uvalive 7331 Hovering Hornet 半平面交+概率期望

题意：一个骰子在一个人正方形内，蜜蜂在任意一个位置可以出现，问看到点数的期望。

思路：半平面交+概率期望

  1 #include<cstdio>
  2 #include<cstring>
  3 #include<algorithm>
  4 #include<iostream>
  5 #include<cstdlib>
  6 #include<string>
  7 #include<cmath>
  8 #include<vector>
  9 using namespace std;
 10 const int maxn=1e5+7;
 11 const double eps=1e-8;
 12 const double pi=acos(-1);
 13 
 14 double dcmp(double x)
 15 {
 16     if(fabs(x) < eps) return 0;
 17     else return x < 0 ? -1 : 1;
 18 }
 19 
 20 struct Point
 21 {
 22     double x, y;
 23     Point(double x=0, double y=0):x(x),y(y) { }
 24 };
 25 
 26 typedef Point Vector;
 27 
 28 Vector operator + (const Point& A, const Point& B)
 29 {
 30     return Vector(A.x+B.x, A.y+B.y);
 31 }
 32 
 33 Vector operator - (const Point& A, const Point& B)
 34 {
 35     return Vector(A.x-B.x, A.y-B.y);
 36 }
 37 
 38 Vector operator * (const Point& A, double v)
 39 {
 40     return Vector(A.x*v, A.y*v);
 41 }
 42 
 43 Vector operator / (const Point& A, double v)
 44 {
 45     return Vector(A.x/v, A.y/v);
 46 }
 47 
 48 double Cross(const Vector& A, const Vector& B)
 49 {
 50     return A.x*B.y - A.y*B.x;
 51 }
 52 
 53 double Dot(const Vector& A, const Vector& B)
 54 {
 55     return A.x*B.x + A.y*B.y;
 56 }
 57 
 58 double Length(const Vector& A)
 59 {
 60     return sqrt(Dot(A,A));
 61 }
 62 
 63 Vector Rotate(Vector A,double rad)
 64 {
 65     return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
 66 }
 67 
 68 bool operator < (const Point& p1, const Point& p2)
 69 {
 70     return p1.x < p2.x || (p1.x == p2.x && p1.y < p2.y);
 71 }
 72 
 73 bool operator == (const Point& p1, const Point& p2)
 74 {
 75     return p1.x == p2.x && p1.y == p2.y;
 76 }
 77 
 78 Vector Normal(Vector A)
 79 {
 80     double L=Length(A);
 81     return Vector(-A.y/L,A.x/L);
 82 }
 83 struct Line
 84 {
 85     Point P;
 86     Vector v;
 87     double ang;
 88     Line() {}
 89     Line(Point P, Vector v):P(P),v(v)
 90     {
 91         ang = atan2(v.y, v.x);
 92     }
 93     bool operator < (const Line& L) const
 94     {
 95         return ang < L.ang;
 96     }
 97 };
 98 
 99 bool OnLeft(const Line& L, const Point& p)
100 {
101     return Cross(L.v, p-L.P) > 0;
102 }
103 
104 
105 Point GetLineIntersection(const Line& a, const Line& b)
106 {
107     Vector u = a.P-b.P;
108     double t = Cross(b.v, u) / Cross(a.v, b.v);
109     return a.P+a.v*t;
110 }
111 
112 const double INF = 1e8;
113 
114 Point ansPoly[maxn];
115 int HalfplaneIntersection(vector<Line> L)     //L为切割平面的直线集合，求半平面交，返回点的个数，点存在anspoly数组中
116 {
117     int n = L.size();
118     sort(L.begin(), L.end()); // 按极角排序
119     int first, last;         // 双端队列的第一个元素和最后一个元素的下标
120     vector<Point> p(n);      // p[i]为q[i]和q[i+1]的交点
121     vector<Line> q(n);       //
122     q[first=last=0] = L[0];  //
123     for(int i = 1; i < n; i++)
124     {
125         while(first < last && !OnLeft(L[i], p[last-1])) last--;
126         while(first < last && !OnLeft(L[i], p[first])) first++;
127         q[++last] = L[i];
128         if(fabs(Cross(q[last].v, q[last-1].v)) < eps)   //
129         {
130             last--;
131             if(OnLeft(q[last], L[i].P)) q[last] = L[i];
132         }
133         if(first < last) p[last-1] = GetLineIntersection(q[last-1], q[last]);
134     }
135     while(first < last && !OnLeft(q[first], p[last-1])) last--; //
136     if(last - first <= 1) return 0; //
137     p[last] = GetLineIntersection(q[last], q[first]); //
138     // 从deque复制到输出中
139     int index=0;
140     for(int i = first; i <= last; i++) ansPoly[index++]=p[i];
141     return index;
142 }
143 
144 double PolygonArea(int n,Point *p)
145 {
146     double area=0;
147     for(int i=1; i<n-1; i++)
148         area+=Cross(p[i]-p[0],p[i+1]-p[0]);
149     return area/2;
150 }
151 // vector<Line>  vec;
152 //        vec.push_back(Line(Point(0,0),Point(1,0)));
153 //        vec.push_back(Line(Point(10000,0),Point(0,1)));
154 //        vec.push_back(Line(Point(10000,10000),Point(-1,0)));
155 //        vec.push_back(Line(Point(0,10000),Point(0,-1)));
156 //        Vector v=(p[1]-p[0]);
157 //        vec.push_back(Line((p[1]+p[0])*0.5,Normal(v)));
