斯特林公式（Stirling）:

    

对右端取以10为的对数再加1就是n！的位数：

    位数=（lg2πn）/2+nlg(n/e)+1

代码如下：

    #include<stdio.h>
    #include<stdlib.h>
    #include<iostream>
    #include<algorithm>
    #include<cmath>
    #define e 2.7182818
    #define pi 3.14159
    using namespace std;
    int main()
    {
         int n;
    double x;
    cin >> n;
    x = int(log10(2 * pi*n) / 2 + n*log10(n / e))+1;
    printf("%d", int(x));

    }

hdu1018题可用此法求解

图片转载自(代码仓库)[https://github.com/LzyRapx] QAQ https://blog.csdn.net/liangzhaoyang1/article/details/511458