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Self Dividing Numbers

Difficulty: Easy

Problem Description

A self-dividing number is a number that is divisible by every digit it contains. A self-dividing number is not allowed to contain the digit zero. Given two integers left and right, return a list of all the self-dividing numbers in the range [left, right] (both inclusive).

Key Insights

  • A self-dividing number must be divisible by each of its non-zero digits.
  • The number should not contain the digit zero.
  • We can check each number in the given range to determine if it is self-dividing.
  • The maximum limit for left and right is 10,000, allowing for a straightforward iteration approach.

Space and Time Complexity

Time Complexity: O(n * d), where n is the range size (right - left + 1) and d is the maximum number of digits in a number (which is constant, at most 5 for numbers up to 10,000). Space Complexity: O(m), where m is the number of self-dividing numbers found.

Solution

To determine self-dividing numbers, we will iterate through each number in the specified range. For each number, we will extract its digits and check if the number is divisible by each digit. If a number contains the digit zero, we will skip it. We will use a list to store all valid self-dividing numbers.

Code Solutions

def selfDividingNumbers(left: int, right: int) -> List[int]:
    result = []
    for num in range(left, right + 1):
        if isSelfDividing(num):
            result.append(num)
    return result

def isSelfDividing(num: int) -> bool:
    original_num = num
    while num > 0:
        digit = num % 10
        if digit == 0 or original_num % digit != 0:
            return False
        num //= 10
    return True
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