POJ-2661Factstone Benchmark

Factstone Benchmark

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 5577		Accepted: 2524

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

Source

Waterloo local 2005.09.24

OJ-ID：
poj-2661

author：
Caution_X

date of submission：
20191010

tags：
math

description modelling：
给定一个数x(x可以达到256位)，找到一个数n满足n!<=x&&(n+1)!>x

major steps to solve it：
1.因为x可以达到256位，所以我们同时对n!<=x和(n+1)!>x去对数
2.得到log(n)+log(n-1)+.......+log(1)<=log(x)&&log(n+1)+log(n)+......+log(1)>log(x)

AC Code:

#include<cstdio>
#include<cmath>
using namespace std;
int main()
{
    int n;
    double w;
    while(~scanf("%d",&n)&&n) {
        w=log(4);
        for(int i=1960;i<=n;i+=10) {
            w*=2;
        }
        int i=1;
        double f=0;
        while(f<w) {
            f+=log((double)++i);
        }
        printf("%d\n",i-1);
    }
}