158 //        v=(p[2]-p[0]);
159 //        vec.push_back(Line((p[2]+p[0])*0.5,Normal(v)));
160 //        int m=HalfplaneIntersection(vec);
161 //        double ans=PolygonArea(m,ansPoly);
162 //        printf("%.3f\n",ans/(1.0*10000*10000));
163 Point p[5];
164 void CC(Point *p)
165 {
166     for(int i=0; i<maxn; i++)
167     {
168         p[i].x=0;
169         p[i].y=0;
170     }
171 }
172 int main()
173 {
174 //  freopen("in.txt","r",stdin);
175     double a1,a2,a3,a4,a5,a6;
176     a5=(5.0*5*4)/(5*5*5-1);
177     a2=0;
178     while(cin>>p[0].x>>p[0].y>>p[1].x>>p[1].y>>p[2].x>>p[2].y>>p[3].x>>p[3].y)
179     {
180         CC(ansPoly);
181         vector<Line>vec;
182         vec.push_back(Line(Point(p[0].x,p[0].y),Point(p[1].x-p[0].x,p[1].y-p[0].y)));
183         vec.push_back(Line(Point(p[1].x,p[1].y),Point(p[2].x-p[1].x,p[2].y-p[1].y)));
184         vec.push_back(Line(Point(p[2].x,p[2].y),Point(p[3].x-p[2].x,p[3].y-p[2].y)));
185         vec.push_back(Line(Point(p[3].x,p[3].y),Point(p[0].x-p[3].x,p[0].y-p[3].y)));
186         vec.push_back(Line(Point(-0.5,-0.5),Point(-1,0)));
187         int sou_num=HalfplaneIntersection(vec);
188         a1=PolygonArea(sou_num,ansPoly);
189 //        cout<<"a1:"<<a1<<endl;
190 //        cout<<"sou_num:"<<sou_num<<endl;
191 //        CC(ansPoly);
192         vec.clear();
193         vec.push_back(Line(Point(p[0].x,p[0].y),Point(p[1].x-p[0].x,p[1].y-p[0].y)));
194         vec.push_back(Line(Point(p[1].x,p[1].y),Point(p[2].x-p[1].x,p[2].y-p[1].y)));
195         vec.push_back(Line(Point(p[2].x,p[2].y),Point(p[3].x-p[2].x,p[3].y-p[2].y)));
196         vec.push_back(Line(Point(p[3].x,p[3].y),Point(p[0].x-p[3].x,p[0].y-p[3].y)));
197         vec.push_back(Line(Point(-0.5,-0.5),Point(0,1)));
198         int west_num=HalfplaneIntersection(vec);
199 //        cout<<ansPoly[3].y<<endl;
200         a4=PolygonArea(west_num,ansPoly);
201 //        cout<<"a4:"<<a4<<endl;
202 //        cout<<"west_num:"<<west_num<<endl;
203         CC(ansPoly);
204         vec.clear();
205         vec.push_back(Line(Point(p[0].x,p[0].y),Point(p[1].x-p[0].x,p[1].y-p[0].y)));
206         vec.push_back(Line(Point(p[1].x,p[1].y),Point(p[2].x-p[1].x,p[2].y-p[1].y)));
207         vec.push_back(Line(Point(p[2].x,p[2].y),Point(p[3].x-p[2].x,p[3].y-p[2].y)));
208         vec.push_back(Line(Point(p[3].x,p[3].y),Point(p[0].x-p[3].x,p[0].y-p[3].y)));
209         vec.push_back(Line(Point(-0.5,0.5),Point(1,0)));
210         int nor_num=HalfplaneIntersection(vec);
211         a6=PolygonArea(nor_num,ansPoly);
212 //        cout<<"a6:"<<a6<<endl;
213 //        cout<<"nor_num:"<<nor_num<<endl;
214         CC(ansPoly);
215         vec.clear();
216         vec.push_back(Line(Point(p[0].x,p[0].y),Point(p[1].x-p[0].x,p[1].y-p[0].y)));
217         vec.push_back(Line(Point(p[1].x,p[1].y),Point(p[2].x-p[1].x,p[2].y-p[1].y)));
218         vec.push_back(Line(Point(p[2].x,p[2].y),Point(p[3].x-p[2].x,p[3].y-p[2].y)));
219         vec.push_back(Line(Point(p[3].x,p[3].y),Point(p[0].x-p[3].x,p[0].y-p[3].y)));
220         vec.push_back(Line(Point(0.5,0.5),Point(0,-1)));
221         int east_num=HalfplaneIntersection(vec);
222         a3=PolygonArea(east_num,ansPoly);
223 //        cout<<"a3:"<<a3<<endl;
224 //        cout<<"east_num:"<<east_num<<endl;
225         long double ans1,ans2,ans3,ans4,ans5,ans6;
226         double ans;
227 //        anss=(5.0*a1)/(5*5*5-1)+2*(5.0*a2)/(5*5*5-1)+3*(5.0*a3)/(5*5*5-1)+4*(5.0*a4)/(5*5*5-1)+a5*5.0+6*(5.0*a6)/(5*5*5-1);
228         ans1=(5.0*a1)/(5*5*5-1);
229 //        cout<<"ans1:"<<ans1<<endl;
230         ans2=(5.0*a2)/(5*5*5-1);
231 //        cout<<"ans2:"<<ans2<<endl;
232         ans3=3*(5.0*a3)/(5*5*5-1);
233 //        cout<<"ans3:"<<ans3<<endl;
234         ans4=4*(5.0*a4)/(5*5*5-1);
235 //        cout<<"ans4:"<<ans4<<endl;
236         ans5=5*a5;
237 //        cout<<"ans5:"<<ans5<<endl;
238         ans6=6*(5.0*a6)/(5*5*5-1);
239 //        cout<<"ans6:"<<ans6<<endl;
240         ans=ans1+ans2+ans3+ans4+ans5+ans6;
241         printf("%.10lf\n",ans);
242     }
243     return 0;
244 }

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