uva 11796 - Dog Distance

#include<iostream>
#include<cstdio>
#include<cmath>
#define eps 1e-8
#define max(a,b) a>b?a:b

using namespace std;

int sig(double a)
{
    return (a>eps)-(a<-eps);
}

typedef struct point
{
    double x,y;
    point(double xx=0,double yy=0):x(xx),y(yy){}
}vector;

vector operator - (point a,point b)
{
    return vector(a.x-b.x,a.y-b.y);
}
point operator + (point a,vector b)
{
    return point(a.x+b.x,a.y+b.y);
}
vector operator * (vector a,double b)
{
    return vector(a.x*b,a.y*b);
}
double dot(vector a,vector b)
{
    return a.x*b.x+a.y*b.y;
}
double len(vector a)
{
    return sqrt(dot(a,a));
}
double cross(vector a,vector b)
{
    return a.x*b.y-a.y*b.x;
}
vector resiz(vector a,double l)
{
    l/=len(a);
    return vector(a.x*l,a.y*l);
}
double dis(point p,point a,vector v)
{
    point b=a+v;
    vector v1=p-a,v2=p-b;
    if(sig(dot(v,v1))<=0) return len(v1);
    else if(sig(dot(v,v2))>=0) return len(v2);
    return fabs(cross(v1,v))/len(v);
}

int main()
{
    int i,j,m,n,t,c=0;
    double mx,mn,v1,v2,l1,l2,d;
    point p[51],q[51],a,b;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d%d",&m,&n);
        v1=v2=0;
        for(i=0;i<m;i++)
        {
            scanf("%lf%lf",&p[i].x,&p[i].y);
            if(i) v1+=len(p[i]-p[i-1]);
        }
        for(i=0;i<n;i++)
        {
            scanf("%lf%lf",&q[i].x,&q[i].y);
            if(i) v2+=len(q[i]-q[i-1]);
        }
        mn=mx=len(p[0]-q[0]);
        a=p[0];b=q[0];
        for(i=1,j=1;i<m;)
        {
            l1=len(p[i]-a);l2=len(q[j]-b);
            d=l1/v1-l2/v2;
            if(sig(d)>0)
            {
                vector w=resiz(p[i]-a,l2*v1/v2),u=w-(q[j]-b);
                d=dis(b,a,u);
                if(sig(mn-d)>0) mn=d;
                d=max(len(b-a),len(b-a-u));
                if(sig(mx-d)<0) mx=d;
                a=a+w;b=q[j++];
            }
            else if(sig(d)<0)
            {
                vector w=resiz(q[j]-b,l1*v2/v1),u=w-(p[i]-a);
                d=dis(a,b,u);
                if(sig(mn-d)>0) mn=d;
                d=max(len(b-a),len(a-b-u));
                if(sig(mx-d)<0) mx=d;
                b=b+w;a=p[i++];
            }
            else
            {
                vector u=(q[j]-b)-(p[i]-a);
                d=dis(a,b,u);
                if(sig(mn-d)>0) mn=d;
                d=max(len(b-a),len(a-b-u));
                if(sig(mx-d)<0) mx=d;
                a=p[i++];b=q[j++];
            }
        }
        printf("Case %d: %.lf\n",++c,mx-mn);
    }
    return 0;
}