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:
- Count number of step required to reduce N to 1 by following certain rule
- Minimum steps required to reduce all the elements of the array to zero
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- Minimum sum after subtracting multiples of k from the elements of the array
- Check if it is possible to get back to 12'0 clock only by adding or subtracting given seconds
- Count of Numbers in Range where first digit is equal to last digit of the number
- Find the remainder when First digit of a number is divided by its Last digit
- Count 'd' digit positive integers with 0 as a digit
- Largest number less than N with digit sum greater than the digit sum of N
- Minimum sum of the elements of an array after subtracting smaller elements from larger
- Reach A and B by multiplying them with K and K^2 at every step
- Minimum step to reach one
- Count n digit numbers not having a particular digit
- Check if frequency of each digit is less than the digit
- Delete odd and even numbers at alternate step such that sum of remaining elements is minimized
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