Keep track of how many times a recursive function was called

Answer 1

Here's a Python version that uses a wrapper function to simplify the counter, as has been suggested by slebetman's answer — I write this only because the core idea is very clear in this implementation:

from functools import reduce

def single_digit(n: int) -> tuple:
    """Take an integer >= 0 and return a tuple of the single-digit product reduction
    and the number of reductions performed."""

    def _single_digit(n, i):
        if n <= 9:
            return n, i
        else:
            digits = (int(d) for d in str(n))
            product = reduce(lambda x, y: x * y, digits)
            return _single_digit(product, i + 1)

    return _single_digit(n, 0)

>>> single_digit(39)
(4, 3)