Warning: this assignment is not officially released yet. This spec is subject to change until this warning disappears.


Each assignment will have an FAQ linked at the top. You can also access it by adding “/faq” to the end of the URL. The FAQ for Lab 2 is located here.

Before You Begin #

Run git pull skeleton main in your repo. You should get a lab02/ folder. For this, and later labs, we strongly recommend opening up the lab in IntelliJ.

Note: You may notice after pulling and setting up your workspace that two of the files, PathHarness.java and PathTest.java, will have orange coffee mugs next to their name instead of a blue circle. This is ok! We will revisit those files later in the lab.

Also, please note that this lab expects exposure to programming similar to that obtained in a course like CS 61A. We will begin diving deep into Java, and moving fast. If you are not as comfortable with this material, we recommend you take a look at this Java Crash Course as supplemental material.

Learning Goals #

This lab will focus on Java primitives and objects. Our goals for this lab will be as follows:

  • Learn the different Java primitives and when to use them.
  • Learn how to define classes and use reference-typed variables.
  • Learn how to work with box-and-pointer diagrams to identify common usage errors.
  • Get some more practice with Arrays
  • Start Project 0!

Primitives #

As you may have noticed, when initializing a variable in Java you must put the type next to it. Notice that this is different than Python, where you can simply assign any arbitrary data type to a variable name.

int number = 10;

The above line tells Java that the variable number is an integer that holds the value 10. A variable’s type tells us what kind of data is stored in that variable. In the case of the variable number, its data type is an integer. In Java, there are a predefined set of primitive types.

  • boolean : a boolean represents the two possible values of true and false.

  • byte : a byte represents an 8-bit signed integer.

  • short : a short represents a 16-bit signed integer.

  • int : an int represents a 32-bit signed integer. This is the most commonly used integer type and can hold values between -2,147,483,648 to 2,147,483,647 inclusive.

  • long : a long represents a 64-bit signed integer. Sometimes when we need to express large integral numbers we will use this as it ranges from -9,223,372,036,854,775,808 to 9,223,372,036,854,775,807.

  • float : a float represents a 32-bit single precision floating point number. Floating point numbers can approximate a range of real numbers including integers, decimals, and special values like infinity. Floating point numbers can only represent a finite number of the infinitely many numbers in existence. Anything that cannot be represented is encoded as “NaN”, which stands for “Not a Number”. How float determines what numbers can be represented is a 61C topic. For the purposes of this class, you can work under the assumption that every number can be represented as a float.

  • double : a double represents a 64-bit double precision floating point number. Most of our decimal numbers will use this type as it provides greater precision.

  • char : a char represents an ASCII letter (like the English alphabet).

These words are reserved in Java. That is, we cannot use int and double in any other context besides declaring a variable of that type. Note that all primitives begin with a lowercase letter.

Declaring a primitive is very simple. For example, if we wanted to declare a double, we can write the following.

double pi = 3.14;

Certain primitives require an extra letter after the initial value. For example, to declare a long or a float, we write the following. Notice the L and the f that signify the end of the value.

long num = 9223372036854775807L;
float num2 = 42.0f;

Finally, we can declare a char using a single-quoted literal. For example, if we want to initialize variable a to the letter “a”, we would write the following.

char a = 'a';

We need not always initialize the value of a primitive. Sometimes, we don’t care about the value at that point in time, and only need a variable to use in later code. We do so by declaring the following:

char a;
double d;

Note that primitives have default values - we’ll talk about this later.

So declaring a variable is like telling Java you have a variable of a certain type. Java sets aside a little container of memory that can perfectly hold that type. Once you’ve declared a variable, initializing a variable is when you actually put a value inside that little container of memory. We can imagine that these little magic memory boxes can only contain objects of a certain type. So if you declare a variable of type int, and then try to initialize its value to false, your code won’t compile because false is not an int!

int a;
int b;
a = 61; //This line will compile with no errors
b = false; //This line will error during compilation as 'b' is of type int and not boolean

Objects #

Java is an object-oriented language. This means that everything we want to represent in Java is defined in terms of objects.

Objects are bundles of code that define the state and behavior of the construct we wish to represent. Suppose we wish to represent a potato. A potato’s state can be described by its variety and age, and it also has behaviors such as grow and flower.

Now suppose Erik and Alex both have potatoes; Erik has a Yukon Gold and Alex has a Red Pontiac. Even though Erik and Alex have different varieties of potatoes, they are both still potatoes. They each have an age, color and variety. Critically, we can describe an entire group of Potatoes with a set of common descriptors.

