BZOJ 1185([HNOI2007]最小矩形覆盖-旋转卡壳+点集几何意义)

1185: [HNOI2007]最小矩形覆盖

Time Limit: 10 Sec   Memory Limit: 162 MBSec   Special Judge
Submit: 258   Solved: 137

Description

 

l要事先改成r，注意把向量的2点设成同一点会出现奇妙的事情

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<functional>
#include<cmath>
using namespace std;
#define MAXN (50000+10)
#define INF (1000000000)
#define eps 1e-6
struct P
{
	double x,y;
	P(){}
	P(double _x,double _y):x(_x),y(_y){}
	friend bool operator<(P a,P b){return (fabs(a.y-b.y)<eps)?a.x<b.x:a.y<b.y;	}
	friend bool operator==(P a,P b){return fabs(a.x-b.x)<eps&&fabs(a.y-b.y)<eps;}
	friend bool operator!=(P a,P b){return !(a==b);}
	
}a[MAXN],s[MAXN],ansp[5];
int size=0;
double ans=INF;
double dis2(P a,P b){return (a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y);}
struct V
{
	double x,y;
	V(){}
	V(double _x,double _y):x(_x),y(_y){}
	V(P a,P b):x(b.x-a.x),y(b.y-a.y){}
	friend double operator*(V a,V b){return	a.x*b.y-a.y*b.x;}
	friend V operator*(double a,V b){return V(a*b.x,a*b.y);}
	friend double operator/(V a,V b){return	a.x*b.x+a.y*b.y;}
	friend P operator+(P a,V b){return P(a.x+b.x,a.y+b.y);}
	friend P operator-(P a,V b){return P(a.x-b.x,a.y-b.y);}
	friend V operator~(V a){return V(a.y,-a.x);}
	double dis2(){return x*x+y*y;	}	
}c[MAXN];
int cmp(P A,P B)
{
	double tmp=V(a[1],A)*V(a[1],B);
	if (tmp>0) return 1;
	else if (fabs(tmp)<eps) return (-dis2(A,a[1])-dis2(B,a[1])>0);
	return 0;
}
int n;

int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%lf%lf",&a[i].x,&a[i].y);
	for (int i=2;i<=n;i++) if (a[i]<a[1]) swap(a[1],a[i]);
	sort(a+2,a+1+n,cmp);
	s[1]=a[1];size=1;
	for (int i=2;i<=n;)
		if (size<2||V(s[size-1],s[size])*V(s[size],a[i])>eps) s[++size]=a[i++];
		else size--;
	s[0]=s[size];
	
	int l=1,r=1,t=1;
	for (int i=0;i<size;i++)
	{
		while (V(s[i],s[i+1])*V(s[i],s[t+1])-V(s[i],s[i+1])*V(s[i],s[t])>-eps) t=(t+1)%size; 
		while (V(s[i],s[i+1])/V(s[i],s[r+1])-V(s[i],s[i+1])/V(s[i],s[r])>-eps) r=(r+1)%size; 
		if (i==0) l=r;
		while (V(s[i],s[i+1])/V(s[i],s[l+1])-V(s[i],s[i+1])/V(s[i],s[l])<eps) l=(l+1)%size; 
		double Dis2=dis2(s[i],s[i+1]),wlxdis=V(s[i],s[i+1])/V(s[i],s[l]),wrxdis=V(s[i],s[i+1])/V(s[i],s[r]),hxdis=V(s[i],s[i+1])*V(s[i],s[t]);
		double tmp=hxdis*(wrxdis-wlxdis)/Dis2;		
		if (tmp<0) tmp=-tmp;
		if (ans>tmp)
		{
			ans=tmp;
			ansp[0]=s[i]-(wlxdis/Dis2)*V(s[i+1],s[i]);
			ansp[1]=s[i]+(wrxdis/Dis2)*V(s[i],s[i+1]);
			ansp[2]=ansp[1]+(hxdis/Dis2)*(~V(s[i+1],s[i]));			
			ansp[3]=ansp[0]+(hxdis/Dis2)*(~V(s[i+1],s[i]));			
		}
	}
	int p=0;
	for (int i=1;i<4;i++) if (ansp[i]<ansp[p]) p=i;//p=0;
	printf("%.5lf\n",ans);	
	for (int i=0;i<4;i++) 
		printf("%.5lf %.5lf\n",ansp[(p+i)%4].x,ansp[(p+i)%4].y);
	return 0;
}