Solution: Add Digits

Explore the add digits problem by applying the digital root concept for constant time computation. Understand how to repeatedly sum digits without loops or recursion, leveraging modular arithmetic to achieve an O(1) runtime and O(1) space complexity solution.

We'll cover the following...

Statement
Solution
- Time complexity
- Space complexity

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 $1 +$ ...