Time complexity of recursive palindrome question, C++

Question

I was just wondering how I can find the time complexity of my recursive function here. I know that for the most part of my program its all in constant time O(1) but how do I calculate the time complexity of recursion functions as well.

int pal(int n, int temp)
{
    // Using division of 10 trick
    if(n == 0)
        return temp;

    // Build the number backwards.
    temp = (temp * 10) + (n % 10);

    // Then advance through the number.
    return pal(n / 10, temp);
}

int main()
{
    int n = 5678;
    int temp = pal(n, 0);
    if(temp == n)
       cout << "Yes it is a palindrome";
    else
       cout << "No its not a palindrome";
]

Answer 1

It's O(log(n)) , where n is the number.

But it's also O(s) , shere s is the input size (pretty standard in computation theory to use input size as a string)

Compiled on any existing C++ platform, you could also argue it is O(k) because int 's have finite size.

So, it depends on the convention you use. Or whatever your professor showed in class. :-)