CC150 17.3

17_3.cpp

/* CC150 17.3 */
// compute the number of tailing zeros in n factorial

#include <iostream>

int tailZeros(int n)
{
	int count = 0;
	for (int fact = 5; fact <= n; fact += 5) {
		for (int j = fact; j % 5 == 0; j /= 5)
			++count; // increase count for each factor 5 in fact
	}
	return count;
}

int tailZeros2(int n)
{
	int count = 0;
	for (int fact = 5; fact <= n; fact *= 5) { // power of 5
		for (int j = fact; j <= n; j += fact) // count all multiples of fact
			++count;
	}
	return count;
}

int main()
{
	int n;
	std::cin >> n;
	std::cout << tailZeros(n) << std::endl;
	std::cout << tailZeros2(n) << std::endl;
	return 0;
}