Self Dividing Numbers

• LeetCode: Self Dividing Numbers

• Problem:

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.

• Note:

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

• Examples:

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

• Analysis:

For left number to right number, we do the core operation to make a number been divided by every digit which is not zero.

If the digit of a number is 0, the number is not a self-dividing number.

If the number can't be divided by it's digit, the number is not a self-dividing number.

• Code - Java:

class Solution {
    public List<Integer> selfDividingNumbers(int left, int right) {
        List<Integer> results = new ArrayList<Integer>();
        for (int i = left; i <= right; i++) {
            int val = i;
            while (val > 0) {
                int digit = val % 10;
                if (digit == 0 || i % digit != 0) {
                    break;
                }
                val /= 10;
            }
            if (val == 0) {
                results.add(i);
            }
        }
        return results;
    }
}

• Code - C++:

class Solution {
public:
    vector<int> selfDividingNumbers(int left, int right) {
        vector<int> results;
        for (int i = left; i <= right; i++) {
            int val = i;
            while (val > 0) {
                int digit = val % 10;
                if (digit == 0 || i % digit != 0) {
                    break;
                }
                val /= 10;
            }
            if (val == 0) {
                results.push_back(i);
            }
        }
        return results;
    }
};

• Code - Python:

class Solution(object):
    def selfDividingNumbers(self, left, right):
        """
        :type left: int
        :type right: int
        :rtype: List[int]
        """
        results = []
        for i in range(left, right + 1):
            val = i
            while val > 0:
                digit = val % 10
                if digit == 0 or i % digit != 0:
                    break
                val /= 10
            if val == 0:
                results.append(i)
        return results

• Time Complexity: O(N), N is the range from left to right

• Space Complexity: O(M), M is the count of self-dividing numbers