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)
log.jpg

解题思路:
求一个数n的位数很容易联想到(int)log10(n)+1,现在变成了n的阶乘,恰好又log里面相乘,直接变相加就行。log1.png

#include <iostream>
#include <stdio.h>
#include<string.h>
#include<math.h>
using namespace std;
int main()
{
    int n,t;scanf("%d",&t);
    while(t--)
    {
        scanf("%d",&n);
        double s=0;
        for(int i=1;i<=n;i++)
            s+=log10(i);
        printf("%d\n",(int)s+1);
    }
    return 0;
}
Last modification:December 4th, 2019 at 08:20 pm
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