HDUOJ 1018 Big Number （斯特林公式）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1018

Big Number

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 34083    Accepted Submission(s): 16111


[align=left]Problem Description[/align]
In many applications very large integers numbers are required. Some of these applications are using keys for secure transmission of data, encryption, etc. In this problem you are given a number, you have to determine the number of
digits in the factorial of the number.

 

[align=left]Input[/align]
Input consists of several lines of integer numbers. The first line contains an integer n, which is the number of cases to be tested, followed by n lines, one integer 1 ≤ n ≤ 107 on each line.

题意：求N！的位数，如果你不知道斯特林公式，就只能暴力的计算位数了，所以多看点数学书还是有好处的；

斯特林公式：

  详细证明可以参考《具体数学》（第二版）第380页到381页

所以利用ceil(log10（n!）)就可以计算出位数；

代码不长；
#include<stdio.h>
#include<math.h>
#define PI 3.1415926535
int main()
{
int t,n,ans;
scanf("%d",&t);
while(t--)
{
scanf("%d",&n);
ans=0.5*ceil(log10(2*PI*n))+ceil(n*log10(n/exp(1)));
printf("%d\n",ans);
}
return 0;
}