HDU1018 （斯特林公式）

Big Number

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 31681    Accepted Submission(s): 14769

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

Source

Asia 2002, Dhaka (Bengal)

 

题意：求n的阶乘的位数

本题可以暴力，正解应该是用斯特林公式，听说斯特林数能够做一切关于阶乘的大数运算，好像很牛逼的样子，要深入学习。。。直接给出公式

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

int main() {
    int T, n;
    scanf("%d", &T);
    while (T --) {
        scanf("%d", &n);
        if (n == 1) printf("1
");
        else printf("%d
", (int)(0.5*log10(2*PI*n)+n*log10(n/e)+1));
    }
    return 0;
}