SPOJ #11 Factorial
Counting trailing 0s of n! It is not very hard to figure out how to count it - simply count how many 5s. Since even numbers are always more than 5s, we don't have to consider even numbers.
But counting 5, is tricky. Naive method is quite slow - I got 12+s for 1000000000. And after reading below article, I got 0.04s. The former counts individually, duplicated; but the latter counts smart:
http://en.wikipedia.org/wiki/Trailing_zeros#Factorial
#include <iostream>
#include <ctime>
using namespace std; int main()
{
int cnt; cin >> cnt;
if(cnt == ) return ; while(cnt --)
{
unsigned long long n; cin >> n;
unsigned cnt = ; for (int d = ; d <= n; d *= ) {
cnt += n / d;
}
cout << cnt << endl;
}
return ;
}
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