uva 10256 The Great Divide

https://vjudge.net/problem/UVA-10256

 

翻了一个小时的uva，竟然没找到题库在哪儿，

蠢哭~~~~(>_<)~~~~

 

题意：

一堆蓝点一堆红点

能否找到一条直线，将蓝点与红点分开

 

构造出蓝点的凸包，红点的凸包

如果能的话

1、两凸包的所有边没有交点

2、蓝点不在红凸包内

3、红点不在蓝凸包内

 

#include<cstdio>
#include<iostream>
#include<algorithm>

using namespace std;

#define N 501

struct Point 
{
    int x,y;
    
    Point (int x=0,int y=0) : x(x),y(y) { }
    
    bool operator < (Point q)
    {
        if(x!=q.x) return x<q.x;
        return y<q.y;
    }
    
    bool operator == (Point q)
    {
        return x==q.x && y==q.y;
    }
    
};

typedef Point Vector;

Point P1[N],P2[N],c1[N],c2[N];

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

void read(int &x)
{
    x=0; int f=1; char c=getchar();
    while(!isdigit(c))  { if(c=='-') f=-1; c=getchar(); }
    while(isdigit(c)) { x=x*10+c-'0'; c=getchar(); }
    x*=f;
}

int dcmp(int x)
{
    if(!x) return 0;
    return x<0 ? -1 : 1;
}

int Cross(Vector A,Vector B)
{
    return A.x*B.y-A.y*B.x;
}

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

bool cmp(Point A,Point B)
{
    if(A.x==B.x) return A.y<B.y;
    return A.x<B.x;
}

int ConvexHull(Point *p,int n,Point *c)
{
    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(c[m-1]-c[m-2],p[i]-c[m-2])<=0) m--;
        c[m++]=p[i];
    }
    int k=m;
    for(int i=n-2;i>=0;--i)
    {
        while(m>k && Cross(c[m-1]-c[m-2],p[i]-c[m-2])<=0) 
            m--;
        c[m++]=p[i];
    }
    return m;
}

bool OnSegment(Point p,Point a1,Point a2)
{
    if(p==a1 || p==a2) return true;
    return dcmp(Cross(a1-p,a2-p))==0 && dcmp(Dot(a1-p,a2-p))<0;
}

bool SegmentIntersection(Point a1,Point a2,Point b1,Point b2)
{
    if(OnSegment(a1,b1,b2) || OnSegment(a2,b1,b2) || OnSegment(b1,a1,a2) || OnSegment(b2,a1,a2))  return true;
    int 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 isPointInPolygon(Point p,Point *c,int n)
{
    if(n==1) return false;
    if(n==3) return OnSegment(p,c[0],c[1]); 
    for(int i=0;i<n-1;++i)
        if(dcmp(Cross(c[i+1]-c[i],p-c[i]))<0) return false;
}

bool check(int n1,int m1,int n2,int m2)
{
    for(int i=0;i<m1-1;++i)
        for(int j=0;j<m2-1;++j)
            if(SegmentIntersection(c1[i],c1[i+1],c2[j],c2[j+1])) return false;
    for(int i=0;i<n1;++i)
        if(isPointInPolygon(P1[i],c2,m2)) return false;
    for(int i=0;i<n2;++i)
        if(isPointInPolygon(P2[i],c1,m1)) return false;
    return true;
}

int main()
{
    int n1,n2;
    int m1,m2;
    while(1)
    {
        read(n1); read(n2);
        if(!n1) return 0;
        for(int i=0;i<n1;++i) read(P1[i].x),read(P1[i].y);
        for(int i=0;i<n2;++i) read(P2[i].x),read(P2[i].y);
        m1=ConvexHull(P1,n1,c1);
        m2=ConvexHull(P2,n2,c2);
        puts(check(n1,m1,n2,m2) ? "Yes" : "No");
    }
}