In Java we define an Object via its Class. Erik’s Yukon Gold and Alex’s Red Pontiac would then be called instances of the Potato class. Let’s see how we can implement a Potato class in Java.

Example #

For this section, we will be using the Potato code found below. This can also be found in lab02/src/Potato.java.

public class Potato {

    /* An instance variable representing the potato's species. */
    private String variety;
    /* An instance variable representing the potato's age. */
    private int age;

    /** A constructor that returns a very young russet burbank potato. */
    public Potato() {
        this.variety = "Russet Burbank";
        this.age = 0;

    /** A constructor that allows you to specify its variety and age. */
    public Potato(String variety, int age) {
        this.variety = variety;
        this.age = age;

    /** A getter method that returns the potato's type. */
    public String getVariety() {
        return this.variety;

    /** A getter method that returns the potato's age. */
    public int getAge() {
        return this.age;

    /** A setter method that sets the potato's age to AGE. */
    public void setAge(int age) {
        this.age = age;

    /** A method that grows the potato. Note it increases its age by 1. */
    public void grow() {
        this.age = this.age + 1;

    /** Did you know potatoes can flower? No? Neither did I... */
    public void flower() {
        System.out.println("I am now a beautiful potato");

We will also be looking at lab02/src/Potato1.java later on!

Defining a Class #

We’ve provided a sample Potato class in the skeleton files. The steps in this section show you how we made it!

To define a Java class, we make a new .java file and encompass the class’s code with the following header:

class Potato {
    /** Potato code goes here! */

There are two things to keep in mind when writing Java classes.

  • Java requires the class name to be the same as the file name. This is why the Potato class is written in Potato.java.

  • By convention, the name of a class always begin with a capital letter and is generally named using camel case (ex: ThisIsCamelCase)

Constructors #

Now, to initialize a Potato object, we must call its constructor. The constructor is a special method that creates and returns a new instance of your class. This method is where we will initialize all the variables associated with the class’s instance. Unlike other methods, there is no return type in the constructor’s signature, and it must have the same name as the class itself. Although we do not specify a return type in the method name and there is no return statement, the constructor creates an instance of the class and returns it. This is a unique property of constructor methods.

It’s possible to define a constructor that takes in no arguments.

public Potato() {
    this.variety = "Russet Burbank";
    this.age = 0;

Creating a constructor that takes in no arguments lets us create a default case. Here, if the user doesn’t give us the type or age of the potato, we’re telling the computer to set the type to “Russet Burbank” and age to 0 by default.

However, we can also give our user the option to specify arguments in our constructor.

public Potato(String variety, int age) {
    this.variety = variety;
    this.age = age;

This constructor returns a Potato with its variety and age set to the values given as arguments. Now we can construct potatoes such as erik’s 3 year old Yukon Gold potato.

We will discuss how to declare objects in more detail during the Boxes and Pointer Diagrams section.

Caveat: if no constructors are defined in the object file, then the Java compiler will provide a default constructor that accepts no argument. However, if a constructor is defined, then the compiler will not provide a default constructor. Read more about it here.

Instance Variables #

Instance variables allow us to represent the state of an object and can be both primitives or objects. The “has a” test is an easy way to see if something should be an instance variable of an object. For example, a potato has an age and variety. Thus, within our Potato class, we see that there are two instance variables: variety and age.

/* An instance variable representing the potato's species. */
private String variety;
/* An instance variable representing the potato's age. */
private int age;

As with any other variable, we must declare what type it is. The String keyword tells us variety is a string object and int tells us the age is an integer primitive.

Instance variables have default values that correspond to the type of the variable. If instance variables are not initialized in the constructor or elsewhere with a value, they will initially contain the default. These defaults will correspond to a zero value. 0 for int, float, double, etc. false for boolean, and null for Object types. However, it is not good practice to rely on default values, as it makes it harder to understand your code. Instead, you should explicitly initialize your instance variables.

We can (usually) access the age and variety of the Potato via dot notation. This is similar to Python’s dot notation, which you may have encountered in CS 61A.

