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:
我叫风骨散人，名字的意思是我多想可以不低头的自由生活，可现实却不是这样。家境贫寒，总得向这个世界低头，所以我一直在奋斗，想改变我的命运给亲人好的生活，希望同样被生活绑架的你可以通过自己的努力改变现状，深知成年人的世界里没有容易二字。目前是一名在校大学生，预计考研，热爱编程，热爱技术，喜欢分享，知识无界，希望我的分享可以帮到你！
如果有什么想看的，可以私信我，如果在能力范围内，我会发布相应的博文！
感谢大家的阅读！😘你的点赞、收藏、关注是对我最大的鼓励！