# Time:  O(nlogn)
# Space: O(1)

# 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.

class Solution(object):
    def selfDividingNumbers(self, left, right):
        """
        :type left: int
        :type right: int
        :rtype: List[int]
        """
        def isDividingNumber(num):
            n = num
            while n > 0:
                if (n%10) == 0 or (num%(n%10)) != 0:
                    return False
                n /= 10
            return True
        
        result = []
        for num in xrange(left, right+1):
            if isDividingNumber(num):
                result.append(num)
        return result

# Time:  O(nlogr) = O(n)
# Space: O(logr) = O(1)

# 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.

class Solution(object):
    def selfDividingNumbers(self, left, right):
        """
        :type left: int
        :type right: int
        :rtype: List[int]
        """
        def isDividingNumber(num):
            n = num
            while n > 0:
                if (n%10) == 0 or (num%(n%10)) != 0:
                    return False
                n /= 10
            return True
        
        result = []
        for num in xrange(left, right+1):
            if isDividingNumber(num):
                result.append(num)
        return result

Update self-dividing-numbers.py