【HDOJ1018】【大数阶乘位数】【斯特林公式】

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): 41932    Accepted Submission(s): 20544

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.

 

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

题目大意：求阶乘位数，数据很大。

题目分析：斯特林公式   X的阶乘位数==llog10(1)+log10(2)+···+long10(n)取整后加1

#include<iostream>
#include<cstdio>
#include<cmath>
using namespace std;
int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        int n;
        double sum=1.0;
        scanf("%d",&n);
        for(double i = 1 ; i <= n ;i++)
        {
            sum+=log10(i);
        }
        cout << (long)sum << endl;
    }
    return 0;
}