UVA-11796-计算几何

题目大意：有两条狗分别沿着自己的折线段跑，他们都是匀速运动并且同时开始同时到达，问中间过程的他们两者距离的最大值减去最小值的值是多少；

题目解析：首先他们运动的过程可以分解成在某一段时间内都在线段上运动，那么在线段上运动，我们就可以考虑运动的相对性，一个看成静止不动，另一个还是匀速运动，那么这就是个点到线段的距离问题了；

AC代码：

#include<bits/stdc++.h>using namespace std;struct Point{    double x,y;    Point(double x=0,double y=0):x(x),y(y){}};typedef Point Vector;Vector operator + (Vector A,Vector B)   {return Vector(A.x+B.x,A.y+B.y);}Vector operator - (Vector A,Vector B)   {return Vector(A.x-B.x,A.y-B.y);}Vector operator * (Vector A,double p)   {return Vector(A.x*p,A.y*p);}Vector operator / (Vector A,double p)   {return Vector(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);}const double eps=1e-10;int dcmp(double x){    if(fabs(x)<eps) return 0;    else return x<0?-1:1;}bool operator == (const Point& a,const Point& b){    return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;}double Dot(Vector A,Vector B) {return A.x*B.x+A.y*B.y;}                     //点的点积double Length(Vector A) {return sqrt(Dot(A,A));}                            //向量的长度double Angle(Vector A,Vector B) {return acos(Dot(A,B)/Length(A)/Length(B));} //向量之间的角度double Cross(Vector A,Vector B) {return A.x*B.y-A.y*B.x;}                    //点的叉积double Area2(Point A,Point B,Point C){return Cross(B-A,C-A);}                    //三点构成的三角形面积的两倍Vector Rotate(Vector A,double rad)    {return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));}     //向量逆时针旋转Vector Normal(Vector A)                                                            //向量的法线{    double L = Length(A);    return Vector(-A.y/L,A.x/L);}//定义直线P+tv，计算两直线的交点，前提是两直线不平行Point GetLineIntersection(Point P,Point v,Point Q,Point w){    Vector u=P-Q;    double t=Cross(w,u)/Cross(v,w);    return P+v*t;} //点到直线的距离double DistanceToLine(Point P,Point A,Point B){    Vector v1=B-A,v2=P-A;    return fabs(Cross(v1,v2))/Length(v1);} //点到线段的距离double DistanceToSegement(Point P,Point A,Point B){    if(A==B)    return Length(P-A);    Vector 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);} //点在直线上的投影Point GetLineProjection(Point P,Point A,Point B){    Vector v=B-A;    return A+v*(Dot(v,P-A)/Dot(v,v));} //判断两直线是否规范相交bool SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2){    double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1),c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1);    return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0;}//判断点是否在线段上并且不在线段的端点上bool OnSegment(Point p,Point a1,Point a2){    return dcmp(Cross(a1-p,a2-p))==0&&dcmp(Dot(a1-p,a2-p))<0;} //计算多边形的有向面积 double PolygonArea(Point* p,int n) {     double area=0;     for(int i=1;i<n-1;i++)     {         area+=Cross(p[i]-p[0],p[i+1]-p[0]);     }     return area/2; }////////////////////////////////////////const int maxn=70;const int inf=0x3fffffff;double Max,Min;Point p[maxn],q[maxn];void update(Point p,Point a,Point b){    Min=min(Min,DistanceToSegement(p,a,b));    Max=max(Max,Length(p-a));    Max=max(Max,Length(p-b));}int main(){    int t,cas=1;    scanf("%d",&t);    while(t--)    {        int a,b;        scanf("%d%d",&a,&b);        for(int i=0;i<a;i++)    scanf("%lf%lf",&p[i].x,&p[i].y);        for(int i=0;i<b;i++)    scanf("%lf%lf",&q[i].x,&q[i].y);        double lena=0,lenb=0;        for(int i=1;i<a;i++)   lena+=Length(p[i]-p[i-1]);        for(int i=1;i<b;i++)   lenb+=Length(q[i]-q[i-1]);        Max=-inf;        Min=inf;        int sa=0,sb=0;        Point pa=p[0],pb=q[0];        while(sa<a-1&&sb<b-1)        {            double la=Length(p[sa+1]-pa);            double lb=Length(q[sb+1]-pb);            double t=min(la/lena,lb/lenb);            Point va=(p[sa+1]-pa)/la*t*lena;            Point vb=(q[sb+1]-pb)/lb*t*lenb;            update(pa,pb,pb+vb-va);            pa=pa+va;            pb=pb+vb;            if(pa==p[sa+1]) sa++;            if(pb==q[sb+1]) sb++;        }        printf("Case %d: %.0lf\n",cas++,Max-Min);    }    return 0;}