CodeForces - 140A New Year Table （几何题）当时没想出来-----补题

A. New Year Table

time limit per test2 seconds

memory limit per test256 megabytes

inputstandard input

outputstandard output

Gerald is setting the New Year table. The table has the form of a circle; its radius equals R. Gerald invited many guests and is concerned whether the table has enough space for plates for all those guests. Consider all plates to be round and have the same radii that equal r. Each plate must be completely inside the table and must touch the edge of the table. Of course, the plates must not intersect, but they can touch each other. Help Gerald determine whether the table is large enough for n plates.

Input

The first line contains three integers n, R and r (1 ≤ n ≤ 100, 1 ≤ r, R ≤ 1000) — the number of plates, the radius of the table and the plates’ radius.

Output

Print “YES” (without the quotes) if it is possible to place n plates on the table by the rules given above. If it is impossible, print “NO”.

Remember, that each plate must touch the edge of the table.

Examples

inputCopy

4 10 4

outputCopy

YES

inputCopy

5 10 4

outputCopy

NO

inputCopy

1 10 10

outputCopy

YES

Note

The possible arrangement of the plates for the first sample is:

画画图就好做了，当时没做出来。



每个小圆所占的圆心角都是可以计算的，由角度可以计算最多的圆是多少个，和给定的值比较就可以了。

#include <cstdio>
#include <iostream>
#include <cmath>
using namespace std;
const double PI=acos(-1.0);
int main()
{
	int n,R,r;
	cin>>n>>R>>r;
	if(r>R)
	{
		cout<<"NO"<<endl;
		return 0;
	}
	else if(r>(R-r))
	{
		if(n==1)cout<<"YES"<<endl;
		else  cout<<"NO"<<endl;
		return 0;
	}
	double agle=asin((double)r/(double)(R-r));  //计算角度
	if(2.0*PI-2.0*agle*n>=-1e-12)  //精度是真高
		cout<<"YES"<<endl;
	else
		cout<<"NO"<<endl;
	return 0;
}

写在最后:

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