102551: [AtCoder]ABC255 B - Light It Up
Description
Score : $200$ points
Problem Statement
There are $N$ people numbered $1, 2, \dots, N$ in the $xy$-plane. Person $i$ is at the coordinates $(X_i, Y_i)$.
$K$ of these people, Persons $A_1, A_2, \dots, A_K$, will receive lights of the same strength.
When a person at coordinates $(x, y)$ has a light of strength $R$, it lights up the interior of a circle of radius $R$ centered at $(x, y)$ (including the boundary).
Find the minimum strength of the lights needed for every person to be lit by at least one light.
Constraints
- All values in input are integers.
- $1 \le K < N \le 1000$
- $1 \le A_1 < A_2 < \dots < A_K \le N$
- $|X_i|,|Y_i| \le 10^5$
- $(X_i,Y_i) \neq (X_j,Y_j)$, if $i \neq j$.
Input
Input is given from Standard Input in the following format:
$N$ $K$ $A_1$ $A_2$ $\dots$ $A_K$ $X_1$ $Y_1$ $X_2$ $Y_2$ $\vdots$ $X_N$ $Y_N$
Output
Print the answer as a real number.
Your output will be considered correct if its absolute or relative error from the judge's output is at most $10^{-5}$.
Sample Input 1
4 2 2 3 0 0 0 1 1 2 2 0
Sample Output 1
2.23606797749978969
This input contains four people. Among them, Persons $2$ and $3$ will have lights.
Every person will be lit by at least one light if $R \ge \sqrt{5} \approx 2.236068$.
Sample Input 2
2 1 2 -100000 -100000 100000 100000
Sample Output 2
282842.712474619009
Sample Input 3
8 3 2 6 8 -17683 17993 93038 47074 58079 -57520 -41515 -89802 -72739 68805 24324 -73073 71049 72103 47863 19268
Sample Output 3
130379.280458974768
Input
题意翻译
有 $n$ 盏灯,有 $m$ 盏灯是亮的,这 $m$ 盏灯分别为 $A_1$ 到 $A_m$,每盏灯有个坐标,问,当 $m$ 盏灯所能照亮的半径为多少时,所有灯会被照亮Output
问题描述
在$xy$平面上有$N$个人,编号为$1, 2, \dots, N$。第$i$个人在坐标$(X_i, Y_i)$处。
其中的$K$个人,编号为$A_1, A_2, \dots, A_K$,将收到相同强度的灯光。
当一个人在坐标$(x, y)$处有一盏强度为$R$的灯时,它会照亮以$(x, y)$为中心,半径为$R$的圆的内部(包括边界)。
找出使每个人都能被至少一盏灯照亮所需的灯光的最小强度。
约束条件
- 输入中的所有值都是整数。
- $1 \le K < N \le 1000$
- $1 \le A_1 < A_2 < \dots < A_K \le N$
- $|X_i|,|Y_i| \le 10^5$
- 如果$i \neq j$,则$(X_i,Y_i) \neq (X_j,Y_j)$。
输入
输入从标准输入中给出,格式如下:
$N$ $K$ $A_1$ $A_2$ $\dots$ $A_K$ $X_1$ $Y_1$ $X_2$ $Y_2$ $\vdots$ $X_N$ $Y_N$
输出
以实数形式打印答案。
如果您的输出与法官的输出绝对或相对误差不超过$10^{-5}$,则将被认为是正确的。
样例输入1
4 2 2 3 0 0 0 1 1 2 2 0
样例输出1
2.23606797749978969
此输入包含四个人。其中,第$2$和$3$个人将有灯光。
如果$R \ge \sqrt{5} \approx 2.236068$,那么每个人将至少被一盏灯照亮。
样例输入2
2 1 2 -100000 -100000 100000 100000
样例输出2
282842.712474619009
样例输入3
8 3 2 6 8 -17683 17993 93038 47074 58079 -57520 -41515 -89802 -72739 68805 24324 -73073 71049 72103 47863 19268
样例输出3
130379.280458974768