Check if a number can be represented as the sum of numbers with at least one digit equal to K

Given integers N and K, the task is to check if a number can be represented as the sum of numbers that have at least one digit equal to K.

Example:

Input: N = 68, K = 7
Output: YES
Explanation: 68 = (27 + 17 + 17 + 7). Each number has atleast one digit equal to 7.

Input: N = 23, K = 3
Output: YES
Explanation: 23 itself contains a digit equal to 3.

Approach: The given problem can be solved by using simple concepts of math. Follow the steps below to solve the problem:

• Initialize a variable temp to k, and also take a counter say count, assign it with 0
• Iterate till the last digits of temp and N are not equal and at each iteration
  • Increment the value of temp by k
  • Keep a count of iterations and break the loop if the count becomes greater than 10
• Check if the last digits of temp and N are equal, and if the value of temp <= N:
  • If the above condition is satisfied return true
  • Else return false
• Also if k * 10 <= N, return true
• Else return false

Below is the implementation of the above approach:

YES

Time Complexity: O(1)
Auxiliary Space: O(1)