Potato eriksPotato = new Potato("Yukon Gold", 3); // erik's potato!
eriksPotato.variety; // returns the variety of erik's potato
eriksPotato.age; // returns the age of erik's potato

Notice that we had to first instantiate a new Potato object before we could access variety or age. The order of the variables that we pass into the new Potato call must match the order of the parameters of the constructor. Remember that instance variables are particular to the object. Thus we need to create an object first in order to have variety and age. Also notice that we have both declared and instantiated eriksPotato within the same line to make our code a little more compact.

Doing something like:

Potato eriksPotato;
eriksPotato = new Potato("Yukon Gold", 3);

is practically the same. You may want to declare a variable before instantiating it if the initial assignment of the variable should not be set (e.g. we don’t know that Erik’s potato is currently 3 years old).

When writing object code within its class, we can also employ the this keyword. Its usage is similar to that of self in Python.

this.variety; // returns the current instance's variety
this.age; // returns the current instance's age

One notable difference, however, is that this cannot be reassigned whereas self in Python can be reassigned.

Outside of the Potato class, we can’t use this to refer to eriksPotato since we only use this to refer to the current instance while inside the class. Instead, we’re trying to refer specifically to eriksPotato.

We also have a private keyword placed in front of the variety and age declaration. This means we cannot access the variety and age via dot notation outside of Potato.java. We will see more about why we may want to do this in the Getter and Setter Method section later on.

Finally, it’s important to stress that even though all instances of Potato will have the variables variety and age, their values will be specific to each instance of Potato - hence the name instance variable.

Instance Methods #

To facilitate behavior, we can define instance methods. For example, Potato has defined in it the grow() method.

/** A method that grows the potato. Note it increases its age by 1. */
public void grow() {
    this.age = this.age + 1;

Like instance variables, we can access instance methods using dot notation as well.

eriksPotato.grow(); // Erik's potato grows!

We also have a few special instance methods prefixed by the words “get” and “set”. These are aptly named getters and setters, which we’ll learn more about below!

Getter and Setter Methods #

As we have seen, the private keyword limits our ability to access instance variables directly. This is called an access modifier and we will be discussing them in more detail later on in the course.

For now, just know that in general it is good practice to make instance variables private. One consequence of making our instance variables private is that we must now define instance methods to access them.

This is where we introduce getter and setter methods. Within Potato we have these methods.

/** A getter method that returns the potato's type. */
public String getVariety() {
    return this.variety;

/** A getter method that returns the potato's age. */
public int getAge() {
    return this.age;

The above two blocks are called getter methods since they get the value of their respective instance variables for programs outside of Potato.java. Of course, due to advancements in genetic modification technology, it is also possible to set the age of our potato.

/** A setter method that sets the potato's age to AGE. */
public void setAge(int age) {
    this.age = age;

This is called a setter method as it allows us to set the value of an instance variable.

Interestingly enough, we don’t have a setter method for the variety instance variable. This is because until we develop the technology to support spud-transmutation (#PotatoDreams), Erik’s Yukon Gold potato will forever remain a Yukon Gold potato.

Of course, this is important in an application sense because now external programs cannot maliciously change the identity of a potato. Take a look at Potato1.java

/* An instance variable representing the potato's species. */
public String variety;
/* An instance variable representing the potato's age. */
public int age;

The variety and age are public, meaning we can write a program to change the identity of Erik’s potato.

/* eriksPotato is an instance with variety = "Yukon Gold" */
eriksPotato.variety = "Red Pontiac"; // A POTATO IMPOSTER!

The practice of using getters and setters is called information hiding and it prevents external programs from unintentionally (or intentionally!) changing the value of our instance variables.

In one of exercises later, we will be considering a bank account. Without a doubt, we will want the balance of our bank account to be private, so that other programs cannot simply set account.balance = 0;.

Box and Pointer Diagrams #

Throughout this class it will be extraordinarily helpful to draw pictures of the variables in our programs to help us with debugging by visualizing the state and changes of objects throughout the code. The diagrams we’ll teach you to use in this class are often referred to as box and pointer diagrams, which are similar to the Environment Diagrams you saw in CS 61A.

Let’s start off with something simple. When we declare a primitive, we draw a box for it, and label the box with the type of primitive, and the name of the variable. Here, primitives will be in red boxes. For example,

int x;


(We could also have drawn a 0 in the box.) When we assign a value to the primitive, we fill in the box with the value of the primitive.

x = 3;


Variables can also refer to objects. For example, a variable can refer to a Potato instance. We can declare a Potato object the same way as we declare an int.

