[USACO5.1]圈奶牛Fencing the Cows /【模板】二维凸包

二维凸包板子

#include<iostream>
#include<algorithm>
#include<cmath>
#include<math.h>
using namespace std;
const double eps = 1e-10;
struct Point 
{
    double x,y;
    Point(double x=0,double y=0):x(x),y(y){}
};
typedef Point Vector;

Vector operator + (Vector A,Vector B)
{
    return Vector(A.x+B.x,A.y+B.y);
}
Vector operator - (Vector A,Vector B)
{
    return Vector(A.x-B.x,A.y-B.y);
}
Vector operator * (Vector A,double p)
{
    return Vector(A.x*p,A.y*p);
}
Vector operator / (Vector A,double p)
{
    return Vector(A.x/p,A.y/p);
}

bool operator < (const Point& a,const Point& b)
{
    return a.x<b.x|| (a.x==b.x&&a.y<b.y);
}

int dcmp(double x)
{
    if(fabs(x)<eps) return 0;
    if(x<0)     return -1;
    return 1;
}

bool operator == (const Point& a,const Point& b)
{
    return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;
}

Point read_point()
{
    double x,y;
    cin>>x>>y;
    return Vector(x,y);
}
double dot(Vector A,Vector B)
{
    return A.x*B.x+A.y*B.y;
}

double cross(Vector A,Vector B)
{
    return A.x*B.y-B.x*A.y;
}
double length(Vector A)
{
    return sqrt(dot(A,A));
}
double convexhull(Point* p,int n,Point* ch)
{
    double res=0;
    int m=0;
    sort(p,p+n);
    for(int i=0;i<n;i++)
    {
        while(m>1&&cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0)  m--;
        ch[m++]=p[i];
    }
    int k=m;
    for(int i=n-2;i>=0;i--)
    {
        while(m>k&&cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0)  m--;
        ch[m++]=p[i];
    }
    if(n>1) m--;

    for(int i=1;i<=m;i++)
    {
        res+=length(ch[i]-ch[i-1]);
    }

    return res;
}


int main()
{
    int n;
    cin>>n;
    Point p[10010],ch[10010];
    for(int i=0;i<n;i++)
    {
        p[i]=read_point();
    }

    double res=convexhull(p,n,ch);

    printf("%.2lf",res);
    return 0;
}