P742圈奶牛

题目链接：https://www.luogu.com.cn/problem/P2742

思路：要把奶牛喜欢吃草的所有地点都圈起来，且围栏的长度要尽量小。可以想到凸包，先求出凸包，再求凸包的周长即可。

#include<bits/stdc++.h>
using namespace std;
struct point{
    double x,y;
    point friend operator -(point a,point b)
    {return {a.x-b.x,a.y-b.y};}
}p[100005],s[100005];
double dis(point a,point b)
{
    point c=a-b;
    return sqrt(c.x*c.x+c.y*c.y);
}
double X(point a,point b)
{
    return a.x*b.y-a.y*b.x;
}
int cmp(point a,point b)
{
    double x=X(a-p[1],b-p[1]);

    if(x>0) return 1;
    if(x==0&&dis(a,p[1])<dis(b,p[1])) return 1;
    return 0;
}
double multi(point p1,point p2,point p3)
{
    return X(p2-p1,p3-p1);
}
int main()
{
    int N;
    while(~scanf("%d",&N))
    {
        if(N==0)
            break;
        for(int i=1;i<=N;i++) 
            scanf("%lf%lf",&p[i].x,&p[i].y);
            //cin>>p[i].x>>p[i].y;
        if(N==1)
        {
            printf("0.00\n");
            continue;
        }
        else if(N==2)
        {
            printf("%.2lf\n",dis(p[1],p[2]));
            continue;
        }

        int k=1;
        for(int i=2;i<=N;i++)
        if(p[i].y<p[k].y||(p[i].y==p[k].y&&p[i].x<p[k].x))k=i;
        swap(p[1],p[k]);

        sort(p+2,p+1+N,cmp);

        s[1]=p[1];
        s[2]=p[2];
        int t=2;
        for(int i=3;i<=N;i++)
        {
            while(t>=2&&multi(s[t-1],s[t],p[i])<=0) t--;
            s[++t]=p[i];
        }
        double sum=0;
        for(int i=1;i<t;i++)
        {
            sum+=dis(s[i],s[i+1]);
        }
        printf("%.2lf\n",sum+dis(s[1],s[t]));
    }
    return 0;
}