LA 4127 - The Sky is the Limit (离散化 扫描线 几何模板)

  1 #include<iostream>
  2 #include<cmath>
  3 #include<cstdio>
  4 #include<algorithm>
  5 #include<vector>
  6 const double eps=1e-8;
  7 using namespace std;
  8 
  9 struct Point{    //定义点
 10     double x;
 11     double y;
 12     Point(double x=0,double y=0):x(x),y(y){}   //构造函数
 13     //void operator<<(Point &A) {cout<<A.x<<‘ ‘<<A.y<<endl;}
 14 };
 15 
 16 int dcmp(double x)  {return (x>eps)-(x<-eps); }   //判断精度
 17 
 18 typedef  Point  Vector;    //自定义别名
 19 
 20 Vector  operator +(Vector A,Vector B) { return Vector(A.x+B.x,A.y+B.y);} //向量+向量=向量，点+向量=点
 21 
 22 Vector  operator -(Vector A,Vector B) { return Vector(A.x-B.x,A.y-B.y); }  //点-点=向量
 23 
 24 Vector  operator *(Vector A,double p) { return Vector(A.x*p,A.y*p);  }   //向量*数=向量
 25 
 26 Vector  operator /(Vector A,double p) {return Vector(A.x/p,A.y/p);}    //向量/数=向量
 27 
 28 ostream &operator<<(ostream & out,Point & P) { out<<P.x<<‘ ‘<<P.y<<endl; return out;}  //输出点的 符号重载
 29 
 30 bool  operator< (const Point &A,const Point &B) { return A.x<B.x||(A.x==B.x&&A.y<B.y); }  //小于号 重载
 31 
 32 bool  operator== ( const Point &A,const Point &B) { return dcmp(A.x-B.x)==0&&dcmp(A.y-B.y)==0;}  //等于号 重载
 33 
 34 double  Dot(Vector A,Vector B) {return A.x*B.x+A.y*B.y;}  //点积
 35 
 36 double  Cross(Vector A,Vector B)  {return A.x*B.y-B.x*A.y; } //叉积
 37 
 38 double  Length(Vector A)  { return sqrt(Dot(A, A));}  //向量长度
 39 
 40 double  Angle(Vector A,Vector B) {return acos(Dot(A,B)/Length(A)/Length(B));}  //向量夹角
 41 
 42 double  Area2(Point A,Point B,Point C ) {return Cross(B-A, C-A);}  //三角形面积
 43 
 44 Vector Rotate(Vector A,double rad) { return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));} //向量旋转，rad为逆时针旋转的弧度
 45 Vector Normal(Vector A) {double L=Length(A);return Vector(-A.y/L,A.x/L);}  //计算向量的单位法线，需确保A不是零向量。
 46 
 47 Point GetLineIntersection(Point P,Vector v,Point Q,Vector w)  //两直线的交点。需确保直线 P+tv 和 Q+tw有唯一交点，cross(v,w)需非0。
 48 {                                                             //t是参数，v，w分别为两直线的向量。
 49     Vector u=P-Q;
 50     double t=Cross(w, u)/Cross(v,w);
 51     return P+v*t;
 52 }
 53 
 54 double DistanceToLine(Point P,Point A,Point B)  //点到直线的距离，p到ab的距离
 55 {
 56     Vector v1=P-A; Vector v2=B-A;
 57     return fabs(Cross(v1,v2))/Length(v2);
 58 }
 59 
 60 double DistanceToSegment(Point P,Point A,Point B)  //点到线段的距离，p到ab
 61 {
 62     if(A==B)  return Length(P-A);
 63     Vector v1=B-A;
 64     Vector v2=P-A;
 65     Vector v3=P-B;
 66 
 67     if(dcmp(Dot(v1,v2))==-1)    return  Length(v2);
 68     else if(Dot(v1,v3)>0)    return Length(v3);
 69     else return DistanceToLine(P, A, B);
 70 
 71 }
 72 
 73 Point GetLineProjection(Point P,Point A,Point B)  //点在直线的投影，p到ab
 74 {
 75     Vector v=B-A;
 76     Vector v1=P-A;
 77     double t=Dot(v,v1)/Dot(v,v);
 78     return  A+v*t;
 79 }
 80 
 81 bool  SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2)  //判断线段相交，交点不在端点上（如果交点在端点上可以借助下面的OnSegment来判断）
