Question

Define a procedure that takes three numbers as arguments and returns the sum of the squares of the two larger numbers.

Short answer

Sort the numbers, pick the two largest, square them, and return their sum.

Step-by-step solution

Identify the Task

The task is to create a procedure (or function) that accepts three numbers as inputs. It should calculate and return the sum of the squares of the two largest numbers among those provided.

Understand the Logic Behind the Task

To solve this, you need to identify which two numbers are the largest out of the three provided. A straightforward way to do this is by sorting the three numbers and selecting the two largest ones.

Implement Sorting Mechanism

Sort the three input numbers in non-decreasing order. This will position the smallest number first and the two largest numbers last. For example, if the input numbers are 3, 1, and 2, sorting them gives us 1, 2, and 3.

Select the Two Largest Numbers

From the sorted list of three numbers, pick the last two numbers. These are the largest two numbers in the original list. Using the previous example, after sorting 1, 2, 3, the two largest numbers are 2 and 3.

Square the Two Largest Numbers

Square both of the largest numbers obtained in the previous step.For example, if our largest numbers are 2 and 3, calculate \(2^2 = 4\) and \(3^2 = 9\).

Calculate the Sum of Squares

Add the squares of the two largest numbers. This will provide the result that the procedure needs to return.From our example: \(4 + 9 = 13\).

Write the Function

Create a function in your chosen programming language using the previous steps. Here is a Python example: ```python def sum_of_squares_of_two_largest(a, b, c): numbers = sorted([a, b, c]) return numbers[1]**2 + numbers[2]**2 ``` This function sorts the inputs and returns the sum of the squares of the two largest numbers.

Key concepts

Sorting Algorithms

When tackling problems that involve selecting specific elements from a set, sorting algorithms can be invaluable. In the provided exercise, sorting helps us identify the two largest numbers from a set of three. The aim is to arrange the numbers in a sequence where they go from the smallest to the largest. By sorting the numbers, it becomes straightforward to access the largest ones. Sorting algorithms, such as the simple sort used here, can often be executed in a single line of code using built-in functions in many programming languages. These functions are efficient because they automatically handle the rearrangement of elements:

• They reorder the list so that you can easily identify positions — the last two elements in a sorted list of three elements are guaranteed to be the largest.
• Sorting ensures that no manual comparison is required, simplifying the task and reducing the risk of errors.

Using sorting reduces complexity, making the logic more manageable and easier to follow.

Function Definition

A function in programming is a reusable block of code designed to perform a specific task. In our exercise, the task is to build a function that calculates the sum of the squares of the two largest numbers from a given set of three. Understanding how to define a function is crucial: - **Function Name:** Should clearly represent its purpose. Here, `sum_of_squares_of_two_largest` immediately describes what the function does. - **Parameters:** Functions can take inputs; in this case, our function requires three numbers. These numbers are passed as parameters when the function is called. - **Return Statement:** This specifies what the function will output. After processing, the function returns the result — the sum of squares of the two largest numbers in the given example. Writing functions allows for code modularity and reusability, making your programs cleaner and more structured. Functions simplify complex problems into smaller, manageable tasks.

Mathematical Operations

Mathematical operations form the core of our calculation in this exercise. Once we've identified the two largest numbers using sorting, we must square them and find their sum.- **Squaring a Number:** This involves multiplying the number by itself. For example, squaring a number like 3 is performed as follows: \[ 3^2 = 3 \times 3 = 9 \] Squaring each of the largest numbers ensures we amplify their values, which is crucial for specific calculations or transformations.- **Summing Values:** After squaring, the final task is to add these values together. Adding allows us to combine results into a single output, which our function will return. If the results from squaring are, for example, 4 and 9, the summation is computed as: \[ 4 + 9 = 13 \]Through these operations, we're able to manipulate the provided inputs to achieve the desired outcome. It's essential to get comfortable with these simple operations to handle more complex algorithms and computations effectively.