POJ 2661 Factstone Benchmark

Description

Amtel has announced that it will release a 128-bit computer chip by 2010, a 256-bit computer by 2020, and so on, continuing its strategy of doubling the word-size every ten years. (Amtel released a 64-bit computer in 2000, a 32-bit computer in 1990, a 16-bit computer in 1980, an 8-bit computer in 1970, and a 4-bit computer, its first, in 1960.) 
Amtel will use a new benchmark - the Factstone - to advertise the vastly improved capacity of its new chips. The Factstone rating is defined to be the largest integer n such that n! can be represented as an unsigned integer in a computer word. 
Given a year 1960 <= y <= 2160, what will be the Factstone rating of Amtel's most recently released chip?

Input

There are several test cases. For each test case, there is one line of input containing y. A line containing 0 follows the last test case.

Output

For each test case, output a line giving the Factstone rating.

Sample Input

1960
1981
0

Sample Output

3
8

由于这是高精度没法用普通方式计算阶乘，否则会TLE
可以用斯特林(Stirling)公式求解
    
    
    
    

     
     
     
     
 
      
 
       
 
        

          斯特林（Stirling）公式： 
        
 
      
 
     
    
    
    
    
#include <stdio.h>
int main()
{
    int year;
    int endflag;
    int n;
    double sum;
    while(scanf("%d", &year),year)
    {
        endflag = 1<<((year - 1960) / 10 + 2);
        n = 2;
        sum = 0;
        while(sum <= endflag)
        {
            sum += log(n) / log(2);
            ++n;
        }
        printf("%d\n", n - 2);
    }
    return 0;
}