Luogu 1452 Beauty Contest

Luogu 1452 Beauty Contest

• 求平面最远点对,先求出凸包,再找凸包的直径.
• 使用旋转卡壳,直径一定出现在对踵点对间.比较不同点到同一直线距离可以用叉积算三角形面积来比较.
• 实现时注意关于栈的 \(top\) 的细节.

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define mp make_pair
#define pii pair<int,int>
inline int read()
{
	int x=0;
	bool pos=1;
	char ch=getchar();
	for(;!isdigit(ch);ch=getchar())
		if(ch=='-')
			pos=0;
	for(;isdigit(ch);ch=getchar())
		x=x*10+ch-'0';
	return pos?x:-x;
}
const int MAXN=5e4+10;
const double eps=1e-9;
struct v2{
	ll x,y;
	v2(ll x=0,ll y=0):x(x),y(y) {}
	v2 operator + (const v2 &rhs) const
		{
			return v2(x+rhs.x,y+rhs.y);
		}
	v2 operator / (const double &rhs) const
		{
			return v2(x/rhs,y/rhs);
		}
	v2 operator - (const v2 &rhs) const
		{
			return v2(x-rhs.x,y-rhs.y);
		}
	ll operator * (const v2 &rhs) const
		{
			return x*rhs.y-y*rhs.x;
		}
	ll modulus2()
		{
			return x*x+y*y;
		}
	bool operator < (const v2 &rhs) const
		{
			return x==rhs.x?y<rhs.y:x<rhs.x;
		}
};
v2 origin;
bool cmp(const v2 &a,const v2 &b)
{
	double A=atan2(a.y-origin.y,a.x-origin.x),B=atan2(b.y-origin.y,b.x-origin.x);
	return A==B?a.x<b.x:A<B;
}
v2 stk[MAXN];
int tp;
void ConvexHull(v2 *p,int n)
{
	for(int i=2;i<=n;++i)
		if(p[i]<p[1])
			swap(p[i],p[1]);//p1为左下角的点
	origin=p[1];
	sort(p+2,p+n+1,cmp);
	stk[tp]=p[1];//从0开始存
	for(int i=2;i<=n;++i)
		{
			while(tp>=2 && (stk[tp]-stk[tp-1])*(p[i]-stk[tp])<=0)
				--tp;
			stk[++tp]=p[i];
		}
}
ll RotatingCaliper()
{
	if(tp==1)
		return (stk[0]-stk[1]).modulus2();
	stk[++tp]=stk[0];
	ll ans=0;
	int j=2;
	for(int i=0;i<tp;++i)
		{
			while(abs((stk[i]-stk[j])*(stk[i+1]-stk[j]))<abs((stk[i]-stk[j+1])*(stk[i+1]-stk[j+1])))
				j=(j+1)%tp;
			ans=max(ans,(stk[i]-stk[j]).modulus2());
			ans=max(ans,(stk[i+1]-stk[j]).modulus2());
		}
	return ans;
}
int n;
v2 p[MAXN];
int main()
{
//	freopen("testdata.in","r",stdin);
	n=read();
	for(int i=1;i<=n;++i)
		scanf("%lld%lld",&p[i].x,&p[i].y);
	ConvexHull(p,n);
	ll ans=RotatingCaliper();
	printf("%lld\n",ans);
	return 0;
}
//785190749