（2）K - Big Number

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最新推荐文章于 2022-02-09 12:21:06 发布

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本文介绍了一种计算大数阶乘位数的方法，并提供了一个C++实现示例。该方法利用数学公式简化计算过程，适用于加密和数据安全等场景。

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

2
10
20

Sample Output

7
19

求大数阶乘位数，有公式，，，s=log10(2*PI*n)/2+n*log10(n/e);

#include<iostream>
#include<cstdio>
#include<cmath>
using namespace std;
#define p 0.798179868358
#define e 0.434294481903
int main()
{
 int n;
 long double m;
 long long temp;
 cin>>n;
 while(n--)
 {
  cin>>m;
  if(m>3)
  {
   temp=(p+log10((double)m))/2+m*(log10((double)m)-e)+1;
  }
  else
  {
   temp=1;
  }
  cout<<temp<<endl;
 }
 
}