# Homework 4: Binary Search Trees Solution

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## Description

Binary Search Tree

You are to code a binary search tree. A binary search tree is a collection of nodes, each having a data item and a reference pointing to the left and right child nodes. The left child node and all of its children are less than the data. The right child node and all of its children are greater than the data. Therefore, all elements added to the tree must implement Java’s generic Comparable interface. This means that ALL comparison logic should be using the compareTo method.

All methods in the BST that are not O(1) must be implemented recursively, except for one speci c edge case in remove(), see Javadoc for details).

Your binary search tree implementation will implement the BST interface provided. It will have two constructors: the no-argument constructor (which should initialize an empty tree), and a constructor that takes in data to be added to the tree, and initializes the tree with this data. Any attempts to add data that is already in the tree should be ignored (the tree shouldn’t be changed, and the duplicate item shouldn’t get added).

Nodes

The binary search tree consists of nodes. The BSTNode class will be given to you; do not modify it.

Methods

You will implement all standard methods for a Java data structure (add, remove, etc.). See the interface for details. Note that some methods are worth more than others. If add is incorrect, then you are likely to fail most tests, as adding is crucial to the usability of a data structure.

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Homework 4: Binary Search Trees Due: See T-Square

Traversals

You will implement 3 di erent ways of traversing a tree: pre-order traversal, in-order traversal, and post-order traversal. They must be implemented recursively! You may import Java’s LinkedList/ArrayList classes as appropriate for these methods (but they may only be used for these methods and the Find-PathBetween method).

FindPathBetween

You will implement a method to calculate the path between two elements in the tree. You will treat the rst parameter as your starting point and the second as your ending point. Note that either piece of data could be anywhere in the tree, meaning you will have to at some point make a separate traversal for each piece of data. You may import Java’s LinkedList/ArrayList classes as appropriate for these methods (but they may only be used for this method and the traversal methods). However, you are only allowed to use 1 instance of a List (determining which type of List to use is an exercise to you and is subject to e ciency deductions) to store the path. You must only traverse to each element once and any common ancestors may only be traversed once in total. This path must only include the deepest common ancestor only. Including other ancestors will result in 0 points. If the rst data parameter is equivalent to the second data parameter, then the path between the data is simply the data in the tree itself (note that the length of the list should be 1 in this case).

Height

You will implement a method to calculate the height of the tree. The height of any given node is max(left.height, right.height) + 1. A leaf node has a height of 0.

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: add 24pts remove 16pts get 6pts contains 6pts traversals 6pts path between 7pts height 3pts clear 2pts constructor 5pts Other: Checkstyle 10pts E ciency 15pts Total: 100pts

Keep in mind that add functions are necessary to test other functions, so if an add doesn’t work, remove tests might fail as the items to be removed were not added correctly. Additionally, the size function is used many times throughout the tests, so if the size isn’t updated correctly or the method itself doesn’t work, many tests can fail.

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Homework 4: Binary Search Trees Due: See T-Square

A note on JUnits

We have provided a very basic set of tests for your code, in BSTStudentTests.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 (when it comes up).

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. 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.

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 ArrayList<Integer>() instead of new ArrayList(). 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

System.arraycopy()

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Homework 4: Binary Search Trees Due: See T-Square

clone() assert()

Arrays class Array class

Collections class

Collection.toArray()

Re ection APIs

Inner or nested classes

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.

Provided

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

1. BSTInterface.java

This is the interface you will implement in BST. All instructions for what the methods should do are in the javadocs. Do not alter this le.

1. BST.java

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

1. BSTNode.java

This class represents a single node in the BST. It encapsulates the data, left, and right reference. Do not alter this le.

1. BSTStudentTests.java

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