# Homework 6: Sorting Solution

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## Description

Sorting

For this assignment you will be coding 3 di erent sorts: insertion sort, merge sort, and LSD radix sort. You will also be coding the kth select algorithm that follows the quick sort algorithm. In addition to the requirements for each sort, we will be looking at the number of comparisons made between elements while grading.

Comparator

Each sorting method (except radix sort) will take in a comparator and use it to sort the elements of the array using various sorting algorithms described below and in the sorting le.

Note that comparator.compare(x, y) is equivalent to x.compareTo(y).

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 array or list. Note that you can still create variables that hold only one item; you cannot create another 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).

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Homework 6: Sorting Due: See T-Square

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

Your implementation of quick sort must match the method shown in lecture; otherwise, you may not receive full credit for the sort.

Merge Sort

Merge sort should be 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).

Your radix sort implementation will be with the least signi cant digit (LSD). 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 sorting ints. Note that you CANNOT change the ints into Strings at any point in the sort for this exercise. In addition, the sorts must be done in base 10.

LSD radix sort should be stable.

If you need to calculate the result of a number raised to a power, you should use the pow() method we have provided. You may only use Math.abs() from the Math class.

Kth Select

Kth select should be inplace. It should have a worst case running time of O(n2) and a best case running time of O(n). Logically, it is similar to a one-sided quick sort. When asked for the kth smallest, it would be equivalent to say that if the array was perfectly sorted you would be returning the element at index

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Important Implementation Note

Your implementation of all sorts and kth Selection must match the method shown in lecture; otherwise, you may not receive full credit for the sort.

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 10pts mergeSort 25pts kthSelect 25pts lsdRadixSort 15pts Other: Checkstyle 10pts E ciency 15pts Total: 100pts

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Homework 6: Sorting Due: See T-Square

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 does it 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 T-Square under Resources, 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 in T-Square, under Resources, 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 Grayson Bianco (gbianco6@gatech.edu) with the subject header of \CheckStyle XML”.

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.

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.

For example:

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 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.

break may only be used in switch-case statements

continue package

Integer.toString() String.parseInt()

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Homework 6: Sorting Due: See T-Square

System.arraycopy() clone()

assert()

Arrays class Array class

Collections class

Collection.toArray()

Re ection APIs

Inner, nested, or anonymous classes

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

Debug print statements are ne, but nothing should be printed when we run them. We expect clean runs – printing to the console when we’re grading will result in a penalty. If you use these, we will take o points.

Provided

The following le(s) have been provided to you. There are several, but you will edit only one of them.

1. 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.

1. 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. T-Square does not delete les from old uploads; you must do this manually. Failure to do so may result in a penalty.

DO NOT ZIP HOMEWORK FILES.