Stirling Formula and its application

The Stirling formula is a mathematical formula used to obtain an approximate value of n factorial. Generally speaking, when N is very large, n factorial calculation is very large, so the Stirling formula is very useful, and even when N is very small, the value of the Stirling formula is very accurate.

The formula is:

The programming of the Stirling formula: N. =SQRT (2*pi*n) * (n/e) ^n; (Pi=3.1415926=acos ( -1.0), e=2.718)

Conversion of the Stirling formula: LgN. = (LG (2*PI) +LGN)/2+n* (Lgn-lge);//+1 is the length.

Always ask for the decimal length to change LG to LOG10.

Template code:

#include <bits/stdc++.h>
using namespace std;
const int PI = ACOs ( -1.0);
int main ()
{
    int n;
    while (Cin>>n)
    {
        double ans;
        Ans= (0.5*log (2*pi*n) +n* (log (n)-1))/log (a);
        cout<< (Long Long) ans+1<<endl;
    }
}