail shaker sort, merge sort, quick sort, LSD radix sort, and heap sort. In addition to the requirements for each sort, to test for efficiency, we will be looking at the number of comparisons made between elements while grading.

For each of the sorting algorithms, you may assume that the arrays you are sorting will not contain null. You should also assume that arrays may contain any number of duplicate elements.

Your implementations must match what was taught in lecture and recitation to receive credit. Implementing a different sort or a different implementation for a sort will receive no credit even if it passes comparison checks.

Comparator

Each method (except radix and heap sort) will take in a Comparator and use it to compare the elements of the array in various algorithms described below and in the sorting file. Youmust use this Comparator as the number of comparisons performed with it will be used when testing your assignment. See the Java API for details about how the Comparator works and the meaning of the returned value.






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Homework 8: Sorting Algorithms    Due: See Canvas



Generic Methods

Most of the assignments for this class so far have utilized generics by incorporating them into the class declaration. However, the rest of the assignments will have you implement various algorithms as static methods in a utility class. Thus, the generics from here on will use generic methods instead of generic classes (hence the <T> in each of the method headers and javadocs). This also means any helper methods you create will also need to be static with the same <T> in the method header.

In-Place Sorts

Some of the sorts below are in-place sorts. This means that the items in the array passed in should not get copied over to another data structure. Note that you can still create variables that hold only one item; you cannot create another data structure such as an array or list in the method.

Stable Sorts

Some of the sorts below are stable sorts. This means that duplicates must remain in the same relative positions after sorting as they were before sorting. Furthermore, these elements must remain in the same relative order in all intermediate steps of the sorting algorithm.

Adaptive Sorts

Some of the sorts below are adaptive sorts. This means that the algorithm takes advantage of existing order in the input array.

Selection Sort

Selection sort should be in-place, unstable, and not adaptive. It should have a worst case running time of O(n2) and a best case running time of O(n2). You can implement either the minimum version or the maximum version; both are acceptable since they will both yield the same number of comparisons.

Cocktail Sort

Cocktail sort should be in-place, stable, and adaptive. It should have a worst case running time of O(n2) and a best case running time of O(n). Note: Implement cocktail sort with the optimization where it utilizes the last swapped index. Remembering where you last swapped will enable some optimization for cocktail sort. For example, traversing the array from smaller indices to larger indices, if you remember the index of your last swap, you know after that index, there are only the largest elements in order. Therefore, on the next traversal down the array, you start at the last swapped index, and on the next traversal up the array, you stop at the last swapped index. Make sure that both on the way up and on the way down, you only look at the indices that you do not know are sorted. Do not make extra comparisons.

Example of one pass of cocktail sort with last swapped optimization:

Start of cocktail sort:


1

2

6

5

3

4

7

8

9

Start going up the array:


Compare 1 (at index 0) with 2 (at index 1) and don’t swap


1

2

6

5

3

4

7

8

9


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Homework 8: Sorting Algorithms    Due: See Canvas



Compare 2 (at index 1) with 6 (at index 2) and don’t swap


1    2    6    5    3    4    7    8    9


Compare 6 (at index 2) with 5 (at index 3) and swap


1    2    5    6    3    4    7    8    9


Compare 6 (at index 3) with 3 (at index 4) and swap


1    2    5    3    6    4    7    8    9


Compare 6 (at index 4) with 4 (at index 5) and swap


1    2    5    3    4    6    7    8    9


Compare 6 (at index 5) with 7 (at index 6) and don’t swap


1    2    5    3    4    6    7    8    9


Compare 7 (at index 6) with 8 (at index 7) and don’t swap


1    2    5    3    4    6    7    8    9


Compare 8 (at index 7) with 9 (at index 8) and don’t swap


1    2    5    3    4    6    7    8    9


Start going down the array:

Note: Skip over indices 5 - 8 since no swaps occurred there.

Compare 4 (at index 4) with 3 (at index 3) and don’t swap


1    2    5    3    4    6    7    8    9


Compare 3 (at index 3) with 5 (at index 2) and swap


1    2    3    5    4    6    7    8    9


Compare 3 (at index 2) with 2 (at index 1) and don’t swap


1    2    3    5    4    6    7    8    9


Compare 2 (at index 1) with 1 (at index 0) and don’t swap


1    2    3    5    4    6    7    8    9


Finished one pass of cocktail sort.

Note: Next time going up, skip over indices 0 - 2 as well as indices 5 - 8 since no swaps occurred there.

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Homework 8: Sorting Algorithms    Due: See Canvas



Merge Sort

Merge sort should be out-of-place, stable, and not adaptive. It should have a worst case running time of O(n log n) and a best case running time of O(n log n). When splitting an odd size array, the extra data should go on the right.

Quick Sort

Quick sort should be inplace, unstable, and not adaptive. It should have a worst case running time of O(n2) and a best case running time of O(n log n). Your implementation must be randomized as specified in the method’s interface.

LSD Radix Sort

LSD Radix sort should be out-of-place, stable, and not adaptive. It should have a worst case running time of O(kn) and a best case running time of O(kn), where k is the number of digits in the longest number. You will be implementing the least significant digit version of the sort. You will be sorting ints. Note that you CANNOT change the ints into Strings at any point in the sort for this exercise. The sort must be done in base 10. Also, as per the forbidden statements section, you cannot use anything from the Math class besides Math.abs(). However, be wary of handling overflow if you use Math.abs()!

Heap Sort

Heap sort should be out-of-place, unstable, and not adaptive. It should have a worst case running time of O(nlogn) and a best case running time of O(nlogn). Use java.util.PriorityQueue as the heap. Refer to the javadocs for more details. You may also find this heap sort video helpful.

