Week 1 Exercises: 2D and 3D Arrays

Instructions

Answer all questions to test your understanding of 2D and 3D arrays. Remember: The computer only understands 1D arrays! A 2D array is an array of arrays - an array of references where each reference points to a 1D array.

Part 1: 2D Arrays (Array of Arrays)

Multiple Choice

What does this declaration create? Think in terms of "array of arrays".

Declaration.java

int[][] matrix = new int[3][4];

An array of 4 references, each pointing to a 1D array of 3 integers

An array of 3 references, each pointing to a 1D array of 4 integers

A single 1D array with 12 elements

A 3D array

Understanding: Array of Arrays Structure

Code Tracing

Given this 2D array, what is the value of arr[1][2]?

Access2D.java

int[][] arr = {
    {10, 20, 30, 40},
    {50, 60, 70, 80},
    {90, 100, 110, 120}
};
                    

Array of Arrays Structure

60

70

30

110

Fill in the Blank

Using the same array from Question 2, what is the value of arr.length?

arr.length =

Fill in the Blank

Using the same array, what is the value of arr[0].length?

arr[0].length =

Code Tracing

What is the output of this code?

LastElement.java

int[][] arr = {
    {1, 2, 3},
    {4, 5, 6}
};

int lastRow = arr.length - 1;
int lastCol = arr[lastRow].length - 1;

System.out.println(arr[lastRow][lastCol]);
                    

3

6

5

4

Part 2: Ragged Arrays (Proof of Array of Arrays!)

True / False

In Java, all "rows" in a 2D array must have the same number of elements.

TRUE

FALSE

Why Ragged Arrays Are Possible: Each 1D Array is Independent!

Code Tracing

What is the value of ragged[2].length?

RaggedArray.java

int[][] ragged = {
    {1, 2},           // Row 0: 2 elements
    {3, 4, 5, 6},     // Row 1: 4 elements
    {7, 8, 9}         // Row 2: 3 elements
};
                    

2

3

4

9

Code Tracing

Using the same ragged array, what is ragged[1][3]?

5

6

9

ArrayIndexOutOfBoundsException

Part 3: 3D Arrays (Array of 2D Arrays)

Multiple Choice

What does this declaration create?

ThreeDArray.java

int[][][] cube = new int[2][3][4];

2 layers, each with 3 rows and 4 columns (total: 24 elements)

3 layers, each with 2 rows and 4 columns

4 layers, each with 3 rows and 2 columns

A 2D array with 3×4 elements

Code Tracing

What is the value of building[1][0][2]?

Building3D.java

int[][][] building = {
    // Layer 0
    {
        {1, 2, 3},
        {4, 5, 6}
    },
    // Layer 1
    {
        {7, 8, 9},
        {10, 11, 12}
    }
};
                    

3

6

9

12

Fill in the Blank

Using the same building array, what is building.length?

building.length =

Fill in the Blank

Using the same building array, what is building[0][1].length?

building[0][1].length =

Part 4: Advanced Questions

Code Tracing

What is the output of this code?

SumDiagonal.java

int[][] matrix = {
    {1, 2, 3},
    {4, 5, 6},
    {7, 8, 9}
};

int sum = 0;
for (int i = 0; i < matrix.length; i++) {
    sum += matrix[i][i];
}

System.out.println(sum);
                    

6

12

15

45

Code Tracing

What is the output of this code?

CountElements.java

int[][] ragged = {
    {1},
    {2, 3},
    {4, 5, 6}
};

int count = 0;
for (int i = 0; i < ragged.length; i++) {
    count += ragged[i].length;
}

System.out.println(count);
                    

3

6

9

21

True / False

A 2D array in Java is stored as a single contiguous block of memory (all elements next to each other).

TRUE

FALSE

Memory Layout: Why 2D Arrays Are NOT Contiguous

Your Results

0 Correct

0 Incorrect

2D & 3D Arrays Exercises

Instructions