Question

Consider a two-by-three integer array t. a) Write a statement that declares and creates t. b) How many rows does t have? c) How many columns does t have? d) How many elements does t have? e) Write access expressions for all the elements in row 1 of \(t\) f) Write access expressions for all the elements in column 2 of t. g) Write a single statement that sets the element of t in row 0 and column 1 to zero. h) Write a series of statements that initializes each element of t to zero. Do not use a repetition statement. i) Write a nested for statement that initializes each element of t to zero. j) Write a nested for statement that inputs the values for the elements of t from the user. k) Write a series of statements that determines and displays the smallest value in t. I) Write a printf statement that displays the elements of the first row of t. Do not use repetition. m) Write a statement that totals the elements of the third column of t. Do not use repetition. n) Write a series of statements that displays the contents of \(t\) in tabular format. List the column indices as headings across the top, and list the row indices at the left of each row.

Short answer

The array \( t \) is declared as `int t[2][3];` with 2 rows, 3 columns, and 6 elements total.

Step-by-step solution

Declare and Create Array

To declare and create a two-by-three integer array named \( t \), use the following statement in C: ```cint t[2][3];```

Determine Number of Rows

The array \( t \) has 2 rows, as it is declared as a two-by-three array.

Determine Number of Columns

The array \( t \) has 3 columns, as specified in the declaration `int t[2][3];`.

Calculate Number of Elements

The array \( t \) has a total of \( 2 \times 3 = 6 \) elements.

Access Elements in Row 1

The access expressions for all elements in row 1 (second row) are:- \( t[1][0] \)- \( t[1][1] \)- \( t[1][2] \)

Access Elements in Column 2

The access expressions for all elements in column 2 (third column) are:- \( t[0][2] \)- \( t[1][2] \)

Set Element in Row 0 Column 1 to Zero

To set the element of \( t \) in row 0 and column 1 to zero, use the following statement:```ct[0][1] = 0;```

Initialize All Elements to Zero Without Loop

To initialize each element of \( t \) to zero without using repetition:```ct[0][0] = 0;t[0][1] = 0;t[0][2] = 0;t[1][0] = 0;t[1][1] = 0;t[1][2] = 0;```

Initialize All Elements to Zero with Nested Loop

Using a nested for loop to initialize each element of \( t \) to zero:```cfor (int i = 0; i < 2; i++) { for (int j = 0; j < 3; j++) { t[i][j] = 0; }}```

Input Elements Using Nested Loop

To input values for the elements of \( t \) from the user with a nested loop:```cfor (int i = 0; i < 2; i++) { for (int j = 0; j < 3; j++) { printf("Enter value for t[%d][%d]: ", i, j); scanf("%d", &t[i][j]); }}```

Find and Display Smallest Element

To find and display the smallest element in \( t \), use:```cint smallest = t[0][0];for (int i = 0; i < 2; i++) { for (int j = 0; j < 3; j++) { if (t[i][j] < smallest) { smallest = t[i][j]; } }}printf("Smallest value in t: %d", smallest);```

Print Elements of First Row

To print the elements of the first row of \( t \) without using repetition:```cprintf("%d %d %d", t[0][0], t[0][1], t[0][2]);```

Total Elements of Third Column

To total the elements of the third column of \( t \) without using repetition:```cint total = t[0][2] + t[1][2];```

Display Array in Tabular Format

To display the contents of \( t \) in tabular format:```cprintf(" 0 1 2");for (int i = 0; i < 2; i++) { printf("%d ", i); for (int j = 0; j < 3; j++) { printf("%d ", t[i][j]); } printf("");}```

Key concepts

Array Initialization

In C programming, an array is a collection of elements stored under a single variable name. To initialize an array, you need to define its dimensions. This involves specifying the number of rows and columns it contains. For example, the declaration `int t[2][3];` creates a 2x3 integer array. Here, '2' represents the number of rows, and '3' represents the number of columns. This initialization prepares the space in memory to store 6 integers, as the total elements in the array equals the number of rows multiplied by the number of columns. Both dimensions must be declared to manage the array's shape effectively.

Nested Loops

Nested loops are loops within loops. They are particularly useful for working with multi-dimensional arrays, like the 2x3 array we discussed. Nested loops can iterate over each element in the array by iterating over each row, and for each row, iterating over each column. This is crucial for operations like initializing values, inputting data, or processing elements in a structured manner.

For example, to set all elements of the array `t` to zero, a nested loop works as follows:

• The outer loop iterates over the rows.
• The inner loop iterates over the columns within a given row.

This technique ensures each element in the array is addressed and updated efficiently.

Array Access Expressions

Array access expressions allow you to reference or manipulate specific elements in an array. Each element is identified by its row and column indices. For example, `t[1][0]` accesses the first element of the second row in array `t`.

Understanding how to properly use access expressions is key when performing operations such as updating or retrieving the value of a specific element. The indices within the brackets `[i][j]` help specify which element you are trying to access, where `i` is the row index and `j` is the column index. Proper array access is crucial for correct data manipulation and retrieval in a program.

Array Elements Manipulation

Manipulating array elements is an essential part of working with arrays in C. This involves modifying, calculating, or using elements for further operations. You can use assignment statements to change values, such as `t[0][1] = 0;` to set the element in the first row and second column of array `t` to zero.

Apart from simple assignments, manipulations often include finding the smallest or largest element, summing values, or reading user input into an array. For these tasks, loops are commonly employed to apply operations across multiple elements. For example, a nested loop can evaluate each element to find the smallest value, or accumulate values in a specific dimension, such as summing elements in one column.