UVA 11796 Dog Distance 几何
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给两个点的序列,表示两只狗的运动路径,保证a,b同时出发同时到达终点,求运动过程中a,b的最远距离-最近距离。
因为同时出发,同时到达,所以可以把两条路径的总长看做时间来做。更新最大最小值可以拆分成子过程来做,每次从当前点---某一个点到达拐点,这样每个子过程都是两个直线的运动,更新一下这段过程的最大最小值就行,之后当前点向后移动。
#include <iostream>#include <cstdio>#include <algorithm>#include <cstring>#include <cmath>#include <string>typedef double type;using namespace std;struct Point{ type x,y; Point(){} Point(type a,type b) { x=a; y=b; } void read() { scanf("%lf%lf",&x,&y); } void print() { printf("%.6lf %.6lf",x,y); }};typedef Point Vector;Vector operator + (Vector A,Vector B){ return Vector(A.x+B.x,A.y+B.y);}Vector operator - (Point A,Point B){ return Vector(A.x-B.x,A.y-B.y);}Vector operator * (Vector A,type p){ return Vector(A.x*p,A.y*p);}Vector operator / (Vector A,type 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;}//atan2(x,y) :向量(x,y)的极角,即从x轴正半轴旋转到该向量方向所需要的角度。type Dot(Vector A,Vector B){ return A.x*B.x+A.y*B.y;}type Cross(Vector A,Vector B){ return A.x*B.y-A.y*B.x;}type Length(Vector A){ return sqrt(Dot(A,A));}type Angle(Vector A,Vector B){ return acos(Dot(A,B))/Length(A)/Length(B);}type Area2(Point A,Point B,Point C){ return Cross(B-A,C-A);}Vector Rotate(Vector A,double rad){ return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));}Vector Normal(Vector A)//单位法线,左转90度,长度归一{ double L=Length(A); return Vector(-A.y/L,A.x/L);}Point GetLineIntersection(Point P,Vector v,Point Q,Vector w){ Vector u=P-Q; double t=Cross(w,u)/Cross(v,w); return P+v*t;}double DistanceToLine(Point P,Point A,Point B){ Vector v1=B-A,v2=P-A; return fabs(Cross(v1,v2))/Length(v1);}double DistanceToSegment(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);}Point GetLineProjection(Point P,Point A,Point B)//P在AB上的投影{ Vector v=B-A; return A+v*(Dot(v,P-A)/Dot(v,v));}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;}bool OnSegment(Point p,Point a1,Point a2){ return dcmp(Cross(a1-p,a2-p))==0 && dcmp(Dot(a1-p,a2-p))<0;}double ConvexPolygonArea(Point* p,int n)//多边形面积{ double area=0; for (int i=1; i<n-1; i++) area+=Cross(p[i]-p[0],p[i+1]-p[0]); return area/2.0;}double PolygonArea(Point* p,int n)//有向面积{ double area=0; for (int i=1; i<n-1; i++) area+=Cross(p[i]-p[0],p[i+1]-p[0]); return area/2.0;}Point a[120],b[120];int na,nb,num,n;int tt;double lena,lenb;double la[120],lb[120];double minn,maxx;void updata(Point p,Point a,Point b){ minn=min(minn,DistanceToSegment(p,a,b)); maxx=max(maxx,Length(p-a)); maxx=max(maxx,Length(p-b));}int main(){// freopen("in.txt","r",stdin); scanf("%d",&tt); for (int ii=1; ii<=tt; ii++) { scanf("%d%d",&na,&nb); lena=lenb=0.0; for (int i=0; i<na; i++) { a[i].read(); if (i>0) { la[i]=Length(a[i]-a[i-1]); lena+=la[i]; } } for (int i=0; i<nb; i++) { b[i].read(); if (i>0) { lb[i]=Length(b[i]-b[i-1]); lenb+=lb[i]; } } int pa,pb; pa=pb=1; double t; Point sa,sb; sa=a[0]; sb=b[0]; minn=999999999.9; maxx=0.0; while(pa<na && pb<nb) { double lla=Length(a[pa]-sa); double llb=Length(b[pb]-sb); t=min(lla/lena,llb/lenb); Vector va=(a[pa]-sa)/lla*lena*t; Vector vb=(b[pb]-sb)/llb*lenb*t; updata(sa,sb,sb+vb-va); sa=sa+va; sb=sb+vb; if (sa==a[pa]) pa++; if (sb==b[pb]) pb++; } printf("Case %d: %.0lf\n",ii,maxx-minn+eps); } return 0;}
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