Problem
Add up the digits of n. If the result has more than one digit, add up its digits again. Repeat until a single digit remains.
Implement digital_root(n).
Input
n: A positive integer.
Output
Return the final single digit.
Constraints
1 ≤ n ≤ 10¹⁸
Examples
Example 1
Input:
n = 999
Expected output:
expected = 9Input:
long long n = 999;
Expected output:
long long expected = 9;Input:
long n = 999;
Expected output:
long expected = 9;Explanation
9 + 9 + 9 = 27, then 2 + 7 = 9.
Example 2
Input:
n = 38
Expected output:
expected = 2Input:
long long n = 38;
Expected output:
long long expected = 2;Input:
long n = 38;
Expected output:
long expected = 2;Explanation
3 + 8 = 11, then 1 + 1 = 2.
How to approach it
Try on your own first, then open one hint at a time.
Hint 1
Adding digits repeatedly eventually collapses the number to one digit.
Hint 2
You can simulate the repeated summing process until the value is less than 10.
Hint 3
Watch out for very large inputs; the process is simple, but repeated passes over the digits are the main work.
Expected complexity
O(d log n) time, O(1) extra space