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