Homework 5: MaxHeap Solution

Heap

You are to code a Heap, speci cally a MaxHeap, that is backed by an array of contiguous elements. Here is a tree and array representation of the same MaxHeap:



















A MaxHeap is a type of binary tree with two main properties.

Shape Property: The tree must be complete. All levels of the tree must be full except the bottom-most level. If the bottom-most level is not full, it must be lled from left to right.

Order Property: Each node’s data is larger than the data in its two children. There is no explicit relationship between sibling nodes.

These properties guarantee that the largest element in the heap will be at the root of the heap.

Although heaps are usually classi ed as a type of tree, they are commonly implemented using an array due to their completeness. In your implementation, you should leave index 0 empty and begin your heap at index 1. This will make the arithmetic to nd parents and children simpler.

To nd the children of index i, 2i is the index of the left child (if one exists) and 2i + 1 is the in-dex of the right child (if one exists).

You should implement two constructors for this heap. One constructor initializes an empty heap with the capacity speci ed by a constant in MaxHeap.java. The other constructor should implement the BuildHeap algorithm that was taught in lecture, which is an algorithm that creates a heap in O(n) time. Simply adding the elements one by one will not receive credit since it would be O(n log(n)) in the worst case; see the javadocs for this constructor for more speci cations.

You may assume that your implementation does not need to handle duplicate elements. That is, the add method will never be passed duplicates and the remove method will never have to deal with the heap having duplicates. To be clear, your implementation would most likely work even if we were to test for duplicates; however, this will help remove ambiguity surrounding grading and testing your implementation.

Unlike your BST homework, you are not required to use recursion in this assignment. Use whatever you nd most intuitive - recursion, iteration, or both. However, regardless of the technique you use, make sure to meet e ciency requirements as discussed in lecture.



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Homework 5: MaxHeap    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:



constructor / buildHeap
20pts


add
20pts


remove
20pts


getMax
5pts


isEmpty
5pts


clear
5pts


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. MaxHeap.java

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

    2. MaxHeapStudentTest.java

This is the test class that contains a set of tests covering the basic operations on the MaxHeap 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. MaxHeap.java






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