牛客国庆集训派对Day1L-New Game!

版权声明：不念过去，不畏未来，一切都是过眼云烟。 https://blog.csdn.net/qq_34531807/article/details/83119537

题解：
数学知识+最短路
$Code：$

#include<bits/stdc++.h>
using namespace std;
const int N=1e3+3,inf=1e9;
int n,a,b,c1,c2,x[N],y[N],r[N],tot,head[N*N],vis[N];
double dist[N];
priority_queue<pair<int,int>,vector<pair<int,int> >,greater<pair<int,int> > >Q;
double max(double X,double Y)
{
    return X>Y?X:Y;
}
double Abs(double a)
{
    return a>0?a:-a;
}
struct node
{
    int vet,next;
    double len;
}edge[N*N];
void add(int u,int v,double w)
{
    edge[++tot].vet=v;
    edge[tot].next=head[u];
    head[u]=tot;
    edge[tot].len=w;
}
void work(int X,int Y)
{
    double len=max((double)0,(double)(sqrt(Abs((double)(y[Y]-y[X]))*Abs((double)(y[Y]-y[X]))+Abs((double)(x[X]-x[Y]))*Abs((double)(x[X]-x[Y])))-r[X]-r[Y]));
    add(X,Y,len);add(Y,X,len);
}
inline int read()
{
    int x=0,f=1;
    char s=getchar();
    while(s>'9'||s<'0'){if(s=='-')f=-1;s=getchar();}
    while(s<='9'&&s>='0'){x=x*10+s-'0';s=getchar();}
    return x*f;
}
int main()
{
    n=read(),a=read(),b=read(),c1=read(),c2=read();
    memset(head,-1,sizeof(head));
    for(int i=1;i<=n;i++)
    {
        x[i]=read();y[i]=read();r[i]=read();
    }
    for(int i=1;i<n;i++)
        for(int j=i+1;j<=n;j++)
        {
            work(i,j);
        }
    double len;
    for(int i=1;i<=n;i++)
    {
        len=max((double)0,Abs((double)(a*x[i]+b*y[i]+c1)/(double)(sqrt(a*a+b*b)))-r[i]);
        add(0,i,len);add(i,0,len);
        len=max((double)0,Abs((double)(a*x[i]+b*y[i]+c2)/(double)(sqrt(a*a+b*b)))-r[i]);
        add(n+1,i,len);add(i,n+1,len);
    }
    for(int i=0;i<=n+1;i++)
    {
        dist[i]=inf;
    }
    dist[0]=0;
    Q.push(make_pair(dist[0],0));
    while(!Q.empty())
    {
        int u=Q.top().second;
        vis[u]=1;
        Q.pop();
        for(int i=head[u];i!=-1;i=edge[i].next)
        {
            int v=edge[i].vet;
            if(dist[u]+edge[i].len<dist[v]&&!vis[v])
            {
                dist[v]=dist[u]+edge[i].len;
                Q.push(make_pair(dist[v],v));
            }
        }
    }
    printf("%.10lf",dist[n+1]);
    return 0;
}