凸包讲解
例题 POJ 2187
模板
#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
#include<cmath>
using namespace std;struct node
{int x,y;
};
node vex[50050];//存入的所有的点
node stackk[50050];//凸包中所有的点
int xx,yy,n;
bool cmp1(node a,node b)//排序找第一个点
{if(a.y==b.y)return a.x<b.x;elsereturn a.y<b.y;
}
int cross(node a,node b,node c)//计算叉积
{return (b.x-a.x)*(c.y-a.y)-(c.x-a.x)*(b.y-a.y);
}
double dis(node a,node b)//计算距离
{return sqrt((a.x-b.x)*(a.x-b.x)*1.0+(a.y-b.y)*(a.y-b.y));
}
int DIS(node a,node b)
{return (a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y);
}
bool cmp2(node a,node b)//极角排序
{if(atan2(a.y-yy,a.x-xx)!=atan2(b.y-yy,b.x-xx))return (atan2(a.y-yy,a.x-xx))<(atan2(b.y-yy,b.x-xx));return a.x<b.x;
}
int main()
{scanf("%d",&n);for(int i=0; i<n; i++){scanf("%d%d",&vex[i].x,&vex[i].y);}memset(stackk,0,sizeof(stackk));sort(vex,vex+n,cmp1);stackk[0]=vex[0];xx=stackk[0].x;yy=stackk[0].y;sort(vex+1,vex+n,cmp2);stackk[1]=vex[1];int top=1;for(int i=2; i<n; i++){while(i>=1&&cross(stackk[top-1],stackk[top],vex[i])<0)top--;stackk[++top]=vex[i];}int ans=0;stackk[++top]=vex[0];//for(i=1; i<=top+1; i++)//输出凸包上的点//cout<<stackk[i].x<<" "<<stackk[i].y<<endl;for(int i=1; i<=top+1; i++){for(int j=1; j<=top+1; j++){ans=max(ans,DIS(stackk[i],stackk[j]));}}printf("%d\n",ans);
}