Check Whether a Number is a Disarium Number in Java

Number Classification & Special Numbers

Topic: Check Whether a Number is a Disarium Number

A Disarium number is a number in which the sum of its digits powered with their respective positions is equal to the number itself.

For example, in the number 135:

  • 11 + 32 + 53 = 1 + 9 + 125 = 135

This concept uses basic arithmetic operations and the use of Math.pow to raise digits to a power, as well as converting numbers to strings to get digit positions easily.

Examples

Example 1:

Input: 89

Calculation: 81 + 92 = 8 + 81 = 89

Output: Disarium Number

Example 2:

Input: 75

Calculation: 71 + 52 = 7 + 25 = 32

Output: Not a Disarium Number

Example 3 (Edge Case):

Input: 1

Output: Disarium Number — Since 11 = 1

Interviewer Expectations

The interviewer is checking whether you can:

  • Understand digit manipulation in numbers
  • Use string operations and indexing
  • Apply loops and arithmetic operations effectively
  • Write clean and readable code with correct logic

Approach

  1. Convert the number to a string so that each digit’s position can be easily tracked.
  2. Initialize a variable to store the sum.
  3. Loop through each digit and compute digitposition using Math.pow().
  4. Sum all powered digits.
  5. Compare the sum with the original number.

Dry Run (with 135):

  • Digits: 1 (pos 1), 3 (pos 2), 5 (pos 3)
  • Sum = 11 + 32 + 53 = 1 + 9 + 125 = 135
  • Since the sum equals the original number, it is a Disarium number.

Java Program

public class DisariumNumber {
    public static void main(String[] args) {
        int num = 135;
        String strNum = Integer.toString(num);
        int sum = 0;
        
        for (int i = 0; i < strNum.length(); i++) {
            int digit = Character.getNumericValue(strNum.charAt(i));
            sum += Math.pow(digit, i + 1);
        }

        if (sum == num) {
            System.out.println(num + " is a Disarium Number");
        } else {
            System.out.println(num + " is Not a Disarium Number");
        }
    }
}
135 is a Disarium Number

Possible Followup Questions with Answers

1. Can we solve it without converting to String?

Yes. We can count digits first using a loop, then extract digits from right to left and process their position accordingly. However, it’s more complex and less readable.

2. What is the time complexity of this program?

O(n), where n is the number of digits in the number, because we loop once through all digits.

3. Can we generalize this for a list of numbers?

Yes. Just wrap the logic inside a method and call it for multiple values using a loop or from user input.

4. What other numbers fall in the special category?

Some other interesting number types:

  • Armstrong Number
  • Perfect Number
  • Harshad Number
  • Automorphic Number


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