```
/**
* @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
* 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)
*/
#include <cassert> /// for assert
#include <iostream> /// for IO operations
/**
* @namespace bit_manipulation
* @brief Bit manipulation algorithms
*/
namespace bit_manipulation {
/**
* @namespace count_of_trailing_ciphers_in_factorial_n
* @brief Functions for the [Count the number of
* ciphers](https://www.tutorialspoint.com/count-trailing-zeros-in-factorial-of-a-number-in-cplusplus)
* in `n!` implementation
*/
namespace count_of_trailing_ciphers_in_factorial_n {
/**
* @brief Function to count the number of the trailing ciphers
* @param n number for which `n!` ciphers are returned
* @return count, Number of ciphers in `n!`.
*/
uint64_t numberOfCiphersInFactorialN(uint64_t n) {
// count is to store the number of 5's in factorial(n)
uint64_t count = 0;
// Keep dividing n by powers of
// 5 and update count
for (uint64_t i = 5; n / i >= 1; i *= 5) {
count += static_cast<uint64_t>(n) / i;
}
return count;
}
} // namespace count_of_trailing_ciphers_in_factorial_n
} // namespace bit_manipulation
/**
* @brief Self-test implementations
* @returns void
*/
static void test() {
// 1st test
std::cout << "1st test ";
assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::
numberOfCiphersInFactorialN(395) == 97);
std::cout << "passed" << std::endl;
// 2nd test
std::cout << "2nd test ";
assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::
numberOfCiphersInFactorialN(977) == 242);
std::cout << "passed" << std::endl;
// 3rd test
std::cout << "3rd test ";
assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::
numberOfCiphersInFactorialN(871) == 215);
std::cout << "passed" << std::endl;
// 4th test
std::cout << "4th test ";
assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::
numberOfCiphersInFactorialN(239) == 57);
std::cout << "passed" << std::endl;
// 5th test
std::cout << "5th test ";
assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::
numberOfCiphersInFactorialN(0) == 0);
std::cout << "passed" << std::endl;
}
/**
* @brief Main function
* @returns 0 on exit
*/
int main() {
test(); // run self-test implementations
return 0;
}
```