Question

Write C++ statements to do the following: a. Declare an array beta of 20 components of type double. b. Initialize each component of the array beta to 0. c. Output the value of the fifth component of the array beta. d. Set the value of the ninth component of the array beta to 70.50. e. Set the value of the twelth component of beta to four times the value of the eighth component of beta minus 15. f. Use a for loop to output the value of a component of beta if its index is a multiple of 3. g. Output the value of the last component of beta. h. Output the value of beta so that ten components per line are printed.

Short answer

Declare, initialize, modify, and output elements of the `beta` array with specific conditions.

Step-by-step solution

Declare the Array

First, we need to declare an array named `beta` with 20 components of type double. In C++, this is done using the following code: ```cpp double beta[20]; ```

Initialize the Array

To initialize each component of `beta` to 0, we can use a for loop that iterates through each index of the array and sets it to 0: ```cpp for (int i = 0; i < 20; ++i) { beta[i] = 0.0; } ```

Output the Fifth Component

The fifth component has the index 4 (since array indices start at 0). Output its value using: ```cpp std::cout << "Fifth component: " << beta[4] << std::endl; ```

Set the Ninth Component

Set the ninth component of `beta` (index 8) to 70.50: ```cpp beta[8] = 70.50; ```

Compute the Twelfth Component

Set the twelfth component (index 11) to four times the value of the eighth component (index 7) minus 15: ```cpp beta[11] = 4 * beta[7] - 15; ```

Output Components with Index Multiple of 3

Use a for loop to output the values of components whose indices are multiples of 3: ```cpp for (int i = 0; i < 20; i += 3) { std::cout << "Component at index " << i << ": " << beta[i] << std::endl; } ```

Output Last Component

Output the value of the last component of the array (index 19): ```cpp std::cout << "Last component: " << beta[19] << std::endl; ```

Output the Array with 10 Components per Line

Use a for loop to output the entire array with ten components per line: ```cpp for (int i = 0; i < 20; ++i) { std::cout << beta[i] << " "; if ((i + 1) % 10 == 0) { std::cout << std::endl; } } ```

Key concepts

Array Initialization

In C++, initializing an array is a fundamental operation that sets the stage for using arrays effectively. An array is a collection of elements of the same data type, and it's essential to allocate memory for these elements through initialization. In the context of our task, we start by declaring an array named `beta` which consists of 20 elements, all of type `double`.

Here's how you declare it:

• `double beta[20];`

This line of code explicitly states that we want an array capable of holding 20 floating-point numbers. Once declared, it's often desirable to initialize the array's elements to specific values. In our exercise, each element is set to zero.

The initialization step ensures that when we subsequently use the array's elements, we begin with a clean slate rather than arbitrary values, which could lead to computational errors.

For Loop

The `for loop` is a powerful loop structure in C++ that allows for repeated execution of a block of code. It's often used for iterating over arrays because it can efficiently traverse array elements.

In our current task, the `for loop` is used in multiple steps. For instance, to initialize all elements of the array `beta` to zero, we use:
```cpp for (int i = 0; i < 20; ++i) { beta[i] = 0.0; } ```

• The loop starts with `int i = 0;` which initializes the loop counter (in this case `i`) at 0.
• `i < 20;` indicates the loop should continue as long as `i` is less than 20.
• `++i` increments the value of `i` after each iteration.

Thus, this loop initializes each element in `beta` from 0 to 19.

For loops can also be optimized for specific conditions, such as stepping through the array by multiples of three or outputting every component after completion. This modularity makes `for loops` a versatile choice for array operations.

Array Indexing

Array indexing is at the heart of accessing specific elements within an array. In C++, arrays are zero-indexed, meaning the first element has an index of 0. Understanding and using the correct index is crucial to ensure your code interacts with the intended components.

Accessing an element is simple with the syntax `array[index]`. For example, to access the fifth element of the array `beta`, you use the index 4:

• `beta[4]` accesses the fifth component.

Array indexing allows setting values as well. For instance, the statement:

• `beta[8] = 70.50;`

will set the ninth component of the array to 70.50 because the index starts at 0.

Correct use of indices is critical to avoid off-by-one errors and unintended memory access. Arrays are stored in contiguous memory locations, and accessing indices beyond the declared size may lead to undefined behaviors in C++.

Array Output

Outputting array elements effectively requires understanding both indexing and loop structures in C++. One goal is to print or display the elements in a way that is understandable and organized for the user. In our exercise, several output tasks help illustrate this process.

To output a single component, such as the fifth element, you use: ```cpp std::cout << "Fifth component: " << beta[4] << std::endl; ``` For more complex output requirements, like displaying elements at indices which are multiples of three, you can structure a loop as follows: ```cpp for (int i = 0; i < 20; i += 3) { std::cout << "Component at index " << i << ": " << beta[i] << std::endl; } ``` This loop skips by three indices per iteration, printing only the desired components.

Finally, when asked to output the entire array with ten components per line, a nested approach can be effective: ```cpp for (int i = 0; i < 20; ++i) { std::cout << beta[i] << " "; if ((i + 1) % 10 == 0) { std::cout << std::endl; } } ``` This straightforward chunking approach formats output into clear and manageable sections, enhancing readability.