【hdu - 1018 n! 的位数】

最新推荐文章于 2024-07-28 10:45:00 发布

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最新推荐文章于 2024-07-28 10:45:00 发布

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文章标签： java

原文链接：http://www.cnblogs.com/ismdeep/archive/2012/07/19/2598783.html

本文介绍了一个计算大整数阶乘位数的方法，使用C++实现，通过斯特林公式估算给定整数n的阶乘有多少位。适用于加密、数据安全等应用场景。

Big Number

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 15735 Accepted Submission(s): 6954

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

2 10 20

Sample Output

7 19

Source

Asia 2002, Dhaka (Bengal)

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 1 #include <iostream>
 2 #include <cmath>
 3 using namespace std;
 4 
 5 const double pi = acos(-1.0);
 6 const double E  = exp(1.0);
 7 int main()
 8 {
 9     int t;
10     cin >> t;
11     while (t--)
12     {
13         int n;
14         cin >> n;
15         int len;
16         len = (int)(log10l(sqrtl(2*pi*n))+n*log10l(n/E)+1);
17         if (n == 1)
18         {
19             len = 1;
20         }
21 
22         cout << len << endl;
23     }
24 
25     return 0;
26 }
27 
28 // end
29 // ism