Digital Root Function

A Go implementation of the digital root algorithm that repeatedly sums the digits of a number until a single digit is obtained.

What is Digital Root?

The digital root (also called the repeated digit sum) of a non-negative integer is the single digit obtained by an iterative process of summing digits:

1. Sum all digits of the number
2. If the result has more than one digit, repeat step 1
3. Continue until you get a single digit

Examples

• 467 → 4 + 6 + 7 = 17 → 1 + 7 = 8
• 21 → 2 + 1 = 3
• 1000 → 1 + 0 + 0 + 0 = 1
• 1 → 1 (already single digit)
• -36 → 36 → 3 + 6 = 9 (handles negatives by taking absolute value)

Features

✨ Simple & Efficient - Clean recursive implementation ✨ Handles Negatives - Converts to absolute value ✨ Well-Tested - Includes multiple test cases in main()

Usage

Basic Example

package main

import (
	"fmt"
)

func main() {
	result := singleDigit(467)
	fmt.Println(result)  // Output: 8
}

Available Function

func singleDigit(n int) int

Parameters:

• n (int) - The number to calculate the digital root for

Returns:

• (int) - The single digit digital root

How It Works

The singleDigit() function:

1. Converts negative numbers to their absolute value
2. Returns immediately if the number is already single-digit (< 10)
3. Sums all digits by converting to string and iterating through characters
4. Recursively calls itself on the sum if it's greater than 9
5. Returns the final single digit

Running the Code

go run main.go

Output:

8
3
1
1
9

Algorithm Complexity

• Time Complexity: O(log n) where n is the input number
• Space Complexity: O(log n) due to recursion depth

Mathematical Note

The digital root has a mathematical property: For any positive integer n, the digital root equals:

• (n - 1) % 9 + 1 (when n ≠ 0)

This could be used for a more efficient O(1) implementation, but the current approach is more intuitive.

License

This project is open source and available under the MIT License.

Author

Created by Israel-light