Debugging the recursion couldn't solve my Issue

I wrote this function below in Python and I am expecting to see 4 as the result but get 2. Why is that?

Here is my function:

def persistence(n):
    if 0 <= n <= 9:
        return n
    else:
        result = 0
        counter = 0
        while True:
            result += n % 10 * persistence(n // 10)
            counter += 1
            if result > 9:
                n = result
                result = 0
                continue
            return counter

print(persistence(999))  # Output should be 4 but gives me 2

The goal of the function is to calculate how many times to multiply the digits of the number until you get to a one digit number.

For example: when given n = 999 I want the process below to happen:

// 999 -> 9 * 9 * 9 = 729
// 729 -> 7 *2 *9 = 126
// 126 -> 1 *2 *6 = 12
// 12 -> 1 * 2 = 2

See? It takes four iterations to get from 999 to 2 which is a single digit number. So I want my function to return 4 which is the number of iterations to get to a one digit number but returns 2 which is not what I have expected.

I know where the problem exactly happens. It is in the line in which I wrote result += n % 10 * persistence(n // 10). when I debug it in the first iteration, instead of giving me the number 729 (the multiplication of 9 * 9 * 9) it gives me 18. Why is that? What is wrong with my code that instead of getting 729 as the output for result in the first iteration I get 18 and therefore the value of persistence(999) is not what I expect it to be?

Solution

It's unclear, what your function is supposed to do, as commented.

My best guess is that you want to multiply the digits of a number.

In that case, you either use recursion without a while or just iterate using a loop.

def persistence(n):
    counter = 0
    result = 1
    while n:
        last_digit = n % 10
        result *= last_digit
        n //= 10
        counter += 1

    print(result)
    return counter


print(persistence(999))
print(persistence(9999))

Prints

Notes:

The return counter in your code is inside the while loop. That's probability not what you had in mind.
When you write your base case in a recursive functiono, you no longer have to define an else.

Edit

If you want to count the number of operations until reaching one digit, we only add a few conditions:

def persistence(n):
    if -10 < n < 10:
        return 0
    if n < 0:
        n *= -1
    counter = 0
    result = 1
    while n > 9:
        last_digit = n % 10
        result *= last_digit
        n //= 10
        counter += 1

    return counter


print(persistence(999))
print(persistence(9999))
print(persistence(123456))
print(persistence(1))

print(persistence(-999))
print(persistence(-9999))
print(persistence(-123456))
print(persistence(-1))

Prints

This may have a minor issue, did not check. Test it and modify it.

def persistence(n, counter=0):
    if -10 < n < 10:
        return 0
    if n < 0:
        n *= -1
    result = 1
    while n > 9:
        last_digit = n % 10
        result *= last_digit
        n //= 10

    counter += 1
    if result > 9:
        return persistence(result, counter + 1)
    return counter + 1


print(persistence(999))
print(persistence(9999))
print(persistence(123456))
print(persistence(1))

print(persistence(-999))
print(persistence(-9999))
print(persistence(-123456))
print(persistence(-1))

Logic

Your code has logic issues. Logic bugs are among the most difficult "bugs". If you want to fully understand, put a print statement in each line.
Another way to solve the problem is to write multiple functions, so that each function does a specific task. You don't have to write the whole algorithm in one function.