杭电 1141

最新推荐文章于 2020-02-21 10:00:19 发布

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本文详细解析了Amtel的芯片发展策略及其引入的Factstone基准测试，通过比较阶乘数值与位数之间的关系，揭示了如何计算Factstone评级。文中包括多个测试案例，演示了如何为不同年份的芯片计算Factstone评级。

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杭电 1141

Factstone Benchmark

Time Limit: 10000/5000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 1839 Accepted Submission(s): 1011

Problem 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?

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

196019810

Sample Output

分析：

阶乘数字太大，大数阶乘时间复杂度又太高，且大数之间不好进行比较，因此考虑优化，主要是比较 m! 和 2^n 的大小，可以用换底公式，这样就变成了比较log10（m！) 和2*log10（n）的大小。即log10（1）+log10（2）+........+log10（m）和2*log10（n）。

#include<iostream>
#include<cmath>
using namespace std;
int main()
{
	int year;
	while (cin >> year, year)
	{
		year = pow(2,year / 10 - 194);
		double max = year * log10(2);
		double changdu = 0, i = 1;
		while (changdu < max)
		{
			changdu += log10(i);
			i++;
		}
		i--;
		cout << i-1 << endl;
	}
	return 0;
}