 82 {
 83     double c1=Cross(b1-a1, a2-a1);
 84     double c2=Cross(b2-a1, a2-a1);
 85     double c3=Cross(a1-b1, b2-b1);
 86     double c4=Cross(a2-b1, b2-b1);
 87     return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0 ;
 88 }
 89 
 90 bool  OnSegment(Point P,Point A,Point B)  //判断一个点是否在一条线段上
 91 {
 92     return dcmp(Cross(P-A, P-B))==0&&dcmp(Dot(P-A,P-B))<0;
 93 }
 94 
 95 double PolygonArea(Point *p,int n)  //多边形的有向面积
 96 {
 97     double area=0;
 98 
 99     for(int i=1;i<n-1;i++)
100     {
101         area+=Cross(p[i]-p[0], p[i+1]-p[0]);
102     }
103     return area/2;
104 
105 }
106 
107 Point  read_point()   //输入点
108 {
109     Point P;
110     scanf("%lf%lf",&P.x,&P.y);
111     return  P;
112 }
113 
114 int n;
115 Point L[110][2][2];
116 double x[20000];   //  存放离散化的x坐标
117 
118 int main()
119 {
120     double X,H,B;
121     int cas=0;
122     while(cin>>n && n)
123     {
124         int c=0;
125         for(int i=0;i<n;i++)
126         {
127             scanf("%lf%lf%lf",&X,&H,&B);
128             L[i][0][0]=Point(X-B*0.5,0);
129             L[i][0][1]=L[i][1][0]=Point(X,H);
130             L[i][1][1]=Point(X+B*0.5,0);
131 
132             x[c++]=X-B*0.5;
133             x[c++]=X;
134             x[c++]=X+B*0.5;
135         }
136             for(int i=0;i<n;i++)
137                 for(int a=0;a<2;a++)
138                     for(int j=i+1;j<n;j++)
139                         for(int b=0;b<2;b++)
140                         {
141                             Point A=L[i][a][0];
142                             Point B=L[i][a][1];
143                             Point C=L[j][b][0];
144                             Point D=L[j][b][1];
145 
146                             if(SegmentProperIntersection(A, B, C, D))
147                             {
148                                 x[c++]=GetLineIntersection(A, B-A, C, D-C).x;
149                             }
150                         }
151 
152         sort(x,x+c);
153         c=unique(x, x+c)-x; //unique()函数去重函数，在头文件algorithm中
154         double ans=0;
155         Point lastp=Point(x[0],0);
156 
157         for(int i=0;i<c;i++)
158         {
159             Point P=Point(x[i],0);
160             Vector v=Vector(0,1);
161             double maxy=-1;
162             Point inter;
163 
164             for(int j=0;j<n;j++)
165                 for(int a=0;a<2;a++)
166                 {
167                     Point A=L[j][a][0];
168                     Point B=L[j][a][1];
169                     if(dcmp(A.x-x[i])<=0&&dcmp(B.x-x[i])>=0)
170                     {
171                         inter=GetLineIntersection(A, B-A, P, v);
172                         maxy=max(maxy,inter.y);
173                     }
174                 }
175             if(i>0&&(dcmp(maxy)>0||dcmp(lastp.y)>0))   ans+=Length(Point(x[i],maxy)-lastp);
176             lastp=Point(x[i],maxy);
177         }
178         printf("Case %d: %.0f\n\n",++cas,ans);
179     }
180 }