Check Narcissistic Number in C++

Check Narcissistic Number in C++ (4 Programs).

IntermediateAdvanced Number ProgramsExample 12 of 13

check-narcissistic-number.cpp

1#include <iostream>
2#include <cmath>
3using namespace std;
4
5bool isNarcissistic(int num) {
6    int original = num;
7    int n = 0, sum = 0;
8    
9    // Count digits
10    int temp = num;
11    while (temp != 0) {
12        temp /= 10;
13        n++;
14    }
15    
16    // Calculate sum of digits raised to power n
17    temp = num;
18    while (temp != 0) {
19        int digit = temp % 10;
20        sum += pow(digit, n);
21        temp /= 10;
22    }
23    
24    return sum == original;
25}
26
27int main() {
28    int num;
29    cout << "Enter a number: ";
30    cin >> num;
31    
32    if (isNarcissistic(num)) {
33        cout << num << " is a Narcissistic number" << endl;
34    } else {
35        cout << num << " is not a Narcissistic number" << endl;
36    }
37    
38    return 0;
39}

Output

Enter a number: 153
153 is a Narcissistic number

What's going on

The program checks whether a given number is a Narcissistic number. For example:

Input: 153

Number of digits: 3

Calculation: 1³ + 5³ + 3³ = 1 + 125 + 27 = 153

Since 153 equals 153, it is a Narcissistic number.

A Narcissistic number must satisfy: sum of (each digit^number_of_digits) = number

Example:

153 is Narcissistic: 1³ + 5³ + 3³ = 1 + 125 + 27 = 153 ✓

9474 is Narcissistic: 9⁴ + 4⁴ + 7⁴ + 4⁴ = 6561 + 256 + 2401 + 256 = 9474 ✓

123 is NOT Narcissistic: 1³ + 2³ + 3³ = 1 + 8 + 27 = 36 ≠ 123 ✗

Header Files Used

1.#include <iostream>

Provides cout and cin for input/output operations.

2.#include <cmath>

Provides pow() function for calculating powers.

Essential for raising digits to the power of number of digits.

Understanding Narcissistic Numbers

Definition

A Narcissistic number (Armstrong number) is a number that equals the sum of its digits, each raised to the power of the number of digits.

Mathematical Expression

If n has d digits and digits are d₁, d₂, ..., dₐ, then:

n = d₁^d + d₂^d + ... + dₐ^d

Examples

153 (3 digits): 1³ + 5³ + 3³ = 1 + 125 + 27 = 153 ✓

9474 (4 digits): 9⁴ + 4⁴ + 7⁴ + 4⁴ = 6561 + 256 + 2401 + 256 = 9474 ✓

371 (3 digits): 3³ + 7³ + 1³ = 27 + 343 + 1 = 371 ✓

123 (3 digits): 1³ + 2³ + 3³ = 1 + 8 + 27 = 36 ≠ 123 ✗

Known Narcissistic Numbers

1-digit: 1, 2, 3, 4, 5, 6, 7, 8, 9 (all single digits)

3-digit: 153, 370, 371, 407

4-digit: 1634, 8208, 9474

And more...

Function: isNarcissistic()

bool isNarcissistic(int num) {

int original = num;

int n = 0, sum = 0;

int temp = num;

while (temp != 0) {

temp /= 10;

n++;

}

// Calculate sum of digits raised to power n

temp = num;

while (temp != 0) {

int digit = temp % 10;

sum += pow(digit, n);

temp /= 10;

}

return sum == original;

}

This function:

Takes a number as input.

Counts the number of digits.

Calculates sum of each digit raised to power of digit count.

Returns true if sum equals original number.

1// Count digits

Step-by-Step Algorithm

Let's trace through the algorithm for num = 153:

Step 1: Count Digits

Initialize: n = 0, temp = 153

Iteration 1:

temp = 153 / 10 = 15, n = 1

Iteration 2:

temp = 15 / 10 = 1, n = 2

Iteration 3:

temp = 1 / 10 = 0, n = 3

Result: n = 3 (153 has 3 digits)

Step 2: Calculate Sum of Digit Powers

Initialize: sum = 0, temp = 153

Iteration 1:

digit = 153 % 10 = 3

sum = 0 + 3³ = 0 + 27 = 27

temp = 153 / 10 = 15

Iteration 2:

digit = 15 % 10 = 5

sum = 27 + 5³ = 27 + 125 = 152

temp = 15 / 10 = 1

Iteration 3:

digit = 1 % 10 = 1

sum = 152 + 1³ = 152 + 1 = 153

temp = 1 / 10 = 0

Step 3: Compare

sum = 153, original = 153

153 == 153 → return true

Result: 153 is a Narcissistic number.

