求平面最远点对
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
using namespace std;
const int N=50005;
int n,w=1,top;
double ans;
struct dian
{
double x,y;
dian(double X=0,double Y=0)
{
x=X,y=Y;
}
dian operator + (const dian &a) const
{
return dian(x+a.x,y+a.y);
}
dian operator - (const dian &a) const
{
return dian(x-a.x,y-a.y);
}
}p[N],s[N];
int read()
{
int r=0,f=1;
char p=getchar();
while(p>‘9‘||p<‘0‘)
{
if(p==‘-‘)
f=-1;
p=getchar();
}
while(p>=‘0‘&&p<=‘9‘)
{
r=r*10+p-48;
p=getchar();
}
return r*f;
}
double dis(dian a,dian b)
{
return (a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y);
}
double cj(dian a,dian b)
{
return a.x*b.y-a.y*b.x;
}
bool cmp(const dian &a,const dian &b)
{
int ar=cj(a-p[1],b-p[1]);
return ar>0||(ar==0&&a.x<b.x);
}
double mj(dian a,dian b,dian c)
{
return cj(b-a,c-a);
}
int main()
{
n=read();
for(int i=1;i<=n;i++)
{
int x=read(),y=read();
p[i]=dian(x,y);
if(p[i].x<p[w].x||(p[i].x==p[w].x&&p[i].y<p[w].y))
w=i;
}
swap(p[w],p[1]);
sort(p+2,p+1+n,cmp);
s[++top]=p[1],s[++top]=p[2];
for(int i=3;i<=n;i++)
{
while(top>1&&cj(s[top]-p[i],s[top-1]-p[i])>=0)
top--;
s[++top]=p[i];
}
w=2;s[top+1]=s[1];
for(int i=1;i<=top;i++)
{
while(cj((s[i]-s[w]),(s[i+1]-s[w]))<cj((s[i]-s[w+1]),(s[i+1]-s[w+1])))
w=(w+1)>top?1:w+1;
ans=max(ans,dis(s[w],s[i]));
}
printf("%.0f\n",ans);
return 0;
}