maximum shortest distance

maximum shortest distance

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)

Total Submission(s): 60 Accepted Submission(s): 27

Problem Description

There are n points in the plane. Your task is to pick k points (k>=2), and make the closest points in these k points as far as possible.

 

Input

For each case, the first line contains two integers n and k. The following n lines represent n points. Each contains two integers x and y. 2<=n<=50, 2<=k<=n, 0<=x,y<10000.

 

Output

For each case, output a line contains a real number with precision up to two decimal places.

 

Sample Input

3 2
0 0
10 0
0 20

 

Sample Output

22.36

 

Author

alpc50

 

Source

2010 ACM-ICPC Multi-University Training Contest（15）——Host by NUDT

 

Recommend

zhouzeyong

 

/*
题意：给出n个点，现在让你选k个点，这k个点中，最近的两个点的距离最大

初步思路：刚好做到最大团这里，转化成最大团问题，二分，用二分的距离建边，比这条边长的两点才连线

#wa了一发：为啥double等于的时候 用减法判断开1e-6就不对，1e-8就对
*/
#include<bits/stdc++.h>
#define eps 1e-8
using namespace std;
/***********************************最大团模板************************************/
struct MAX_CLIQUE {
    static const int N=60;

    bool G[N][N];//存储图
    int n;//图的定点数
    int Max[N];//保存每个节点为根节点搜索到的最大团的定点数
    int Alt[N][N];//用来存储第i层的节点
    int    ans;//用来存储最大团的定点数

    bool DFS(int cur, int tot) {//cur表示当前层数的顶点数 tot表示搜索到的当前层数
        if(cur==0) {//不能扩展了就停止
            if(tot>ans) {
                ans=tot;
                return 1;
            }
            return 0;
        }
        for(int i=0; i<cur; i++) {
            if(cur-i+tot<=ans) return 0;//剪枝如果子图的节点数 加上 所有的定点数加上当前的层数 小于 前面找到的最大团
            
            int u=Alt[tot][i];
            if(Max[u]+tot<=ans) return 0;
            
            int nxt=0;
            for(int j=i+1; j<cur; j++)
                if(G[u][Alt[tot][j]]) 
                    Alt[tot+1][nxt++]=Alt[tot][j];
            
            if(DFS(nxt, tot+1)) return 1;
        }
        return 0;
    }

    int MaxClique(){
        ans=0, memset(Max, 0, sizeof Max);
        for(int i=n-1; i>=0; i--) {
            int cur=0;
            for(int j=i+1; j<n; j++) 
                if(G[i][j]) 
                    Alt[1][cur++]=j;
            DFS(cur, 1);
            Max[i]=ans;
        }
        return ans;
    }
};
struct Point{
    int x,y;
    Point(){}
    Point(int a,int b){
        x=a;
        y=b;
    }
    void input(){
        scanf("%d%d",&x,&y);
    }
    double dis(Point b){
        return sqrt((x-b.x)*(x-b.x)+(y-b.y)*(y-b.y));
    }
};
MAX_CLIQUE fuck;
Point p[55];
/***********************************最大团模板************************************/
void build(double r){
    for(int i=0;i<fuck.n;i++){
        for(int j=0;j<fuck.n;j++){
            if(p[i].dis(p[j])-r>=eps)
                fuck.G[i][j]=1;
            else fuck.G[i][j]=0;
        }
    }
}
int k;

int main(){
    // freopen("in.txt","r",stdin);
    while(scanf("%d%d",&fuck.n,&k)!=EOF){
        for(int i=0;i<fuck.n;i++){
            p[i].input();
        }
        double l=0.0,r=20000.0;
        while(r-l>eps){
            double m=(l+r)/2.0;
            build(m);
            if(fuck.MaxClique()>=k)//满足 
                l=m;
            else r=m;
        }
        printf("%.2lf
",l);
    }
    return 0;
}