Uva 10256 The Great Divide（凸包）

题目地址：https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1197

思路：

分离两种点，即为分离两种点组成的两个凸包：

1.任取A凸包中的一点，判断是否在B凸包中；任取B凸包中的一点，判断是否在A凸包中；

2.任取A凸包上一条线段，判断是否与B凸包中线段相交；任取B凸包上一条线段，判断是否与A凸包中线段相交。

#include<cmath>#include<cstdio>#include<cstring>#include<iostream>#include<algorithm>#define debugusing namespace std;struct Point{    double x,y;    Point(double x=0.0,double y=0.0):x(x),y(y) {}    void read()    {        scanf("%lf%lf",&x,&y);    }};typedef Point Vector;int dcmp(double x){    if(fabs(x)<0) return 0;    else return x<0?-1:1;}bool operator < (Point A,Point B){    if(A.x==B.x) return A.y<A.y;    else return A.x<B.x;}Vector operator - (Vector A,Vector B){    return Vector(A.x-B.x,A.y-B.y);}double Cross(Vector A,Vector B){    return A.x*B.y-A.y*B.x;}double Dot(Vector A,Vector B){    return A.x*B.x+A.y*B.y;}bool SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2){    double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1),           c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1);    return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0;}bool isPointOnSegment(Point p,Point a1,Point a2){    return dcmp(Cross(a1-p,a2-p))==0&&dcmp(Dot(a1-p,a2-p))<0;}int ConvexHull(Point* p,int n,Point* ch){    sort(p,p+n);    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++)    {        if(isPointOnSegment(p,poly[i],poly[(i+1)%n])) return -1;        int k=dcmp(Cross(poly[(i+1)%n]-poly[i],p-poly[i]));        int d1=dcmp(poly[i].y-p.y);        int d2=dcmp(poly[(i+1)%n].y-p.y);        if(k>0&&d1<=0&&d2>0) wn++;        if(k<0&&d2<=0&&d1>0) wn--;    }    if(wn!=0) return 1;    return 0;}const int maxn=500+50;int m,c;int num1,num2;Point p1[maxn],p2[maxn];Point convex1[maxn],convex2[maxn];int checkIn(){    for(int i=0; i<num1; i++)    {        if(isPointInPolygon(convex1[i],convex2,num2))        {            return 1;        }    }    for(int i=0; i<num2; i++)    {        if(isPointInPolygon(convex2[i],convex1,num1))        {            return 1;        }    }    return 0;}int checkIntersection(){    for(int i=0; i<num1; i++)    {        for(int j=0; j<num2; j++)        {            if(SegmentProperIntersection(convex1[i],convex1[(i+1)%num1],convex2[j],convex2[(j+1)%num2]))            {                return 1;            }        }    }    return 0;}int main(){#ifdef debu    freopen("in.txt","r",stdin);#endif // debug    while(scanf("%d%d",&m,&c)!=EOF&&(m+c))    {        for(int i=0; i<m; i++) p1[i].read();        for(int i=0; i<c; i++) p2[i].read();        num1=ConvexHull(p1,m,convex1);        num2=ConvexHull(p2,c,convex2);        if(!checkIn()&&!checkIntersection())        {            printf("Yes\n");        }        else        {            printf("No\n");        }    }    return 0;}