poj2187 Beauty Contest

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旋转卡壳

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旋转卡壳 刚开始要用第二个点卡第一条边

Code

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//Code by Lucida
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#define red(x) scanf("%d",&x)
#define fred(x) scanf("%lf",&x)
template <class T> inline bool chkmx(T &a,const T &b){return a<b?a=b,1:0;}
template <class T> inline bool chkmn(T &a,const T &b){return a>b?a=b,1:0;}
using std::sort;
using std::swap;
using std::unique;
const int MAXN=50000+1;
typedef double ld;
const ld eps=1e-7;
int fcmp(ld x)
{
	if(-eps<x && x<eps) return 0;
	return x<0?-1:1;
}
template <class T> T sqr(T a){return a*a;}
template <class T> T abs(T a){return a>0?a:-a;}
struct vec
{
	ld x,y;
	vec(ld _x=0,ld _y=0):x(_x),y(_y){}
	bool operator <(const vec &a) const
	{
		if(x!=a.x) return x<a.x;
		return y<a.y;
	}
	void operator +=(vec a){x+=a.x,y+=a.y;}
	void operator -=(vec a){x-=a.x,y-=a.y;}
	bool operator ==(const vec &a) const{return x==a.x && y==a.y;}
	ld norm(){return sqrt(x*x+y*y);}
};
typedef vec point;
vec operator +(vec a,vec b){return vec(a.x+b.x,a.y+b.y);}
vec operator -(vec a,vec b){return vec(a.x-b.x,a.y-b.y);}
vec operator *(vec a,ld t){return vec(a.x*t,a.y*t);}
vec operator /(vec a,ld t){return vec(a.x/t,a.y/t);}
ld inner(vec a,vec b){return a.x*b.x+a.y*b.y;}
ld outer(vec a,vec b){return a.x*b.y-a.y*b.x;}
struct line
{
	point a;vec v;
	line(point _a,vec _v):a(_a),v(_v){}
};
bool cmp(vec a,vec b)
{
	if(fcmp(outer(a,b))!=0)
		return fcmp(outer(a,b))>0;
	return inner(a,a)<inner(b,b);
}
void Graham(point *p,int n,point *stack,int &top)
{
	top=0;
	int mi=1;
	for(int i=1;i<=n;i++) if(p[i]<p[mi]) mi=i;
	swap(p[1],p[mi]),p[0]=p[1];
	for(int i=1;i<=n;i++) p[i]-=p[0];
	sort(p+2,p+1+n,cmp);
	n=unique(p+1,p+1+n)-p-1;
	p[n+1]=p[1];
	for(int i=1;i<=n+1;i++) p[i]+=p[0];
	for(int i=1;i<=n+1;i++)
	{
		while(top>=2 && fcmp(outer(p[i]-stack[top],stack[top]-stack[top-1]))>=0) top--;
		stack[++top]=p[i];
	}
	top--;
}
ld dist(point a,point b){return sqrt(sqr(a.x-b.x)+sqr(a.y-b.y));}
ld dist(point a,line l){return abs(outer(a-l.a,l.v))/l.v.norm();}
ld dist2(point a,point b){return sqr(a.x-b.x)+sqr(a.y-b.y);}
int main()
{
	freopen("input","r",stdin);
	static point p[MAXN],hull[MAXN];
	int n,nb;red(n);
	for(int i=1;i<=n;i++) fred(p[i].x),fred(p[i].y);
	Graham(p,nb=n,hull,n);
	ld ANS=0;
	if(n==1)
	{
		n=nb;
		sort(p+1,p+1+n);
		ANS=dist2(p[1],p[n]);
	}
	else
	{
		#define suc(i) (i+1>n?1:i+1)
		for(int i=1,cur=2;i<=n;i++)
		{
			line now(hull[i],hull[suc(i)]-hull[i]);
			while(fcmp(dist(hull[cur],now)-dist(hull[suc(cur)],now))<0) 
				cur=suc(cur);
			chkmx(ANS,dist2(hull[i],hull[cur]));
			chkmx(ANS,dist2(hull[suc(i)],hull[cur]));
		}
		#undef suc
	}
	printf("%.0f\n",ANS);
	return 0;
}