Determine Perfect Square in C++

Introduction

In this lab, you will learn how to determine if a given number is a perfect square in C++. A perfect square is a number that can be expressed as the product of an integer with itself. For example, 1, 4, 9, 16, and 25 are perfect squares because they can be expressed as 1×1, 2×2, 3×3, 4×4, and 5×5 respectively.

We will create a C++ program that uses the sqrt() function from the standard library to calculate the square root of a number and determine if it is a perfect square. This lab will introduce you to basic C++ programming concepts including functions, conditional statements, and mathematical operations.

Create a New C++ File and Include Necessary Libraries

In this step, we will create a new C++ file and include the necessary libraries for our program.

First, let's create a new file named main.cpp in the project directory:

In the WebIDE, click on the Explorer icon in the left sidebar
Right-click on the project folder and select "New File"
Name the file main.cpp and press Enter

Now, let's add the necessary libraries to our program. We need two main libraries:

iostream: This library provides functionality for input and output operations
cmath: This library contains mathematical functions, including the sqrt() function that we will use

Add the following code to your main.cpp file:

#include <iostream>
#include <cmath>

using namespace std;

int main() {
    cout << "\nWelcome to the Perfect Square Checker Program\n\n";

    // We will add more code here in the next steps

    return 0;
}

This code:

Includes the required libraries
Uses the namespace std to avoid having to write std:: before standard library functions
Creates a basic main() function that displays a welcome message
Returns 0 to indicate successful program execution

Save your file by pressing Ctrl+S or selecting File > Save from the menu.

Implement the Perfect Square Checking Function

Now, we will create a function that determines whether a number is a perfect square. A perfect square has an integer square root. For example, 16 is a perfect square because its square root is exactly 4.

Add the following function above the main() function in your main.cpp file:

bool isPerfectSquare(int number) {
    // Calculate the square root of the number
    double squareRoot = sqrt(number);

    // Convert the square root to an integer
    int intSquareRoot = static_cast<int>(squareRoot);

    // A number is a perfect square if squaring its integer square root gives the original number
    return (intSquareRoot * intSquareRoot == number);
}

Let's understand how this function works:

The function takes an integer parameter number and returns a boolean value (true or false)
We use the sqrt() function from the cmath library to calculate the square root of the input number
We convert the square root to an integer using static_cast<int>(), which removes any decimal portion
If the number is a perfect square, then multiplying the integer square root by itself will give the original number
The function returns true if the number is a perfect square, and false otherwise

For example:

For number 16:
- sqrt(16) = 4.0
- Converting 4.0 to an integer gives 4
- 4 × 4 = 16, which equals the original number, so 16 is a perfect square
For number 10:
- sqrt(10) ≈ 3.16227766
- Converting 3.16227766 to an integer gives 3
- 3 × 3 = 9, which does not equal the original number, so 10 is not a perfect square

Your complete code so far should look like this:

#include <iostream>
#include <cmath>

using namespace std;

bool isPerfectSquare(int number) {
    // Calculate the square root of the number
    double squareRoot = sqrt(number);

    // Convert the square root to an integer
    int intSquareRoot = static_cast<int>(squareRoot);

    // A number is a perfect square if squaring its integer square root gives the original number
    return (intSquareRoot * intSquareRoot == number);
}

int main() {
    cout << "\nWelcome to the Perfect Square Checker Program\n\n";

    // We will add more code here in the next step

    return 0;
}

Save your file before proceeding to the next step.

Complete the Main Function with User Input and Output

Now, let's enhance the main() function to:

Prompt the user to enter a number
Get the user's input
Use our isPerfectSquare() function to check if the number is a perfect square
Display an appropriate message based on the result

Update your main() function with the following code:

int main() {
    cout << "\nWelcome to the Perfect Square Checker Program\n\n";

    int userNumber;

    // Prompt the user to enter a number
    cout << "Please enter a positive integer: ";
    cin >> userNumber;

    // Check if the entered number is a perfect square
    if (isPerfectSquare(userNumber)) {
        int squareRoot = static_cast<int>(sqrt(userNumber));
        cout << "\nThe number " << userNumber << " is a perfect square!" << endl;
        cout << "It is equal to " << squareRoot << " × " << squareRoot << endl;
    } else {
        cout << "\nThe number " << userNumber << " is not a perfect square." << endl;
    }

    cout << "\nThank you for using the Perfect Square Checker Program!\n" << endl;

    return 0;
}

Let's understand what this code does:

