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Finding sum of digits of a number until sum becomes single digit

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  • Difficulty Level : Medium
  • Last Updated : 13 Feb, 2022

Given a number n, we need to find the sum of its digits such that: 

If n < 10    
    digSum(n) = n
Else         
    digSum(n) = Sum(digSum(n))

Examples : 

Input : 1234
Output : 1
Explanation : The sum of 1+2+3+4 = 10, 
              digSum(x) == 10
              Hence ans will be 1+0 = 1

Input : 5674
Output : 4 

A brute force approach is to sum all the digits until the sum < 10. 
Flowchart: 

Below is the brute force program to find the sum. 

C++




// C++ program to find sum of
// digits of a number until
// sum becomes single digit.
#include<bits/stdc++.h>
  
using namespace std;
 
int digSum(int n)
{
    int sum = 0;
    
    // Loop to do sum while
    // sum is not less than
    // or equal to 9
    while(n > 0 || sum > 9)
    {
        if(n == 0)
        {
            n = sum;
            sum = 0;
        }
        sum += n % 10;
        n /= 10;
    }
    return sum;
}
 
// Driver program to test the above function
int main()
{
    int n = 1234;
    cout << digSum(n);
    return 0;
}


Java




// Java program to find sum of
// digits of a number until
// sum becomes single digit.
import java.util.*;
 
public class GfG {
     
    static int digSum(int n)
    {
        int sum = 0;
 
        // Loop to do sum while
        // sum is not less than
        // or equal to 9
        while (n > 0 || sum > 9)
        {
            if (n == 0) {
                n = sum;
                sum = 0;
            }
            sum += n % 10;
            n /= 10;
        }
        return sum;
    }
     
    // Driver code
    public static void main(String argc[])
    {
        int n = 1234;
        System.out.println(digSum(n));
    }
}
 
// This code is contributed by Gitanjali.


Python




# Python program to find sum of
# digits of a number until
# sum becomes single digit.
import math
 
# method to find sum of digits
# of a number until sum becomes
# single digit
def digSum( n):
    sum = 0
     
    while(n > 0 or sum > 9):
     
        if(n == 0):
            n = sum
            sum = 0
         
        sum += n % 10
        n /= 10
     
    return sum
 
# Driver method
n = 1234
print (digSum(n))
 
# This code is contributed by Gitanjali.


C#




// C# program to find sum of
// digits of a number until
// sum becomes single digit.
using System;
 
class GFG {
     
    static int digSum(int n)
    {
        int sum = 0;
 
        // Loop to do sum while
        // sum is not less than
        // or equal to 9
        while (n > 0 || sum > 9)
        {
            if (n == 0)
            {
                n = sum;
                sum = 0;
            }
            sum += n % 10;
            n /= 10;
        }
        return sum;
    }
     
    // Driver code
    public static void Main()
    {
        int n = 1234;
        Console.Write(digSum(n));
    }
}
 
// This code is contributed by nitin mittal


PHP




<?php
// PHP program to find sum of
// digits of a number until
// sum becomes single digit.
 
function digSum( $n)
{
    $sum = 0;
     
    // Loop to do sum while
    // sum is not less than
    // or equal to 9
    while($n > 0 || $sum > 9)
    {
        if($n == 0)
        {
            $n = $sum;
            $sum = 0;
        }
        $sum += $n % 10;
        $n = (int)$n / 10;
    }
    return $sum;
}
 
// Driver Code
$n = 1234;
echo digSum($n);
 
// This code is contributed
// by aj_36
?>


Javascript




<script>
// Javascript program to find sum of
// digits of a number until
// sum becomes single digit.
    let n = 1234;
    //Function to get sum of digits
    function getSum(n) {
        let sum = 0;
        while (n > 0 || sum > 9) {
             if(n == 0) {
                n = sum;
                sum = 0;
             }
             sum = sum + n % 10;
             n = Math.floor(n / 10);
        }
        return sum;
    }
 //function call  
    document.write(getSum(n));
     
//This code is contributed by Surbhi Tyagi
</script>


Output : 

1

So, another challenge is “Could you do it without any loop/recursion in O(1) runtime?”

YES!!
There exists a simple and elegant O(1) solution for this too. The answer is given simply:- 

If n == 0
   return 0;

If n % 9 == 0      
    digSum(n) = 9
Else               
    digSum(n) = n % 9 

How does the above logic works? 

The logic behind this approach is :

To check if a number is divisible by 9, add the digits of the number and check if the sum is divisible by 9 or not. If yes, is the case,  the number is divisible by 9, otherwise, it’s not.

let’s take 27  i.e (2+7 = 9) hence divisible by 9.
If a number n is divisible by 9, then the sum of its digit until the sum becomes a single digit is always 9. For example, 
Let, n = 2880 
Sum of digits = 2 + 8 + 8 = 18: 18 = 1 + 8 = 9

Therefore,
A number can be of the form 9x or 9x + k. For the first case, the answer is always 9. For the second case, and is always k which is the remainder left.

The problem is widely known as the digit root problem.

You may find this Wikipedia article useful. -> https://en.wikipedia.org/wiki/Digital_root

Below is the implementation of the above idea : 

C++




#include<bits/stdc++.h>
using namespace std;
 
int digSum(int n)
{
    if (n == 0)
       return 0;
    return (n % 9 == 0) ? 9 : (n % 9);
}
 
// Driver program to test the above function
int main()
{
    int n = 9999;
    cout<<digSum(n);
    return 0;
}


Java




import java.io.*;
 
class GFG {
 
    static int digSum(int n)
    {
        if (n == 0)
        return 0;
        return (n % 9 == 0) ? 9 : (n % 9);
    }
     
    // Driver program to test the above function
    public static void main (String[] args)
    {
        int n = 9999;
        System.out.println(digSum(n));
    }
}
 
// This code is contributed by anuj_67.


Python3




def digSum(n):
 
    if (n == 0):
        return 0
    if (n % 9 == 0):
        return 9
    else:
       return (n % 9)
 
# Driver program to test the above function
n = 9999
print(digSum(n))
 
# This code is contributed by
# Smitha Dinesh Semwal


C#




using System;
 
class GFG
{
    static int digSum(int n)
    {
        if (n == 0)
        return 0;
        return (n % 9 == 0) ? 9 : (n % 9);
    }
     
    // Driver Code
    public static void Main ()
    {
        int n = 9999;
        Console.Write(digSum(n));
     
    }
}
 
// This code is contributed by aj_36


PHP




<?php
 
function digSum($n)
{
    if ($n == 0)
        return 0;
    return ($n % 9 == 0) ? 9 : ($n % 9);
}
 
// Driver program to test the above function
$n = 9999;
echo digSum($n);
 
//This code is contributed by anuj_67.
?>


Javascript




<script>
     
function digSum(n)
{
    if (n == 0)
        return 0;
         
    return (n % 9 == 0) ? 9 : (n % 9);
}
 
// Driver code
n = 9999;
document.write(digSum(n));
 
// This code is contributed by code_hunt
 
</script>


Output: 

9

Related Post : 
https://www.geeksforgeeks.org/digital-rootrepeated-digital-sum-given-integer/

This article is contributed by Ayush Khanduri. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 


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