APCS Chapter 6: 2D Arrays and ArrayLists

Alright, it’s time to tackle 2D arrays and arrayLists. 2D arrays are basically arrays of arrays. First off, 2D arrays:

2D Arrays

To start off with, the declaration and instantiation. Since 2D arrays are objects, we will use the new operator. There are several ways to do this:

The “normal” way:

data type [] [] name = new data type [# of rows] [# of collumns];

Example: I want to create a 2D array called nums containing int data with 2 rows and 3 collumns:

int[] [] nums = new int[2][3];

If you want to create a jagged array where each row is of a different length, then you can input your values directly into the 2D array. There are several ways to do this but I’m going to show you guys the simplest one:

int[] [] nums =


{4, 5, 6, 4},

{7, 234, 34, 1},

{23, 57, 2}


(Of course, you can write this all on one line but this layout looks more intuitive.)

So, this is what the 2D array would look like visually:


If this were a rectangular 2D array and not a jagged array, any attempt to retrieve a data value from the index position (3, 2) would return null so keep that in mind if you are manipulating or accessing a 2D array. There is also a thing called sparseArrays and an FRQ concerning sparseArrays has popped up on the AP exams (although I don’t think it’s likely to pop up again but hey, the more you know…) so here’s a link that kind of explains it but I don’t really think you need to know it for this class because it’s a little more high-level.

Traversing Through a 2D Array

With 2D arrays, you also need to know how to traverse through them. You can do this through the basic three types of loops. I’m going to show an example of each.

For Loops

You can use both the for loop and a for each loop. In my examples, I’m going to use the loops to add up all the numbers in the 2D array. I’m going to use the nums array that I instantiated above (all of the loops work with regular 2D arrays as well as jagged 2D arrays). This is how to use a regular nested for loop to go through every element in a 2D array and add them up.

int sum = 0;

for (int row = 0; row < nums.length; row++)

for (int col = 0; col < nums[row].length; col++)

sum += nums[row][col];

For Each Loop

For each loops are a little less intuitive to use but in the first part of the parameters denote which type of data type you’re trying to handle within the array and the second part is the array that you want to traverse through.

int sum = 0;

for (int[] num : nums)  //this looks at each row of thes 2D array

for (int i : num)  //this looks at all the data values within each row

sum+= num;

Both of these loops do the same thing.

While Loops

As a rule of thumb, while loops are used when you don’t know how many times iterations you need the loop to go through. I’m just going to use the basic example I used above and write a while loop instead.

int row = 0, col = 0, sum = 0;

while (row < nums.length) {

while (col < nums[row].length) {

sum += nums[row][col];

col++; }

row++; }


APCS Ch 6: Sorting and Searching Methods

Sorting methods as it pertains to arrays isn’t the simplest thing to wrap your head around but the concept and the way they should work should be pretty intuitive. You would need to know about two main sorting methods in APCS; the selection sort and the insertion sort. Like the different types of loops, both of these sorting methods have pros and cons attached to them.

Selection Sort

A selection sort is a tedious affair. Basically, what it does is takes each value in each index position and compares that value to all the other values to the right of it (after it) in the array. When it finds the smallest/largest value that exists to the right of its index position, it swaps places with it. In this way, this method sorts all of its value in either ascending or descending order of value.

Let’s take a look at what a selection sort in ascending order looks like in code:

//nums is an array of int values

//the variables min and minIndex both hold int values

for (int i = 0; i < nums.length – 1; i++)


min = nums[i];

minIndex = i;

for (int j = i; j < nums.length; j++)


if (nums[j] < min)


min = nums[j];

minIndex = j;



int temp = nums[i];

nums[i] = nums[minIndex];

nums[minIndex] = temp;


This is a daunting bit of code at first. However, if we understand mechanically how this sorting method works, it might help you understand better. For example, if I had an array of int values, this is what the array would look like after every pass of the outer loop:


(1) The outer loop started at index position 0, took the number 16 at index 0 and started to loop through the values after it to find the smallest number, which happened to be the number 1 at index position 5. Then, the numbers 1 and 16 swapped places due to the inner loop. That was the first pass of the outer loop.

(2) Then, the outer loop looked at index position 1 and picked up the number 3 at index 1 and looped through the values to the right to find the smallest number. Since there were no values to the right that was smaller than 3, the inner loop swapped the 3 at index 1 with 3 at index 1, which meant the 3 swapped with itself and stayed where it is.

This process would repeat until it got to the second to last number by which time, the last number in the array would already be in its final sorted position so the number of passes the outer loop needs to fully sort an array is always the length of the array minus 1. By this rule, if we were on the fourth pass of the outer loop, the first four values of the array would have been in their final sorted places.

Let’s break down the code and see what the first pass of the outer loop looks like:

for (int i = 0; i < nums.length – 1; i++)

The outer loop just goes through the whole length of the array. In the first pass, i would be set to 0.

min = nums[i];

minIndex = i;

This sets min to the number currently at the index position of whatever element the outer loop is currently looking at. So, min would be set to the number at index 0 on the first pass, which would be the number 16. The index of the smallest number would be default set to the index of the number that we’re currently looking at, which would be index 0.

 for (int j = i; j < nums.length; j++)

This inner loop would loop through all the index positions to the right of the number at the index position we’re currently looking at, which would be all the values stored in the index positions after index 0.

if (nums[j] < min){

min = nums[j];

minIndex = j; }

This if statement compares the current min value (16) to all the values right of its index position (0). If it finds a number that is smaller, it will set the smaller value to min and set its index position to minIndex. The inner loop would cause this if statement to compare whatever smallest number it has found so far to the numbers in the index positions to the right. When it came to the number 1 at index 5, it set min to 1 and minIndex to 5. After going through the rest of the array, it didn’t find any smaller value so those variables stayed the same and we exit out of the inner loop.

int temp = nums[i];

nums[i] = nums[minIndex];

nums[minIndex] = temp;

This piece of code should look familiar; after all, it should be a simple puzzle that confronts many beginner programmers. Basically, what this does is it swaps the two numbers at the two index positions. In this case, temp would be set to 16, then the index position 1 would be overridden with the value at minIndex(5) which is 1. Then, temp (16) would override what was at index 5, effectively swapping the 16 and 1. This repeats until it has touched all but the last index position in the array, at which point the array is fully sorted and the outer loop terminates.

See next page for Insertion Sort

APCS Ch 6: Arrays Basics

Arrays are basically lists of things. This list can contain both objects and primitive data. The basic array can be declared and instantiated as such:

(data type)[ ] (arrayname) = new (data type) [(number of elements)];

Since arrays are considered as objects, the declaration and instantiation follow the pattern of other objects. So, if I wanted the array to store a total of ten names, I would make the array like so:

String[ ] names = new String[10];

Arrays have index values for every element they contain. If I had an array called nums that contained the numbers 1, 2, and 3, the number 1 would have the index position of 0, the number 2 would have index position 1 and the number 3 would have the index position 2 and so on.

Like Strings, arrays have a method that returns the length of the object. In the case of arrays, you would call the method .length. The  .length method for arrays does not need the double parentheses.

So, if you wanted to know the length (or number of elements) of the array names, you would do this:


We now go on to loops. This is quite simple. Looping through an array is pretty easy and intuitive. If I were to use a for loop to go through every element of the array names which contains 10 String objects, it would look something like this:

for (int i = 0; i < names.length; i++)


//body of the loop