Question

An application of function floor is rounding a value to the nearest integer. The statement y=floor( x + .5 ); rounds the number x to the nearest integer and assigns the result to y. Write a program that reads several numbers and uses the preceding statement to round each of these numbers to the nearest integer. For each number processed, print both the original number and the rounded number.

Short answer

To round numbers to the nearest integer: Read input numbers, use floor(x + 0.5) to round each, and print both original and rounded numbers.

Step-by-step solution

Initialize the Program

Start by including the necessary headers and then initiate the main function of the program. Inside the main function, declare an array or list to store the numbers which will be rounded.

Read Input Numbers

Use a loop to prompt the user for each number. Read the input numbers one by one and store them in the earlier declared array or list.

Include the Floor Function

Make sure to include the library or its equivalent to use the floor function in your program. This function will be needed to round the numbers.

Round Each Number

Iterate through the array or list of input numbers. For each number, apply the floor function with the addition of 0.5 to round the number to the nearest integer and store it in a new array or list of rounded numbers.

Output Results

Loop through the array or list of original numbers and their corresponding rounded numbers. Print both the original and rounded number for each entry.

End the Program

After processing all the input numbers, end the loop and terminate the program. Make sure your program correctly handles all user input and edge cases.

Key concepts

Floor Function in C++

Rounding numbers is a common task in programming, and in C++, the floor function is one of the tools for such operations. The floor function is part of the C++ Standard Library and can be found within the cmath header. In mathematical terms, the floor function takes a floating-point number and rounds it down to the nearest integer less than or equal to the original number.

When the goal is to round a number to the nearest integer, you can add 0.5 to the number and apply the floor function. This approach capitalizes on the behavior of the floor function, ensuring that any decimal portion of 0.5 or greater causes the input value to round up to the nearest integer. For decimals less than 0.5, adding 0.5 won't be sufficient to round the number up, so the floor function will naturally round it down.

For example, the expression floor(2.7 + .5) will yield 3.0, because 2.7 + .5 equals 3.2, and the floor function then rounds down to 3. This method provides a reliable means to round floating-point numbers efficiently.

User Input Handling in C++

Handling user input is a fundamental part of interactive C++ programs. Ensuring robust user input handling helps create a user-friendly and error-resistant application. To read numbers from users, you commonly use the cin object, which is part of the C++ Standard Library's iostream header.

To continuously request user input within a program, a loop structure is usually implemented. This could be a for, while, or do-while loop, depending on the specific requirements and conditions for ending the input phase. Within these loops, you must prepare to handle potential input errors — such as the user entering a non-numeric value when a number is expected — by using input validation techniques or by clearing and resetting the input stream to avoid infinite loops or crashes.

When collecting multiple numbers, it's typical to store these inputs in a data structure like an array or a std::vector. This facilitates later manipulation, such as rounding each number and pairing it with its original value as required by our rounding example.

Cmath Library in C++

The cmath library in C++ is a compilation of mathematical functions that programmers can utilize to perform a variety of calculations and operations. It is the C++ equivalent of the C library math.h and contains functions for mathematical operations like power calculations, trigonometric operations, exponentials and logarithms, as well as rounding numbers.

Including the cmath library is essential when you want to make use of mathematic functions such as floor, ceil, round, and abs. To use it, simply include the statement #include <cmath> at the beginning of your program. This gives your program access to these predefined functions, which are optimized for performance and accuracy.

Using the cmath library not only helps in carrying out mathematical operations confidently but also ensures consistency and compatibility across different platforms and compilers, which is crucial for producing reliable and portable code.