Question

(Double Array Questions) Answer the following questions regarding an array called table: a) Declare the array to be an integer array and to have 3 rows and 3 columns. Assume that the constant variable arraysize has been defined to be 3 b) How many elements does the array contain? c) Use a for statement to initialize each element of the array to the sum of its subscripts. Assume that the integer variables \(i\) and \(j\) are declared as control variables. d) Write a program segment to print the values of each element of array table in tabular format with 3 rows and 3 columns. Assume that the array was initialized with the declaration int table[ arraySize ][ arraySize ] = { { 1, 8 }, { 2, 4, 6 }, { 5 } }; and the integer variables i and j are declared as control variables. Show the output.

Short answer

a) int table[arraysize][arraysize]; b) 9 elements c) for(i = 0; i < arraysize; i++) { for(j = 0; j < arraysize; j++) { table[i][j] = i + j; } } d) The output will be a 3x3 table reflecting the initial values and any uninitialized elements will be set to zero.

Step-by-step solution

- Declaring the array

Declare the array with the name 'table' as an integer 2-dimensional array with 3 rows and 3 columns using the provided constant variable 'arraysize'. In C-like languages, you would write: int table[arraysize][arraysize];

- Calculating the total number of elements

Calculate the total number of elements in the array by multiplying the number of rows by the number of columns. Since the array is a square with 'arraysize' rows and 'arraysize' columns, you have a total of arraysize * arraysize elements.

- Initializing the elements

Write a nested for loop to iterate over the array indexing variables 'i' and 'j' and set each element of 'table' to the sum of its indices. The code will look like this: for(i = 0; i < arraysize; i++) { for(j = 0; j < arraysize; j++) { table[i][j] = i + j; } }

- Printing the array elements

Write a nested for loop similar to the one in the previous step but this time to print the values of each element in the array 'table' in a 3x3 tabular format. You'll also need to handle the formatting to make sure elements are properly aligned. The code will look like this: for(i = 0; i < arraysize; i++) { for(j = 0; j < arraysize; j++) { printf('%d ', table[i][j]); } printf(''); }

Key concepts

2D Arrays in C++

In C++, a 2D array is essentially an array of arrays, often used to represent a matrix or a grid. 2D arrays are declared with two dimensions, the first specifying the number of rows and the second the number of columns. Easy to visualize as a table, a 2D array is structured in rows and columns, just like a chessboard or an excel sheet.

For example, if we want to declare a 2D array called 'table' that consists of 3 rows and 3 columns, we would write it as:

int table[3][3]; 

Here, we've specifically used the number 3, but if a constant variable like 'arraysize' is defined, you can use it to set both dimensions to ensure consistent array sizes.
In the provided exercise, since 'arraysize' equals 3, our declaration would look like this:

int table[arraysize][arraysize]; 

This declaration sets up our grid-like structure where 'arraysize' indicates both the number of rows and columns.

Nested For Loops in C++

Whenever we work with 2D arrays, nested for loops become our essential tool. These are simply loops within loops that allow us to iterate over each row and then each column within that row. This is similar to traversing each cell in our table grid one by one.

Let's look at how we would initialize our array 'table' using nested loops:

for(int i = 0; i < arraysize; i++) {   for(int j = 0; j < arraysize; j++) {     table[i][j] = i + j;   }}

This code will set each element of 'table' to the sum of its indices. The outer for loop iterates through each row, while the inner loop iterates through each column of the current row. It's like going through each box of a checkers board, row by row and within those rows, square by square.

Array Indexing in C++

Array indexing is how we access elements within our array using their location. In a 2D array, the location of an element is specified by two indices: one for the row and one for the column. The indices usually start from 0 in C++, so the first element is at index [0][0], the next element in the same row but next column is at [0][1], and so forth.

Considering 'table' as our example 2D array, the expression 'table[i][j]' refers to the element in the 'i-th' row and 'j-th' column. In the initialization loop, 'i' and 'j' are the control variables used to index into 'table'. In the provided exercise, each element of 'table' is set to the sum of its row index and column index, demonstrating a direct application of array indexing in array manipulation.
When printing the array, we again make use of indexing within a nested loop structure to access each element and print it, resulting in a formatted output on screen.