Program to find super digit of a number in Python

Suppose we have a number n. We have to find the super digit of this number. The super digit of a single digit number is the digit itself, but for multi-digit numbers, super digit is the sum of all digits repeatedly until the sum is a single digit number.

So, if the input is like n = 513682, then the output will be 7 because (5+1+3+6+8+2) = 25, (2 + 5) = 7.

Algorithm

To solve this, we will follow these steps ?

• s := 0
• while n > 0 or s > 9, do
  • if n is same as 0, then
    • n := s
    • s := 0
  • s := s + n mod 10
  • n := floor value of n/10
• return s

Method 1: Using While Loop

This approach processes each digit one by one and calculates the sum repeatedly ?

def solve(n):
    s = 0
    while(n > 0 or s > 9):
        if n == 0:
            n = s
            s = 0
        
        s += n % 10
        n //= 10
    
    return s

n = 513682
print(f"Super digit of {n} is: {solve(n)}")

Super digit of 513682 is: 7

Method 2: Using String Conversion

A more intuitive approach that converts the number to string and sums the digits ?

def super_digit_string(n):
    while n >= 10:
        digit_sum = sum(int(digit) for digit in str(n))
        n = digit_sum
    return n

# Test with different numbers
numbers = [513682, 123, 999, 7]
for num in numbers:
    result = super_digit_string(num)
    print(f"Super digit of {num} is: {result}")

Super digit of 513682 is: 7
Super digit of 123 is: 6
Super digit of 999 is: 9
Super digit of 7 is: 7

Method 3: Mathematical Formula (Digital Root)

The super digit is also known as the digital root, which can be calculated using a mathematical formula ?

def digital_root(n):
    if n == 0:
        return 0
    return 1 + (n - 1) % 9

# Test the formula approach
numbers = [513682, 123, 999, 7, 0]
for num in numbers:
    result = digital_root(num)
    print(f"Digital root of {num} is: {result}")

Digital root of 513682 is: 7
Digital root of 123 is: 6
Digital root of 999 is: 9
Digital root of 7 is: 7
Digital root of 0 is: 0

Comparison

Conclusion

The super digit (digital root) can be calculated using iterative digit summation or the mathematical formula 1 + (n - 1) % 9. The formula approach is most efficient with O(1) time complexity, while iterative methods help understand the concept better.