Sicily 1119. Factstone Benchmark

1119. Factstone Benchmark
      Constraints
      Time Limit: 1 secs, Memory Limit: 32 MB
      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.
      Input
      Given a year 1960 ≤ y ≤ 2160, what will be the Factstone rating of Amtel’s most recently released chip?
      Output
      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. For each test case, output a line giving the Factstone rating.
      Sample Input
      1960
      1981
      0
      Sample Output
      3
      8
      这道题先给出年份，根据年份求出位数n，然后需要求出一个x，使得x!正好小于2的n次方，在这里我们可以通过对两边同时取对数减少运算量， 即log2+…+logn<n，代码如下
      

#include<iostream>
#include<cmath>
using namespace std;
int main(){
	int year;
	while(cin>>year&&year!=0){
		year/=10;
		int k=year-194;
		k=pow(2,k);
		double n=1;
		double sum=0;
		while(sum<k){
			n++;
			sum+=log(n)/log(2);
		}
		cout<<n-1<<endl;
	}
}