Potato p;

This variable is called a reference, because it will refer to an object. When we first declare the reference but don’t assign an object to it like in the code above, we say the reference contains nothing, or null. This also occurs when an instance variable is not assigned a value in the constructor. Here’s how we draw it:


Here we’re drawing references in green to emphasize that they are different from primitives.

Now let’s assign a reference to the Potato object by calling its constructor. This instantiates, or creates, a new instance of the Potato class. Instantiating an object via its constructor always requires the new keyword.

p = new Potato();

Objects in Box and Pointer Diagrams are each drawn as their own separate boxes. Here, there is a large blue box that represents one instance of the Potato class. Inside the large blue box are smaller boxes that represent the instance variables of the class. In our example, the Potato class has one primitive variable, the int ‘age’, and one object variable, the String variety. Therefore there are two smaller boxes in the Potato box. Notice how the value for age is inside a red box because it is a primitive, just like int x.


Here an object is drawn in blue, to emphasize that it is different from a primitive and a reference. We can now store primitives within the object as instance variables!

One critical thing about the object: unlike the primitive integer, 3, drawn inside the box for x, the Potato object is not drawn inside the variable p. Instead p simply contains an arrow that points to the Potato object. This is why p is called a reference or pointer because it just refers to the object but does not contain it. The true value of the variable p is a pointer to a Potato object rather than the Potato object itself. A pointer is essentially just a location in memory where the actual Potato object is stored.

This is a very, very important distinction!

Of course, when we call the no argument constructor, it will initialize the variety to "Russet Burbank" and the age to 0. Our diagram looks like the following.


Is this what you expected?

Remember that a String in Java is an object, not a primitive. As a result, the String instance variable representing the variety of the potato must contain a pointer to the actual String object containing the name we’ve chosen. For the sake of simplicity we don’t show the instance variables of the String object. Although it’s very much out of scope for the purposes of this class, you can take a look at the source code for the String class in Java, if you’re interested.

For another explanation, you may read Section 2.1 from the CS 61B textbook, starting from the section titled “The Mystery of the Walrus” and stopping just before “The Law of the Broken Futon”.

Discussion: Intuition for Drawing Objects #

See if you can come up with intuition as to why these diagrams are drawn the way they are:

  • Why does it make sense that objects are not stored inside variables, but are only referred to them?
  • Why isn’t the blue object box labeled with the name of the variable?

There aren’t necessarily correct answers to these questions, so just see if you can come up with explanations that make sense to you.

Pass-by-Value #

Java is pass-by-value. Methods are given copies of the actual parameters during execution. The original parameters cannot be changed by the method.

Consider the following code, right before tryToIncrement returns.

public class passByValue{

    public static void tryToIncrement(int x) {
	      x = x + 1;
    public static void main(String[] args) {
	    int x = 10;


When we pass a variable into a method, we copy whatever is inside the box of the variable and put that copy into a new box in the method. For primitives, like x, we copy whatever is inside the box for x (in this case 10), and put that data into the method’s stack frame, the space in memory that this method uses to track its variables. This means that, like we saw in tryToIncrement(), when we modify primitives in a method we modify the copy of that primitive, not the original. For objects, this is different. Remember, in our box and pointer diagrams, the object itself is not stored inside the box for the object variable. Instead, what is stored is a pointer to the object in memory (represented by an arrow). Therefore, what is copied over is that pointer, not an entirely new copy of the object. In more technical terms, when we pass in an object, what is copied is not the object itself, but the reference to the object.

public static void refresh(Potato p) {
    p.age = 0;

public static void main(String[] args) {
    Potato potat = new Potato("Red La Soda", 5);


What is copied over into the parameter of the refresh method is not a copy of the Potato object, but a copy of the reference (the arrow) to the Potato Object.

static #

There’s something that we’ve been kind of waving off up until now: the static keyword. In Java, static fields belong to the class instead of a particular instance. We call these static fields or class variables. During execution, only one instance of a static field exists throughout, no matter how many instances of the class are created. You can think of them as living in their own special space, away from each instance. Static fields can be referenced the same as instance variables from within a instance method. They can also be directly referenced as ClassName.staticVariable, or by the instance reference (although this is not recommended for style).

