Question

Write \(\mathrm{C}++\) statements to do the following: a. Declare an array alpha of 15 components of type int. b. Output the value of the tenth component of the array alpha. c. Set the value of the fifth component of the array alpha to 35. d. Set the value of the ninth component of the array alpha to the sum of the sixth and thirteenth components of the array alpha. e. Set the value of the fourth component of the array alpha to three times the value of the eighth component minus 57. f. Output alpha so that five components per line are printed.

Short answer

Declare and initialize `alpha` array in C++, manipulate specific elements, and print with appropriate formatting.

Step-by-step solution

Declaring the Array

To declare an array of 15 components in C++, use the following syntax: ```cpp int alpha[15]; ```This line creates an integer array named `alpha` capable of storing 15 integer values.

Outputting the Tenth Component Value

To output the value of the tenth component of the array `alpha`, use this statement: ```cpp std::cout << alpha[9] << std::endl; ```This line accesses the tenth element via index 9 (since C++ uses zero-based indexing) and prints it to the console.

Setting Fifth Component to 35

Assign the value 35 to the fifth component of the `alpha` array: ```cpp alpha[4] = 35; ```Index 4 targets the fifth element of the array, setting its value to 35.

Setting Ninth Component to Sum of Sixth and Thirteenth Components

To set the ninth component to be the sum of the sixth and thirteenth components, use: ```cpp alpha[8] = alpha[5] + alpha[12]; ```Here, index 8 refers to the ninth element, which is set to the sum of the elements at indices 5 and 12.

Setting Fourth Component to Calculated Value

Assign the fourth element a value based on the given formula: ```cpp alpha[3] = 3 * alpha[7] - 57; ```The expression multiplies the eighth component (index 7) by 3 and subtracts 57 to determine the value for index 3.

Output Array with Five Components Per Line

Iterate over the array and print five components per line with the following loop: ```cpp for (int i = 0; i < 15; i++) { std::cout << alpha[i] << " "; if ((i + 1) % 5 == 0) { std::cout << std::endl; } } ```This loop outputs each element of `alpha`, adding a newline character after every five elements.

Key concepts

Array Declaration

In C++, arrays are a fundamental way of storing multiple values of the same type in a single variable. They allow us to manage data more efficiently. When declaring an array, you specify:

• The data type of the elements it will hold, like int for integers.
• The name of the array, which is the identifier you will use to access it.
• The size of the array, which is the total number of elements it can store.

For example, to declare an array named alpha with 15 integer components, you would write:
int alpha[15];
This statement sets aside memory for 15 integer elements and associates them with the name alpha.

Zero-based Indexing

Zero-based indexing is a common convention in C++ and many other programming languages. It means that the first element in an array has an index of 0, the second element an index of 1, and so on. This is important to remember when accessing or manipulating elements. For an array declared as int alpha[15];, accessing elements is done like this:

• alpha[0] accesses the first element.
• alpha[9] accesses the tenth element.

Keep in mind this zero-based rule as you write code; otherwise, you'll end up accessing incorrect elements, or even cause runtime errors by trying to access out-of-bounds indices.

Array Element Access

Accessing elements within an array is straightforward once you understand zero-based indexing. You can both retrieve and modify elements by their index.
For instance, to output the tenth element of the array alpha, you would use:
std::cout << alpha[9];
This retrieves the value from the tenth position. To modify the fifth element and assign it a new value of 35, you use:
alpha[4] = 35;
This assigns the value 35 to the fifth position in the array. Indexing makes direct manipulation of data convenient, whether updating values or using them in expressions.

Loop Iteration

Looping through arrays is a common task in programming, allowing us to process each element systematically. In C++, the `for` loop is a popular choice for iterating over arrays. When you use a loop with a condition that runs for the length of the array, you can access each element sequentially.
For example, to print all elements of the array alpha with five elements per line, you'd write:
for (int i = 0; i < 15; i++) { std::cout << alpha[i] << " "; if ((i + 1) % 5 == 0) { std::cout << std::endl; }}
This loop iterates over each index from 0 to 14, printing each element. The conditional inside the loop, (i + 1) % 5 == 0, adds a newline after every five elements, formatting the output neatly.