UVALive7461

  1 //UVALive7461 - Separating Pebbles 判断两个凸包相交
  2 
  3 #include <bits/stdc++.h>
  4 using namespace std;
  5 #define LL long long
  6 typedef pair<int,int> pii;
  7 const int inf = 0x3f3f3f3f;
  8 const int N =1e5+10;
  9 #define clc(a,b) memset(a,b,sizeof(a))
 10 const double eps = 1e-8;
 11 const int MOD = 1e9+7;
 12 void fre() {freopen("in.txt","r",stdin);}
 13 void freout() {freopen("out.txt","w",stdout);}
 14 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;}
 15 
 16 int sgn(double x) {
 17     if(fabs(x) < eps)return 0;
 18     if(x < 0)return -1;
 19     else return 1;
 20 }
 21 
 22 struct Point {
 23     int x,y;
 24     Point() {}
 25     Point(int _x,int _y) {
 26         x = _x;
 27         y = _y;
 28     }
 29     Point operator -(const Point &b)const {
 30         return Point(x - b.x,y - b.y);
 31     }
 32     int operator ^(const Point &b)const {
 33         return x*b.y - y*b.x;
 34     }
 35     int operator *(const Point &b)const {
 36         return x*b.x + y*b.y;
 37     }
 38     friend int dis2(Point a) {
 39         return a.x*a.x+a.y*a.y;
 40     }
 41     friend bool operator<(const Point &a,const Point &b){
 42         if(fabs(a.y-b.y)<eps) return a.x<b.x;
 43         return a.y<b.y;
 44     }
 45 };
 46 typedef Point Vector;
 47 double Dot(Point A, Point B){return A.x*B.x+A.y*B.y;}//点积
 48 double Cross(Vector A,Vector B){return A.x*B.y-A.y*B.x;}//叉积 
 49 double Length(Vector A){return sqrt(Dot(A,A));}//OA长  
 50 double Angle(Point A,Point B){return acos(Dot(A,B)/Length(A)/Length(B));}//OA和OB的夹角  
 51 //判断线段相交,不在端点相交  
 52 bool SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2){  
 53     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);  
 54     return sgn(c1)*sgn(c2)<0&&sgn(c3)*sgn(c4)<0;  
 55 }
 56 
 57 int graham(Point p[],int n,Point q[]){
 58      int top=1;
 59      sort(p,p+n);
 60      if(n==0) return 0;
 61      q[0]=p[0];
 62      if(n==1) return 1;
 63      q[1]=p[1];
 64      if(n==2) return 2;
 65      q[2]=p[2];
 66      for(int i=2;i<n;i++){
 67          while(top&&(Cross(q[top]-q[top-1],p[i]-q[top-1])<=0)) top--;
 68          q[++top]=p[i];
 69      }
 70      int len=top;
 71      q[++top]=p[n-2];
 72      for(int i=n-3;i>=0;i--){
 73          while(top!=len&&(Cross(q[top]-q[top-1],p[i]-q[top-1])<=0)) top--;
 74          q[++top]=p[i];
 75      }
 76      return top;
 77 }
 78 
 79 bool C_S(Point *ch1,int t1,Point *ch2,int t2)//判断凸包是否相交  
 80 {  
 81     double angle[1010],x;  
 82     int i,j,k,m;  
 83     if(t1==1)return true;  
 84     if(t1==2)  
 85     {  
 86         for(i=0;i<t2;i++)  
 87         {  
 88             k=sgn(Cross(ch1[1]-ch1[0],ch2[i]-ch1[0]));  
 89             if(k==0&&Dot(ch1[1]-ch1[0],ch2[i]-ch1[0])>0)  
 90             {  
 91                 if(Length(ch2[i]-ch1[0])<Length(ch1[1]-ch1[0]))break;  
 92             }  
 93         }  
 94         if(i<t2)return false;  
 95         if(t2==2&&SegmentProperIntersection(ch1[0],ch1[1],ch2[0],ch2[1]))return false;  
 96         return true;  
 97     }  
 98     angle[0]=0;  
 99     for(i=2;i<t1;i++)  
100     angle[i-1]=Angle(ch1[1]-ch1[0],ch1[i]-ch1[0]);  
101     for(i=0;i<t2;i++)  
102     {  
103         j=sgn(Cross(ch1[1]-ch1[0],ch2[i]-ch1[0]));  
104         if(j<0||(j==0&&Dot(ch1[1]-ch1[0],ch2[i]-ch1[0])<0))continue;  
105         j=sgn(Cross(ch1[t1-1]-ch1[0],ch2[i]-ch1[0]));  
106         if(j>0||(j==0&&Dot(ch1[t1-1]-ch1[0],ch2[i]-ch1[0])<0))continue;  
107         x=Angle(ch1[1]-ch1[0],ch2[i]-ch1[0]);  
108         m=lower_bound(angle,angle+t1-1,x)-angle;  
109         if(m==0)j=0;  
110         else j=m-1;  
111         k=sgn(Cross(ch1[j+1]-ch2[i],ch1[j+2]-ch2[i]));  
112         if(k>=0)break;  
113     }  
114     if(i<t2)return false;  
115     return true;  
116 }
117 
118 Point p1[300],p2[300],ch1[300],ch2[300];
119 int main(){
120     int T;
121     scanf("%d",&T);
122     while(T--){
123         int n;
124         scanf("%d",&n);
125         int cnt1=0,cnt2=0;
126         for(int i=0;i<n;i++){
127             int x,y,c;
128             scanf("%d%d%d",&x,&y,&c);
129             if(c==0){
130                 p1[cnt1++]=Point(x,y);
131             }
132             else p2[cnt2++]=Point(x,y);
133         }
134         int t1=graham(p1,cnt1,ch1);
135         int t2=graham(p2,cnt2,ch2);
136         if(C_S(ch1,t1,ch2,t2)&&C_S(ch2,t2,ch1,t1)) printf("1
");  
137         else printf("0
");  
138     }
139 }