The code block below shows some of the different ways in which static and non-static methods and variables interact with each other. Read through the code and the comments to get a sense what is happening. Then, run the code using the link to the Java Visualizer and see if your predictions were correct.

public class Bicycle {

    // Non-static instance variables, each Bicycle(object) has its own copy
    private int speed;
    // Static class variable, shared by all Bicycles(objects)
    private static int numberOfBicycles = 0;

    /* Constructor, called when we create a new Bicycle object.
        can reference (use) both static and non-static variables */
    public Bicycle(int startSpeed) {
        speed = startSpeed;

        numberOfBicycles += 1;

    /* Static methods, belong to the class, can only reference (use) static variables and methods. Can not use 'this' in the function body.*/
    public static int getNumberOfBicycles() {
        return numberOfBicycles;

    /* Instance methods, belong to the object, can reference (use) both static and non-static variables and methods. Can use 'this' in the function body. */  
    public int getSpeed() {
        return this.speed;
    public void speedUp(int increment) {
        this.speed += increment;

    public static void main(String[] args){
        Bicycle b1 = new Bicycle(10); // create a new Bicycle object b1
        System.out.println("Number of bicycles: " + b1.getNumberOfBicycles()); // valid call to static method using instance reference
        Bicycle b2 = new Bicycle(10); // create a new Bicycle object b2
        System.out.println("Number of bicycles: " + b1.getNumberOfBicycles()); // Updated number of bicycles when called from b1
        System.out.println("Number of bicycles: " + b2.getNumberOfBicycles()); // valid call to same static method using instance reference
        System.out.println("Number of bicycles: " + Bicycle.getNumberOfBicycles()); // valid call to same static method using class name
        System.out.println("Speed of b1: " + b1.getSpeed()); // valid call to instance method using instance reference
        System.out.println("Speed of b2: " + b2.getSpeed()); // valid call to instance method using instance reference
        // System.out.println("Speed of b1: " + Bicycle.getSpeed()); // invalid call to instance method using class name
        b1.speedUp(10); // change the speed of b1, b2 is unaffected
        System.out.println("Number of bicycles: " + getNumberOfBicycles()); // valid call to static method when called from within the class
        // System.out.println("Speed of b1: " + speed); // invalid call to instance variable from within static method
        // System.out.println("Speed of b1: " + getSpeed()); // invalid call to instance variable from within static method


We really recommend you play around with the code above, specifically in the main method, and see what happens when you change things. Use the Java Visualizer to help you understand what is happening. You can also read the oracle documentation on class variables for more information.

The True Meaning of this #

Did you notice that there was something different between the setAge method and the refresh method? Look at the code segments and think about why that may be.

setAge is an instance method, which means that it must always be called through dot notation on an object. Instance methods always have a this variable, which references the object that the method was called on. In contrast, refresh is a static method (marked with the static keyword). Static methods do not have a this reference in their frame; they belong to the class rather than to an instance of the class.

We call being inside a static method during execution being in a static context. You cannot directly reference instance variables from a static context. Instead, you must do so through an object reference (due to the lack of a this reference). Note that static methods can be called from a static context (like in main) and do not need to be called with an instance associated with them.

Exercise: Account Management #

The next several exercises involve modifications to the Account class, which models a bank account. You should’ve pulled the skeleton code for this class in the Getting Started section at the beginning of this lab. The file you will be working with is Account.java. Open IntelliJ to access this file.

Tests are also provided in the tests/ folder, you can run AccountTest.java in Intellij to check the correctness of your code.

Task: Modifying Withdrawal Behavior #

The withdraw method is currently returns void. Modify it to return a boolean: true if the withdrawal succeeds (along with actually performing the withdrawal) and false if it fails.

Task: Merging Accounts #

Implement the merge method. This method should transfer all of the money from the argument account to the current account. In other words, the argument account balance should be zeroed while the current account’s balance increases by the argument’s old balance. We’ve provided a skeleton of the method in Account.java.

Task: Overdraft Protection #

A convenient feature of some bank accounts is overdraft protection: rather than bouncing a check when the balance would go negative, the bank will deduct the necessary funds from a second account. One might imagine such a setup for a student account, provided the student’s parents are willing to cover any overdrafts (!). Another use is to have a checking account that is tied to a savings account where the savings account covers overdrafts on the checking account. In our system, we’ll be keeping things simple with only one type of account so we don’t have to worry about student or savings accounts.

Implement and test overdraft protection for Account objects by completing the following steps.

