Add Digits - Implementation

Here's the mathematical solution:

function addDigits(n)
    if n = 0 then
        return 0
    return 1 + ((n - 1) mod 9)

For $n = 38$: $(38 - 1) \bmod 9 = 37 \bmod 9 = 1$, so the answer is $1 + 1 = 2$. This matches the loop result but finishes in constant time.