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
1 #include<iostream> 2 using namespace std; 3 int main(){ 4 double a,min=100005; 5 int n; 6 cin>>a>>n; 7 double b,c; 8 c=b=1; 9 int p=1,q=1; 10 while(c<=n&&b<=n){ 11 if(c/b>a){ 12 if(c/b-a<min){ 13 min=c/b-a; 14 p=c; 15 q=b; 16 } 17 b++; 18 } 19 else{ 20 if(a-c/b<min){ 21 min=a-c/b; 22 p=c; 23 q=b; 24 } 25 c++; 26 } 27 } 28 cout<<p<<" "<<q<<endl; 29 return 0; 30 }