bzoj1185 最小矩形覆盖 旋转卡壳

       先求出凸包，显然至少需要有一条边在凸包上（我只会感性理解不会证明QAQ），那么旋转卡壳一下就好了。

AC代码如下：

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<algorithm>
#define eps 1e-12
#define N 50005
using namespace std;

struct point{ double x,y; }a[N],q[N],t[4]; int n;
point operator +(point u,point v){ u.x+=v.x; u.y+=v.y; return u; }
point operator -(point u,point v){ u.x-=v.x; u.y-=v.y; return u; }
point operator *(point u,double v){ u.x*=v; u.y*=v; return u; }
double crs(point u,point v){ return u.x*v.y-u.y*v.x; }
double dot(point u,point v){ return u.x*v.x+u.y*v.y; }
double dist(point u,point v){ return sqrt(dot(v-u,v-u)); }
bool cmp(point u,point v){
	double t=crs(u-a[1],v-a[1]);
	return (t>eps || t>-eps && t<eps && dist(a[1],u)<dist(a[1],v));
}
int main(){
	scanf("%d",&n); int i,k;
	for (i=1; i<=n; i++) scanf("%lf%lf",&a[i].x,&a[i].y);
	k=1;
	for (i=2; i<=n; i++)
		if (a[i].y<a[k].y || fabs(a[i].y-a[k].y)<eps && a[i].x<a[k].x) k=i;
	swap(a[1],a[k]); sort(a+2,a+n+1,cmp);
	int tp=1; q[1]=a[1];
	for (i=2; i<=n; i++){
		while (tp>1 && crs(q[tp]-q[tp-1],a[i]-q[tp-1])<eps) tp--;
		q[++tp]=a[i];
	}
	q[tp+1]=q[1];
	int l=1,r=1; k=1; double ans=1e100;
	for (i=1; i<=tp; i++){
		double len=dist(q[i],q[i+1]);
		while (crs(q[i+1]-q[i],q[k]-q[i])<crs(q[i+1]-q[i],q[k+1]-q[i])+eps) k=k%tp+1;
		while (dot(q[i+1]-q[i],q[r]-q[i])<dot(q[i+1]-q[i],q[r+1]-q[i])+eps) r=r%tp+1;
		if (i==1) l=r;
		while (dot(q[i+1]-q[i],q[l]-q[i])+eps>dot(q[i+1]-q[i],q[l+1]-q[i])) l=l%tp+1;
		double ls=dot(q[i+1]-q[i],q[l]-q[i])/len,rs=dot(q[i+1]-q[i],q[r]-q[i])/len;
		double ht=crs(q[i+1]-q[i],q[k]-q[i])/len,tmp=ht*(rs-ls);
		if (tmp<0) tmp=-tmp;
		if (tmp<ans){
			ans=tmp; t[0]=q[i]+(q[i+1]-q[i])*(rs/len);
			t[1]=t[0]+(q[r]-t[0])*(ht/dist(q[r],t[0]));
			t[2]=t[1]+(q[k]-t[1])*((rs-ls)/dist(q[k],t[1]));
			t[3]=t[0]+t[2]-t[1];
		}
	}
	printf("%.5f\n",ans); k=0;
	for (i=1; i<4; i++)
		if (t[i].y<t[k].y || fabs(t[i].y-t[k].y)<eps && a[i].x<a[k].x) k=i;
	for (i=0; i<4; i++,k=(k+1)%4) printf("%.5f %.5f\n",t[k].x,t[k].y);
	return 0;
}

by lych

2016.4.14