Two-dimensional arrays in Java - Step-by-Step Execution

Concept Flow - Two-dimensional arrays

Declare 2D array

↓

Allocate memory for rows

↓

Allocate memory for columns in each row

↓

Access or modify element at [row

↓

Use nested loops to traverse rows and columns

↓

Process or print elements

↓

End

This flow shows how a two-dimensional array is declared, allocated, accessed, and traversed using nested loops.

Execution Sample

Java

int[][] matrix = new int[2][3];
matrix[0][1] = 5;
for(int i=0; i<2; i++) {
  for(int j=0; j<3; j++) {
    System.out.print(matrix[i][j] + " ");
  }
  System.out.println();
}

This code creates a 2x3 integer array, sets one element, and prints all elements row by row.

Execution Table

Step	Action	Indices (i,j)	Value Assigned/Accessed	Output	Notes
1	Declare 2D array	-	-	-	matrix created with 2 rows and 3 columns, all initialized to 0
2	Assign value	[0,1]	5	-	matrix[0][1] set to 5
3	Start outer loop	i=0	-	-	Begin first row
4	Start inner loop	i=0, j=0	-	0	Print matrix[0][0], default 0
5	Inner loop	i=0, j=1	-	5	Print matrix[0][1], assigned 5
6	Inner loop	i=0, j=2	-	0	Print matrix[0][2], default 0
7	End inner loop	i=0	-	Line break	End of first row print
8	Outer loop	i=1	-	-	Begin second row
9	Inner loop	i=1, j=0	-	0	Print matrix[1][0], default 0
10	Inner loop	i=1, j=1	-	0	Print matrix[1][1], default 0
11	Inner loop	i=1, j=2	-	0	Print matrix[1][2], default 0
12	End inner loop	i=1	-	Line break	End of second row print
13	End outer loop	-	-	-	All rows printed, loops end

💡 Outer loop i=2 is not less than 2, so loop ends

Variable Tracker

Variable	Start	After Step 2	After Step 5	After Step 11	Final
matrix[0][0]	0	0	0	0	0
matrix[0][1]	0	5	5	5	5
matrix[0][2]	0	0	0	0	0
matrix[1][0]	0	0	0	0	0
matrix[1][1]	0	0	0	0	0
matrix[1][2]	0	0	0	0	0
i	-	0	0	1	2
j	-	-	2	2	-

Key Moments - 3 Insights

Why do we need two loops to print a 2D array?

Because a 2D array has rows and columns, the outer loop goes through rows and the inner loop goes through columns. See execution_table steps 3-12 where nested loops access each element.

What happens if we try to access matrix[2][0]?

It causes an error because the array has only 2 rows (indices 0 and 1). The loops stop at i=2 as shown in exit_note.

Why is matrix[0][1] 5 but others are 0?

Because only matrix[0][1] was assigned 5 at step 2; all other elements keep default int value 0 as shown in variable_tracker.

Visual Quiz - 3 Questions

Look at the execution_table at step 5, what value is printed for matrix[0][1]?

A 0

B 1

C 5

D Error

💡 Hint

Check the 'Value Assigned/Accessed' and 'Output' columns at step 5 in execution_table.

At which step does the outer loop variable i become 1?

A Step 8

B Step 3

C Step 12

D Step 13

💡 Hint

Look at the 'Action' and 'Indices (i,j)' columns in execution_table for when i changes.

If we change the array size to new int[3][3], how many times will the inner loop run per outer loop iteration?

A 2

B 3

C 6

D 9

💡 Hint

Inner loop runs for the number of columns, check the code in execution_sample and relate to array dimensions.

Concept Snapshot

Two-dimensional arrays in Java are arrays of arrays.
Declare with: int[][] name = new int[rows][cols];
Access elements with name[row][col].
Use nested loops to traverse rows and columns.
Default int values are 0.
Indexing starts at 0 for both rows and columns.

Full Transcript

This lesson shows how to work with two-dimensional arrays in Java. First, you declare and allocate the array with rows and columns. Then you can assign values to specific positions using two indices. To read or print all elements, you use nested loops: the outer loop goes through each row, and the inner loop goes through each column in that row. The example code creates a 2x3 array, sets one element to 5, and prints all elements. The execution table traces each step, showing how loops run and values are accessed or printed. The variable tracker shows how each element changes or stays the same. Key moments clarify why nested loops are needed, what happens if you access out-of-bounds indices, and why only one element is changed. The quiz tests understanding of values printed, loop variables, and array size effects. Remember, two-dimensional arrays are like tables with rows and columns, and you always use two indices to work with them.

