uva 1453

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(-1);

int dcmp(double x)
{
    return fabs(x) < eps ? 0 : (x > 0 ? 1 : -1);
}

struct Point
{
    double x;
    double y;

    Point(double x = 0, double y = 0):x(x), y(y) {}

    bool operator < (const Point& e) const
    {
        return dcmp(x - e.x) < 0 || (dcmp(x - e.x) == 0 && dcmp(y - e.y) < 0);
    }

    bool operator == (const Point& e) const
    {
        return dcmp(x - e.x) == 0 && dcmp(y - e.y) == 0;
    }
};

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=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;
}
bool onsegment(Point p,Point a,Point b)
{
    return dcmp(cross(a-p,b-p))==0&&dcmp(dot(a-p,b-p))<0;
}


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) < 0 && dcmp(c3) * dcmp(c4) < 0;
}

int ispointinpolygon(Point p,int n,Point *poly)
{
    int wn=0;
    for(int i=0; i<n; i++)
    {
        if(onsegment(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;
}

bool Check(int n,Point *ch,int m,Point *th)
{
    for(int i=0; i<n; i++)
    {
        if(ispointinpolygon(ch[i],m,th)!=0)return 1;
    }
    for(int i=0; i<m; i++)
        if(ispointinpolygon(th[i],n,ch)!=0)return 1;
    ch[n]=ch[0];
    th[m]=th[0];
    for(int i=0; i<n; i++)
        for(int j=0; j<m; j++)
            if(SegmentProperIntersection(ch[i],ch[i+1],th[j],th[j+1]))return 1;
    return 0;
}
double rotating_calipers(Point *ch,int n)
{
    int q=1;
    double ans=0;
    ch[n]=ch[0];
    for ( int i = 0; i < n; ++i )
     {
         while ( cross( ch[i + 1] - ch[i], ch[q + 1] - ch[i] ) > cross( ch[i + 1] - ch[i], ch[q] - ch[i] ) )
            q = ( q + 1 ) % n;
         ans = max( ans, max( dot( ch[i]- ch[q],ch[i]-ch[q] ),dot( ch[i + 1]-ch[q + 1],ch[i + 1]-ch[q + 1] ) ));
    }
    return ans;
}
Point p[400009],ch[400009];
int main()
{
    int n,m;
    double x,y,w;
    int t;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d",&n);
        int cnt=0;
        for(int i=0; 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
",rotating_calipers(ch,n1));
    }
    return 0;
}