旋转卡壳求最远点对；
#include<iostream>
#include<cmath>
using namespace std;
int n,k;
double dt;
typedef struct point
{
double x,y;
point(double xx=0,double yy=0):x(xx),y(yy){}
}vector;
point p[50010],q[50010];
struct line
{
vector v;
}li,lj;
void sort1(point *a,int x,int y,point *t)
{
int m,u,v,i;
if(y-x>1)
{
m=x+(y-x)/2;
u=x,v=m,i=x;
sort1(a,x,m,t);
sort1(a,m,y,t);
while(u<m || v<y)
{
if(v>=y || (u<m && (a[u].x<a[v].x || (a[u].x==a[v].x && a[u].y<=a[v].y)))) t[i++]=a[u++];
else t[i++]=a[v++];
}
for(i=x;i<y;i++) a[i]=t[i];
}
}
vector operator - (point a,point b) {return vector(a.x-b.x,a.y-b.y);}
double cross(vector a,vector b)
{
return a.x*b.y-a.y*b.x;
}
int convex(point *a,point *t)
{
int m=0,i;
for(i=0;i<n;i++)
{
while(m>1 && cross(t[m-1]-t[m-2],a[i]-t[m-2])<=0) m--;
t[m++]=a[i];
}
k=m;
for(i=n-1;i>=0;i--)
{
while(m>k && cross(t[m-1]-t[m-2],a[i]-t[m-2])<=0) m--;
t[m++]=a[i];
}
if(n>1) m--;
return m;
}
vector rotate(vector a,double rad)
{
return vector(a.x*cos(rad)-a.y*sin(rad),a.x*sin(rad)+a.y*cos(rad));
}
double dot(vector a,vector b)
{
return a.x*b.x+a.y*b.y;
}
double length(vector a)
{
return sqrt(dot(a,a));
}
double angle(vector a,vector b)
{
return acos(dot(a,b)/length(a)/length(b));
}
void f(int m,double &dt)
{
int i=0,j=k-1;
double th1,th2,d;
while(i!=k-1 || j!=m)
{
th1=angle(li.v,q[i+1]-q[i]);
th2=angle(lj.v,q[(j+1)%m]-q[j]);
if(th1<th2)
{
li.v=rotate(li.v,th1);
lj.v=rotate(lj.v,th1);
i++;
d=dot(q[j]-q[i],q[j]-q[i]);
if(d>dt) dt=d;
}
else if(th1>th2)
{
li.v=rotate(li.v,th2);
lj.v=rotate(lj.v,th2);
j++;
d=dot(q[j%m]-q[i],q[j%m]-q[i]);
if(d>dt) dt=d;
}
else
{
li.v=rotate(li.v,th1);
lj.v=rotate(lj.v,th2);
d=dot(q[j]-q[i+1],q[j]-q[i+1]);
if(d>dt) dt=d;
d=dot(q[(j+1)%m]-q[i],q[(j+1)%m]-q[i]);
if(d>dt) dt=d;
i++;j++;
d=dot(q[j%m]-q[i],q[j%m]-q[i]);
if(d>dt) dt=d;
}
}
}
int main()
{
int i,m;
cin>>n;
for(i=0;i<n;i++)
cin>>p[i].x>>p[i].y;
sort1(p,0,n,q);
m=convex(p,q);
li.v=vector(0,-1);
lj.v=vector(0,1);
dt=dot(q[k-1]-q[0],q[k-1]-q[0]);
f(m,dt);
cout<<(int)dt<<endl;
return 0;
}