Given two positive integers N and K. Find the minimum number of digits that can be removed from the number N such that after removals the number is divisible by 10K or print -1 if it is impossible.
Input : N = 10904025, K = 2 Output : 3 Explanation : We can remove the digits 4, 2 and 5 such that the number becomes 10900 which is divisible by 102. Input : N = 1000, K = 5 Output : 3 Explanation : We can remove the digits 1 and any two zeroes such that the number becomes 0 which is divisible by 105 Input : N = 23985, K = 2 Output : -1
Approach : The idea is to start traversing the number from the last digit while keeping a counter. If the current digit is not zero, increment the counter variable, otherwise decrement variable K. When K becomes zero, return counter as answer. After traversing the whole number, check if the current value of K is zero or not. If it is zero, return counter as answer, otherwise return answer as number of digits in N – 1, since we need to reduce the whole number to a single zero which is divisible by any number. Also, if the given number does not contain any zero, return -1 as answer.
Below is the implementation of above approach.
3 3 -1
Time Complexity :Number of digits in the given number.
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