N阶乘的长度

#include<stdio.h>  

#include<math.h>  
int main()  
{  
    int n;  
    double sum=0;  
    scanf("%d",&n);  
    for(int i=1;i<=n;i++)  
    {  
        sum+=log10(i);  //log(i)/log(10)等价于log10(i)
    }  
    printf("%d\n",(int)sum+1);  
    return 0;  
}

lg(N!)=[lg(N*(N-1)*(N-2)*......*3*2*1)]+1=[lgN+lg(N-1)+lg(N-2)+......+lg3+lg2+lg1]+1