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hdu——Big Number

发布日期：2022-02-02 02:58:03 浏览次数：1 分类：技术文章

本文共 1046 字，大约阅读时间需要 3 分钟。

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 ≤ 10 ⁷ on each line.

Output

The output contains the number of digits in the factorial of the integers appearing in the input.

Sample Input

Sample Output

719  



 
   题目是要求出n!的位数，用到了斯特林数：  



 
   log10(n!)=1.0/2*log10(2*pi*n)+n*log10(n/e)  



 
   分析：  



 

  
   #include
    
     #include
     
      const double PI=3.14159265;using namespace std;int main(){
      
int t,n;
      
double sum;
      
cin>>t;
      
while(t--)
      
{
      
   cin>>n;
      
   sum=(n*log(n) - n + 0.5*log(2*n*PI))/log(10)+1;
      
   cout<<(int)sum<
      
       
}
       
return 0;}

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