Codeforces 140A New Year Table（大圆带小圆）

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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:

$\text{[math]}$

题意：

给定一个大圆的半径 R 以及 n 个小院的半径 r 。

问能否把这 n 个小圆贴着大圆边缘 one by one 的放下。

思路：

如图所示，将此问题转化为数学问题。（其实 coderforces 的很多问题都是数学问题）。我们求出 ∠BCD 即可，知道 BC = R - r , BD = r 利用 arcsin() 即可。

注意：

精度问题！卡在第 6 组数据！只有加了 0.0000005才通过。

AC CODE：

#include<cstdio>
#include<cstring>
#include<iostream>
#include<cmath>
#include<algorithm>
using namespace std;const double PI = acos(-1.0);int main()
{double n, R, r;cin >> n >> R >> r;if(n == 1) {if(R >= r) puts("YES");else puts("NO");} else {if(R < r) puts("NO");else {double jiao = 2.0 * asin(r/(R-r));double Get_n = 2.0*PI / jiao;/* 最多可以放置的小圆个数*/Get_n += 0.00000000005;/* 务必留意精度问题 */if(Get_n - n >= 0) puts("YES");else puts("NO");}}return 0;
}

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