hdu 1018 计算一个数阶乘的位数

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

21020

Sample Output

719

题意：求一个数的阶乘的位数

因为根据数学知识可以知道：

log10(1*2*3*4.........*n)=log10(1)+log10(2)+log10(3)+log10(4)...........+log10(n);

又因为阶乘很可能超出整形，不容易计算，所以就应用log进行计数

#include<stdio.h>
#include<math.h>
int main()
{
    int t,m;
    scanf("%d",&t);
    while(t--)
    {
        double sum=0;
        scanf("%d",&m);
        for(int i=1;i<=m;i++)
         sum+=log10(i);
         printf("%d\n",((int)sum)+1);    
    }
    return 0;
}