简单的二分
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<cstring>
using namespace std;
int n,m;
struct po{
int x;
int y;
}p[1005];
int x,y;
int r[1005];
bool cmp(po x,po j){
return x.x<j.x;
}
double l,rr,mid;
double ans;
double dis[1005][1005];
int vis[1005];
bool dfs(int x,double mid){
//cout<<x<<endl;
if((n-p[x].x)*2<=mid){
return 1;
}else{
for(int i=1;i<=m;++i){
if(dis[x][i]<=mid&&i!=x&&!vis[i]){
vis[i]=1;
if(dfs(i,mid)) return 1;
}
}
return 0;
}
return 0;
}
bool check(double aim){
if(aim>=p[1].x&&aim>=(n-p[m].x)){
for(int i=1;i<=m;++i){
if(p[i].x>aim)
break;
if(vis[i]) continue;
vis[i]=1;
if(dfs(i,aim*2))
return 1;
}
}
return 0;
}
int main(){
scanf("%d%d",&n,&m);
for(int i=1;i<=m;++i){
scanf("%d%d",&p[i].x,&p[i].y);
}
rr=n;
// for(int i=1;i<=m;++i){
// cout<<r[i]<<endl;
// }
sort(p+1,p+m+1,cmp);
for(int i=1;i<=m;++i){
for(int j=i+1;j<=m;++j){
double di=(double)sqrt((p[i].x-p[j].x)*(p[i].x-p[j].x)+(p[i].y-p[j].y)*(p[i].y-p[j].y));
dis[i][j]=dis[j][i]=di;
}
}
while(l+1e-6<=rr){
mid=(l+rr)/2;
if(check(mid)){
rr=mid;
ans=mid;
} else{
l=mid;
}
memset(vis,0,sizeof(vis));
}
printf("%.2lf",ans);
return 0;
}