Given a number . Reduce this number to zero by subtracting the number by it’s most significant digit(Left most digit) at every step. The task is to count the number of steps it takes to be reduced to zero.
Input: 14 Output: 6 Steps: 14 - 1 = 13 13 - 1 = 12 12 - 1 = 11 11 - 1 = 10 10 - 1 = 9 9 - 9 = 0 Input: 20 Output: 12 Numbers after series of steps: 20, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 0
Naive Approach: A naive approach is to reduce the number by its first digit step-wise and find the count of steps, but the time complexity will be huge if a large number is provided.
Efficient Approach: The main idea of the efficient approach is to reduce the number of steps in the naive approach. We can skip the steps whose leading digits are the same in consecutive numbers, and count them. The algorithm of skipping those numbers with the same leading digits is as follows:
- Let the number be last, count the digits in last and reduce it by 1, because the smallest number with same leading digit with the same count of digits will have that number of zeros in it.
- Find the first digit of the number of last, by last/count.
- Hence the smallest number of same number of count of digits with same leading number will be [first digit * (count-1)]
- the number of steps skipped can be achieved by [(last-smallest number)/first digit].
- Hence the next number last will be last – (first*skipped)
Below is the implementation of the above approach:
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