Narcissistic Number Checker - Problem

A narcissistic number (also known as an Armstrong number) is an N-digit number that equals the sum of its digits each raised to the power of N.

For example:

153 is a 3-digit narcissistic number: 1³ + 5³ + 3³ = 1 + 125 + 27 = 153
9474 is a 4-digit narcissistic number: 9⁴ + 4⁴ + 7⁴ + 4⁴ = 6561 + 256 + 2401 + 256 = 9474

Write a function to check if a given number is narcissistic. Additionally, find all 3-digit and 4-digit narcissistic numbers.

Input & Output

Example 1 — 3-digit narcissistic number

$ Input: num = 153

› Output: true

💡 Note: 153 has 3 digits: 1³ + 5³ + 3³ = 1 + 125 + 27 = 153, which equals the original number

Example 2 — Non-narcissistic number

$ Input: num = 123

› Output: false

💡 Note: 123 has 3 digits: 1³ + 2³ + 3³ = 1 + 8 + 27 = 36, which does not equal 123

Example 3 — Single digit (always narcissistic)

$ Input: num = 5

› Output: true

💡 Note: 5 has 1 digit: 5¹ = 5, which equals the original number. All single digits are narcissistic.

Constraints

0 ≤ num ≤ 10⁶
Input will be a non-negative integer

Visualization

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Asked in

M Microsoft 15 GS Goldman Sachs 12 A Adobe 8

The key insight is to extract digits mathematically using modulo and division operations, then check if the sum of each digit raised to the power of digit count equals the original number. Best approach uses mathematical digit extraction for O(1) space complexity. Time: O(d), Space: O(1) where d is number of digits.

Common Approaches

✓ Mathematical Digit Extraction

⏱️ Time: O(d) Space: O(1)

Extract digits using mathematical operations: modulo 10 gets the last digit, integer division by 10 removes the last digit. Count digits first, then extract and calculate powers.

String Conversion Method

⏱️ Time: O(d) Space: O(d)

Convert the number to a string to easily count digits and iterate through each character. Convert each character back to an integer, raise to the power of digit count, and sum up.

Mathematical Digit Extraction — Algorithm Steps

Count digits by repeatedly dividing by 10
Extract last digit using modulo 10
Raise digit to power and add to sum
Remove last digit using integer division by 10

Visualization

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Step-by-Step Walkthrough

Count Digits

153 → 15 → 1 → 0 (3 divisions = 3 digits)

Extract Digits

153%10=3, 15%10=5, 1%10=1

Calculate Powers

3³ + 5³ + 1³ = 27 + 125 + 1 = 153

Code -

solution.c — C

#include <stdio.h>
#include <math.h>
#include <stdbool.h>

bool solution(int num) {
    if (num < 0) return false;
    if (num == 0) return true;
    
    // Count digits
    int temp = num;
    int digitCount = 0;
    while (temp > 0) {
        digitCount++;
        temp /= 10;
    }
    
    // Calculate sum of powers
    temp = num;
    int total = 0;
    while (temp > 0) {
        int digit = temp % 10;
        total += (int)pow(digit, digitCount);
        temp /= 10;
    }
    
    return total == num;
}

int main() {
    int num;
    scanf("%d", &num);
    
    bool result = solution(num);
    printf(result ? "true\n" : "false\n");
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(d)

Two passes through d digits: once to count, once to calculate

✓ Linear Growth

Space Complexity

O(1)

Only uses a few integer variables regardless of input size

✓ Linear Space

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Narcissistic Number Checker - Problem

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Mathematical Digit Extraction — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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