hdu 1018 Big Number(对数的性质)

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#C++ #数论

Big Number

Time Limit: 20000/10000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 921 Accepted Submission(s): 522

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)

题目分析：算位数很容易想到用对数的性质

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#define MAX 5000001

using namespace std;

int t,n;

int main ( )
{
    scanf ( "%d" , &t );
    while ( t-- )
    {
        scanf ( "%d" , &n );
        double ans;
        ans = 0;
        for ( int i = 1 ; i <= n ; i++ )
            ans += log10(i);
        printf ( "%.lf\n" , ceil(ans) );
    }
}