pku 2187

cdy20 — Tue, 03 Mar 2009 15:24:00 GMT

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))
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;

}

cdy20 2009-03-03 23:24 发表评论

C++博客-Think! Action!-随笔分类-computing geometry

pku 2187