uva 10652

大意：有n块矩形木板，你的任务是用一个面积尽量小的凸多边形把它们包起来，并计算出木板站整个包装面积的百分比。

思路：按照题意将所有矩形顶点坐标存起来，旋转时先旋转从中心出发的向量，求得各个坐标之后，求凸包即可。

水。。。。

 #include<cstdio>
 #include<cmath>
 #include<cstring>
 #include<algorithm>
 #include<iostream>
 #include<memory.h>
 #include<cstdlib>
 #include<vector>
 #define clc(a,b) memset(a,b,sizeof(a))
 #define LL long long int
 #define up(i,x,y) for(i=x;i<=y;i++)
 #define w(a) while(a)
 using namespace std;
 const int inf=0x3f3f3f3f;
 const int N = ;
 const double eps = *1e-;
 const double pi = acos(-);

 const double PI = acos(-1.0);
 double torad(double deg)
 {
     return deg/ * PI;
 }

 struct Point
 {
     double x, y;
     Point(double x=, double y=):x(x),y(y) { }
 };

 typedef Point Vector;

 Vector operator + (const Vector& A, const Vector& B)
 {
     return Vector(A.x+B.x, A.y+B.y);
 }
 Vector operator - (const Point& A, const Point& B)
 {
     return Vector(A.x-B.x, A.y-B.y);
 }
 double Cross(const Vector& A, const Vector& B)
 {
     return A.x*B.y - A.y*B.x;
 }

 Vector Rotate(const Vector& A, double rad)
 {
     return Vector(A.x*cos(rad)-A.y*sin(rad), A.x*sin(rad)+A.y*cos(rad));
 }

 bool operator < (const Point& p1, const Point& p2)
 {
     return p1.x < p2.x || (p1.x == p2.x && p1.y < p2.y);
 }

 bool operator == (const Point& p1, const Point& p2)
 {
     return p1.x == p2.x && p1.y == p2.y;
 }

 // 点集凸包
 // 如果不希望在凸包的边上有输入点，把两个 <= 改成 <
 // 如果不介意点集被修改，可以改成传递引用
 vector<Point> ConvexHull(vector<Point> p)
 {
     // 预处理，删除重复点
     sort(p.begin(), p.end());
     p.erase(unique(p.begin(), p.end()), p.end());

     int n = p.size();
     int m = ;
     vector<Point> ch(n+);
     for(int i = ; i < n; i++)
     {
         while(m >  && Cross(ch[m-]-ch[m-], p[i]-ch[m-]) <= ) m--;
         ch[m++] = p[i];
     }
     int k = m;
     for(int i = n-; i >= ; i--)
     {
         while(m > k && Cross(ch[m-]-ch[m-], p[i]-ch[m-]) <= ) m--;
         ch[m++] = p[i];
     }
     if(n > ) m--;
     ch.resize(m);
     return ch;
 }

 // 多边形的有向面积
 double PolygonArea(vector<Point> p)
 {
     double area = ;
     int n = p.size();
     for(int i = ; i < n-; i++)
         area += Cross(p[i]-p[], p[i+]-p[]);
     return area/;
 }

 int main()
 {
     int T;
     scanf("%d", &T);
     while(T--)
     {
         int n;
         double area1 = ;
         scanf("%d", &n);
         vector<Point> P;
         for(int i = ; i < n; i++)
         {
             double x, y, w, h, j, ang;
             scanf("%lf%lf%lf%lf%lf", &x, &y, &w, &h, &j);
             Point o(x,y);
             ang = -torad(j);
             P.push_back(o + Rotate(Vector(-w/,-h/), ang));
             P.push_back(o + Rotate(Vector(w/,-h/), ang));
             P.push_back(o + Rotate(Vector(-w/,h/), ang));
             P.push_back(o + Rotate(Vector(w/,h/), ang));
             area1 += w*h;
         }
         double area2 = PolygonArea(ConvexHull(P));
         printf("%.1lf %%\n", area1*/area2);
     }
     return ;
 }