What is Digital Root ?

 What is a Digital root? if you have done little competitive programming or practice for Data Structure or anything else you have got a problem where you need to sum all digits of the number and do this process until the number becomes a single-digit number. so that is Digital Root, let's talk about it.

So you might have seen digital root , some Example

Examples:

123 => 1 + 2 + 3 => 6

455 => 4 + 5 + 5 => 14 => 1+4 = 5 

So here you can attempt brute force too. but that will be slow. Then how will you solve this problem?

Some points which we use in the digital root concept(properties),

• when you multiply any number(>0) by 9 then the sum of all digits of that number will always be 9. Example :  345*9 = 3105 => 3+1+0+5 => 9 , you can check yourself this condition (try different numbers)
• When we add 9 to any number(here add means concatenating ) sum of all digits won't get effected, Example : 345 => 3+4+5 => 12 => 1+2 => 3, now add 9 , 3459 => 21 => 2+1=>3
• when we divide any number by 9, then what remainder we get is the same as the digital root of that number. Example : 15/9 => 6 and 15=> 1+5=>6
• Any Perfect Square's digital root will be 1,4,7,9 (16=>1+6=>7, 36=>3+6=>9 etc)

So Condition for digital root will be,

Here n = number, b= base value (for decimal b=10)

if n==0 then  digital_root(n)  = 0 

if n!=0 && n%(b-1) ==0 then digital_root(n) = b-1

if n%(b-1) != 0  then digital_root(n) = n mod (b-1) 

OR

we can put this in little more simpler form,

if n==0 then digital_root(n) = 0

else , 1 + ( (n-1)%9)

So let's put this all in code 

C++:

#include <iostream>

using namespace std;

int digital_root(int n){

if (n==0)return 0;

else{

return 1 + ((n-1)%9);

}

}

int main() {

int n;

cout << "Enter Number: ";

cin >> n;

cout <<endl;

cout << "Digital Root Value :" << digital_root(n);

return 0;

} 

Python3:

def digital_root(n):

if n==0:

return 0

else:

return 1 + ((n-1)%9)

n = int(input("Enter Number: "))

print("Digital Root :",digital_root(n))

LeetCode Question About Digital Root

If you want to know more about Digital Root --> Wikipedia

Thank You 😊😊