# 2.3: Exercise 2

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$

( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\id}{\mathrm{id}}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\kernel}{\mathrm{null}\,}$$

$$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$

$$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$

$$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

$$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$

$$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$

$$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vectorC}[1]{\textbf{#1}}$$

$$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$

$$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$

$$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

$$\newcommand{\avec}{\mathbf a}$$ $$\newcommand{\bvec}{\mathbf b}$$ $$\newcommand{\cvec}{\mathbf c}$$ $$\newcommand{\dvec}{\mathbf d}$$ $$\newcommand{\dtil}{\widetilde{\mathbf d}}$$ $$\newcommand{\evec}{\mathbf e}$$ $$\newcommand{\fvec}{\mathbf f}$$ $$\newcommand{\nvec}{\mathbf n}$$ $$\newcommand{\pvec}{\mathbf p}$$ $$\newcommand{\qvec}{\mathbf q}$$ $$\newcommand{\svec}{\mathbf s}$$ $$\newcommand{\tvec}{\mathbf t}$$ $$\newcommand{\uvec}{\mathbf u}$$ $$\newcommand{\vvec}{\mathbf v}$$ $$\newcommand{\wvec}{\mathbf w}$$ $$\newcommand{\xvec}{\mathbf x}$$ $$\newcommand{\yvec}{\mathbf y}$$ $$\newcommand{\zvec}{\mathbf z}$$ $$\newcommand{\rvec}{\mathbf r}$$ $$\newcommand{\mvec}{\mathbf m}$$ $$\newcommand{\zerovec}{\mathbf 0}$$ $$\newcommand{\onevec}{\mathbf 1}$$ $$\newcommand{\real}{\mathbb R}$$ $$\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$$ $$\newcommand{\laspan}[1]{\text{Span}\{#1\}}$$ $$\newcommand{\bcal}{\cal B}$$ $$\newcommand{\ccal}{\cal C}$$ $$\newcommand{\scal}{\cal S}$$ $$\newcommand{\wcal}{\cal W}$$ $$\newcommand{\ecal}{\cal E}$$ $$\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$$ $$\newcommand{\gray}[1]{\color{gray}{#1}}$$ $$\newcommand{\lgray}[1]{\color{lightgray}{#1}}$$ $$\newcommand{\rank}{\operatorname{rank}}$$ $$\newcommand{\row}{\text{Row}}$$ $$\newcommand{\col}{\text{Col}}$$ $$\renewcommand{\row}{\text{Row}}$$ $$\newcommand{\nul}{\text{Nul}}$$ $$\newcommand{\var}{\text{Var}}$$ $$\newcommand{\corr}{\text{corr}}$$ $$\newcommand{\len}[1]{\left|#1\right|}$$ $$\newcommand{\bbar}{\overline{\bvec}}$$ $$\newcommand{\bhat}{\widehat{\bvec}}$$ $$\newcommand{\bperp}{\bvec^\perp}$$ $$\newcommand{\xhat}{\widehat{\xvec}}$$ $$\newcommand{\vhat}{\widehat{\vvec}}$$ $$\newcommand{\uhat}{\widehat{\uvec}}$$ $$\newcommand{\what}{\widehat{\wvec}}$$ $$\newcommand{\Sighat}{\widehat{\Sigma}}$$ $$\newcommand{\lt}{<}$$ $$\newcommand{\gt}{>}$$ $$\newcommand{\amp}{&}$$ $$\definecolor{fillinmathshade}{gray}{0.9}$$

The exercise for this chapter is to implement a List that uses a Java array to store the elements.

In the code repository for this book (see Section 0.1), you’ll find the source files you’ll need:

• MyArrayList.java contains a partial implementation of the List interface. Four of the methods are incomplete; your job is to fill them in.
• MyArrayListTest.java contains JUnit tests you can use to check your work.

You’ll also find the Ant build file build.xml. From the code directory, you should be able to run ant MyArrayList to run MyArrayList.java, which contains a few simple tests. Or you can run ant MyArrayListTest to run the JUnit test.

When you run the tests, several of them should fail. If you examine the source code, you’ll find four TODO comments indicating the methods you should fill in.

Before you start filling in the missing methods, let’s walk through some of the code. Here are the class definition, instance variables, and constructor.

public class MyArrayList<E> implements List<E> {
int size;                    // keeps track of the number of elements
private E[] array;           // stores the elements

public MyArrayList() {
array = (E[]) new Object[10];
size = 0;
}
}


As the comments indicate, size keeps track of how many elements are in MyArrayList, and array is the array that actually contains the elements.

The constructor creates an array of 10 elements, which are initially null, and sets size to 0. Most of the time, the length of the array is bigger than size, so there are unused slots in the array.

One detail about Java: you can’t instantiate an array using a type parameter; for example, the following will not work:

array = new E[10];


To work around this limitation, you have to instantiate an array of Object and then typecast it. You can read more about this issue at thinkdast. com/generics.

Next we’ll look at the method that adds elements to the list:

public boolean add(E element) {
if (size >= array.length) {
// make a bigger array and copy over the elements
E[] bigger = (E[]) new Object[array.length * 2];
System.arraycopy(array, 0, bigger, 0, array.length);
array = bigger;
}
array[size] = element;
size++;
return true;
}


If there are no unused spaces in the array, we have to create a bigger array and copy over the elements. Then we can store the element in the array and increment size.

It might not be obvious why this method returns a boolean, since it seems like it always returns true. As always, you can find the answer in the documentation: thinkdast.com/colladd. It’s also not obvious how to analyze the performance of this method. In the normal case, it’s constant time, but if we have to resize the array, it’s linear. I’ll explain how to handle this in Section 3.2.

Finally, let’s look at get; then you can get started on the exercises.

public T get(int index) {
if (index < 0 || index >= size) {
throw new IndexOutOfBoundsException();
}
return array[index];
}


Actually, get is pretty simple: if the index is out of bounds, it throws an exception; otherwise it reads and returns an element of the array. Notice that it checks whether the index is less than size, not array.length, so it’s not possible to access the unused elements of the array.

In MyArrayList.java, you’ll find a stub for set that looks like this:

public T set(int index, T element) {
// TODO: fill in this method.
return null;
}

Read the documentation of set at thinkdast.com/listset, then fill in the body of this method. If you run MyArrayListTest again, testSet should pass.

HINT

Try to avoid repeating the index-checking code.

Your next mission is to fill in indexOf. As usual, you should read the documentation at thinkdast.com/listindof so you know what it’s supposed to do. In particular, notice how it is supposed to handle null.

I’ve provided a helper method called equals that compares an element from the array to a target value and returns true if they are equal (and it handles null correctly). Notice that this method is private because it is only used inside this class; it is not part of the List interface.

When you are done, run MyArrayListTest again; testIndexOf should pass now, as well as the other tests that depend on it.

Only two more methods to go, and you’ll be done with this exercise. The next one is an overloaded version of add that takes an index and stores the new value at the given index, shifting the other elements to make room, if necessary.

Again, read the documentation at thinkdast.com/listadd, write an implementation, and run the tests for confirmation.

HINT

Avoid repeating the code that makes the array bigger.

Last one: fill in the body of remove. The documentation is at thinkdast.com/listrem. When you finish this one, all tests should pass.

Once you have your implementation working, compare it to mine, which you can read at thinkdast.com/myarraylist.

This page titled 2.3: Exercise 2 is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Allen B. Downey (Green Tea Press) .