BZOJ 1185 [HNOI2007]最小矩形覆盖

#include<cmath>
#include<cstdio>
#include<algorithm>
#define calc(a,b,c) cross(p[b]-p[a],p[c]-p[a])
#define N 50005
using namespace std;
struct point
{
double x, y;
point operator - (point a)
{
return (point){x-a.x,y-a.y};
}
point operator + (point a)
{
return (point){x+a.x,y+a.y};
}
point operator * (double a)
{
return (point){x*a,y*a};
}
point operator / (double a)
{
return (point){x/a,y/a};
}
}p
, print[4];
const double eps = 1e-8;
double ans=10000000000000000.0;
int n, con
, top;
bool cmp(point a, point b)
{
return a.x<b.x||(a.x==b.x && a.y<b.y);
}
double cross(point a, point b)
{
return a.x*b.y-a.y*b.x;
}
double dot(point a, point b)
{
return a.x*b.x+a.y*b.y;
}
void Convex()
{
sort(p+1,p+1+n,cmp);
top=0;
for(int i = 1; i <= n; i++)
{
while(top>1 && calc(con[top-2],i,con[top-1]) >= 0)top--;
con[top++]=i;
}
int temp=top;
for(int i = n-1; i >= 1; i--)
{
while(top>temp && calc(con[top-2],i,con[top-1]) >= 0)top--;
con[top++]=i;
}
con[top]=con[0];
top--;
}
double dis(point a, point b)
{
return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
void rotate()
{
int up=1, left=1, right=1;
for(int i = 0; i < top; i++)
{
while(calc(con[i],con[i+1],con[up])<calc(con[i],con[i+1],con[up+1]))up=(up+1)%top;
while(dot(p[con[i]]-p[con[left]],p[con[i+1]]-p[con[i]]) < 0 || dot(p[con[i]]-p[con[left]],p[con[i+1]]-p[con[i]])<dot(p[con[i]]-p[con[left+1]],p[con[i+1]]-p[con[i]]))left=(left+1)%top;
while(dot(p[con[i+1]]-p[con[right]],p[con[i]]-p[con[i+1]])<dot(p[con[i+1]]-p[con[right+1]],p[con[i]]-p[con[i+1]]))right=(right+1)%top;
double la=dis(p[con[i]],p[con[i+1]]);
double RRR=dot((p[con[right]]-p[con[i]]),(p[con[i+1]]-p[con[i]]))/la;
double LLL=dot((p[con[left]]-p[con[i]]),(p[con[i+1]]-p[con[i]]))/la;
if(LLL<0)LLL=-LLL;
double length=LLL+RRR;
double height=cross((p[con[i+1]]-p[con[i]]),(p[con[up]]-p[con[i]]))/la;
if(height*length<ans)
{
ans=height*length;
print[0]=p[con[i]]+((p[con[i+1]]-p[con[i]])*(RRR/la));
print[1]=print[0]+(p[con[right]]-print[0])*(height/dis(p[con[right]],print[0]));
print[2]=print[1]+(p[con[up]]-print[1])*(length/dis(p[con[up]],print[1]));
print[3]=print[2]+(p[con[left]]-print[2])*(height/dis(p[con[left]],print[2]));
}
}
}
int main()
{
scanf("%d",&n);
for(int i = 1; i <= n; i++)
scanf("%lf%lf",&p[i].x,&p[i].y);
Convex();
rotate();
printf("%.5lf\n",ans);
int pre=0;
for(int i=1;i<=3;i++)
{
if(print[i].y<print[pre].y)pre=i;
else if(fabs(print[i].y-print[pre].y)<eps&&print[i].x<print[pre].x)pre=i;
}
for(int i=0;i<4;i++)
printf("%.5lf %.5lf\n",print[(pre+i)%4].x,print[(pre+i)%4].y);
}