hdu-Big Number

Big Number

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 26872    Accepted Submission(s): 12225

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

21020

 

Sample Output

719

 

Source

Asia 2002, Dhaka (Bengal)

 

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

</pre><pre class="cpp" name="code">#include <iostream>//斯特林公式求对数#include <cmath>using namespace std;#define PI 3.141592654int main(){    int n,t;    cin>>t;    while(t--)    {        cin>>n;        cout<<(int)((0.5*log(PI*2*n)+n*log(n)-n)/log(10))+1<<endl;    }    return 0;}