728. Self Dividing Numbers


A self-dividing number is a number that is divisible by every digit it contains.

For example, 128 is a self-dividing number because 128 % 1 == 0, 128 % 2 == 0, and 128 % 8 == 0.

Also, a self-dividing number is not allowed to contain the digit zero.

Given a lower and upper number bound, output a list of every possible self dividing number, including the bounds if possible.

Example 1:

Input: 
left = 1, right = 22
Output: [1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 22]

Note:

  • The boundaries of each input argument are 1 <= left <= right <= 10000.


    • Approach #1: Brute Force [Accepted]

    Intuition and Algorithm

    For each number in the given range, we will directly test if that number is self-dividing.

    By definition, we want to test each whether each digit is non-zero and divides the number. For example, with 128, we want to test d != 0 && 128 % d == 0 for d = 1, 2, 8. To do that, we need to iterate over each digit of the number.

    A straightforward approach to that problem would be to convert the number into a character array (string in Python), and then convert back to integer to perform the modulo operation when checking n % d == 0.

    We could also continually divide the number by 10 and peek at the last digit. That is shown as a variation in a comment.

    Complexity Analysis

    • Time Complexity: , where is the number of integers in the range , and assuming is bounded. (In general, the complexity would be .)

    • Space Complexity: , the length of the answer.

    Analysis written by: @awice.

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