uva10256 凸包

链接：http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1197

题意：平面上n个红点，m个蓝点，问是否存在一条直线，使得任取一个红点和一个蓝点都在直线异侧。

思路：可以把《训练指南》上的两个思路换一下顺序，求出两个凸包之后，先判断一个凸包上的点是否在另一个凸包内侧，不需要判断所有红色的点是否在蓝色凸包内，只要判断红凸包上的顶点就够了。再来判断线段相交，这时只要判断是否是规范相交就好了。觉得数据有点水。

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
const int maxn=510;
const double eps=1e-8;
struct Point
{
    int x,y;
    Point(int x=0,int y=0):x(x),y(y) {}
};
int n,m;
Point red[maxn],blue[maxn];
typedef Point Vector;

Vector operator + (Vector A,Vector B)
{
    return Vector(A.x+B.x,A.y+B.y);
}

Vector operator - (Vector A,Vector B)
{
    return Vector(A.x-B.x,A.y-B.y);
}
double Dot(Vector A,Vector B)
{
    return A.x*B.x+A.y*B.y;
}

double Length(Vector A)
{
    return sqrt(Dot(A,A));
}
double Cross(Vector A,Vector B)
{
    return A.x*B.y-A.y*B.x;
}
int dcmp(double x)
{
    if(fabs(x)<eps) return 0;
    else return x<0?-1:1;
}

bool operator == (const Point& a,const Point& b)
{
    return dcmp(a.x-b.x)==0 && dcmp(a.y-b.y)==0;
}
bool OnSegment(Point p,Point a1,Point a2)
{
    return dcmp(Cross(a1-p,a2-p))==0 && dcmp(Dot(a1-p,a2-p))<0;
}
int cmp(const Point &a,const Point &b)
{
    if(a.x<b.x) return 1;
    else if(a.x==b.x)
    {
        if(a.y<b.y) return 1;
        else return 0;
    }
    else return 0;
}
int ConvexHull(Point *p,int n,Point *ch)
{
    sort(p,p+n,cmp);
    n=unique(p,p+n)-p;
    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--;
    return m;
}
int isPointInPolygon(Point p,Point* poly,int n)
{
    int wn=0;
    for(int i=0;i<n;i++)
    {
        Point& p1=poly[i],p2=poly[(i+1)%n];
        if(p==p1 || p==p2 || OnSegment(p,p1,p2)) return -1;
        int k=dcmp(Cross(p2-p1,p-p1));
        int d1=dcmp(p1.y-p.y);
        int d2=dcmp(p2.y-p.y);
        if(k>0 && d1<=0 && d2>0) ++wn;
        if(k<0 && d2<=0 && d1>0) --wn;
    }
    if(wn) return 1;
    return 0;
}
bool SegmentProperIntersect(Point a1,Point a2,Point b1,Point b2)

{
    double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1);
    double c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1);
    return dcmp(c1)*dcmp(c2)<0 && dcmp(c3)*dcmp(c4)<0;
}

//Point read()
//{
//    Point p;
//    scanf("%d%d",&p.x,&p.y);
//    return p;
//}
void read(Point& p)
{
    scanf("%d%d",&p.x,&p.y);
}
bool solve()
{
    Point chr[maxn],chb[maxn];
    int mr,mb;
    mr=ConvexHull(red,n,chr);
    mb=ConvexHull(blue,m,chb);
    for(int i=0;i<mr;i++)
        if(isPointInPolygon(chr[i],chb,mb))
           return 0;
    for(int i=0;i<mb;i++)
        if(isPointInPolygon(chb[i],chr,mr))
           return 0;
    for(int i=0;i<mr;i++)
        for(int j=0;j<mb;j++)
        {
            if(SegmentProperIntersect(chr[i],chr[(i+1)%mr],chb[j],chb[(j+1)%mb]))
               return 0;
        }
    return 1;
}
int main()
{
  //  freopen("ine.cpp","r",stdin);
    while(scanf("%d%d",&n,&m) && n && m)
    {
        for(int i=0;i<n;i++)
            read(red[i]);//red[i]=read();//
        for(int i=0;i<m;i++)
            read(blue[i]);//blue[i]=read();//
        if(solve()) printf("Yes\n");
        else printf("No\n");
    }
    return 0;
}