Armstrong Number - Video Solutions

Problem Overview: You are given an integer n. A number is called an Armstrong number if it equals the sum of its digits raised to the power of the number of digits. For example, 153 has three digits and satisfies 1^3 + 5^3 + 3^3 = 153. The task is to check whether the given number satisfies this property.

Approach 1: Digit Extraction Simulation (O(d) time, O(1) space)

This approach directly follows the definition of an Armstrong number. First determine the number of digits d in n. Then iterate through each digit by repeatedly taking n % 10 and dividing by 10. For every extracted digit, compute digit^d and add it to a running sum. After processing all digits, compare the computed sum with the original number.

The key insight is that digit extraction with modulo and integer division allows you to process digits without allocating additional memory. Every digit is visited exactly once, so the runtime is proportional to the number of digits in the number. This technique appears frequently in math and number theory problems where operations are performed digit by digit.

Because the algorithm stores only a few integer variables, the extra memory usage stays constant. This makes it the most efficient and interview-friendly solution.

Approach 2: String Conversion (O(d) time, O(d) space)

Another straightforward method converts the integer to a string and iterates over each character. The length of the string gives the digit count d. For every character, convert it back to an integer digit and compute digit^d, accumulating the result in a sum.

This approach is easier to read and implement in many languages because string iteration avoids manual modulo operations. However, it requires additional memory to store the string representation of the number. The time complexity remains linear in the number of digits, but the space complexity increases to O(d).

This pattern is common in beginner-friendly math problems where clarity matters more than micro-optimizations. Many developers prefer this method in scripting languages like Python or JavaScript.

Recommended for interviews: The digit extraction simulation is the preferred solution. It demonstrates comfort with numeric operations such as modulo and integer division, which interviewers often expect in math-focused problems. The string approach still works and clearly shows the logic, but the constant-space simulation signals stronger algorithmic fundamentals.