2015
09-17

# Rain on your Fat brother

After retired form the ACM/ICPC competition, Fat brother starts his civil servant’s life with his pretty girl friend Maze. As far as we known for this holy job, we can imagine how a decadent life they are dealing with!

But one day, Fat brother and Maze have a big quarrel because of some petty things and Maze just run away straight from him. It’s raining cats and dogs outside, our hero Fat brother feel very worried about the little princess so he decide to chase her. As Maze is a tsundere girl, she would feel angry when she touches the rain until she meets the Fat brother.

To simplify this problem, we can just consider each person as a point running along the X coordinate from right to left and the rain as a combination of an isosceles triangle and a half round. The speed of Maze is v1 unit per second and the speed of Fat brother is v2 unit per second (v1 < v2). The place where they have a quarrel is (x, 0) and Fat brother start to chase Maze after T second. You can assume that the rain is doing the uniform linear motion (drop with the same speed forever). Your task is calculating how long (time) the Maze is in the rain. The Maze is considered in the rain even if the point representing her is just touch the border. See the picture for more detail.

The first line contains only one integer T (T<=200), which is the number of test cases. For each test case, first line comes five positive integer v1, v2, v, t, x (v1<v2). v1 is the speed of Maze, v2 is the speed of Fat brother, v is the speed of the rain, you can assume that all rain is in a same speed, t means Fat brother starts to chase Maze after t second, x means they have a quarrel in (x, 0). Then a line with an integer n means that there is n rain begin to drop when Maze start running, 1<=n<=1000. Then n lines describe the rain. Each line contains four integers x0, y0, r, h. (x0, y0) is the center of the circle, r is the radius of the circle, h is the height of the triangle. All the number mentioned before except x0 are positive and no large than 1000. x0 is no large than 1000 and no less than -1000. Note that the point (x, 0) may in the rain in the beginning. Two rains may intersect with each other. See the picture for more detail.

The first line contains only one integer T (T<=200), which is the number of test cases. For each test case, first line comes five positive integer v1, v2, v, t, x (v1<v2). v1 is the speed of Maze, v2 is the speed of Fat brother, v is the speed of the rain, you can assume that all rain is in a same speed, t means Fat brother starts to chase Maze after t second, x means they have a quarrel in (x, 0). Then a line with an integer n means that there is n rain begin to drop when Maze start running, 1<=n<=1000. Then n lines describe the rain. Each line contains four integers x0, y0, r, h. (x0, y0) is the center of the circle, r is the radius of the circle, h is the height of the triangle. All the number mentioned before except x0 are positive and no large than 1000. x0 is no large than 1000 and no less than -1000. Note that the point (x, 0) may in the rain in the beginning. Two rains may intersect with each other. See the picture for more detail.

4
1 2 1 100 1
1
1 1 1 1
1 2 1 100 1
1
2 1 1 1
1 2 1 100 1
1
-9 9 10 10
2 3 1 100 1
1
-9 9 10 10