Grading

Here is the grading breakdown for the assignment. There are various deductions not listed that are incurred when breaking the rules listed in this PDF, and in other various circumstances.

Methods:



selectionSort
10pts


cocktailSort
10pts


mergeSort
15pts


quickSort
15pts


lsdRadixSort
15pts


heapSort
10pts


Other:



Checkstyle
10pts


Efficiency
15pts


Total:
100pts



JUnits

We have provided a very basic set of tests for your code. These tests do not guarantee the correctness of your code (by any measure), nor do they guarantee you any grade. You may additionally post your own set of tests for others to use on the Georgia Tech GitHub as a gist. Do NOT post your tests on the public GitHub. There will be a link to the Georgia Tech GitHub as well as a list of JUnits other students have posted on the class Piazza.

If you need help on running JUnits, there is a guide, available on Canvas under Files, to help you run JUnits on the command line or in IntelliJ.


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Homework 8: Sorting Algorithms    Due: See Canvas



Collaboration Policy

Every student is expected to read, understand and abide by the Georgia Tech Academic Honor Code.

When working on homework assignments, you may not directly copy code from any source (other than your own past submissions). You are welcome to collaborate with peers and consult external re-sources, but you must personally write all of the code you submit. You must list, at the top of each file in your submission, every student with whom you collaborated and every resource you consulted while completing the assignment.

You may not directly share any files containing assignment code with other students or post your code publicly online. If you wish to store your code online in a personal private repository, you can use Github Enterprise to do this for free.

The only code you may share is JUnit test code on a pinned post on the official course Piazza. Use JUnits from other students at your own risk; we do not endorse them. See each assignment’s PDF for more details. If you share JUnits, they must be shared on the site specified in the Piazza post, and not anywhere else (including a personal GitHub account).

Violators of the collaboration policy for this course will be turned into the Office of Student Integrity.

Style and Formatting

It is important that your code is not only functional, but written clearly and with good programming style. Your code will be checked against a style checker. The style checker is provided to you, and is located on Canvas. It can be found under Files, along with instructions on how to use it. A point is deducted for every style error that occurs. If there is a discrepancy between what you wrote in accordance with good style and the style checker, then address your concerns with the Head TA.

Javadocs

Javadoc any helper methods you create in a style similar to the existing javadocs. If a method is overridden or implemented from a superclass or an interface, you may use @Override instead of writing javadocs. Any javadocs you write must be useful and describe the contract, parameters, and return value of the method. Random or useless javadocs added only to appease checkstyle will lose points.

Vulgar/Obscene Language

Any submission that contains profanity, vulgar, or obscene language will receive an automatic zero on the assignment. This policy applies not only to comments/javadocs, but also things like variable names.

Exceptions

When throwing exceptions, you must include a message by passing in a String as a parameter. The message must be useful and tell the user what went wrong. “Error”, “BAD THING HAP-PENED”, and “fail” are not good messages. The name of the exception itself is not a good message. For example:

Bad: throw new IndexOutOfBoundsException(‘‘Index is out of bounds.’’);

Good: throw new IllegalArgumentException(‘‘Cannot insert null data into data structure.’’);

In addition, you may not use try catch blocks to catch an exception unless you are catching an exception you have explicitly thrown yourself with the throw new ExceptionName(‘‘Exception Message’’); syntax (replacing ExceptionName and Exception Message with the actual exception name and message respectively).


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Homework 8: Sorting Algorithms    Due: See Canvas



Generics

If available, use the generic type of the class; do not use the raw type of the class. For example, use new LinkedList<Integer>() instead of new LinkedList(). Using the raw type of the class will result in a penalty.

Forbidden Statements

You may not use these in your code at any time in CS 1332.

    • package

    • System.arraycopy()

    • clone()

    • assert()

    • Arrays class

    • Array class

    • Thread class

    • Collections class

    • Collection.toArray()

    • Reflection APIs

    • Inner or nested classes

    • Lambda Expressions

    • Method References (using the :: operator to obtain a reference to a method)

    • Anything besides Math.abs() in the Math class (for this homework only)

    • String class (for this homework only)


If you’re not sure on whether you can use something, and it’s not mentioned here or anywhere else in the homework files, just ask.

Debug print statements are fine, but nothing should be printed when we run your code. We expect clean runs - printing to the console when we’re grading will result in a penalty. If you submit these, we will take off points.

Provided

The following file(s) have been provided to you. There are several, but we’ve noted the ones to edit.

    1. Sorting.java

This is the class in which you will implement the different sorting algorithms. Feel free to add private helper methods but do not add any new public methods, inner/nested classes, instance variables, or static variables.



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Homework 8: Sorting Algorithms    Due: See Canvas



    2. SortingStudentTests.java

This is the test class that contains a set of tests covering the basic algorithms in the Sorting class. It is not intended to be exhaustive and does not guarantee any type of grade. Write your own tests to ensure you cover all edge cases.


Deliverables

You must submit all of the following file(s) to the course Gradescope. Make sure all file(s) listed below are in each submission, as only the last submission will be graded. Make sure the filename(s) matches the filename(s) below, and thatonly the following file(s) are present. If you resubmit, be sure only one copy of each file is present in the submission. If there are multiple files, do not zip up the files before submitting; submit them all as separate files.

Once submitted, double check that it has uploaded properly on Gradescope. To do this, download your uploaded file(s) to a new folder, copy over the support file(s), recompile, and run. It is your sole responsibility to re-test your submission and discover editing oddities, upload issues, etc.

    1. Sorting.java










































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