POJ 1423.Big Number

Big Number

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 26943		Accepted: 8608

DescriptionIn 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.InputInput 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 <= m <= 10^7 on each line.OutputThe 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

灰常灰常大的数的阶乘的位数，用了个斯特林公式，感觉酷炫吊炸天

#include<cstdio>#include<cmath>#include<iostream>#include<algorithm>using namespace std;#define pi acos(-1.0)#define e exp(1.0)double length(int n){    return 0.5*log10(2*pi*n)+n*log10(n/e);}int main(){    int t,m;    scanf("%d",&t);    while(t--)    {        scanf("%d",&m);        printf("%d\n",(int)length(m)+1);    }    return 0;}