Case 1: 1.0000
Case 2: 0.0000
Case 3: 12.0534
Case 4: 8.0428

//cas忘了++ WA了20次你敢信   第一次做圆的几何   还以为模板有问题一直检查

//代码包含了本题没有用到的模板 所以略长  另外代码也写龊了

//大白p263
#include <cmath>
#include <cstdio>
#include <cstring>
#include <set>
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
const double eps=1e-10;//精度
const int INF=1<<29;
const double PI=acos(-1.0);
int doublecmp(double x){//判断double等于0或。。。
if(fabs(x)<eps)return 0;else return x<0?-1:1;
}
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);}//向量+向量=向量
Vector operator-(Point a,Point b){return Vector(a.x-b.x,a.y-b.y);}//点-点=向量
Vector operator*(Vector a,double p){return Vector(a.x*p,a.y*p);}//向量*实数=向量
Vector operator/(Vector a,double p){return Vector(a.x/p,a.y/p);}//向量/实数=向量
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 doublecmp(a.x-b.x)==0&&doublecmp(a.y-b.y)==0;
}
bool operator!=(const Point&a,const Point&b){return a==b?false:true;}
struct Segment{
Point a,b;
Segment(){}
Segment(Point _a,Point _b){a=_a,b=_b;}
bool friend operator<(const Segment& p,const Segment& q){return p.a<q.a||(p.a==q.a&&p.b<q.b);}
bool friend operator==(const Segment& p,const Segment& q){return (p.a==q.a&&p.b==q.b)||(p.a==q.b&&p.b==q.a);}
};
struct Circle{
Point c;
double r;
Circle(){}
Circle(Point _c, double _r):c(_c),r(_r) {}
Point point(double a)const{return Point(c.x+cos(a)*r,c.y+sin(a)*r);}
bool friend operator<(const Circle& a,const Circle& b){return a.r<b.r;}
};
struct Line{
Point p;
Vector v;
double ang;
Line() {}
Line(const Point &_p, const Vector &_v):p(_p),v(_v){ang = atan2(v.y, v.x);}
bool operator<(const Line &L)const{return  ang < L.ang;}
};
double Dot(Vector a,Vector b){return a.x*b.x+a.y*b.y;}//|a|*|b|*cosθ 点积
double Length(Vector a){return sqrt(Dot(a,a));}//|a| 向量长度
double Angle(Vector a,Vector b){return acos(Dot(a,b)/Length(a)/Length(b));}//向量夹角θ
double Cross(Vector a,Vector b){return a.x*b.y-a.y*b.x;}//叉积 向量围成的平行四边形的面积
double Area2(Point a,Point b,Point c){return Cross(b-a,c-a);}//同上 参数为三个点
double DegreeToRadius(double deg){return deg/180*PI;}
double GetRerotateAngle(Vector a,Vector b){//向量a顺时针旋转theta度得到向量b的方向
double tempa=Angle(a,Vector(1,0));
if(a.y<0) tempa=2*PI-tempa;
double tempb=Angle(b,Vector(1,0));
if(b.y<0) tempb=2*PI-tempb;
if((tempa-tempb)>0) return tempa-tempb;
else return tempa-tempb+2*PI;
}
}
Vector Normal(Vector a){//计算单位法线
double L=Length(a);
return Vector(-a.y/L,a.x/L);
}
Point GetLineProjection(Point p,Point a,Point b){//点在直线上的投影
Vector v=b-a;
return a+v*(Dot(v,p-a)/Dot(v,v));
}
Point GetLineIntersection(Point p,Vector v,Point q,Vector w){//求直线交点 有唯一交点时可用
Vector u=p-q;
double t=Cross(w,u)/Cross(v,w);
return p+v*t;
}
int ConvexHull(Point* p,int n,Point* ch){//计算凸包
sort(p,p+n);
int m=0;
for(int i=0;i<n;i++){
while(m>1&&Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=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>0) m--;
return m;
}
double Heron(double a,double b,double c){//海伦公式
double p=(a+b+c)/2;
return sqrt(p*(p-a)*(p-b)*(p-c));
}
bool SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2){//线段规范相交判定
double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1);
double c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1);
return doublecmp(c1)*doublecmp(c2)<0&&doublecmp(c3)*doublecmp(c4)<0;
}
double CutConvex(const int n,Point* poly, const Point a,const Point b, vector<Point> result[3]){//有向直线a b 切割凸多边形
