275 lines
7.4 KiB
C++
275 lines
7.4 KiB
C++
#include<iostream>
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#include<cmath>
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#include<cstdio>
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#include<algorithm>
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using namespace std;
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const int maxn = 50100;
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const double eps = 1e-8;
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const double pi = acos( -1.0 );
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const double inf = 1e100;
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#define _sign(x) ((x)>eps?1:((x<-eps)?2:0))
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int D( double x ) { return ( x < -eps ? -1 : x > eps ); }
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struct point {
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double x, y;
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point( double _x = 0, double _y = 0 ) : x( _x ), y( _y ) { }
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void input( ) { scanf( "%lf%lf", &x, &y ); }
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bool operator < (const point a)const
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{
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if(y==a.y)
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return x<a.x;
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return y<a.y;
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}
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};
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typedef struct line
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{
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point a,b;
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}Line;
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point operator + ( const point & a, const point & b ) {
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return point( a.x + b.x, a.y + b.y );
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}
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point operator - ( const point & a, const point & b ) {
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return point( a.x - b.x, a.y - b.y );
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}
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point operator * ( const point & a, const double scale ) {
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return point( a.x * scale, a.y * scale );
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}
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point operator / ( const point & a, const double scale ) {
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return point( a.x / scale, a.y / scale );
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}
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double operator ^ ( const point & a, const point & b ) {
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return ( a.x * b.y - a.y * b.x );
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}
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double operator & ( const point & a, const point & b ) {
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return ( a.x * b.x + a.y * b.y );
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}
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double dis2( const point & a, const point & b ) {
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point p = a - b;
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return ( p.x * p.x + p.y * p.y );
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}
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double dis( const point & a, const point & b ) {
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return sqrt( dis2( a, b ) );
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}
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double displ( const point & a, const point & b, const point & p ) {
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if( D( b - a & p - a ) > 0 && D( a - b & p - b ) > 0 ) {
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return fabs( a - p ^ b - p ) / dis( a, b );
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}
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return min( dis( p, a ), dis( p, b ) );
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}
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double disll( const point & a, const point &b, const point &c, const point &d ) {
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return min( min( displ( a, b, c ), displ( a, b, d ) ),
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min( displ( c, d, a ), displ( c, d, b ) ) );
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}
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double det(double x1,double y1,double x2,double y2)
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{
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return x1*y2-x2*y1;
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}
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double cross (const point & a, const point &b, const point &c)
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{
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return det(b.x-a.x,b.y-a.y,c.x-a.x,c.y-a.y);
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}
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point a[maxn],np[maxn];
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struct poly {
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int n;
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point p[ maxn ];
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void in( ) {
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for( int i = 0; i < n; i++ ) {
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p[ i ].x=np[i].x;
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p[i].y=np[i].y;
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}
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if( get_area( ) < 0 ) {
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reverse( p, p + n );
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}
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}
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double get_area( ) const {
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double area = 0;
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for( int i = 0; i < n; i++ ) {
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area += ( p[ i ] ^ p[ ( i + 1 ) % n ] );
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}
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return area;
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}
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};
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void solve( const poly & g1, const poly & g2 ) {
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int f[ 2 ] = { 0, 0 };
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point p0, p1, p2, p3;
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for( int i = 0; i < g1.n; i++ ) {
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if( g1.p[ i ].y < g1.p[ f[ 0 ] ].y ) {
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f[ 0 ] = i;
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}
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}
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for( int i = 0; i < g2.n; i++ ) {
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if( g2.p[ i ].y > g2.p[ f[ 1 ] ].y ) {
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f[ 1 ] = i;
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}
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}
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int cnt = 0;
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double best = inf;
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while( cnt < g1.n ) {
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p0 = g1.p[ f[ 0 ] ], p1 = g1.p[ ( f[ 0 ] + 1 ) % g1.n ];
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p2 = g2.p[ f[ 1 ] ], p3 = g2.p[ ( f[ 1 ] + 1 ) % g2.n ];
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int tmp = D( p1 - p0 ^ p3 - p2 );
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if( tmp == 0 ) {
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cnt++;
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f[ 0 ] = ( f[ 0 ] + 1 ) % g1.n;
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f[ 1 ] = ( f[ 1 ] + 1 ) % g2.n;
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best = min( best, disll( p0, p1, p2, p3 ) );
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}
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else if( tmp < 0 ) {
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cnt++;
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f[ 0 ] = ( f[ 0 ] + 1 ) % g1.n;
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best = min( best, displ( p0, p1, p2 ) );
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}
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else {
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f[ 1 ] = ( f[ 1 ] + 1 ) % g2.n;
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best = min( best, displ( p2, p3, p0 ) );
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}
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}
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printf( "%.4lf\n", best );
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}
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int covex_hull(int n)
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{
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int sz;
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sort(a,a+n);
