題目連結：點選打開連結
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：判斷在一個半徑為 R 的桌子上放 n 個半徑為 r 的盤子，使得各個盤子不互相重疊，是否合法
思路：
如圖所示，将此問題轉化為數學問題。我們求出 ∠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) // 一個盤子就過圓心了，是以隻能放一個
{
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) // 這裡卡精度
puts("YES");
else
puts("NO");
}
return 0;
}