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Update bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp

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Co-authored-by: David Leal <halfpacho@gmail.com>
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Swastika Gupta
2021-07-23 19:53:41 +05:30
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bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp
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* @file
* @brief [Count the number of ciphers](https://www.tutorialspoint.com/count-trailing-zeros-in-factorial-of-a-number-in-cplusplus) in `n!` implementation
* @details
* We are given a number. The algorithm finds all
* the zeroes at the end of factorial of that number.
* Given an integer number as input. The goal is to find the number of trailing zeroes in the factorial calculated for
* that number. A factorial of a number N is a product of all numbers in the range [1, N].
* We know that we get a trailing zero only if the number is multiple of 10 or has a factor pair (2,5). In all factorials of
* any number greater than 5, we have many 2s more than 5s in the prime factorization of that number. Dividing a
* number by powers of 5 will give us the count of 5s in its factors. So, the number of 5s will tell us the number of trailing zeroes.
* @author [Swastika Gupta](https://github.com/Swastyy)
*/