UVA10916 - Factstone Benchmark

最新推荐文章于 2016-08-08 20:27:14 发布

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本文解析了一个关于Factstone基准测试的问题，这是一种衡量计算机芯片容量的新标准。文章通过具体实例介绍了如何计算不同年份下计算机芯片所能表示的最大阶乘值，并提供了一段C语言实现的代码。

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第一次TLE了，想到了取对数的方法，但是纠结 2^x-1 后面的 -1 一直保留所以计算超时了。后来实验了一两次，发现 x = 4 的时候 3! = 6 < 2^x-1 < 4!=15 跨度大于 1 了，以后更大，所以 -1 完全可以略去。

题目：

Problem B: Factstone Benchmark

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?

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

Output for Sample Input

3
8

Charles L. A. Clarke and Gordon V. Cormack

解答：

#include<stdio.h>
#include<math.h>
#include<stdlib.h>
int main()
{
	int y;
	while(scanf("%d",&y)!=EOF)
	{
		if(y==0)
			break;
		int n;
		double x,s=0,res;
		y/=10;
		n=y-196+2;
		x=pow(2,(double)n);
		res=x*log(2);
		n=1;
		while(s<res)
		{
			s+=log(n);
			n++;
		}
		printf("%d\n",n-2);
	}
}