uva 1453 - Squares

旋转卡壳算法；

直接在这个上面粘的模板

主要用途：用于求凸包的直径、宽度，两个不相交凸包间的最大距离和最小距离···

这题就是求凸包的直径

 #include <cstdio>
 #include <cmath>
 #include <cstring>
 #include <algorithm>
 #include <vector>
 #define eps 1e-9
 using namespace std;
 const double pi = acos(-);

 int dcmp(double x)
 {
     return fabs(x) < eps ?  : (x >  ?  : -);
 }

 struct Point
 {
     double x;
     double y;

     Point(double x = , double y = ):x(x), y(y) {}

     bool operator < (const Point& e) const
     {
         return dcmp(x - e.x) <  || (dcmp(x - e.x) ==  && dcmp(y - e.y) < );
     }

     bool operator == (const Point& e) const
     {
         return dcmp(x - e.x) ==  && dcmp(y - e.y) == ;
     }
 };

 typedef Point Vector;

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

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

 Vector operator * (Point A, double p)
 {
     return Vector(A.x * p, A.y * p);
 }

 Vector operator / (Point A, double p)
 {
     return Vector(A.x / p, A.y / p);
 }
 double dot(Point a,Point b)
 {
     return a.x*b.x+a.y*b.y;
 }
 double cross(Point a,Point b)
 {
     return a.x*b.y-a.y*b.x;
 }
 Point rotate(Point a,double ang)
 {
     return Point(a.x*cos(ang)-a.y*sin(ang),a.x*sin(ang)+a.y*cos(ang));
 }
 int convexhull(Point *p,int n,Point *ch)
 {
     sort(p,p+n);
     int m=;
     for(int i=; i<n; i++)
     {
         while(m>&&cross(ch[m-]-ch[m-],p[i]-ch[m-])<=)m--;
         ch[m++]=p[i];
     }
     int k=m;
     for(int i=n-; i>=; i--)
     {
         while(m>k&&cross(ch[m-]-ch[m-],p[i]-ch[m-])<=)m--;
         ch[m++]=p[i];
     }
     if(n>)m--;
     return m;
 }
 bool onsegment(Point p,Point a,Point b)
 {
     return dcmp(cross(a-p,b-p))==&&dcmp(dot(a-p,b-p))<;
 }

 bool SegmentProperIntersection( Point a1, Point a2, Point b1, Point b2 )  //线段相交，交点不在端点
 {
     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) <  && dcmp(c3) * dcmp(c4) < ;
 }

 int ispointinpolygon(Point p,int n,Point *poly)
 {
     int wn=;
     for(int i=; i<n; i++)
     {
         if(onsegment(p,poly[i],poly[(i+)%n]))return -;
         int k=dcmp(cross(poly[(i+)%n]-poly[i],p-poly[i]));
         int d1=dcmp(poly[i].y-p.y);
         int d2=dcmp(poly[(i+)%n].y-p.y);
         if(k>&&d1<=&&d2>)wn++;
         if(k<&&d2<=&&d1>)wn--;
     }
     if(wn!=)return ;
     return ;
 }

 bool Check(int n,Point *ch,int m,Point *th)
 {
     for(int i=; i<n; i++)
     {
         if(ispointinpolygon(ch[i],m,th)!=)return ;
     }
     for(int i=; i<m; i++)
         if(ispointinpolygon(th[i],n,ch)!=)return ;
     ch[n]=ch[];
     th[m]=th[];
     for(int i=; i<n; i++)
         for(int j=; j<m; j++)
             if(SegmentProperIntersection(ch[i],ch[i+],th[j],th[j+]))return ;
     return ;
 }
 double rotating_calipers(Point *ch,int n)
 {
     int q=;
     double ans=;
     ch[n]=ch[];
     for ( int i = ; i < n; ++i )
      {
          while ( cross( ch[i + ] - ch[i], ch[q + ] - ch[i] ) > cross( ch[i + ] - ch[i], ch[q] - ch[i] ) )
             q = ( q +  ) % n;
          ans = max( ans, max( dot( ch[i]- ch[q],ch[i]-ch[q] ),dot( ch[i + ]-ch[q + ],ch[i + ]-ch[q + ] ) ));
     }
     return ans;
 }
 Point p[],ch[];
 int main()
 {
     int n,m;
     double x,y,w;
     int t;
     scanf("%d",&t);
     while(t--)
     {
         scanf("%d",&n);
         int cnt=;
         for(int i=; i<n; i++)
         {
             scanf("%lf%lf%lf",&x,&y,&w);
             p[cnt].x=x,p[cnt++].y=y;
             p[cnt].x=x+w,p[cnt++].y=y;
             p[cnt].x=x,p[cnt++].y=y+w;
             p[cnt].x=x+w,p[cnt++].y=y+w;
         }
         int n1=convexhull(p,cnt,ch);
         printf("%.0lf\n",rotating_calipers(ch,n1));
     }
     return ;
 }