  1. Add a parentAccount instance variable to the Account class; this is the account that will provide the overdraft protection, and it may have overdraft protection of its own.
  2. Add a two-argument constructor. The first argument will be the initial balance as in the existing code. The second argument will be an Account reference with which to initialize the instance variable you defined in step 1.
  3. In the one-argument constructor, set the parent account to null. We’d like to emphasize the fact that there is no parent if the one-argument constructor is used by explicitly setting parentAccount to null.
  4. Modify the withdraw method so that if the requested withdrawal can’t be covered by this account, the difference is withdrawn from the parent account. This may trigger overdraft protection for the parent account, and then its parent, and so on. The number of accounts connected in this way may be unlimited. If the account doesn’t have a parent or if the parent (and its parents and so forth) can’t cover the withdrawal, the withdraw method should merely print an error message as before and not change any account balances.

Note: it is important to check if the parent account is null before executing any changes to the account.

Here’s an example of the desired behavior, with the Account object teresa providing overdraft protection for the Account object dom. Recall this means the parentAccount of dom is teresa.

Suppose, in each scenario below, dom has 100 as their balance while teresa has 500 as their balance.

dom attempts to withdraw 50
dom then has 50 remaining in their balance, while teresa still has 500.
dom attempts to withdraw 200
dom then has 0 remaining in their balance, while teresa needed to cover 100 for dom, leaving 400 as their balance.
dom attempts to withdraw 700
return false without changing either balance as the withdrawal is denied due to insufficient funds.

We recommend approaching this problem recursively. Here are some questions that may help you work through the exercise:

  1. If we trigger overdraft protection, what should the new balance of this account be set to after a successful withdrawal?
  2. If we trigger overdraft protection, how much of the initial withdrawal total will the parent account be responsible for?
  3. How can you use the return value of withdraw to only deduct balance if the parent accounts can complete the withdrawal?

To test your code, try copy and pasting the Account class into the online Java Visualizer. Make sure to add a main method with a few example cases like the ones provided above.

Account teresa = new Account(500);
Account dom = new Account(100, teresa);

Discussion: Merging Revisited #

One proposed solution for merging accounts is the following:

public void merge(Account other) {
    this.balance = this.balance + other.balance;
    other = new Account(0);

This doesn’t work. Explain why not. Highlight the space below to reveal the answer.

When we set `other = new Account(0);`, we lose information regarding the parent account of `other` and this is not intended behavior. .

Exercise: Pursuit Curves #

You will now create a class representing a pursuit curve.

Pursuit curves provide a powerful way to render curves on a computer. The traditional method for drawing a path is to analytically define it via some algebraic formula like \(y(t) = t^2\) and trace it point-wise. Consider an alternative where we define two points: the pursuer and the pursued.

Now suppose the pursued point (in black) follows some fixed path \(F(t)\). Then the pursuer (in red) will seek the pursued in the following manner.


We notice that the pursuer always follows the pursued along its tangent, which gives some serious first order differential equation vibes. Letting the pursuer’s path be given by \(x(t)\), then the closed form solution for its path is given by the following equation.


Of course, we won’t require you to solve a differential equation. In fact, let’s see what your task will be!

Task: Implementing Pursuit Curves #

Here’s a getting started video:

Implement a simpler version of pursuit curves in order to create a cool visual by filling out Path.java. An additional file PathHarness.java is provided containing code that will render your code in Path.java using Java’s graphics framework, uncomment this file after implementing Path.java.

Also, testing code has been provided in PathTest.java. You can uncomment this file and run these tests in Intellij.

As with the previous assignments, these tests are not entirely comprehensive. Feel free to add whatever testing code you desire.

Path.java will represent the path traveled by the pursuer. You will need to keep track of the following two points:

  • curr will represent where the path currently ends. This will be a Point object.

  • next will represent where the path (and thus, curr) will travel to next. This will also be a Point object.

Next, you will need to define a constructor that, given an x and y coordinate, sets next to the starting point (x, y). The constructor may look something like this.

public Path(double x, double y) {
    // more code goes here!

When the Path object is first constructed, curr can be set to a Point instance with any coordinate so long as it is not null. Try playing around with initial curr values to see what you can get!

Finally, you will need to implement the following instance methods.

method name return type functionality
getCurrX() double Returns the x-coordinate of curr
getCurrY() double Returns the y-coordinate of curr
getNextX() double Returns the x-coordinate of next
getNextY() double Returns the y-coordinate of next
getCurrentPoint() Point Returns curr
setCurrentPoint(Point point) void Sets curr to point
iterate(double dx, double dy) void Sets curr to next and updates the position of next to be next with movement defined by dx and dy.

