Homework 8: Sorting Algorithms Solution

For this assignment you will be coding 5 di erent sorts: insertion sort, selection sort, merge sort, quick sort, and LSD radix sort. In addition to the requirements for each sort, to test for e ciency, 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 contains any number of duplicate elements.




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




Comparator




Each method (except radix 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 le. You must use this comparator as the number of comparisons performed with it will be used when testing your assignment.




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).



















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Homework 8: Sorting Algorithms Due: See Canvas










Inplace Sorts




Some of the sorts below are inplace sorts. This means that the items in the array passed in aren’t 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 array or list in the method.




Stable Sorts




Some of the sorts below are stable sorts. This means that duplicates should remain in the same relative positions after sorting as they were before sorting.




Insertion Sort




Insertion sort should be inplace and stable. It should have a worst case running time of O(n2) and a best case running time of O(n).




Note that, for this implementation, you should sort from the beginning of the array. This means that after the rst pass, indices 0 and 1 should be relatively sorted. After the second pass, indices 0-2 should be relatively sorted. After the third pass, indices 0-3 should be relatively sorted, and so on.




Selection Sort




Selection sort should be inplace and unstable. 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.




Merge Sort




Merge sort should be out of place and stable. It should have a worst case running time of O(n log n) and a best case running time of O(n log n).




LSD Radix Sort




LSD Radix sort should be out of place and stable. 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 signi cant 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 over ow if you use Math.abs()!




Quick Sort




Quick sort should be inplace and unstable. 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 speci ed in the method’s interface.











































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Homework 8: Sorting Algorithms Due: See Canvas










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:






insertionSort
12pts




selectionSort
12pts




mergeSort
17pts




quickSort
17pts




lsdRadixSort
17pts




Other:






Checkstyle
10pts




E ciency
15pts




Total:
100pts










A note on JUnits




We have provided a very basic set of tests for your code, in SortingStudentTests.java. 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.




Style and Formatting




It is important that your code is not only functional but is also written clearly and with good style. We will be checking your code against a style checker that we are providing. It is located on Canvas, under Files, along with instructions on how to use it. We will take o a point for every style error that occurs. If you feel like what you wrote is in accordance with good style but still sets o the style checker please email Tim Aveni (tja@gatech.edu) with the subject header of \[CS 1332] CheckStyle XML".




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 may 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 mes-sage must be useful and tell the user what went wrong. \Error", \BAD THING HAPPENED", and \fail" are not good messages. The name of the exception itself is not a good message.







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Homework 8: Sorting Algorithms Due: See Canvas










For example:




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




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







Generics




If available, use the generic type of the class; do not use the raw type of the class. For example, use new LinkedNode<Integer() instead of new LinkedNode(). 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()




Re ection 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 les, just ask.




Debug print statements are ne, 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 o points.

























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Homework 8: Sorting Algorithms Due: See Canvas










Provided




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




 
Sorting.java




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




 
SortingStudentTests.java




This is the test class that contains a set of tests covering the basic operations on 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 le(s). Please make sure the lename matches the lename(s) below, and that only the following le(s) are present. If you make resubmit, make sure only one copy of the le is present in the submission.




After submitting, double check to make sure it has been submitted on Canvas and then download your uploaded les to a new folder, copy over the support les, recompile, and run. It is your responsibility to re-test your submission and discover editing oddities, upload issues, etc.




 
Sorting.java