BZOJ 1185 最小矩形覆盖

Description

Input

Output

Sample Input

Sample Output

HINT

#include<cstdio>
#include<cmath>
#include<ctime>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<queue>
#include<set>
#define eps 1e-8
#define inf 1000000000
using namespace std;
double ans=1e60;
int n,top;
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);
}
friend P operator+(P a,P b){
return P(a.x+b.x,a.y+b.y);
}
friend P operator-(P a,P b){
return P(a.x-b.x,a.y-b.y);
}
friend double operator*(P a,P b){
return a.x*b.y-a.y*b.x;
}
friend P operator*(P a,double b){
return P(a.x*b,a.y*b);
}
friend double operator/(P a,P b){
return a.x*b.x+a.y*b.y;
}
friend double dis(P a){
return sqrt(a.x*a.x+a.y*a.y);
}
}p[50005],q[50005],t[5];
bool cmp(P a,P b)
{
double t=(a-p[1])*(b-p[1]);
if(fabs(t)<eps)return dis(p[1]-a)-dis(p[1]-b)<0;
return t>0;
}
void graham()
{
for(int i=2;i<=n;i++)
if(p[i]<p[1])
swap(p[i],p[1]);
sort(p+2,p+n+1,cmp);
q[++top]=p[1];
for(int i=2;i<=n;i++)
{
while(top>1&&(q[top]-q[top-1])*(p[i]-q[top])<eps)top--;
q[++top]=p[i];
}
q[0]=q[top];
}
void RC()
{
int l=1,r=1,p=1;
double L,R,D,H;
for(int i=0;i<top;i++)
{
D=dis(q[i]-q[i+1]);
while((q[i+1]-q[i])*(q[p+1]-q[i])-(q[i+1]-q[i])*(q[p]-q[i])>-eps)p=(p+1)%top;
while((q[i+1]-q[i])/(q[r+1]-q[i])-(q[i+1]-q[i])/(q[r]-q[i])>-eps)r=(r+1)%top;
if(i==0)l=r;
while((q[i+1]-q[i])/(q[l+1]-q[i])-(q[i+1]-q[i])/(q[l]-q[i])<eps)l=(l+1)%top;
L=(q[i+1]-q[i])/(q[l]-q[i])/D,R=(q[i+1]-q[i])/(q[r]-q[i])/D;
H=(q[i+1]-q[i])*(q[p]-q[i])/D;
if(H<0)H=-H;
double tmp=(R-L)*H;
if(tmp<ans)
{
ans=tmp;
t[0]=q[i]+(q[i+1]-q[i])*(R/D);
t[1]=t[0]+(q[r]-t[0])*(H/dis(t[0]-q[r]));
t[2]=t[1]-(t[0]-q[i])*((R-L)/dis(q[i]-t[0]));
t[3]=t[2]-(t[1]-t[0]);
}
}
}
int main()
{
freopen("1185.in","r",stdin);
freopen("1185.out","w",stdout);
scanf("%d",&n);
for(int i=1;i<=n;i++)
scanf("%lf%lf",&p[i].x,&p[i].y);
graham();
RC();
printf("%.5lf\n",ans);
int fir=0;
for(int i=1;i<=3;i++)
if(t[i]<t[fir])
fir=i;
for(int i=0;i<=3;i++)
printf("%.5lf %.5lf\n",t[(i+fir)%4].x,t[(i+fir)%4].y);
return 0;
}