CF New Year Table

最新推荐文章于 2023-08-13 02:28:59 发布

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#几何

本文介绍了一种算法，用于确定圆形晚宴桌上是否能放置指定数量的圆形盘子，并确保每个盘子都能触及桌子边缘且不相互重叠。通过计算几何的方法解决了这一问题。

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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
inputCopy
4 10 4
output
YES
inputCopy
5 10 4
output
NO
inputCopy
1 10 10
output
YES

Note

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

$\text{[math]}$

精度

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

const int N=100000+5;

const double PI=acos(-1.0);



void solve(){
    int n,R,r;
    cin>>n>>R>>r;

    if(n==1){
        if(R>=r){
            cout<<"YES"<<endl;
        }
        else{
            cout<<"NO"<<endl;
        }
    }
    else{
        if(R<2*r){
            cout<<"NO"<<endl;
        }
        else{
            double x=(R-r)*sin(PI/n);
            //cout<<x<<endl;
            if(x>r-1e-9){
                cout<<"YES"<<endl;
            }
            else{
                cout<<"NO"<<endl;
            }
        }
    }

    return;
}


int main(){
    solve();
    return 0;
}