UVALive 4728 Squares （平面最远点对）

//n个平行于坐标轴的正方形，求出最远点对的平方
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
#define eps 1e-8
#define sgn(x) (x<-eps? -1 : x<eps? 0:1)
#define zero(x) (((x)>0?(x) : -(x))<eps)
const int Max=5e5+7;
struct Point
{
    double x,y;
    Point(double x=0,double y=0):x(x),y(y) {}
    inline Point operator-(const Point& a)const
    {
        return Point(x-a.x,y-a.y);
    }
    inline bool operator<(const Point& a)const
    {
        return sgn(x-a.x)<0||zero(x-a.x)&&sgn(y-a.y)<0;
    }
    inline bool operator!=(const Point& a)const
    {
        return !(zero(x-a.x)&&zero(y-a.y));
    }
};
typedef Point Vector;
double Cross(Vector A,Vector B)
{
    return A.x*B.y-A.y*B.x;
}
double Dis(Point A,Point B)
{
    return sqrt((A.x-B.x)*(A.x-B.x)+(A.y-B.y)*(A.y-B.y));
}
int ConvexHull(Point* p,int n,Point* convex)
{
    sort(p,p+n);
    int m=0,k=1;
    for(int i=0; i<n; ++i)
    {
        if(p[k-1]!=p[i])
        {
            p[k++]=p[i];
        }
    }
    n=k;
    for(int i=0; i<n; ++i)
    {
        while(m>1&&Cross(convex[m-1]-convex[m-2],p[i]-convex[m-2])<0)
            m--;
        convex[m++]=p[i];
    }
    k=m;
    for(int i=n-2; i>=0; --i)
    {
        while(m>k&&Cross(convex[m-1]-convex[m-2],p[i]-convex[m-2])<0)
            m--;
        convex[m++]=p[i];
    }
    if(n>1)
        m--;
    return m;
}
double RotateStuck(Point* convex,int n)//旋转卡壳(前提:一个凸包),注意凸包去重点不要三点共线
{
    double ans=0;
    int q=1;
    convex[n]=convex[0];//避免取模
    for(int p=0; p<n; ++p)//枚举一条边
    {
        while(Cross(convex[p+1]-convex[p],convex[q+1]-convex[p])>//这儿用的是三角形面积的比较
              Cross(convex[p+1]-convex[p],convex[q]-convex[p]))//找到对应p这条个点的最远点（由于单峰函数，所以结果类似双指针）
            q=(q+1)%n;
        ans=max(ans,max(Dis(convex[p],convex[q]),Dis(convex[p+1],convex[q+1])));
    }
    return ans;
}
Point poi[Max],convex[Max];
double Solve(int n)//求出最远点对的平方
{
    double fpp=0;
    int m=ConvexHull(poi,n,convex);//先找凸包
    fpp=RotateStuck(convex,m);//旋转卡壳求对踵点（可以求出凸包上的最远点对）
    return fpp*fpp;
}
int main()
{
    int t,n;
    double w,x,y;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d",&n);
        for(int i=0; i<n; ++i)
        {
            scanf("%lf%lf%lf",&x,&y,&w);
            poi[4*i]=Point(x,y);
            poi[4*i+1]=Point(x+w,y);
            poi[4*i+2]=Point(x,y+w);
            poi[4*i+3]=Point(x+w,y+w);
        }
        printf("%.0f\n",Solve(4*n));
    }
    return 0;
}