http://acm.pku.edu.cn/JudgeOnline/problem?id=2187凸包直径 diameter of a convex polygon
#include <cstdlib>
#include<iostream>
#include<cmath>
using namespace std;
#define MAXN 50005
#define eps 1e-8
#define zero(x) (((x)>0?(x):-(x))<eps)
struct point{double x,y;}p5[MAXN],convex1[MAXN];;
//计算cross product (P1-P0)x(P2-P0)
double xmult(point p1,point p2,point p0){
return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);
}
double dist(point p3,point p4){
return (p3.x-p4.x)*(p3.x-p4.x)+(p3.y-p4.y)*(p3.y-p4.y);
}
//graham算法顺时针构造包含所有共线点的凸包,O(nlogn)
point p1,p2;
int graham_cp(const void* a,const void* b){
double ret=xmult(*((point*)a),*((point*)b),p1);
return zero(ret)?(xmult(*((point*)a),*((point*)b),p2)>0?1:-1):(ret>0?1:-1);
}
void _graham(int n,point* p,int& s,point* ch){
int i,k=0;
for (p1=p2=p[0],i=1;i<n;p2.x+=p[i].x,p2.y+=p[i].y,i++)
if (p1.y-p[i].y>eps||(zero(p1.y-p[i].y)&&p1.x>p[i].x))
p1=p[k=i];
p2.x/=n,p2.y/=n;
p[k]=p[0],p[0]=p1;
qsort(p+1,n-1,sizeof(point),graham_cp);
for (ch[0]=p[0],ch[1]=p[1],ch[2]=p[2],s=i=3;i<n;ch[s++]=p[i++])
for (;s>2&&xmult(ch[s-2],p[i],ch[s-1])<-eps;s--);
}
//构造凸包接口函数,传入原始点集大小n,点集p(p原有顺序被打乱!)
//返回凸包大小,凸包的点在convex中
//参数maxsize为1包含共线点,为0不包含共线点,缺省为1
//参数clockwise为1顺时针构造,为0逆时针构造,缺省为1
//在输入仅有若干共线点时算法不稳定,可能有此类情况请另行处理!
//不能去掉点集中重合的点
int graham(int n,point* p,point* convex,int maxsize=1,int dir=1){
point* temp=new point[n];
int s,i;
_graham(n,p,s,temp);
for (convex[0]=temp[0],n=1,i=(dir?1:(s-1));dir?(i<s):i;i+=(dir?1:-1))
if (maxsize||!zero(xmult(temp[i-1],temp[i],temp[(i+1)%s])))
convex[n++]=temp[i];
delete []temp;
return n;
}
int main()
{
int n,m;//m凸包顶点
double a,b;
//memset()
scanf("%d",&n);
for(int i=0;i<n;i++){
scanf("%lf %lf",&p5[i].x,&p5[i].y);
}
double maxn=0;
m=graham(n,p5,convex1,1,1);
for(int i=0;i<m;i++)
for(int j=0;j<m;j++){
double tmp=dist(convex1[i],convex1[j]);
if(maxn<tmp)maxn=tmp;
}
printf("%d\n",(int)maxn);
//system("pause");
return 0;
}
posted on 2009-03-03 23:24
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computing geometry