UVALive7461 - Separating Pebbles 判断两个凸包相交

//UVALive7461 - Separating Pebbles 判断两个凸包相交

#include <bits/stdc++.h>
using namespace std;
#define LL long long
typedef pair<int,int> pii;
const int inf = 0x3f3f3f3f;
const int N =1e5+10;
#define clc(a,b) memset(a,b,sizeof(a))
const double eps = 1e-8;
const int MOD = 1e9+7;
void fre() {freopen("in.txt","r",stdin);}
void freout() {freopen("out.txt","w",stdout);}
inline int read() {int x=0,f=1;char ch=getchar();while(ch>'9'||ch<'0') {if(ch=='-') f=-1;ch=getchar();}while(ch>='0'&&ch<='9') {x=x*10+ch-'0';ch=getchar();}return x*f;}

int sgn(double x) {
    if(fabs(x) < eps)return 0;
    if(x < 0)return -1;
    else return 1;
}

struct Point {
    int x,y;
    Point() {}
    Point(int _x,int _y) {
        x = _x;
        y = _y;
    }
    Point operator -(const Point &b)const {
        return Point(x - b.x,y - b.y);
    }
    int operator ^(const Point &b)const {
        return x*b.y - y*b.x;
    }
    int operator *(const Point &b)const {
        return x*b.x + y*b.y;
    }
    friend int dis2(Point a) {
        return a.x*a.x+a.y*a.y;
    }
    friend bool operator<(const Point &a,const Point &b){
        if(fabs(a.y-b.y)<eps) return a.x<b.x;
        return a.y<b.y;
    }
};
typedef Point Vector;
double Dot(Point A, Point B){return A.x*B.x+A.y*B.y;}//点积
double Cross(Vector A,Vector B){return A.x*B.y-A.y*B.x;}//叉积 
double Length(Vector A){return sqrt(Dot(A,A));}//OA长  
double Angle(Point A,Point B){return acos(Dot(A,B)/Length(A)/Length(B));}//OA和OB的夹角  
//判断线段相交,不在端点相交  
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 sgn(c1)*sgn(c2)<0&&sgn(c3)*sgn(c4)<0;  
}

int graham(Point p[],int n,Point q[]){
     int top=1;
     sort(p,p+n);
     if(n==0) return 0;
     q[0]=p[0];
     if(n==1) return 1;
     q[1]=p[1];
     if(n==2) return 2;
     q[2]=p[2];
     for(int i=2;i<n;i++){
         while(top&&(Cross(q[top]-q[top-1],p[i]-q[top-1])<=0)) top--;
         q[++top]=p[i];
     }
     int len=top;
     q[++top]=p[n-2];
     for(int i=n-3;i>=0;i--){
         while(top!=len&&(Cross(q[top]-q[top-1],p[i]-q[top-1])<=0)) top--;
         q[++top]=p[i];
     }
     return top;
}

bool C_S(Point *ch1,int t1,Point *ch2,int t2)//判断凸包是否相交  
{  
    double angle[1010],x;  
    int i,j,k,m;  
    if(t1==1)return true;  
    if(t1==2)  
    {  
        for(i=0;i<t2;i++)  
        {  
            k=sgn(Cross(ch1[1]-ch1[0],ch2[i]-ch1[0]));  
            if(k==0&&Dot(ch1[1]-ch1[0],ch2[i]-ch1[0])>0)  
            {  
                if(Length(ch2[i]-ch1[0])<Length(ch1[1]-ch1[0]))break;  
            }  
        }  
        if(i<t2)return false;  
        if(t2==2&&SegmentProperIntersection(ch1[0],ch1[1],ch2[0],ch2[1]))return false;  
        return true;  
    }  
    angle[0]=0;  
    for(i=2;i<t1;i++)  
    angle[i-1]=Angle(ch1[1]-ch1[0],ch1[i]-ch1[0]);  
    for(i=0;i<t2;i++)  
    {  
        j=sgn(Cross(ch1[1]-ch1[0],ch2[i]-ch1[0]));  
        if(j<0||(j==0&&Dot(ch1[1]-ch1[0],ch2[i]-ch1[0])<0))continue;  
        j=sgn(Cross(ch1[t1-1]-ch1[0],ch2[i]-ch1[0]));  
        if(j>0||(j==0&&Dot(ch1[t1-1]-ch1[0],ch2[i]-ch1[0])<0))continue;  
        x=Angle(ch1[1]-ch1[0],ch2[i]-ch1[0]);  
        m=lower_bound(angle,angle+t1-1,x)-angle;  
        if(m==0)j=0;  
        else j=m-1;  
        k=sgn(Cross(ch1[j+1]-ch2[i],ch1[j+2]-ch2[i]));  
        if(k>=0)break;  
    }  
    if(i<t2)return false;  
    return true;  
}

Point p1[300],p2[300],ch1[300],ch2[300];
int main(){
    int T;
    scanf("%d",&T);
    while(T--){
        int n;
        scanf("%d",&n);
        int cnt1=0,cnt2=0;
        for(int i=0;i<n;i++){
            int x,y,c;
            scanf("%d%d%d",&x,&y,&c);
            if(c==0){
                p1[cnt1++]=Point(x,y);
            }
            else p2[cnt2++]=Point(x,y);
        }
        int t1=graham(p1,cnt1,ch1);
        int t2=graham(p2,cnt2,ch2);
        if(C_S(ch1,t1,ch2,t2)&&C_S(ch2,t2,ch1,t1)) printf("1\n");  
        else printf("0\n");  
    }
}