Homework 8: Sorting Solution

For this assignment you will be coding 5 di erent sorts: insertion sort, bubble sort, merge sort, LSD radix sort, and heap sort. You will also be coding the kth select algorithm that is very similar to the quick sort algorithm. In addition to the requirements for each sort (except LSD radix sort and heap 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 / lists you are sorting will not contain null elements. You should also assume that arrays may contain any number of duplicate ele-ments.

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 LSD radix sort 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 le. You must 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.

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.

Adaptive Sorts

Some of the sorts below are adaptive sorts. This means that the algorithm takes advantage of existing order in the input array. The algorithm can detect existing order in the input array and optimize its performance based on that order.

Insertion Sort

Insertion 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 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.


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Homework 8: Sorting    Due: See Canvas



Bubble Sort

Bubble 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 bubble sort with the optimization where it utilizes the last swapped index. Remembering where you last swapped will enable some optimization for bubble 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 iteration, you start at the front but stop at the last swapped index. Make sure you only look at the indices that you do not know are sorted. Do not make extra comparisons.

Example of two iterations of bubble sort with last swapped optimization:

Start of bubble sort:


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Start iteration 1:


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


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


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


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


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


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


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


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


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Homework 8: Sorting    Due: See Canvas



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Start iteration 2:


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

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


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Compare 2 (at index 1) with 5 (at index 2) and don’t swap


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


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Compare 5 (at index 3) with 4 (at index 4) and swap


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Finished iteration 2 of bubble sort.

Note: Next iteration, skip over indices 4 - 8 since no swaps occurred there.

Merge Sort

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

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 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()!

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.

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). Your implementation must be randomized as speci ed in the method’s javadocs. Logically, it is similar to a one-sided quick sort. When asked for the kth smallest, you should return what would be at index k 1 if the array was perfectly sorted.


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Homework 8: Sorting    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
10pts


bubbleSort
10pts


mergeSort
15pts


lsdRadixSort
15pts


heapSort
10pts


kthSelect
15pts


Other:



Checkstyle
10pts


E  ciency
15pts


Total:
100pts



Provided

The following    le(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 di erent 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.

    2. SortingStudentTests.java.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 le(s). Make sure all le(s) listed below are in each submission, as only the last submission will be graded. Make sure the lename(s) matches the lename(s) below, and that only the following le(s) are present. The only exception is that Canvas will automatically append a -n depending on the submission number to the le name(s). This is expected and will be handled by the TAs when grading as long as the le name(s) before this add-on matches what is shown below. If you resubmit, be sure only one copy of each le is present in the submission. If there are multiple les, do not zip up the les before submitting; submit them all as separate les.

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

    1. Sorting.java






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