Solution: Add Digits

Statement

Given an integer num, repeatedly sum all of its digits until the resulting value is a single digit, then return that value.

Note: Could you solve this without any loop or recursion in $O(1)$ runtime?

Constraints:

• $0 \leq$ num $\leq 2^{31} - 1$

Solution

The key insight behind this problem lies in a mathematical concept called the digital root. Rather than repeatedly summing digits in a loop, we can leverage the fact that any positive integer’s repeated digit sum is equivalent to $1+(num-1)$ ...