A note on iterate(double dx, double dy). If you were to implement a pursuit curve in full generality, then this is where you would solve a differential equation. But again, we won’t have you do that. Instead we’re giving you \(dx\) and \(dy\) where, dx represents the distance moved in the x-direction and dy represents the distance moved in the y-direction.

To summarize your task:

  • Keep track of curr and next.

  • Implement a constructor taking in a double x and double y.

  • Implement the methods listed in the table above.

Here are some tips to keep you on the right track!

  • As curr and next are both Point objects, we’ve provided a class defining Point. Make sure to read through and understand what each method and constructor does!

  • When defining iterate(double dx, double dy) you may find that your curr and next are not being set to what they are coded to be. Think about object references and try drawing a box-and-pointer diagram.

If you want to learn more about pursuit curves, Wolfram’s MathWorld provides a very interesting read.

.toString and .equals #

You may have also noticed the .toString and .equals methods in the Point class, which have been copied here for your convenience. Both of these are special methods which you will use often throughout the rest of this class.

public class Point {
    public double x;
    public double y;

    public String toString() {
        return "(" + this.x + ", " + this.y + ")";

The toString method is used by Java to determine how to represent an object as a string, like when printing objects to display to the user. In the example below, we create a new point at the origin, \((0, 0)\). When calling System.out.println, Java needs to figure out what exactly to print, so it invokes the toString method which returns (0.0, 0.0). Then, that string is displayed to the screen.

Point p = new Point();
System.out.println(p);  // (0.0, 0.0)

Likewise, the equals method is used whenever a user calls equals. We might define equality between two points as follows. We first verify if the object passed in is a Point and then check for equality based on the x and y values.

public class Point {
    public double x;
    public double y;

    public boolean equals(Object o) {
        if (o instanceof Point other){
            return (this.x == other.x) && (this.y == other.y);
        else {
            return false;

It is very important to understand the difference between the equality and identity of objects. If you have not already, read over the Identity and Equality section of the Java guide. Many tricky bugs can arise from this if you misuse these two related but different concepts.

Task: Arrays and Project 0 #

The last exercise of this lab is intended to get you started with Project 0, if you have not done so already. This is a fast-paced course and want you to stay on track! Please take a moment to read the Project 0 Spec up to Task 1.

Since Project 0 requires you to manipulate arrays, we have provided some array exercises to warm you up. You can find them in the file ArrayExercises.java in the skeleton code. It is broken down into the following exercises:

  • makeDice: This method returns a new array of integers [1, 2, 3, 4, 5, 6].
  • takeOrder: This method takes in a String and returns a new array containing the orders of the customer. If the customer is Circle, you should return an array of Strings ["beyti", "pizza", "hamburger", "tea"] in that order. If the customer is Erik, you should return an array of Strings ["sushi", "pasta", "avocado", "coffee"]. In any other case, return an empty String array of size 3.

    NOTE: == behaves strangely with Strings, as we discussed in the previous section. You should check strings s1 and s2 for equality using s1.equals(s2) in Java.

  • findMinMax: This method takes an int[] array and returns the the positive difference between the maximum element and minimum element of the given array. You may assume the input array is nonempty.

Your task is to complete the exercises in ArrayExercises.java, then complete Task 1 of the project, which asks you to implement the emptySpaceExists() method. We will only be grading your completion of ArrayExercises.java, but you will thank yourself later if you take the rest of this task seriously and start Project 0!

Conclusion #

Coding is not easy! Keeping track of what references point to what, modifying code (which you first have to understand), and systematically finding bugs are definitely not skills that develop overnight. Make sure to practice! You can generate variants of the lab exercises to provide extra practice.

The exercises on complicated uses of references are easy to produce and can be verified online using tools such as Java Visualizer or by simply running your code through IntelliJ.

The internet is also a great source for more coding practice. Here’s a short list of websites where you can find problems:

Many problems you see will rely on things we haven’t learned yet. If you see a problem that you don’t know how to do, don’t panic! We’ll be covering a lot more data structures in this class that will help you solve them.

For coding, practice is crucial so make sure to do so! Finally, if you or anyone you know is struggling, let a TA know and we’ll be more than happy to help.

Deliverables #

To quickly recap what you need to do for this lab:

  • Make sure you understand Box and Pointer Diagrams
  • Account.java
  • Path.java
  • ArrayExercises.java
  • Start Project 0