PPractick

The problem

A maths-quiz app has a bonus round on Armstrong numbers (also called narcissistic numbers): a number with k digits is an Armstrong number if the sum of each digit raised to the power k equals the number itself. For example, 153 has 3 digits and 1³ + 5³ + 3³ = 1 + 125 + 27 = 153. The app needs a checker, and it also wants to list every Armstrong number below 10,000 for its hint screen. The problem combines two things from earlier: counting digits and extracting them one by one.

Example: 153 → true, 9474 → true (9⁴ + 4⁴ + 7⁴ + 4⁴ = 9474), 123 → false.

Function signature

bool isArmstrong(long long n);  // sum of digits^k equals n, where k is the digit count

Test cases

Input n	Output	Explanation
153	true	1³ + 5³ + 3³ = 153
370	true	3³ + 7³ + 0³ = 370
9474	true	4 digits: 6561 + 256 + 2401 + 256 = 9474
123	false	1 + 8 + 27 = 36
7	true	Every single-digit number: 7¹ = 7
0	true	0¹ = 0
10	false	1² + 0² = 1

(Confirm: the power is the number of digits of n, not always 3; n is non-negative. The Armstrong numbers below 10,000 are 0–9, 153, 370, 371, 407, 1634, 8208 and 9474.)

How interviewers phrase it

• "Check whether a number is an Armstrong number."
• "Print all Armstrong numbers between 1 and N."
• Some versions fix the power at 3 (checking only three-digit numbers). Clarify which one is meant.

Clarifying questions to ask

1. Is the power the number of digits, or always 3?
2. Can the number be negative or zero?
3. What's the range of N? (Decides the integer type for the sum.)

Follow-ups to expect

1. "Why not use pow from <cmath>?"
2. "How do you find the number of digits?"
3. "How many Armstrong numbers are there?"
4. "Complexity?"

Related questions

• Count all Digits of a Number Easy
• Reverse a number Easy
• Palindrome Number Easy
• GCD of Two Numbers Easy
• Print all Divisors Easy
• Check for Prime Number Easy

All 474 dsa interview questions

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