Question

(Dotable Array Questions) Consider a \(2-\mathrm{by}-3\) 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 statement that sets the element of t in the first row and second column 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 to zero. j) Write a statement that inputs the values for the elements of trom the keyboard. 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. \(\mathrm{m}\) ) 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

a) int t[2][3]; b) 2 rows; c) 3 columns; d) 6 elements; e) t[1][0], t[1][1], t[1][2]; f) t[0][1], t[1][1]; g) t[0][1] = 0; h) t[0][0] = 0, ..., t[1][2] = 0; i) for (int i=0; i<2; i++) { for (int j=0; j<3; j++) { t[i][j] = 0; } } j) Use input statements in a loop; k) Determine the smallest value with comparisons; l) Print t[0][0], t[0][1], t[0][2]; m) int sum = t[0][2] + t[1][2]; n) Use nested loops with print statements.

Step-by-step solution

Declare the array

Declare a 2-by-3 integer array named 't'. In most programming languages, this can be done by specifying the type of the elements, the name of the array, and the size of each dimension. For example, in C++/Java: `int t[2][3];`.

Determine the number of rows

Count the number of rows in array 't'. Since it is a 2-by-3 array, it has 2 rows.

Determine the number of columns

Count the number of columns in array 't'. Since it is a 2-by-3 array, it has 3 columns.

Calculate the number of elements

Multiply the number of rows by the number of columns to find the total number of elements in 't'. For a 2-by-3 array, there are 2 * 3 = 6 elements.

Identify elements in row 1

List the names of all elements in row 1 of 't' considering it to be a zero-indexed array. The elements are 't[1][0]', 't[1][1]', and 't[1][2]'.

Identify elements in column 2

List the names of all elements in column 2 of the array 't'. The elements are 't[0][2]' and 't[1][2]'.

Set a specific element to zero

Set the element of 't' in the first row and second column to zero. If the array is zero-indexed, use the statement `t[0][1] = 0;`.

Initialize elements to zero without a loop

Assign the value zero to each element of 't' without using a loop. In a 2-by-3 array, this would look like: `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 elements to zero with a nested loop

Write a nested `for` loop to initialize all elements of 't' to zero. It will have one loop iterating over rows and another over columns, each setting the current element to zero.

Input values from the keyboard

Write a series of statements or a loop structure to input values from the keyboard into the 't' array. Ensure that each element is addressed correctly.

Find and print the smallest value

Initialize a variable to hold the smallest value. Compare each element of 't' with this variable and replace the variable's value if a smaller element is found. Print the smallest value after all elements are compared.

Display elements in row 0

Write a statement that iterates through the elements in the zeroth row of 't' and prints them. This can typically be done with a loop over the columns in row 0.

Total the elements in column 3

Write a statement that sums the elements in the third column of 't'. Since it's a 2-by-3 array, this would involve adding 't[0][2]' and 't[1][2]'.

Print the array in tabular format

Use nested loops to iterate through the rows and columns, printing each element in a structured format. Print the column indices at the top and row indices at the start of each row for clarity.

Key concepts

Array Declaration in C++

In C++, an array is a collection of items stored at contiguous memory locations and accessed using an index. When you declare an array, you're creating a variable that can hold several values of the same type. This is crucial for managing data sets efficiently within a program.

An array declaration involves the following components:

• Type: Indicates the data type of the elements (e.g., int, float).
• Name: The name of the array variable.
• Size: Specifies the number of elements the array will hold.

For example, declaring a single-dimensional array of integers named 'numbers' with space for 10 elements looks like this: int numbers[10];

Following the textbook exercise, a two-dimensional array 't' with two rows and three columns is declared as: int t[2][3];. This creates a grid or matrix of integers where you can store values in a tabular format. Each element in this array can be uniquely identified with a pair of indices – the first for the row and the second for the column.

Nested Loops in C++

Nested loops are a fundamental concept in C++ when dealing with situations that require repetition inside another repetition. They are commonly used with multidimensional arrays to perform operations like initialization, inputting values, or displaying contents.

In a nested loop structure, usually, the outer loop represents rows, while the inner loop represents columns. Here's a simple example of a nested loop that initializes each element of a 2-by-3 array to zero:

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

This series of loops runs through each row (i) and column (j), setting the value at that position to zero. Nested loops are a powerful tool but should be used judiciously as they can create complexity and increase the execution time of a program if not handled correctly.

Multidimensional Arrays

Multidimensional arrays are arrays that contain more than one level of indices to access data. In C++, these are basically arrays of arrays. The most common type is the two-dimensional array, which can be visualized as a table with rows and columns.

For instance, array 't' from our exercise can be imagined as a table with two rows and three columns. Here's how you can access the element on the first row and second column: t[0][1].

A major application of multidimensional arrays is representing matrices in mathematics or other grid-based data structures. They also come in handy for organizing complex data that's logically structured in a tabular format.

A common mistake for beginners is to forget that C++ arrays are zero-indexed, meaning that indexing starts at zero. Thus, for a 2-by-3 array like 't', valid indices range from 't[0][0]' (top-left) to 't[1][2]' (bottom-right). To efficiently work with these arrays, nested loops are indispensable tools.