Understanding the Algorithm Components

Counting Digits

Repeatedly divide by 10 until number becomes 0.

Count how many divisions were needed.

This gives the number of digits.

Extracting Digits

Use modulo (%) to get rightmost digit.

Use division (/) to remove rightmost digit.

Process from right to left.

Raising to Power

pow(digit, n) calculates digit^n.

Example: pow(5, 3) = 5³ = 125

Accumulation

sum += pow(digit, n) adds each digit's power contribution.

Continues until all digits are processed.

Main Function

int num;

cout << "Enter a number: ";

cin >> num;

if (isNarcissistic(num)) {

cout << num << " is a Narcissistic number" << endl;

} else {

cout << num << " is not a Narcissistic number" << endl;

}

return 0;

}

1int main() {

Process Flow

1.User enters a number (e.g., 153).

2.Call isNarcissistic(153) to check.

3.Display result based on return value.

Other Methods (Mentioned but not shown in code)

Method 2: Using String Conversion

string numStr = to_string(num);

int n = numStr.length();

int sum = 0;

for (char c : numStr) {

int digit = c - '0';

sum += pow(digit, n);

}

Converts number to string to count digits.

Iterates through each character.

Converts to digit and calculates power.

1return sum == num;

Method 3: Using Recursion

int countDigits(int num) {

if (num == 0) return 0;

}

int sumDigitPowers(int num, int power) {

if (num == 0) return 0;

return pow(num % 10, power) + sumDigitPowers(num / 10, power);

}

bool isNarcissistic(int num) {

int n = countDigits(num);

return sumDigitPowers(num, n) == num;

}

Recursive approach for counting digits and summing powers.

More complex but demonstrates recursion.

1return 1 + countDigits(num / 10);

Method 4: Using Array

int digits[10], count = 0;

int temp = num;

while (temp != 0) {

digits[count++] = temp % 10;

temp /= 10;

}

int sum = 0;

for (int i = 0; i < count; i++) {

sum += pow(digits[i], count);

}

Stores digits in an array.

Calculates sum from array.

1return sum == num;

Displaying the Result

The program prints:

Output (for input 153):

153 is a Narcissistic number

Or if not a Narcissistic number:

123 is not a Narcissistic number

1cout << num << " is a Narcissistic number" << endl;

Why Are They Called "Narcissistic"?

Origin of Name

The name comes from the concept of "narcissism" - self-love.

These numbers are "in love with themselves" because they equal the sum of their own digits raised to their own power.

Also called "Armstrong numbers" after Michael F. Armstrong.

Mathematical Beauty

They represent a special mathematical property.

Limited in number but fascinating to discover.

Used in number theory and recreational mathematics.

Common Narcissistic Numbers

1-digit (all are Narcissistic)

1, 2, 3, 4, 5, 6, 7, 8, 9

3-digit

153 = 1³ + 5³ + 3³

370 = 3³ + 7³ + 0³

371 = 3³ + 7³ + 1³

407 = 4³ + 0³ + 7³

4-digit

1634 = 1⁴ + 6⁴ + 3⁴ + 4⁴

8208 = 8⁴ + 2⁴ + 0⁴ + 8⁴

9474 = 9⁴ + 4⁴ + 7⁴ + 4⁴

Common Use Cases

Number Theory

Studying special number properties.

Mathematical research and puzzles.

Educational programming exercises.

Algorithm Practice

Digit manipulation techniques.

Understanding exponentiation.

Building complex accumulation patterns.

Interview Questions

Common coding interview problem.

Tests understanding of digit operations and powers.

Foundation for more complex number problems.

Important Considerations

Edge Cases

Single-digit numbers are all Narcissistic (n¹ = n).

0 is Narcissistic (0¹ = 0).

Negative numbers: not typically considered (powers are positive).

Large Numbers

For very large numbers, pow() may cause overflow.

Consider using long long for larger numbers.

Or use iterative power calculation for very large numbers.

Efficiency

Time complexity: O(d × log d) where d is number of digits.

Space complexity: O(1) - constant space.

Can be optimized by pre-calculating digit powers.

return 0;

This ends the program successfully.

PreviousCheck Neon Number NextConvert Char to Int