DataStructures-Algorithms/Leetcode Daily Challenge/November-2020/25. Smallest Integer Divisible by K.cpp at master · sachuverma/DataStructures-Algorithms · GitHub

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/*
Smallest Integer Divisible by K
===============================

Given a positive integer K, you need to find the length of 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.
Note: N may not fit in a 64-bit signed integer.


Example 1:
Input: K = 1
Output: 1
Explanation: The smallest answer is N = 1, which has length 1.

Example 2:
Input: K = 2
Output: -1
Explanation: There is no such positive integer N divisible by 2.

Example 3:
Input: K = 3
Output: 3
Explanation: The smallest answer is N = 111, which has length 3.


Constraints:
1 <= K <= 105

Hint #1
11111 = 1111 * 10 + 1 We only need to store remainders modulo K.

Hint #2
If we never get a remainder of 0, why would that happen, and how would we know that?
*/

class Solution
{
public:
  int smallestRepunitDivByK(int K)
  {
    int rem = 0;
    for (int l = 1; l <= K; l++)
    {
      rem = (rem * 10 + 1) % K;
      if (rem == 0)
        return l;
    }
    return -1;
  }
};