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np[0]=a[0];
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np[1]=a[1];
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sz=1;
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for(int i=2;i<n;i++)
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{
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while(sz>0 && cross(np[sz],a[i],np[sz-1])<=0){
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sz--; }
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np[++sz]=a[i];
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}
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int temp=sz;
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for(int i=n-2;i>=0;i--)
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{
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while(sz>temp && cross(np[sz],a[i],np[sz-1])<=0) {
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sz--; }
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np[++sz]=a[i];
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}
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return sz;
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}
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bool pequal(const point & a,const point & b)
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{
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if(D(a.x-b.x)==0&&D(a.y-b.y)==0)return 1;
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else return 0;
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}
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int intersect(Line a,Line b)
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{
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if(D(cross(a.a,b.a,a.b)*cross(a.a,a.b,b.b))>0)return 1;
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else return 0;
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}
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int dotsOnSeg(const point & p,Line l)
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{
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if(pequal(l.a,l.b)){if(pequal(p,l.a))return 1 ;else return 0;}
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if(D(cross(p,l.a,l.b))==0&&(l.a.x-p.x)*(l.b.x-p.x)<=eps&&(l.a.y-p.y)*(l.b.y-p.y)<=eps)return 1;
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else return 0;
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}
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int intersectSegToSeg(Line a,Line b)
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{
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if(dotsOnSeg(a.a,b)||dotsOnSeg(a.b,b)||dotsOnSeg(b.a,a)||dotsOnSeg(b.b,a))return 1;
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if(intersect(a,b)&&intersect(b,a))return 1;
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else return 0;
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}
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int inside_convex(const point &q,int n,const point *p)
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{
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int i,s[3]={1,1,1};
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for(i=0;i<n&&s[1]|s[2];i++)
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{
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s[_sign(cross(p[i],p[(i+1)%n],q))]=0;
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}
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return s[1]|s[2];
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}
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poly g1, g2;
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int convex_intersect()
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{
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int flag=0;
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Line l1,l2;
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for(int i=1;i<=g1.n&&!flag;i++)
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{
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l1.a=g1.p[i-1];
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l1.b=g1.p[i%g1.n];
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for(int j=1;j<=g2.n;j++)
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{
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l2.a=g2.p[j-1];
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l2.b=g2.p[j%g2.n];
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if(intersectSegToSeg(l1,l2)){flag=1;break;}
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}
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}
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for(int i=0;i<g1.n&&g2.n>=3;i++)
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{
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if(inside_convex(g1.p[i],g2.n,g2.p)){flag=1;break;}
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}
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if(!flag)for(int i=0;i<g2.n&&g1.n>=3;i++)
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{
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if(inside_convex(g2.p[i],g1.n,g1.p)){flag=1;break;}
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}
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return flag;
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}
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int main( ) {
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int n,m;
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while(cin>>n>>m){
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for(int i=0;i<n;i++)
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{
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a[i].input();
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}
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g1.n=covex_hull(n);
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g1.in( );
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for(int i=0;i<m;i++)
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{
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a[i].input();
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}
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g2.n=covex_hull(m);
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g2.in( );
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if(g1.n==1&&g2.n==1)
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{
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double ans=dis(g2.p[0],g1.p[0]);
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printf("%.4lf\n",ans);
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continue ;
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}
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if(!convex_intersect()){
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if(g1.n==1&&g2.n>1)
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{
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double ans=inf;
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for(int i=1;i<=g2.n;i++)
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{
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ans=min(ans,displ(g2.p[i-1],g2.p[i%g2.n],g1.p[0]));
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}
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printf("%.4lf\n",ans);
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continue ;
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}
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if(g2.n==1&&g1.n>1)
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{
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double ans=inf;
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for(int i=1;i<=g1.n;i++)
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{
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ans=min(ans,displ(g1.p[i-1],g1.p[i%g1.n],g2.p[0]));
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}
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printf("%.4lf\n",ans);
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continue ;
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}
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if(g2.n==2&&g1.n>1)
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{
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double ans=inf;
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for(int i=1;i<=g1.n;i++)
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{
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ans=min(ans,disll(g1.p[i-1],g1.p[i%g1.n],g2.p[0],g2.p[1]));
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}
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printf("%.4lf\n",ans);
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continue ;
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}
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if(g1.n==2&&g2.n>1)
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{
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double ans=inf;
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for(int i=1;i<=g2.n;i++)
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{
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ans=min(ans,disll(g2.p[i-1],g2.p[i%g1.n],g1.p[0],g1.p[1]));
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}
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printf("%.4lf\n",ans);
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continue ;
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}
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solve( g1, g2 );
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}
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else printf("%.4lf\n",0);
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}
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return 0;
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}
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