Question

Write C++ statements that do the following: a. Declare an array alpha of 10 rows and 20 columns of type int. b. Initialize the array alpha to 0. c. Store 1 in the first row and 2 in the remaining rows. d. Store 5 in the first column, and make sure that the value in each subsequent column is twice the value in the previous column. e. Print the array alpha one row per line. f. Print the array alpha one column per line.

Short answer

Declare and initialize the array. Fill rows and columns with specified values, then print row by row and column by column.

Step-by-step solution

Declare the Array

To declare an array `alpha` with 10 rows and 20 columns of type `int`, we use the following C++ statement: ```cpp int alpha[10][20]; ```

Initialize the Array to 0

We initialize all elements of the array to 0 using nested loops: ```cpp for (int i = 0; i < 10; i++) { for (int j = 0; j < 20; j++) { alpha[i][j] = 0; } } ```

Set First Row to 1 and Remaining Rows to 2

Set the first row's elements to 1, and all other rows' elements to 2: ```cpp for (int j = 0; j < 20; j++) { alpha[0][j] = 1; // Set first row elements to 1 } for (int i = 1; i < 10; i++) { for (int j = 0; j < 20; j++) { alpha[i][j] = 2; // Set remaining row elements to 2 } } ```

Assign Values to Columns

Assign 5 to the first column and double the value for each subsequent column. Use nested loops: ```cpp for (int i = 0; i < 10; i++) { alpha[i][0] = 5; // First column is 5 for (int j = 1; j < 20; j++) { alpha[i][j] = alpha[i][j - 1] * 2; // Double the previous column's value } } ```

Print Array Row by Row

To print the array row by row, use a loop through the rows: ```cpp for (int i = 0; i < 10; i++) { for (int j = 0; j < 20; j++) { std::cout << alpha[i][j] << " "; } std::cout << std::endl; } ```

Print Array Column by Column

To print the array column by column, you need to loop through each column and print each element: ```cpp for (int j = 0; j < 20; j++) { for (int i = 0; i < 10; i++) { std::cout << alpha[i][j] << std::endl; } std::cout << std::endl; // Separate columns with a new line } ```

Key concepts

Array Initialization

In C++, array initialization is the process of setting initial values to the elements of an array when it is created. This can be crucial, as you often want arrays to start with known values. For a multidimensional array like `alpha` with 10 rows and 20 columns, initialization to a specific value, such as zero, ensures uniform starting conditions. To declare and initialize the array `alpha` to zero, use: ```cpp int alpha[10][20]; ``` In combination with nested loops: ```cpp for (int i = 0; i < 10; i++) { for (int j = 0; j < 20; j++) { alpha[i][j] = 0; } } ```

• First declare the array dimensions.
• Use a loop to traverse the array and set each element to the desired initial value.

This method ensures each entry of `alpha` is explicitly initialized, which is vital in preventing unintentional default values.

Nested Loops

In C++, nested loops are a powerful tool for traversing multidimensional arrays. When dealing with a 2D array like `alpha`, nested loops allow you to iterate over all elements in a structured manner. Nested loops involve a loop within another loop, where the outer loop typically iterates over the rows and the inner loop iterates over the columns: ```cpp for (int i = 0; i < 10; i++) { // Outer loop for rows for (int j = 0; j < 20; j++) { // Inner loop for columns // Access element alpha[i][j] } } ```

• The outer loop is for row traversal.
• The inner loop is for column traversal.

This technique is not just for array initialization, but can be employed for any operation requiring access to array elements, such as assigning values or printing elements. Nested loops give you complete control over array operations.

Array Manipulation

Array manipulation in C++ involves modifying the contents of an array based on specific criteria or operations. In this exercise, we manipulate the array `alpha` to store different values under certain conditions: - **First Row**: Assign `1` to all elements. - **Remaining Rows**: Assign `2` to all elements. This requires operations on arrays using nested loops. For values in specific columns: - Set the first column to `5` and each subsequent column to twice the value of the previous one. This operation requires consistently updating values based on their location in the array: ```cpp for (int i = 0; i < 10; i++) { alpha[i][0] = 5; // Initialize first column to 5 for (int j = 1; j < 20; j++) { alpha[i][j] = alpha[i][j - 1] * 2; // Double previous column value } } ```

• Always check conditions or positions for manipulation.
• This helps in storing values dynamically based on logic within your C++ program.

These practices in array manipulation are essential for writing modular and efficient code.

Printing Arrays in C++

Printing arrays in C++ allows you to visualize the data contained within, which is especially helpful when debugging or checking your work. For a 2D array like `alpha`, you can print it by rows or by columns using nested loops. **Row by Row Printing** To print each row of the array `alpha`, you iterate through each row and then through each column: ```cpp for (int i = 0; i < 10; i++) { for (int j = 0; j < 20; j++) { std::cout << alpha[i][j] << " "; } std::cout << std::endl; // New line at the end of each row } ```

• This prints each row on a separate line, which makes the data easier to read.

**Column by Column Printing** To print each column separately, you swap the order of the loops: ```cpp for (int j = 0; j < 20; j++) { for (int i = 0; i < 10; i++) { std::cout << alpha[i][j] << std::endl; // New line after each element } std::cout << std::endl; // New line between columns } ```

• This method can be useful when you need a vertical representation of the array data.

By mastering these simple techniques, printing arrays becomes an accessible task, allowing you to effectively communicate and validate your stored data in C++.