10916 - Factstone Benchmark

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 integern 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

这道题大致就是求出最大的n，条件是n！在2^N的氛围内。告诉你N。

这道题肯定是会超出int类型的。不过N的值是确定的十几二十个吧，所以可以一开始的时候用打表的方式打出所有的值。

这里打表是有技巧的，每次乘2之后，都要看看能不能再除以n+1,这样数据范围始终不会超了

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<string>
#include<ctype.h>
#include<algorithm>
#include<queue>
#include<stack>
using namespace std;
int a[25]={0};
int n,t=0;
double shang;
int go(int x)
{
    int i;
    for (i=x+1; i<=2*x; i++)
    {
        shang*=2;
        if (shang/(n+1)>=1)
        {
            shang/=(n+1);
            n=n+1;
        }
    }
    a[t]=n;
    t++;
    if (t>22) return 0;
    go(2*x);
}
int main ()
{
    int y,i;
    shang=4*1.0/6.0;
    n=3;
    go(2);
    while(cin>>y)
    {
        if (y==0) break;
        cout<<a[(y-1960)/10]<<endl;
    }
    return 0;
}