UVA 10652 凸包问题

  1 #include <cstdio>
  2 #include <cstring>
  3 #include <algorithm>
  4 #include <cmath>
  5 #include <iostream>
  6 using namespace std;
  7
  8 const double eps = 1e-10;
  9 const int N = 610;
 10 int dcmp(double x)
 11 {
 12     if(abs(x) < eps) return 0;
 13     if(x < 0) return -1;
 14     else return 1;
 15 }
 16
 17 struct Point{
 18     double x,y;
 19     Point(double x = 0,double y = 0):x(x),y(y){}
 20     bool operator<(const Point &m)const{
 21         return dcmp(x - m.x) < 0 || (dcmp(x - m.x) == 0 && dcmp(y - m.y) < 0);
 22     }
 23
 24     bool operator==(const Point &m)const{
 25         return dcmp(x - m.x) == 0 && dcmp(y - m.y) == 0;
 26     }
 27 };
 28
 29 Point ch[N<<2],p[N<<2];
 30
 31 typedef Point Vector;
 32
 33 Vector operator+(Vector a , Vector b)
 34 {
 35     return Vector(a.x + b.x , a.y + b.y);
 36 }
 37
 38 Vector operator-(Point a , Point b)
 39 {
 40     return Vector(a.x - b.x , a.y - b.y);
 41 }
 42
 43 Vector operator*(Vector a , double b)
 44 {
 45     return Vector(a.x * b , a.y * b);
 46 }
 47
 48 Vector operator/(Vector a , double b)
 49 {
 50     return Vector(a.x / b , a.y/b);
 51 }
 52
 53 double Cross(Vector a , Vector b)
 54 {
 55     return a.x * b.y - a.y * b.x;
 56 }
 57
 58 Vector GetReverse(Vector a , double rad)
 59 {
 60     double x = a.x * cos(rad) - a.y * sin(rad);
 61     double y = a.x * sin(rad) + a.y * cos(rad);
 62     return Vector(x,y);
 63 }
 64 //计算多边形面积
 65 double ConvexPolygonArea(Point *p , int n)
 66 {
 67     double area = 0;
 68     for(int i=1;i<n-1;i++){
 69         area += Cross(p[i] - p[0] , p[i+1] - p[0]);
 70     }
 71     return area / 2;
 72 }
 73 //求形成凸包的最大范围
 74 int ConvexHull(Point *p, int n, Point *ch) //凸包
 75 {
 76     sort(p, p+n);
 77     n = unique(p, p+n) - p; //去重
 78     int m = 0;
 79     for(int i = 0; i < n; i++)
 80     {
 81         while(m > 1 && Cross(ch[m-1]-ch[m-2], p[i]-ch[m-2]) <= 0) m--;
 82         ch[m++] = p[i];
 83     }
 84     int k = m;
 85     for(int i = n-2; i >= 0; i--)
 86     {
 87         while(m > k && Cross(ch[m-1]-ch[m-2], p[i]-ch[m-2]) <= 0) m--;
 88         ch[m++] = p[i];
 89     }
 90     if(n > 1) m--;
 91     return m;
 92 }
 93 int main()
 94 {
 95   //  freopen("test.in","rb",stdin);
 96
 97     int T,n;
 98     double x,y,w,h,_angle; //_angle表示度数，自己还要转化成弧度
 99     scanf("%d",&T);
100     while(T--){
101         scanf("%d",&n);
102         int k=0;
103         double area = 0;
104         for(int i=0;i<n;i++)
105         {
106             scanf("%lf%lf%lf%lf%lf",&x,&y,&w,&h,&_angle);
107             area += w*h;
108             double rad = -_angle * acos(-1) / 180;
109             Point o(x,y);
110             //cout<<"  rad:  "<<rad<<endl;
111             p[k++] = GetReverse(Vector(-w/2 , h/2),rad) + o;
112             p[k++] = GetReverse(Vector(w/2 , h/2),rad) + o;
113             p[k++] = GetReverse(Vector(w/2 , -h/2),rad) + o;
114             p[k++] = GetReverse(Vector(-w/2 , -h/2),rad) + o;
115         }
116
117         int m = ConvexHull(p , k , ch);
118         double sumOfArea = ConvexPolygonArea(ch , m);
119         double ans = area / sumOfArea * 100;
120
121         printf("%.1f %%\n",ans);
122     }
123     return 0;
124 }