M - Arctic Network
Time Limit:2000MS     Memory Limit:65536KB     64bit IO Format:%lld & %llu
Appoint description:

Description

The Department of National Defence (DND) wishes to connect several northern outposts by a wireless network. Two different communication technologies are to be used in establishing the network: every outpost will have a radio transceiver and some outposts will in addition have a satellite channel.

Any two outposts with a satellite channel can communicate via the satellite, regardless of their location. Otherwise, two outposts can communicate by radio only if the distance between them does not exceed D, which depends of the power of the transceivers. Higher power yields higher D but costs more. Due to purchasing and maintenance considerations, the transceivers at the outposts must be identical; that is, the value of D is the same for every pair of outposts.

Your job is to determine the minimum D required for the transceivers. There must be at least one communication path (direct or indirect) between every pair of outposts.


Input

The first line of input contains N, the number of test cases. The first line of each test case contains 1 <= S <= 100, the number of satellite channels, and S < P <= 500, the number of outposts. P lines follow, giving the (x,y) coordinates of each outpost in km (coordinates are integers between 0 and 10,000).


Output

For each case, output should consist of a single line giving the minimum D required to connect the network. Output should be specified to 2 decimal points.


Sample Input



1
2 4
0 100
0 300
0 600
150 750


Sample Output




  212.13
//求最小生成树中的第S长边
#include <iostream>
#include <stdio.h>
#include <queue>
#include <stack>
#include <set>
#include <vector>
#include <math.h>
#include <string.h>
#include <algorithm>
using namespace std;
#define N 502
double dis(double x,double y,double a,double b)
{
    return sqrt((x-a)*(x-a)+(y-b)*(y-b));
}
double d[N][2];
double map[N][N];
int P;
bool b[N];
double rd[N];
int id;
void Prim()
{
    int i,k;
    memset(b,0,sizeof(b));
    double Min;
    int t=P;
    while(--t)
    {
        Min=1000000;
        for(i=1;i<P;i++)
         if(!b[i]&&Min>map[0][i])
         {
             Min=map[0][i];
             k=i;
         }
        b[k]=1;
        rd[id++]=Min;
        for(i=1;i<P;i++)
        if(!b[i]&&map[k][i]<map[0][i])
         map[0][i]=map[k][i];
    }
}
int main()
{
    int S;
    int T;
    int i,j,k;
    scanf("%d",&T);
    while(T--)
    {
        scanf("%d %d",&S,&P);
        for(i=0;i<P;i++)
         scanf("%lf %lf",&d[i][0],&d[i][1]);
        for(i=0;i<P;i++)
         for(j=i+1;j<P;j++)
          map[i][j]=map[j][i]=dis(d[i][0],d[i][1],d[j][0],d[j][1]);
        id=0;
        Prim();
        sort(rd,rd+id);
        printf("%.2lf\n",rd[id-S]);
    }
    return 0;
}