We declare an integer variable userNumber to store the user's input
We prompt the user to enter a positive integer using cout
We read the user's input using cin and store it in userNumber
We call our isPerfectSquare() function with userNumber as the argument
If the number is a perfect square:
- We calculate its square root and store it in squareRoot
- We display a message indicating that the number is a perfect square
- We show what two identical integers multiply to give the original number
If the number is not a perfect square:
- We display a message indicating that the number is not a perfect square
Finally, we display a thank-you message and return from the main() function

Your complete program should now look like this:

#include <iostream>
#include <cmath>

using namespace std;

bool isPerfectSquare(int number) {
    // Calculate the square root of the number
    double squareRoot = sqrt(number);

    // Convert the square root to an integer
    int intSquareRoot = static_cast<int>(squareRoot);

    // A number is a perfect square if squaring its integer square root gives the original number
    return (intSquareRoot * intSquareRoot == number);
}

int main() {
    cout << "\nWelcome to the Perfect Square Checker Program\n\n";

    int userNumber;

    // Prompt the user to enter a number
    cout << "Please enter a positive integer: ";
    cin >> userNumber;

    // Check if the entered number is a perfect square
    if (isPerfectSquare(userNumber)) {
        int squareRoot = static_cast<int>(sqrt(userNumber));
        cout << "\nThe number " << userNumber << " is a perfect square!" << endl;
        cout << "It is equal to " << squareRoot << " × " << squareRoot << endl;
    } else {
        cout << "\nThe number " << userNumber << " is not a perfect square." << endl;
    }

    cout << "\nThank you for using the Perfect Square Checker Program!\n" << endl;

    return 0;
}

Save your file before proceeding to the next step.

Compile and Test the Program

Now that we have completed our C++ program, it's time to compile and run it. Compiling converts our human-readable code into a machine-executable program.

Compile the Program

Open a terminal in the WebIDE by clicking on "Terminal" in the menu and selecting "New Terminal".

In the terminal, navigate to the project directory:

cd ~/project

Compile the program using the g++ compiler:

g++ main.cpp -o perfect_square_checker

This command tells the compiler to:

Take our source file main.cpp
Compile it into an executable named perfect_square_checker

If the compilation is successful, you will not see any output. If there are errors, read the error messages, fix the issues in your code, and try compiling again.

Run the Program

After successfully compiling the program, run it using:

./perfect_square_checker

The program will start and prompt you to enter a positive integer.

Test with Different Inputs

Let's test our program with different inputs to verify it works correctly:

Test Case 1: A Perfect Square

Enter 16 when prompted. You should see output similar to:

Please enter a positive integer: 16

The number 16 is a perfect square!
It is equal to 4 × 4

Thank you for using the Perfect Square Checker Program!

Test Case 2: Not a Perfect Square

Run the program again and enter 10 when prompted. You should see output similar to:

Please enter a positive integer: 10

The number 10 is not a perfect square.

Thank you for using the Perfect Square Checker Program!

Test Case 3: Another Perfect Square

Run the program again and enter 25 when prompted. You should see output similar to:

Please enter a positive integer: 25

The number 25 is a perfect square!
It is equal to 5 × 5

Thank you for using the Perfect Square Checker Program!

By testing with different inputs, you can verify that your program correctly identifies perfect squares and non-perfect squares.

Congratulations! You have successfully created a C++ program that determines whether a number is a perfect square.

Summary

In this lab, you successfully created a C++ program that determines whether a number is a perfect square. Let's review what you accomplished:

You learned how to include necessary libraries in a C++ program:
- iostream for input and output operations
- cmath for mathematical functions like sqrt()
You implemented the isPerfectSquare() function that uses a mathematical approach to determine if a number is a perfect square:
- Calculate the square root of the number
- Check if squaring the integer part of the square root equals the original number
You created a user-friendly interface in the main() function that:
- Prompts the user to enter a number
- Uses the isPerfectSquare() function to check if the number is a perfect square
- Displays an appropriate message based on the result
You compiled and tested your program with different inputs to verify its functionality.

Through this lab, you gained practical experience with several important C++ programming concepts:

Creating and calling functions
Using conditional statements (if-else)
Working with user input and output
Performing type conversions
Using mathematical functions from the standard library
Compiling and running a C++ program

You can further enhance this program by adding features such as:

Input validation to ensure the user enters a positive integer
The ability to check multiple numbers without restarting the program
Finding the closest perfect square to a non-perfect square number

By continuing to practice and build upon these fundamental concepts, you will develop stronger C++ programming skills that you can apply to more complex problems.