凸包模板（codevs1298）（洛谷2742）

Posted 2020-09-23

就是给你若干个点，求凸包的周长。

#include<bits/stdc++.h>
#define maxn 2000000
using namespace std;

struct Point {
	double x,y;
	Point(double x=0,double y=0):x(x),y(y){}
}p[maxn],ch[maxn];
int n;
typedef Point Vector;//将点和向量区分开来 
double Dot(Vector A,Vector B){return A.x*B.x+A.y*B.y;}//点积
double Cross(Vector A,Vector B){return A.x*B.y-A.y*B.x;}//叉积 
double dis(Point A,Point B){return sqrt((A.x-B.x)*(A.x-B.x)+(A.y-B.y)*(A.y-B.y));}
Vector operator -(Point A,Point B) {return Vector(A.x-B.x,A.y-B.y);}//点-点等于向量 
bool operator < (Point a,Point b){return a.x<b.x||(a.x==b.x&&a.y<b.y);}

double CovexHull(Point* p,int n,Point* ch)
{
	sort(p,p+n);
	int m=0;
	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--;
	double ans=0;
	for(int i=0;i<m;i++)
		ans+=dis(ch[i],ch[i+1]);
	return ans;
}
 
int main()
{
    cin>>n;
    for(int i=0;i<n;i++)
    	cin>>p[i].x>>p[i].y;
    printf("%.1f\n",CovexHull(p,n,ch));
    return 0;
}