KotlinJava

# Multidimensional Arrays

int[][] pixels = new int[32][32];
for (int i = 0; i < pixels.length; i++) {
for (int j = 0; j < pixels[i].length; j++) {
pixels[i][j] = i + j;
}
}
System.out.println(pixels[8][18]);

This is another extremely exciting lesson. Because now, we’ll learn how to work with even more data. We’ll break free from our linear shackles into full multi-dimensional splendor. Let’s get started!

## Debugging PracticeDebugging Practice

But first, let’s get a bit more debugging practice!

## Multidimensional DataMultidimensional Data

So far we’ve worked with single data values, arrays of values, and `String`s—which on some level or just character arrays with features. But all of the plural data that we’ve worked with so far has been linear. We’ve learned how to put things in order. But just try linearizing this guy:

It turns out that a lot of the data around us is multidimensional. Photos are just one example.

## Multidimensional ArraysMultidimensional Arrays

Of course Java has a way to work with multidimensional data. And, in many ways, it’s a straightforward extension of what we’ve already seen.

Here’s our first multidimensional array:

int[][] values = new int[8][8];

The syntax is similar to what we saw with single-dimensional arrays. But instead of a single `[]` in the variable declaration, we have two, indicating a two-dimensional array. How would we do three?

int[][][] values = new int[8][88][8];

Same idea. Also note that on the right side of the initial assignment we can specify sizes for each of the dimensions. The 3-d array shown above has size 8 in the first dimension, 88 in the second dimension, and 8 in the third dimension.

Array indexing in multidimensional arrays works just the same as we’ve seen in the past:

int[][][] values = new int[8][4][2];
System.out.println(values[4][2][1]);
values[2][2][1] = 10;
System.out.println(values[2][2][1]);

And we can still have problems with our bounds if we’re not careful:

int[][][] values = new int[8][4][2];
System.out.println(values[4][2][2]);

### Forget Rows and ColumnsForget Rows and Columns

A bi-yearly rant. Forget about rows and columns. Do you want to work with spreadsheets your entire life? This limited mental model will utterly fail you when you need it most!

int[][] samples = new int[2][64];

### Arrays of Arrays of ArraysArrays of Arrays of Arrays

Let’s explore how multidimensional arrays in Java actually work. Specifically, we’ll talk about why something like this works:

int[][] twod = new int[2][];
int[] oned = new int[8];
twod[1] = oned;
twod[0] = new int[4];
System.out.println(twod.length);
System.out.println(twod[0].length);
System.out.println(twod[1].length);
int[][] twod = new int[4][];

### Non-Rectangular ArraysNon-Rectangular Arrays

Note one important consequence of the fact that Java arrays are arrays of arrays. They do not need to be rectangular! Specifically, an innermost array can have a different size at each index. Some may even be `null`! Let’s look at how.

int[][] nonrectangular = new int[8][];

If this doesn’t make perfect sense to you, don’t worry. Next we’ll show you patterns that you can use below to work with any array, rectangular or non.

### Multidimensional Array LiteralsMultidimensional Array Literals

These exist, but they are awful. We’ll never do this to you:

// Holy terrible syntax, Batman!
int[][][] values = new int[][][] {new int[][] {new int[] {1, 2}, new int[] {3}}};
System.out.println(values[0][1][0]);

## Practice: Array Sum (Two Dimensional)

Created By: CS 124 Staff
/ Version: 2020.9.0

Declare and implement a function called `arraySum` that receives a two-dimensional array of `double` values as its only parameter and returns the sum of the values in the array as a `double`. If the array is `null` you should return 0. None of the inner arrays will be `null`.

## Multidimensional Array Programming PatternsMultidimensional Array Programming Patterns

Just like single-dimensional arrays, we can develop similar programming patterns for working with multidimensional arrays. Let’s look at an example together.

int[] values = {1, 2, 4};

## Practice: 2D Array Max Subarray Sum

Created By: CS 124 Staff
/ Version: 2021.8.0

Write a method `maxSubarraySum` that, given a non-rectangular two-dimensional `int` array, returns the sum of the subarray that sums to the largest value.

So given the following array, with each subarray on a separate line:

``````1, 2, 4
4, 1, -1
6, 8, -10, -9
-1
``````

You would return 7.

`assert` that the passed array is not `null`. However, if the passed array is not `null` it will contain no empty subarrays.

One hint for this problem is that you may need both an `int` variable to store the max and a `boolean` variable to record whether the maximum value has been initialized. Once you have summed each subarray, check whether either your `boolean` value is `false` or the sum is larger than the largest you've seen so far. After you check the sum of the first subarray, set your `boolean` value to `true`. Another approach is to use the counter that you use to proceed through each subarray to determine whether you have initialized the max value.

## Homework: Validate Magic Square

Created By: CS 124 Staff
/ Version: 2022.8.0

A magic square is a NxN square where the rows, columns, and diagonals all sum to the same value: https://en.wikipedia.org/wiki/Magic_square.

Write a method `validateMagicSquare` that, given a two-dimensional array of `int` values, returns whether the array contains a magic square. The passed array may be `null`, in which case you should return `false`. However, if it is not `null` it will contain a non-empty square array, meaning that the size of the array in the first and second dimensions will be the same and greater than zero.

You should check all rows and columns and both diagonals. To determine if all sums are the same, we suggest that you compute an initial sum of any row or column, and then compare all other sums to that value. The choice of how to create the initial sum is arbitrary, but if all sums are the same, then any sum you choose to compare against will work!

We've provided some incomplete starter code to get you going with this problem.

(Note that you do not and should not validate that the magic square is normal, meaning it contains only the numbers from 1 to the size squared. We will pass magic squares that do not have this property.)

## Hack4ImpactHack4Impact

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## More Practice

Need more practice? Head over to the practice page.