SPOJ FCTRL

11 - Factorial
https://www.spoj.com/problems/FCTRL/

Summary
This problem required us to determine the number of trailing zeroes for factorial n, where n is a integer between 1 and 1 billion. Obviously calculating n! itself and determining the number of trailing zeroes would result in a TLE, but if we research a bit we find a simple mathematical formula to determine Z(N):

$$Z(N)=\sum_{k=1}^{\lfloor log_5N\rfloor} \lfloor \frac{N}{5^{k}}\rfloor$$

Implementations
This is just a straightforward translation of the formula above:

int zeta(int n) { int ret = 0; for (int p = 5; p <= n; p*=5) ret += n/p; return ret; }

Input
6 3 60 100 1024 23456 8735373

Output
0 14 24 253 5861 2183837