Description

Thousands of thousands years ago there was a small kingdom located in the middle of the Pacific Ocean. The territory of the kingdom consists two separated islands. Due to the impact of the ocean current, the shapes of both the islands became convex polygons. The king of the kingdom wanted to establish a bridge to connect the two islands. To minimize the cost, the king asked you, the bishop, to find the minimal distance between the boundaries of the two islands.

Input

Output

Sample Input

4 4
0.00000 0.00000
0.00000 1.00000
1.00000 1.00000
1.00000 0.00000
2.00000 0.00000
2.00000 1.00000
3.00000 1.00000
3.00000 0.00000
0 0

Sample Output

1.00000

经典题目

代码：

/* ***********************************************
Author :_rabbit
Created Time :2014/5/10 16:26:51
File Name :20.cpp
************************************************ */
#pragma comment(linker, "/STACK:102400000,102400000")
#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <sstream>
#include <stdlib.h>
#include <string.h>
#include <limits.h>
#include <string>
#include <time.h>
#include <math.h>
#include <queue>
#include <stack>
#include <set>
#include <map>
using namespace std;
#define INF 0x3f3f3f3f
#define eps 1e-5
#define pi acos(-1.0)
typedef long long ll;
int dcmp(double x){
	if(fabs(x)<eps)return 0;
	return x>0?1:-1;
}
struct Point{
	double x,y;
	Point(double _x=0,double _y=0){
		x=_x;y=_y;
	}
};
Point operator + (const Point &a,const Point &b){  
    return Point(a.x+b.x,a.y+b.y);  
}  
Point operator - (const Point &a,const Point &b){  
    return Point(a.x-b.x,a.y-b.y);  
}  
Point operator * (const Point &a,const double &p){  
    return Point(a.x*p,a.y*p);  
}  
Point operator / (const Point &a,const double &p){  
    return Point(a.x/p,a.y/p);  
}  
bool operator < (const Point &a,const Point &b){  
    return a.x<b.x||(a.x==b.x&&a.y<b.y);  
}  
bool operator == (const Point &a,const Point &b){  
    return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;  
}  
double Dot(Point  a,Point b){  
    return a.x*b.x+a.y*b.y;  
}  
double Length(Point a){  
    return sqrt(Dot(a,a));  
}  
double Angle(Point a,Point b){  
    return acos(Dot(a,b)/Length(a)/Length(b));  
}  
double angle(Point a){  
    return atan2(a.y,a.x);  
}  
double Cross(Point a,Point b){  
    return a.x*b.y-a.y*b.x;  
}  
Point vecunit(Point a){  
    return a/Length(a);  
}  
Point Normal(Point a){  
    return Point(-a.y,a.x)/Length(a);  
}  
Point Rotate(Point a,double rad){  
    return Point(a.x*cos(rad)-a.y*sin(rad),a.x*sin(rad)+a.y*cos(rad));  
}  
double Area2(Point a,Point b,Point c){  
    return Length(Cross(b-a,c-a));  
}  
double DistanceToSegment(Point p, Point a, Point b)  {  
    if(a == b) return Length(p-a);  
    Point v1 = b-a, v2 = p-a, v3 = p-b;  
    if(dcmp(Dot(v1, v2)) < 0) return Length(v2);  
    else if(dcmp(Dot(v1, v3)) > 0) return Length(v3);  
    else return fabs(Cross(v1, v2)) / Length(v1);  
}  
double dis_pair_seg(Point p1, Point p2, Point p3, Point p4)  {  
    return min(min(DistanceToSegment(p1, p3, p4), DistanceToSegment(p2, p3, p4)),  
     min(DistanceToSegment(p3, p1, p2), DistanceToSegment(p4, p1, p2)));  
}  
vector<Point> CH(vector<Point> p){
	sort(p.begin(),p.end());
	p.erase(unique(p.begin(),p.end()),p.end());
	int n=p.size();
	int m=0;
	vector<Point> ch(n+1);
	for(int i=0;i<n;i++){
		while(m>1&&Cross(ch[m-1]-ch[m-2],p[i]-ch[m-1])<=0)m--;
		ch[m++]=p[i];
	}
	int k=m;
	for(int i=n-2;i>=0;i--){
		while(m>k&&Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0)m--;
		ch[m++]=p[i];
	}
	if(n>1)m--;
	ch.resize(m);
	return ch;
}
double RC_Distance(vector<Point> ch1,vector<Point> ch2)  
{  
    int q=0, p=0,n=ch1.size(),m=ch2.size();
    for(int i=0;i<n;i++) if(ch1[i].y-ch1[p].y < -eps) p=i;  
    for(int i=0;i<m;i++)if(ch2[i].y-ch2[q].y > eps) q=i;  
    ch1.push_back(ch1[0]);ch2.push_back(ch2[0]); 
  
    double tmp, ans=1e100;  
    for(int i=0;i<n;i++) 
    {  
        while((tmp = Cross(ch1[p+1]-ch1[p], ch2[q+1]-ch1[p]) - Cross(ch1[p+1]-ch1[p], ch2[q]- ch1[p])) > eps)  
            q=(q+1)%m;  
        if(tmp < -eps) ans = min(ans,DistanceToSegment(ch2[q],ch1[p],ch1[p+1]));  
        else ans = min(ans,dis_pair_seg(ch1[p],ch1[p+1],ch2[q],ch2[q+1]));  
        p=(p+1)%n;  
    }  
    return ans;  
}  

int main()
{
     //freopen("data.in","r",stdin);
     //freopen("data.out","w",stdout);
     int n,m;
	 while(cin>>n>>m){
		 if(n==0&&m==0)break;
		 vector<Point> ch1,ch2;
		 Point p;
		 while(n--)scanf("%lf%lf",&p.x,&p.y),ch1.push_back(p);
		 while(m--)scanf("%lf%lf",&p.x,&p.y),ch2.push_back(p);
		 ch1=CH(ch1);ch2=CH(ch2);
		 printf("%.5lf\n",RC_Distance(ch1,ch2));
	 }
     return 0;
}