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 a 10x20 `int` array, initialize to 0, fill rows and columns appropriately, then print by rows and columns.

Step-by-step solution

Declare the Array

To declare a 2D 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 Zero

To initialize the entire array `alpha` to zero, we use nested loops to iterate through each element and set its value to 0: ```cpp for (int i = 0; i < 10; i++) { for (int j = 0; j < 20; j++) { alpha[i][j] = 0; } } ```

Fill Rows with Specific Values

Set the values in the first row to 1 and the rest to 2. This can be done using a loop: ```cpp for (int j = 0; j < 20; j++) { alpha[0][j] = 1; // First row } for (int i = 1; i < 10; i++) { for (int j = 0; j < 20; j++) { alpha[i][j] = 2; // Remaining rows } } ```

Fill Columns with Incremental Values

For the first column, set values to 5 in all rows and make each element in subsequent columns twice the value of the previous column: ```cpp for (int i = 0; i < 10; i++) { alpha[i][0] = 5; // First column for (int j = 1; j < 20; j++) { alpha[i][j] = 2 * alpha[i][j-1]; } } ```

Print the Array Row by Row

To print the array `alpha` with each row on a new line, use the following loop: ```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 the Array Column by Column

To print the array `alpha` with each column on a new line, iterate through the columns first: ```cpp for (int j = 0; j < 20; j++) { for (int i = 0; i < 10; i++) { std::cout << alpha[i][j] << ' '; } std::cout << std::endl; } ```

Key concepts

2D Arrays in C++

A 2D array in C++ is essentially an array of arrays. It is used to store data in a tabular form like a matrix and is defined with multiple indexes. This can be visualized as a grid with rows and columns. For instance, in the exercise, we declare an array `alpha` having `10` rows and `20` columns as: ```cpp int alpha[10][20]; ``` Here, `10` specifies the number of rows, and `20` specifies the number of columns. Such arrays allow us to work with a large amount of structured data conveniently. They are particularly useful in applications involving matrices, images, or where data can be naturally represented in 2D form.

Nested Loops

Nested loops in C++ are loops within loops and they are vital when dealing with multi-dimensional arrays. In the exercise, nested loops are used to initialize and manipulate the values within `alpha`. - **Initialization:** To set all elements to `0` initially: ```cpp for (int i = 0; i < 10; i++) { for (int j = 0; j < 20; j++) { alpha[i][j] = 0; } } ``` - **Row values:** Setting the first row to `1` and all other rows to `2`: ```cpp for (int j = 0; j < 20; j++) { alpha[0][j] = 1; } for (int i = 1; i < 10; i++) { for (int j = 0; j < 20; j++) { alpha[i][j] = 2; } } ``` The outer loop controls the row iteration, while the inner loop iterates over the columns. This setup is efficient for working with data in a 2D format.

Incrementing Array Values

When configuring values within a 2D array, sometimes you need to increment or modify existing values based on certain rules or patterns. In the given exercise, each element in the first column of `alpha` is initialized to `5`. Subsequent columns double the value of the element in the preceding column: ```cpp for (int i = 0; i < 10; i++) { alpha[i][0] = 5; // First column for (int j = 1; j < 20; j++) { alpha[i][j] = 2 * alpha[i][j-1]; } } ``` This code snippet uses the previous column's value to determine the current column's value, enhancing understanding of both multiplication and indexing in arrays. The simple arithmetic operation of doubling helps illustrate the power of nested loops combined with arithmetic progressions in modifying and filling arrays programmatically.

Printing Arrays in C++

To display the contents of a 2D array, you'll often print it with each element shown clearly. This exercise requires printing the array both row by row and column by column. Here is how it can be achieved: - **Row by Row:** ```cpp for (int i = 0; i < 10; i++) { for (int j = 0; j < 20; j++) { std::cout << alpha[i][j] << ' '; } std::cout << std::endl; } ``` This loop iterates over each row and column, displaying elements horizontally across the entire array. - **Column by Column:** ```cpp for (int j = 0; j < 20; j++) { for (int i = 0; i < 10; i++) { std::cout << alpha[i][j] << ' '; } std::cout << std::endl; } ``` Here, the focus is on iterating column-wise. This structure is helpful in scenarios where you might want to analyze data that is naturally column-first, such as in some kinds of datasets or visualizations.