vector<Point> points;
Point p;
Point p1=a,p2=b;
int cur,pre;
result[0].clear();
result[1].clear();
result[2].clear();
if(n==0) return 0;
double tempcross;
tempcross=Cross(p2-p1,poly[0]-p1);
if(doublecmp(tempcross)==0) pre=cur=2;
else if(tempcross>0) pre=cur=0;
else pre=cur=1;
for(int i=0;i<n;i++){
tempcross=Cross(p2-p1,poly[(i+1)%n]-p1);
if(doublecmp(tempcross)==0) cur=2;
else if(tempcross>0) cur=0;
else cur=1;
if(cur==pre){
result[cur].push_back(poly[(i+1)%n]);
}
else{
p1=poly[i];
p2=poly[(i+1)%n];
p=GetLineIntersection(p1,p2-p1,a,b-a);
points.push_back(p);
result[pre].push_back(p);
result[cur].push_back(p);
result[cur].push_back(poly[(i+1)%n]);
pre=cur;
}
}
sort(points.begin(),points.end());
if(points.size()<2){
return 0;
}
else{
return Length(points.front()-points.back());
}
}
double DistanceToSegment(Point p,Segment s){//点到线段的距离
if(s.a==s.b) return Length(p-s.a);
Vector v1=s.b-s.a,v2=p-s.a,v3=p-s.b;
if(doublecmp(Dot(v1,v2))<0) return Length(v2);
else if(doublecmp(Dot(v1,v3))>0) return Length(v3);
else return fabs(Cross(v1,v2))/Length(v1);
}
bool isPointOnSegment(Point p,Segment s){//点在线段上
return doublecmp(DistanceToSegment(p,s))==0;
}
int isPointInPolygon(Point p, Point* poly,int n){//点与多边形的位置关系
int wn=0;
for(int i=0;i<n;i++){
Point& p2=poly[(i+1)%n];
if(isPointOnSegment(p,Segment(poly[i],p2))) return -1;//点在边界上
int k=doublecmp(Cross(p2-poly[i],p-poly[i]));
int d1=doublecmp(poly[i].y-p.y);
int d2=doublecmp(p2.y-p.y);
if(k>0&&d1<=0&&d2>0)wn++;
if(k<0&&d2<=0&&d1>0)wn--;
}
if(wn) return 1;//点在内部
else return 0;//点在外部
}
double PolygonArea(vector<Point> p){//多边形有向面积
double area=0;
int n=p.size();
for(int i=1;i<n-1;i++)
area+=Cross(p[i]-p[0],p[i+1]-p[0]);
return area/2;
}
int PSLGtoPolygons(Segment arr[],int n,vector<Point>* Polygons){//通过n/2个线段组成的PSLG求所有多边形 返回个数
int count=n-1;
bool vis[9999];memset(vis,0,sizeof vis);//先求一次外包围 去掉多余线段
Point star=arr[0].a,pre=arr[0].a,cur=arr[0].b,purpose=arr[0].b;vis[0]=true;
int mark;
while(purpose!=star){
double theta=-INF;
for(int i=0;i<n;i++)if(!vis[i]&&arr[i].a==cur&&arr[i].b!=pre){
if(theta<GetRerotateAngle(pre-cur,arr[i].b-cur)){
theta=GetRerotateAngle(pre-cur,arr[i].b-cur);
purpose=arr[i].b;
mark=i;
}
}
vis[mark]=true;count--;
pre=cur;cur=purpose;
}//接下来卷包裹最大角度求多边形
int polyidx=0;
while(count>0){//线段个数不为0
for(int i=0;i<n;i++)if(!vis[i]){//找一个出发线段
star=arr[i].a,pre=arr[i].a,cur=arr[i].b,purpose=arr[i].b;vis[i]=true;count--;
Polygons[polyidx].clear();
Polygons[polyidx].push_back(cur);
break;
}
while(purpose!=star){
double theta=-INF;
for(int i=0;i<n;i++)if(!vis[i]&&arr[i].a==cur&&arr[i].b!=pre){
if(theta<GetRerotateAngle(pre-cur,arr[i].b-cur)){
theta=GetRerotateAngle(pre-cur,arr[i].b-cur);
purpose=arr[i].b;
mark=i;
}
}
vis[mark]=true;count--;
Polygons[polyidx].push_back(purpose);
pre=cur;cur=purpose;
}
polyidx++;
}
return polyidx;
}
int GetLineCircleIntersection(Line L,Circle C,Point& p1,Point& p2){//圆与直线交点 返回交点个数
double a = L.v.x, b = L.p.x - C.c.x, c = L.v.y, d = L.p.y-C.c.y;
double e = a*a + c*c, f = 2*(a*b+c*d), g = b*b + d*d -C.r*C.r;
double delta = f*f - 4*e*g;
if(doublecmp(delta) < 0)  return 0;//相离
if(doublecmp(delta) == 0) {//相切
p1=p1=C.point(-f/(2*e));
return 1;
}//相交
p1=(L.p+L.v*(-f-sqrt(delta))/(2*e));
p2=(L.p+L.v*(-f+sqrt(delta))/(2*e));
return 2;
}

