Question

Consider a 2-by-3 integer array t. a. Write a declaration for t. b. How many rows does t have? c. How many columns does t have? d. How many elements does t have? e. Write the names of all the elements in row 1 of t. f. Write the names of all the elements in column 2 of t. g. Write a single statement that sets the element of t in row 1 and column 2 to zero. h. Write a series of statements that initialize each element of t to zero. Do not use a loop. i. Write a nested for statement that initializes each element of t to zero. j. Write a statement that inputs the values for the elements of t from the terminal. k. Write a series of statements that determine and print the smallest value in array t. l. Write a statement that displays the elements in row 0 of t. m. Write a statement that totals the elements in column 3 of t. n. Write a series of statements that prints the array t in neat, tabular format. List the column subscripts as headings across the top and list the row subscripts at the left of each row.

Short answer

Array t has 2 rows, 3 columns, and 6 elements. Elements of row 1 are t[1][0], t[1][1], t[1][2]; column 2 are t[0][2], t[1][2].

Step-by-step solution

Declaring Array t

To declare a 2-by-3 integer array named `t`, use the following syntax for a static array in most programming languages like C++: ```cpp int t[2][3]; ``` This creates an array `t` with 2 rows and 3 columns.

Determine Number of Rows

The number of rows in array `t` is 2. This is specified in the array declaration as the first dimension: `t[2][3]`.

Determine Number of Columns

The number of columns in array `t` is 3. This is specified in the array declaration as the second dimension: `t[2][3]`.

Determine Number of Elements

The total number of elements in the array `t` is given by the product of its dimensions: \[2 \times 3 = 6\]Thus, `t` has 6 elements.

List Elements in Row 1

In a 2D array, rows and columns are typically indexed starting from 0. The elements in row 1 (second row) of array `t` are: `t[1][0]`, `t[1][1]`, and `t[1][2]`.

List Elements in Column 2

The elements in column 2 (third column) of array `t`, across both rows, are: `t[0][2]` and `t[1][2]`.

Set Specific Element to Zero

To set the element in row 1, column 2 of `t` to zero, use the statement: ```cpp t[1][2] = 0; ```

Initialize Each Element to Zero (without Loop)

Set each element of `t` to zero individually: ```cpp t[0][0] = 0; t[0][1] = 0; t[0][2] = 0; t[1][0] = 0; t[1][1] = 0; t[1][2] = 0; ```

Initialize Each Element to Zero (with Loop)

Use a nested loop structure to set each element of `t` to zero: ```cpp for (int i = 0; i < 2; ++i) { for (int j = 0; j < 3; ++j) { t[i][j] = 0; } } ```

Input Values for Array Elements

Use a nested loop to input values for the array elements: ```cpp for (int i = 0; i < 2; ++i) { for (int j = 0; j < 3; ++j) { cin >> t[i][j]; } } ```

Find and Print the Smallest Element

Determine the smallest value in `t` using a nested loop: ```cpp int min = t[0][0]; for (int i = 0; i < 2; ++i) { for (int j = 0; j < 3; ++j) { if (t[i][j] < min) { min = t[i][j]; } } } cout << "Smallest element: " << min << endl; ```

Display Elements in Row 0

To display the elements of row 0 (first row) of `t`, use: ```cpp cout << t[0][0] << " " << t[0][1] << " " << t[0][2] << endl; ```

Total Elements in Column 3

Column 3 does not exist in a 2-by-3 array. It only has columns 0, 1, and 2. Make sure to clarify the correct column to total or adjust the task requirements.

Print Array in Tabular Format

Use nested loops to print the array in a tabular format with headers: ```cpp cout << " 0 1 2" << endl; for (int i = 0; i < 2; ++i) { cout << i << " | "; for (int j = 0; j < 3; ++j) { cout << t[i][j] << " "; } cout << endl; } ```

Key concepts

Multidimensional Arrays

Understanding multidimensional arrays is crucial in programming as they allow you to store and manage data in a structured way. A multidimensional array is essentially an array of arrays, providing a way to store data in a grid or matrix form. This is particularly useful when dealing with more complex data structures in applications such as spreadsheets, image processing, and game development.
In C++, a multidimensional array is declared by specifying more than one set of square brackets, indicating the levels of dimensions. For instance, an array with two dimensions is generally called a two-dimensional array, commonly used to represent a table with rows and columns. Each additional dimension can be thought of as additional layers or more complex matrices.
This concept is a stepping stone toward understanding more complex data structures, and it introduces programmers to handling data in a scalable and organized manner.

Array Initialization

Initializing arrays correctly is essential to prevent undefined behaviors and errors during program execution. In C++, arrays can be initialized in several ways, including during declaration or at runtime through loops. When declaring an array like `int t[2][3];`, it's possible to assign initial values at the same time:

• ```cpp
  int t[2][3] = {{0, 0, 0}, {0, 0, 0}};
  ```

Here, every element in the array is explicitly set to zero.
For more dynamic scenarios where initial values are not known at compilation time, arrays might be initialized later in the code. This approach often involves using nested loops to assign values to each element systematically. Proper initialization ensures that all elements have known values and prevents unexpected behaviors in your code.

Array Looping

Looping through arrays is a common operation when you need to process or update data stored in array elements. In C++, the `for` loop is commonly used for this purpose, as it allows precise control over the iteration process.
When dealing with a two-dimensional array, nested loops are typically used: an outer loop iterates over rows, and an inner loop processes each column of the current row. Consider an example where you reset all elements of a 2x3 array `t` to zero:

• ```cpp
  for (int i = 0; i < 2; ++i) {
  for (int j = 0; j < 3; ++j) {
  t[i][j] = 0;
  }
  }
  ```

This structure ensures that all elements are accessed in an orderly fashion, allowing you to apply consistent operations to each one. Understanding how loops work with arrays is a fundamental skill for any programmer, aiding in efficient data manipulation.

Two-Dimensional Arrays

Two-dimensional arrays are a subtype of multidimensional arrays, perfectly suited for representing rectangular grids or matrices. This form is quite intuitive as it mirrors many structures we encounter daily, such as spreadsheets or chess boards.
In C++, a two-dimensional array is specified by two index values: one for rows and the other for columns. For example, an array declared as `int t[2][3];` creates a matrix with 2 rows and 3 columns, resulting in a total of 6 elements.
Accessing these elements typically involves two indices, `t[i][j]`, where `i` corresponds to the row and `j` to the column. Mastering this access pattern is crucial when interfacing with data that naturally fits into a grid format, enabling clearer, more organized coding when solving real-world problems that involve spatial data.