by A Neon number is an intriguing concept in the realm of mathematics and computer science. It is a number where the sum of the digits of its square equals the number itself. For instance, 9 is a neon number because 9^2 = 81, and the sum of the digits of 81 (8 + 1) equals 9.
Understanding Neon Numbers
To identify neon numbers, one must perform the following steps for each number in the given range:
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Square the Number:
First, compute the square of the number.
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Sum the Digits:
Next, calculate the sum of the digits of the squared number.
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Compare with Original:
Finally, check if the sum of the digits equals the original number. If so, the number is a neon number.
This process involves fundamental operations like multiplication and digit extraction, the latter typically achieved through division and modulus operations.
Algorithm for Finding Neon Numbers in a Range
Before implementing the program, let’s outline the algorithm to find and display all neon numbers within a specified range:
- Input Range: Obtain the lower and upper bounds of the range from the user.
- Iterate Through the Range: For each number in the range, perform the following steps:
- Square the number.
- Calculate the sum of the digits of the square.
- Check if the sum equals the original number.
- If so, display the number as a neon number.
- Repeat until all numbers in the range have been checked.
Implementing the Program
Now, let’s translate the above algorithm into a C++ program:
#include <iostream>
using namespace std;
// Function to calculate the sum of digits of a number
int sumOfDigits(int n) {
int sum = 0;
while (n > 0) {
sum += n % 10; // Add the rightmost digit to sum
n /= 10; // Remove the rightmost digit from n
}
return sum;
}
// Function to check if a number is a Neon Number
bool isNeon(int num) {
int square = num * num; // Calculate square of num
int sum = sumOfDigits(square); // Sum the digits of the square
return sum == num; // Return true if sum of digits equals num
}
int main() {
int lower, upper;
// Prompt user for the range
cout << “Enter the lower and upper bounds of the range: “;
cin >> lower >> upper;
cout << “Neon numbers between ” << lower << ” and ” << upper << ” are:” << endl;
// Iterate through the range and check for Neon Numbers
for (int i = lower; i <= upper; ++i) {
if (isNeon(i)) {
cout << i << ” “;
}
}
return 0;
}
Program Explanation
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Sum of Digits Function (sumOfDigits):
This helper function takes an integer n and returns the sum of its digits. It does so by repeatedly extracting the rightmost digit (using n % 10), adding it to the sum, and then removing this digit from n (using n /= 10).
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Neon Number Checker Function (isNeon):
The isNeon function checks whether a given number is a neon number. It squares the number, uses sumOfDigits to calculate the sum of the digits of the square, and then checks if this sum equals the original number.
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Main Function:
After obtaining the range from the user, the program iterates through each number in this range, using the isNeon function to determine if it is a neon number. If a number is found to be neon, it is printed to the console.