//直线P+tV
//--------------------------------------
//--------------------------------------
//--------------------------------------
//--------------------------------------
//--------------------------------------
struct Allpoint{
Point p;
int pos;
bool friend operator<(Allpoint a,Allpoint b){
if(a.pos==-1&&a.pos==b.pos) return a.p<b.p;
else if(a.pos==-1) return true;
else if(b.pos==-1) return false;
else return a.p<b.p;
}
}allpoint[8000];//true=右下 false=左上
int idx=0;
int lpint(Line l, Point a, Point b, Point c, Allpoint *sol) {
int ret = 0;
if (doublecmp(Cross(l.v, a - b)) != 0) {
sol[ret].p = GetLineIntersection(l.p,l.v, a, b-a);
if (isPointOnSegment(sol[ret].p, Segment(a, b))) ret++;
}
if (doublecmp(Cross(l.v, c - b)) != 0) {
sol[ret].p = GetLineIntersection(l.p,l.v,c, b-c);
if (isPointOnSegment(sol[ret].p, Segment(c, b))) ret++;
}
if (doublecmp(Cross(l.v, a - c)) != 0) {
sol[ret].p = GetLineIntersection(l.p,l.v, a, c-a);
if (isPointOnSegment(sol[ret].p, Segment(a, c))) ret++;
}
if (ret < 2) return 0;
sort(sol, sol + ret);
if (ret == 3) {
if (sol[0].p == sol[1].p) sol[1].p = sol[2].p;
}
if (sol[0].p == sol[1].p) return 0;
return 2;
}
int main()
{
int T,cas=1;
scanf("%d",&T);
while(T--){
double v1,v2,v,t,x;
int n;
idx=0;
scanf("%lf%lf%lf%lf%lf",&v1,&v2,&v,&t,&x);
scanf("%d",&n);
double time = v2 * t / (v2 - v1);
Line l = Line(Point(x, 0), Point(x - v1 * time, v * time)-Point(x,0));
for(int i=0;i<n;i++){
Point O;
double r,h;
Allpoint ip[4];
scanf("%lf%lf%lf%lf", &O.x, &O.y, &r, &h);
int ipp = lpint(l, Point(O.x + r, O.y), Point(O.x - r, O.y), Point(O.x, O.y + h), ip);
if (ipp) {
if (ip[1] < ip[0]) swap(ip[0], ip[1]);
for (int i = 0; i < 2; i++) ip[i].pos= i & 1, allpoint[idx++] = ip[i];
}
int ipc = GetLineCircleIntersection(l,Circle(O, r), ip[0].p,ip[1].p);
if (ipc==2) {
if (ip[1] < ip[0]) swap(ip[0], ip[1]);
if (doublecmp(ip[1].p.y - O.y) >= 0) continue;
if (doublecmp(ip[0].p.y - O.y) > 0) ip[0].p = GetLineIntersection(l.p,l.v, O, Point(1.0, 0));
for (int i = 0; i < 2; i++) ip[i].pos = i & 1, allpoint[idx++] = ip[i];
}
}
sort(allpoint, allpoint + idx);
int cnt = 0;
double sum = 0, lp = x - v1 * time, rp = x, ls = lp;
for (int i = 0; i < idx; i++) {
if (allpoint[i].p.x > rp) break;
if (allpoint[i].p.x < lp) {
if (allpoint[i].pos) cnt--;
else cnt++;
} else {
if (allpoint[i].pos) {
if (cnt == 1) sum += allpoint[i].p.x - ls;
cnt--;
} else {
if (cnt == 0) ls = allpoint[i].p.x;
cnt++;
}
}
}
if (cnt > 0) sum += rp - ls;
printf("Case %d: %.4f\n", cas++, sum / v1);
}
}