Another from the archive! I’ll confess some annoyance with this style of question (this is not the first or only example) that presents a contrived concept, in this case a “self dividing number“, and define it with the same language as more typical math concepts. I’ve seen it confuse or intimidate students with a nontraditional background as they think “here’s another thing I should have known, but I don’t because of my background”. I just wish these questions would make it clear when they’re making up a concept for the sake of the exercise.

In any case, this is a question that has another interesting-sort of loop. There is a style of using divide-by-10, modulo-by-10 to “iterate” through a number. See the standard atoi question (which I realize I don’t have yet? Something to add.) In binary form we have the implementation of popcount here, or the formatting requirement here.

def selfDividing(n):
    N = n
    while n > 0:
        d = n % 10
        if d == 0:
            return False
        if N % d != 0:
            return False
        n = n // 10
    return True
class Solution:
    def selfDividingNumbers(self, left: int, right: int) -> List[int]:
        res = [i for i in range(left, right+1) if selfDividing(i)]
        return list(res)

Discussion

I like that this has helper functions. For Python you get this cute filtering machinery, and I think that’s also a nice thing for this question. I think even just implementing the single helper function is a good warm-up and could lead into the atoi question, which a question I actually like. Maybe this is a good teaching warm-up before covering atoi. For lack of a better category I called this a numerical question, others of which can be found here.