poj 1650 Integer Approximation

Integer Approximation

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 5326		Accepted: 1750

Description

The FORTH programming language does not support floating-point arithmetic at all. Its author, Chuck Moore, maintains that floating-point calculations are too slow and most of the time can be emulated by integers with proper scaling. For example, to calculate the area of the circle with the radius R he suggests to use formula like R * R * 355 / 113, which is in fact surprisingly accurate. The value of 355 / 113 ≈ 3.141593 is approximating the value of PI with the absolute error of only about 2*10^-7. You are to find the best integer approximation of a given floating-point number A within a given integer limit L. That is, to find such two integers N and D (1 <= N, D <= L) that the value of absolute error |A - N / D| is minimal.

Input

The first line of input contains a floating-point number A (0.1 <= A < 10) with the precision of up to 15 decimal digits. The second line contains the integer limit L. (1 <= L <= 100000).

Output

Output file must contain two integers, N and D, separated by space.

Sample Input

3.14159265358979
10000

Sample Output

355 113

Source

Northeastern Europe 2001, Far-Eastern Subregion

分析：

枚举

#include<iostream>
using namespace std;
int main(){
    double a,min=100005;
    int n;
    cin>>a>>n;
    double b,c;
    c=b=1;
    int p=1,q=1;
    while(c<=n&&b<=n){
         if(c/b>a){
             if(c/b-a<min){
                 min=c/b-a;
                 p=c;
                 q=b;
             }
             b++;
         }
         else{
             if(a-c/b<min){
                 min=a-c/b;
                 p=c;
                 q=b;
             }
             c++;
         }    
    }
    cout<<p<<" "<<q<<endl;
    return 0;
}