Given a number N. Add one to the number in the first step and if the number has trailing zeros, remove all the trailing zeros in the second step. Continue the process for the next generated number. The task is to count the number of unique numbers that can be generated from these operations.
Input: N = 5
5 -> 6 -> 7 -> 8 -> 9 -> 1 -> 2 -> 3 -> 4 -> 5 (same sequence repeats)
Note that 10 is not included as it contained trailing zero
and removing the zero gave 1 as the next element.
Input: N = 28
Approach: The problem can be solved using recursion. Use a unordered_set to store all the unique numbers. In case a number is reached twice, we end the recursion as the same sequence will be repeated and we will not be getting any more unique numbers. Else insert the number to the set and in the first step increase the number by 1 and remove all trailing zeros in the next step if there are any.
Below is the implementation of the above approach:
- Count number of trailing zeros in (1^1)*(2^2)*(3^3)*(4^4)*..
- Count number of trailing zeros in product of array
- Count number of trailing zeros in Binary representation of a number using Bitset
- Count different numbers that can be generated such that there digits sum is equal to 'n'
- Count numbers having N 0's and and M 1's with no leading zeros
- Find the smallest number X such that X! contains at least Y trailing zeros.
- Smallest number divisible by n and has at-least k trailing zeros
- Count of N-bit binary numbers without leading zeros
- Count trailing zeroes in factorial of a number
- All possible numbers of N digits and base B without leading zeros
- K-th smallest element after removing given integers from natural numbers | Set 2
- Numbers having Unique (or Distinct) digits
- Print all numbers less than N with at-most 2 unique digits
- Find ways an Integer can be expressed as sum of n-th power of unique natural numbers
- Count numbers < = N whose difference with the count of primes upto them is > = K
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