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:
- Min steps to convert N-digit prime number into another by replacing a digit in each step
- Minimum steps required to reduce all the elements of the array to zero
- Min number of operations to reduce N to 0 by subtracting any digits from N
- Invert the Kth most significant bit of N
- Find most significant bit of a number X in base Y
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- Find the greater number closest to N having at most one non-zero digit
- Count number of step required to reduce N to 1 by following certain rule
- Count ways to reach the Nth stair using multiple 1 or 2 steps and a single step 3
- Minimum steps to reach N from 1 by multiplying each step by 2, 3, 4 or 5
- Minimize steps to reach K from 0 by adding 1 or doubling at each step
- Number of steps to sort the array by changing order of three elements in each step
- Minimum Decrements on Subarrays required to reduce all Array elements to zero
- Minimum steps to reduce N to 0 by given operations
- Count of N-digit numbers having digit XOR as single digit
- Round-off a number to a given number of significant digits
- Unset least significant K bits of a given number
- Find the remainder when First digit of a number is divided by its Last digit
- Reach A and B by multiplying them with K and K^2 at every step
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