凸包

#include <stdlib.h>#define eps 1e-8#define zero(x) (((x)>0?(x):-(x))<eps)struct point{double x,y;};//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);}//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;}