[Algorithm] 728. Self Dividing Numbers

Posted 2021-03-20 answer1215

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.

 

/**
 * @param {number} left
 * @param {number} right
 * @return {number[]}
 */
var selfDividingNumbers = function(left, right) {
    let result = [];
    let current = left;
    while (current <= right) {
        if (isDividable(current)) {
            result.push(current)
        }
        
        current++;
    }
    
    return result;
};

function isDividable (num) {
    if (num < 10) {
        return true;
    }
    
    const original = num;
    while (num > 0) {
        const temp = num % 10;
        if (original % temp !== 0) {
            return false;
        }
        num = Math.floor(num / 10);
    }
    
    return true;
}

 

• Time Complexity: O(D), where DD is the number of integers in the range [L, R] and assuming log(R) is bounded. (In general, the complexity would be O(DlogR).)

• Space Complexity: O(D), the length of the answer.