OI模板凸包_凸包 oi-优快云博客

本文链接：https://blog.youkuaiyun.com/im_zyINF/article/details/124396426

这篇博客介绍了二维凸包的基本概念，并提供了OI模板——Andrew算法实现凸包的详细过程。该算法用于计算给定点集的凸包，并计算其周长。此外，还给出了一个具体的例子，如LuoguP2742题目，展示了凸包在解决实际问题中的应用。

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OI模板凸包

凸包-Andrew


const int N=1;
const double eps=1e-8;
int is0(double x){return (fabs(x)<eps?0:(x<0)?-1:1);}
struct Point{
	double x,y;
	Point(){}
	Point(double x,double y):x(x),y(y){}
	Point operator+(Point b){return Point(x+b.x,y+b.y);}
	Point operator-(Point b){return Point(x-b.x,y-b.y);}
	bool operator==(Point b){return is0(x-b.x)==0&&is0(y-b.y)==0;}
	bool operator<(Point b){return is0(x-b.x)<0||(is0(x-b.x)==0&&is0(y-b.y)<0);}
}p[N],ch[N];//输入点，凸包上点
typedef Point Vector;
double Cross(Vector a,Vector b){return a.x*b.y-a.y*b.x;}
double Dist(Point a,Point b){return hypot(a.x-b.x,a.y-b.y);}
int Andrew(int n){//计算凸包（n是输入点数，返回凸包点数，计算ch[]为凸包上点
	int v=0,k;
	sort(p,p+n);
	n=unique(p,p+n)-p;
	for(int i=0; i<n; ++i){
		while(v>1 && is0(Cross(ch[v-1]-ch[v-2],p[i]-ch[v-2]))<1) --v;
		ch[v++]=p[i];
	}
	for(int i=n-2,k=v; i>=0; --i){
		while(v>k && is0(Cross(ch[v-1]-ch[v-2],p[i]-ch[v-2]))<1) --v;
		ch[v++]=p[i];
	}
	return (n>1?v-1:v);
}
double Perimeter(int v){//算周长（v是凸包点数）
	double ans=0;
	for(int i=0; i<v; ++i)
		ans+=Dist(ch[i],ch[(i+1)%v]);
	return ans;
}