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

Problem Description

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.

 

Input

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 3.1415926535int 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;}