Question

Describe the contents of the array after the following code segment is run: int [][] matrix = new int[5][5]; for (int row \(=0\); row \(<\) matrix.length; row++) for (int col \(=0 ; \mathrm{col}<\) matrix[row].length; \(\mathrm{col}++\) ) matrix[row \(][c o l]=\) row \(*\) col;

Short answer

The matrix will be: [[0, 0, 0, 0, 0], [0, 1, 2, 3, 4], [0, 2, 4, 6, 8], [0, 3, 6, 9, 12], [0, 4, 8, 12, 16]].

Step-by-step solution

- Initialization

A 5x5 two-dimensional array named `matrix` is declared and initialized. Initially, all elements in the array are set to 0.

- Outer Loop (Rows)

The outer loop iterates over each row of the matrix. The variable `row` goes from 0 to 4 (inclusive), corresponding to the 5 rows.

- Inner Loop (Columns)

The inner loop iterates over each column in the current row. The variable `col` goes from 0 to 4 (inclusive), corresponding to the 5 columns.

- Element Assignment

For each element `matrix[row][col]`, the value is set to the product of `row` and `col`. This means every element is calculated as: `matrix[row][col] = row * col`.

- Resulting Matrix

After executing both loops, the elements of the matrix are filled as follows: the first row (0-th row) will be: [0*0, 0*1, 0*2, 0*3, 0*4] -> [0, 0, 0, 0, 0]the second row (1-st row) will be: [1*0, 1*1, 1*2, 1*3, 1*4] -> [0, 1, 2, 3, 4]the third row (2-nd row) will be: [2*0, 2*1, 2*2, 2*3, 2*4] -> [0, 2, 4, 6, 8]the fourth row (3-rd row) will be: [3*0, 3*1, 3*2, 3*3, 3*4] -> [0, 3, 6, 9, 12]fifth row (4-th row) will be: [4*0, 4*1, 4*2, 4*3, 4*4] -> [0, 4, 8, 12, 16]

Key concepts

Array Initialization

In Java, a multidimensional array is essentially an array of arrays. Specifically, in our example, int [][] matrix = new int[5][5]; initializes a 5x5 two-dimensional array called matrix.
All elements in this array start off with a default value, which for int types, is 0.
Consider this initialization like laying out a grid where each cell is filled with zeroes awaiting assignment.
This step is crucial for setting up the structure you'll work with.

Nested Loops

To manipulate or access data in a multidimensional array, you often use nested loops.
A nested loop is simply one loop inside another loop. In these loops:

• The outer loop tracks the rows.
• The inner loop tracks the columns within each row.

This allows us to visit and manipulate each element in the matrix.
Here's the key part of our example:
for (int row = 0; row < matrix.length; row++) {
  for (int col = 0; col < matrix[row].length; col++) {
   // operations on matrix[row][col]
  }
}

Element Assignment

Once your nested loops are set, you can assign values to each element in the matrix.
In our case, we want each element to be the product of its row and column indices.
The assignment line in the code is:
matrix[row][col] = row * col;
You can think of each element in the array getting filled one by one as the loops iterate over every index.
For instance, matrix[2][3] will store the value obtained by multiplying the row index (2) and the column index (3), resulting in 6.

Two-Dimensional Arrays

Multidimensional arrays, like our 5x5 matrix, are often visualized as a table with rows and columns.
This is useful for handling data that naturally fits this kind of tabular format, like matrices in mathematics.
In Java, you can access elements using the syntax array[row][column].
Initialization and manipulation are handled with nested loops, helping you traverse through every element efficiently.
Two-dimensional arrays bring the capabilities needed for more complex operations and data structures.

Matrix Operations

Matrix operations often extend beyond just filling and accessing elements. They can include:

• Matrix Addition
• Matrix Multiplication
• Transposition of matrix

For our example, the operation is straightforward element assignment based on multiplication of indices.
The resulting matrix looks like this:

• Row 0: [0, 0, 0, 0, 0]
• Row 1: [0, 1, 2, 3, 4]
• Row 2: [0, 2, 4, 6, 8]
• Row 3: [0, 3, 6, 9, 12]
• Row 4: [0, 4, 8, 12, 16]

This visual representation helps solidify understanding of both the loops and how the matrix is populated.