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 = 4010;
const double eps = 5*1e-13;
const double pi = acos(-1);

const double PI = acos(-1.0);
double torad(double deg)
{
    return deg/180 * PI;
}

struct Point
{
    double x, y;
    Point(double x=0, double y=0):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 = 0;
    vector<Point> ch(n+1);
    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 > 1) m--;
    ch.resize(m);
    return ch;
}

// 多边形的有向面积
double PolygonArea(vector<Point> p)
{
    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 main()
{
    int T;
    scanf("%d", &T);
    while(T--)
    {
        int n;
        double area1 = 0;
        scanf("%d", &n);
        vector<Point> P;
        for(int i = 0; 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/2,-h/2), ang));
            P.push_back(o + Rotate(Vector(w/2,-h/2), ang));
            P.push_back(o + Rotate(Vector(-w/2,h/2), ang));
            P.push_back(o + Rotate(Vector(w/2,h/2), ang));
            area1 += w*h;
        }
        double area2 = PolygonArea(ConvexHull(P));
        printf("%.1lf %%
", area1*100/area2);
    }
    return 0;
}