Nude Numbers In C++

Certain mathematical concepts are great examples in programming, and "nude numbers" form one such series. Even if the term is interesting, it goes very deep and has the very essence of mathematical elegance written in the language of simplicity. This article explores an idea as to what it is to understand nude numbers by explaining them and writing the program for C++ using which such numbers can efficiently be obtained.

What Are Nude Numbers?

A nude number is a positive integer that satisfies the following conditions:

✅ It is divisible by each of its digits.
✅ None of its digits can be zero.

For example:

✅ 36 is a nude number because it is divisible by both 3 and 6.
✅ 128 is not a nude number because it contains the digit 0.

The difficulty is determining whether a number given fulfills these requirements by parsing the digits of the number and testing for divisibility.

Breaking the Problem Down:

In order to identify whether a number is a nude number, we have to carry out the following:

✅ Extracting the Digits: Break down the number into its constituent digits.
✅ Checking for Zero: If there is a zero in the digit, the number cannot be a nude number.
✅ Divisibility Test: Confirm that the number is divisible by each of its digits.

Algorithm for Nude Numbers

Step-by-Step Explanation:

Loop Over Numbers:

✅ Select a set of integers to test.

Extract Digits:

✅ Apply modulo and division operations to obtain digits.

Check Each Criterion:

✅ Confirm no digit is zero.
✅ Confirm that the number is divisible by each digit.

Print Results:

✅ Print or save numbers that pass the test as naked numbers.

C++ Implementation:

Below is a C++ program to find and display nude numbers within a given range.

Example


#include <iostream>
using namespace std;

// Function to check if a number is a nude number
bool isNudeNumber(int num) 
{
    int originalNum = num; 

    // Handle the case when the number is zero (0 is not a nude number)
    if (num == 0) {
        return false;
    }

    while (num > 0) 
    {
        int digit = num % 10; // Extract the last digit

        // Here check if the digit is zero or if the original number is not divisible by the digit
        if (digit == 0 || originalNum % digit != 0) 
        {
            return false;
        }

        num /= 10; 
    }
    return true; // All conditions met
}

int main() 
{
    int lowerLimit, upperLimit;

    // Input range from the user
    cout << "Enter the lower limit: ";
    cin >> lowerLimit;
    cout << "Enter the upper limit: ";
    cin >> upperLimit;

    cout << "Nude numbers between " << lowerLimit << " and " << upperLimit << " are:" << endl;

    // Iterate through the range to find nude numbers
    for (int i = lowerLimit; i <= upperLimit; i++) 
    {
        if (isNudeNumber(i)) 
        {
            cout << i << " "; 
        }
    }
    cout << endl;

    return 0;
}

Output:

Here's how the program works when executed:

Input:

Example


Enter the lower limit: 10
Enter the upper limit: 50

Output:

Output


Nude numbers between 10 and 50 are:
12 15 24 36

Explanation:

✅ 12: Divisible by 1 and 2.
✅ 15: Divisible by 1 and 5.
✅ 24: Divisible by 2 and 4.
✅ 36: Divisible by 3 and 6.

Explanation of the Code:

✅ The is nude number Function: Function Accept an integer as the input to it and check if it's a nude number or not. It extracts digits using the modulo operator (%) and checks if they are non-zero and if the original number is divisible by the digit. If any digit fails these tests, the function returns false.
✅ Main Function Logic: The program accepts a range of numbers (lowerLimit and upperLimit) from the user. It calls isNudeNumber for each number in this range. All valid nude numbers are printed on the console.
✅ Function Accept an integer as the input to it and check if it's a nude number or not.
✅ It extracts digits using the modulo operator (%) and checks if they are non-zero and if the original number is divisible by the digit.
✅ If any digit fails these tests, the function returns false.
✅ The program accepts a range of numbers (lowerLimit and upperLimit) from the user.
✅ It calls isNudeNumber for each number in this range.
✅ All valid nude numbers are printed on the console.

Optimization Tips

For large ranges, the performance may be enhanced by

✅ Skip those numbers that contain the digit 0 because they will never be nude numbers.
✅ Using mathematical properties to limit unnecessary computations, like finding patterns in the divisibility rule.

Applications of Nude Numbers

Nude numbers are essentially a theoretical and entertainment concept in mathematics and computer science . However, they help in enhancing important programming techniques, which include:

✅ Digit manipulation.
✅ Effective usage of loops and conditional statements.
✅ Modulo operations for divisibility checks.

Conclusion:

In conclusion, Nude numbers are intriguing to a programmer and math student. It requires a set of steps for a programmer to identify them: extract the digits, apply logical checking, and work under limitations. It is an activity that helps sharpen one's problem-solving skills while improving familiarity with key programming constructs in C++ .

Whether you're a beginner exploring the basics of digit manipulation or a seasoned coder refining your optimization skills, nude numbers offer a perfect playground to experiment and learn. So, grab your compiler and start exploring the fascinating world of nude numbers.