Practice

1. What does a two-dimensional array in Java represent?

easy

A. A collection of unrelated variables

B. A single list of elements

C. A table with rows and columns

D. A method to sort numbers

Solution

1. Step 1: Understand the structure of two-dimensional arrays

   Two-dimensional arrays store data in rows and columns, like a grid or table.

2. Step 2: Compare options with the definition

   Only A table with rows and columns correctly describes this as a table with rows and columns.

3. Final Answer:

   A table with rows and columns -> Option C

4. Quick Check:

   Two-dimensional array = table [OK]

Hint: Think of it as a spreadsheet with rows and columns [OK]

Common Mistakes:

• Confusing with one-dimensional arrays
• Thinking it's a list of unrelated variables
• Mixing arrays with methods

2. Which of the following is the correct way to declare a two-dimensional array of integers in Java?

easy

A. int matrix[3][4];

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

C. int matrix = new int[3,4];

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

Solution

1. Step 1: Recall Java syntax for 2D array declaration

   Java uses int[][] name = new int[rows][columns]; to declare 2D arrays.

2. Step 2: Check each option

   int[][] matrix = new int[3][4]; matches correct syntax. int matrix[3][4]; is C-style, invalid in Java. int matrix = new int[3,4]; uses comma, invalid. int[] matrix = new int[3][4]; declares a 1D array incorrectly.

3. Final Answer:

   int[][] matrix = new int[3][4]; -> Option B

4. Quick Check:

   Correct 2D array syntax = int[][] matrix = new int[3][4]; [OK]

Hint: Use double brackets [][] and new with sizes [OK]

Common Mistakes:

• Using commas instead of separate brackets
• Trying C-style declarations
• Mixing 1D and 2D array syntax

3. What is the output of the following Java code?

int[][] arr = {{1, 2}, {3, 4}, {5, 6}};
System.out.println(arr[1][0]);

medium

A. 3

B. 5

C. 4

D. 2

Solution

1. Step 1: Identify the element at arr[1][0]

   arr[1] is the second row: {3, 4}. The element at index 0 in this row is 3.

2. Step 2: Confirm the printed value

   System.out.println prints arr[1][0], which is 3.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   arr[1][0] = 3 [OK]

Hint: Remember indexing starts at 0 for rows and columns [OK]

Common Mistakes:

• Confusing row and column indices
• Starting count at 1 instead of 0
• Mixing up elements in nested arrays

4. Find the error in the following code snippet:

int[][] grid = new int[2][3];
grid[2][1] = 5;

medium

A. Array index out of bounds error

B. Syntax error in declaration

C. Missing initialization of array

D. No error, code runs fine

Solution

1. Step 1: Check array size and indices used

   Array grid has 2 rows (indices 0 and 1) and 3 columns (indices 0 to 2). Accessing grid[2][1] uses row index 2 which is out of bounds.

2. Step 2: Identify the error type

   Accessing an invalid index causes ArrayIndexOutOfBoundsException at runtime.

3. Final Answer:

   Array index out of bounds error -> Option A

4. Quick Check:

   Index 2 invalid for 2-row array [OK]

Hint: Check array size before accessing indices [OK]

Common Mistakes:

• Using indices equal to array length
• Confusing rows and columns sizes
• Assuming arrays auto-expand

5. Given a 2D array int[][] data = {{1,2},{3,4},{5,6}};, which code snippet correctly calculates the sum of all elements?

hard

A. int sum = 0;
for(int i=0; i

B. int sum = 0;
for(int i=0; i

C. int sum = 0;
for(int i=0; i

D. int sum = 0;
for(int i=0; i

Solution

1. Step 1: Understand array dimensions and iteration

   data.length is number of rows (3). data[i].length is number of columns (2). Nested loops must iterate rows then columns.

2. Step 2: Analyze each option's loop structure

   int sum = 0; for(int i=0; i

3. Final Answer:

   The nested loops with outer loop on data.length and inner on data[i].length -> Option D

4. Quick Check:

   Correct nested loops sum all elements [OK]

Hint: Outer loop rows, inner loop columns for 2D arrays [OK]

Common Mistakes:

• Swapping row and column loops
• Adding arrays directly to int
• Using wrong indices in loops