判断两点间连通性，建图跑floyed
#include<bits/stdc++.h>
using namespace std;
const int N=;
struct node
{
double z[],x;
}q[N];double e[N][N];
double dis(double x1,double y1,double x2,double y2)
{
return sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
}
bool come(int i,int j,int a,int b)
{
if(j-i<)return ;
double x1=q[i].x,x2=q[j].x,y1=q[i].z[a],y2=q[j].z[b];if(x1==x2)return ;
double k=(y1-y2)/(x1-x2),bb=y1-x1*k;
for(i=i+;i<j;++i)
{
double y=q[i].x*k+bb;
if(y<q[i].z[]||(y>q[i].z[]&&y<q[i].z[])||y>q[i].z[])return ;
}
return ;
}
void add(int i,int j,int a,int b)
{
if(come(i,j,a,b))return;
e[i*+a][j*+b]=e[j*+b][i*+a]=dis(q[i].x,q[i].z[a],q[j].x,q[j].z[b]);
}
int main()
{
int n;
scanf("%d",&n);
for(int i=;i<=n;++i)
{
scanf("%lf",&q[i].x);
for(int j=;j<=;++j)scanf("%lf",&q[i].z[j]);
}
q[].x=;q[++n].x=;
for(int i=;i<=;++i)q[].z[i]=q[n].z[i]=;
for(int i=;i<=n*+;++i)for(int j=;j<=n*+;++j)e[i][j]=1e9; for(int i=;i<=n;++i)
for(int j=i+;j<=n;++j)
for(int a=;a<=;++a)
for(int b=;b<=;++b)
add(i,j,a,b);
for(int k=;k<=n*+;++k)
for(int i=;i<=n*+;++i)
for(int j=;j<=n*+;++j)
e[i][j]=min(e[i][j],e[i][k]+e[k][j]);
printf("%.2lf",e[][n*+]);
return ;
}