UVA-10652-凸包

题目大意：平面上给定n个矩形，问用一个面积最小的凸多边形把他们包起来，计算出木板占整个包装面积的百分比；

题目解析：求一个凸包就可以了，注意角度转化；

AC代码：

#include<bits/stdc++.h>using namespace std;const double PI = acos(-1.0);struct Point{    double x,y;    Point(double x=0,double y=0):x(x),y(y){}};typedef Point Vector;Vector operator + (Vector A,Vector B)   {return Vector(A.x+B.x,A.y+B.y);}Vector operator - (Vector A,Vector B)   {return Vector(A.x-B.x,A.y-B.y);}Vector operator * (Vector A,double p)   {return Vector(A.x*p,A.y*p);}Vector operator / (Vector A,double p)   {return Vector(A.x/p,A.y/p);}bool operator < (const Point& a,const Point& b){    return a.x<b.x||(a.x==b.x&&a.y<b.y);}const double eps=1e-10;int dcmp(double x){    if(fabs(x)<eps) return 0;    else return x<0?-1:1;}bool operator == (const Point& a,const Point& b){    return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;}double Dot(Vector A,Vector B) {return A.x*B.x+A.y*B.y;}                     //点的点积double Length(Vector A) {return sqrt(Dot(A,A));}                            //向量的长度double Angle(Vector A,Vector B) {return acos(Dot(A,B)/Length(A)/Length(B));} //向量之间的角度double Cross(Vector A,Vector B) {return A.x*B.y-A.y*B.x;}                    //点的叉积double Area2(Point A,Point B,Point C){return Cross(B-A,C-A);}                    //三点构成的三角形面积的两倍Vector Rotate(Vector A,double rad)    {return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));}     //向量逆时针旋转Vector Normal(Vector A)                                                            //向量的法线{    double L = Length(A);    return Vector(-A.y/L,A.x/L);}//定义直线P+tv，计算两直线的交点，前提是两直线不平行Point GetLineIntersection(Point P,Point v,Point Q,Point w){    Vector u=P-Q;    double t=Cross(w,u)/Cross(v,w);    return P+v*t;} //点到直线的距离double DistanceToLine(Point P,Point A,Point B){    Vector v1=B-A,v2=P-A;    return fabs(Cross(v1,v2))/Length(v1);} //点到线段的距离double DistanceToSegement(Point P,Point A,Point B){    if(A==B)    return Length(P-A);    Vector v1=B-A,v2=P-A,v3=P-B;    if(dcmp(Dot(v1,v2))<0)  return Length(v2);    else if(dcmp(Dot(v1,v3))>0) return Length(v3);    else return fabs(Cross(v1,v2))/Length(v1);} //点在直线上的投影Point GetLineProjection(Point P,Point A,Point B){    Vector v=B-A;    return A+v*(Dot(v,P-A)/Dot(v,v));} //判断两直线是否规范相交bool SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2){    double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1),c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1);    return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0;}//判断点是否在线段上并且不在线段的端点上bool OnSegment(Point p,Point a1,Point a2){    return dcmp(Cross(a1-p,a2-p))==0&&dcmp(Dot(a1-p,a2-p))<0;} //计算多边形的有向面积 double PolygonArea(Point* p,int n) {     double area=0;     for(int i=1;i<n-1;i++)     {         area+=Cross(p[i]-p[0],p[i+1]-p[0]);     }     return area/2; }//凸包int ConvexHull(Point* p,int n,Point* ch){    sort(p,p+n);    int m=0;    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--;    return m;}//角度转化成弧度double torad(double ang){    return ang/180*PI;}////////////////////////////////////////const int maxn=2500;Point p[maxn],ch[maxn];int main(){    int t;    scanf("%d",&t);    while(t--)    {        int n,pc=0;        double area1=0;        scanf("%d",&n);        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[pc++]=o+Rotate(Vector(-w/2,-h/2),ang);            p[pc++]=o+Rotate(Vector(w/2,-h/2),ang);            p[pc++]=o+Rotate(Vector(-w/2,h/2),ang);            p[pc++]=o+Rotate(Vector(w/2,h/2),ang);            area1+=w*h;        }        int m=ConvexHull(p,pc,ch);        double area2=PolygonArea(ch,m);        printf("%.1lf %%\n",area1*100/area2);    }    return 0;}