codeforces-140【A几何】【精度】

题目链接：点击打开链接

A. New Year Table

time limit per test
2 seconds

memory limit per test
256 megabytes

input
standard input

output
standard 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

input

4 10 4

output

YES

input

5 10 4

output

NO

input

1 10 10

output

YES

Note

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



大意：判断在一个半径为 R 的桌子上放 n 个半径为 r 的盘子，使得各个盘子不互相重叠，是否合法

思路：



如图所示，将此问题转化为数学问题。我们求出  ∠BCD 即可，知道 BC = R - r , BD = r 利用 arcsin() 即可。

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
int n,R,r;
int main()
{
while(~scanf("%d%d%d",&n,&R,&r))
{
if(R<r)
{
puts("NO");
continue;
}
if(2*r>R) // 一个盘子就过圆心了，所以只能放一个
{
if(n==1)
puts("YES");
else
puts("NO");
continue;
}
double angle=asin(r*1.0/(R-r));
if(2*acos(-1.0)-angle*2*n>-1e-10) // 这里卡精度
puts("YES");
else
puts("NO");
}
return 0;
}