Formatted question description: https://leetcode.ca/all/1015.html

1015. Smallest Integer Divisible by K

Level

Medium

Description

Given a positive integer K, you need find the smallest positive integer N such that N is divisible by K, and N only contains the digit 1.

Return the length of N. If there is no such N, return -1.

Example 1:

Input: 1

Output: 1

Explanation: The smallest answer is N = 1, which has length 1.

Example 2:

Input: 2

Output: -1

Explanation: There is no such positive integer N divisible by 2.

Example 3:

Input: 3

Output: 3

Explanation: The smallest answer is N = 111, which has length 3.

Note:

  • 1 <= K <= 10^5

Solution

If K is a multiple of 2 or 5, then any number divisible by K can’t end with 1, so return -1.

Otherwise, each time append a 1 to the current number (which is initially 0) and check whether the new number is divisible by K. Use modulo operation to avoid overflow.

class Solution {
    public int smallestRepunitDivByK(int K) {
        if (K % 2 == 0 || K % 5 == 0)
            return -1;
        int value = 1;
        int length = 1;
        while (value % K != 0) {
            value = value % K * 10 + 1;
            length++;
        }
        return length;
    }
}

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