Question

Perform the following tasks for an array called fractions: a) Declare a constant ARRAY_SIZE that is initialized to 10 . b) Declare an array with ARRAY_SIZE elements of type double, and initialize the elements to 0 c) Refer to array element 4 d) Assign the value 1.667 to array element 9 e) Assign the value 3.333 to array element 6 f) Sum all the elements of the array, using a for statement. Declare the integer variable \(x\) as a control variable for the loop.

Short answer

Declare a constant size, set up and initialize the array, access specific elements, assign values, and use a loop to sum elements.

Step-by-step solution

Declare a Constant

Declare a constant named `ARRAY_SIZE` and initialize it to 10. This constant will define the size of our array. In many programming languages like C++ or Java, this can be done as follows: ```c const int ARRAY_SIZE = 10; ```

Declare and Initialize Array

Declare an array named `fractions` with type `double` and size `ARRAY_SIZE`. Initialize all elements of the array to 0. In code, this would typically look like: ```c double fractions[ARRAY_SIZE] = {0.0}; ```

Refer to Element 4

Array elements are typically accessed using their index, starting from 0. Thus, to refer to the 4th element of the array: ```c fractions[4]; ```

Assign Value to Element 9

Assign the value 1.667 to the 9th element of the `fractions` array. The index for the 9th element is 8 (since the index starts from 0): ```c fractions[8] = 1.667; ```

Assign Value to Element 6

Assign the value 3.333 to the 6th element of the `fractions` array. The index for this element is 5: ```c fractions[5] = 3.333; ```

Sum Array Elements

Use a `for` loop to sum all the elements of the `fractions` array. Declare an integer variable `x` to serve as the loop control variable, and a double variable to store the sum of the elements. Here's how you might write it: ```c double sum = 0.0; for (int x = 0; x < ARRAY_SIZE; ++x) { sum += fractions[x]; } ```

Key concepts

Array Initialization

Array initialization is a fundamental concept in programming that sets up an array with a particular size and initial values. When initializing an array, you typically declare it by specifying its data type and size, which can often be set using a constant to help control the size across the program. Using constants is beneficial for code readability and maintainability:

• To declare an array, specify its type and size, such as `double fractions[10];`, where `10` is the number of elements it can hold.
• Initializing involves setting starting values for each element. You can do this by listing values in curly braces, like `{0.0}`, which initializes all array elements to `0.0` in languages like C++ or Java.

Array initialization ensures that the array is ready for use, with a defined size and initial state for each element.

Loop Control Variables

Loop control variables are used to guide loop execution, making them indispensable in programming, especially when working with arrays. In loops, a control variable dictates the number of times the loop executes, with the most common loop structures being `for`, `while`, and `do-while` loops.

A `for` loop is particularly useful when dealing with arrays, as it offers a concise structure for iterating over elements.

• The control variable, such as `int x`, is usually initialized at the start of the loop.
• The loop continues to execute while a condition, often involving the control variable, remains true.
• After each iteration, the control variable is updated, usually incremented or decremented.

The loop control variable is critical because it serves as a counter that helps traverse each element in the array efficiently.

Array Indexing

Array indexing is how you access and manipulate specific elements within an array. In most programming languages, array indexing starts from `0`, which means the first element is at index `0`, the second at index `1`, and so on.

• To access an element, you use its index inside square brackets, like `fractions[4]` to access the fifth element.
• Understanding the zero-based index is crucial, especially when navigating through the array for tasks like reading or modifying data.

Indexing allows programmers to efficiently access and manage an array's elements, enabling specific operations such as updating values or performing calculations on individual elements.

Array Element Assignment

Assigning values to array elements is a straightforward process of updating elements at specific indexes. This concept allows you to modify array contents, crucial for maintaining dynamic data.

• Assignment can be done by directly referencing the element's index. For example, `fractions[8] = 1.667;` updates the 9th element's value.
• This operation is particularly important when working with data updates or computational results.

Understanding element assignment is key for tasks like initializing data sets, applying incoming data to existing structures, and performing calculations. It allows array contents to be dynamically managed, adapting to changing program requirements.