UVA - 10652 Board Wrapping （凸包+多边形面积）

快来打我* 2022-05-27 09:05 263阅读 0赞

#include<cstdio>
    #include<cmath>
    #include<iostream>
    #include<algorithm>
    using namespace std;
    const double ep=1e-10;
    const int maxn=6e3+10;
    int cnt;
    
    struct Point {
    	double x, y;
    	Point(){}
    	Point(double x, double y): x(x), y(y){}
    	bool operator < (const Point A) const{ return x<A.x || (x==A.x&&y<A.y);}
    	
    }p[maxn], ch[maxn];
    typedef Point Vector;
    
    int dcmp(double x){
    	if(fabs(x) < ep) return 0; else return x<0? -1 : 1;
    }
    
    Point operator + (Point A, Vector B) { return Point(A.x+B.x, A.y+B.y); }
    Point operator - (Point A, Point 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 (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; }
    double Cross(Vector A, Vector B){ return A.x*B.y-A.y*B.x; }
    
    bool SegmentProperIntersection(Point a1, Point a2, Point b1, Point b2){
    	double c1=Cross(a2-a1, b1-a1), c2=Cross(a2-a1, b2-a1);
    	double c3=Cross(b2-b1, a1-b1), c4=Cross(b2-b1, a2-b1);
    	return dcmp(c1)*dcmp(c2)<0 && dcmp(c3)*dcmp(c4)<0;
    }
    
    Point GetLineIntersection(Point a1, Vector v1, Point a2, Vector v2){
    	Vector v=a1-a2;
    	double t=Cross(v2, v)/Cross(v1, v2);
    	return a1+v1*t;
    }
    
    bool OnSegment(Point p, Point a, Point b){
    	return dcmp(Cross(a-p, b-p))==0 && dcmp(Dot(a-p, b-p))<0;
    }
    
    Vector Rotate(Vector A, double rad){
    	return Vector(A.x*cos(rad)-A.y*sin(rad), A.x*sin(rad)+A.y*cos(rad));
    }
    
    void GetPoint(Point t, double w, double h, double rad){
    	p[cnt++]=t + Rotate(Vector(w/2, h/2), rad);
    	p[cnt++]=t + Rotate(Vector(-w/2, h/2), rad);
    	p[cnt++]=t + Rotate(Vector(-w/2, -h/2), rad);
    	p[cnt++]=t + Rotate(Vector(w/2, -h/2), rad);
    }
    
    int ConvexHull(){
    	sort(p, p+cnt);
    	
    	int m=0;
    	for(int i=0; i<cnt; 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=cnt-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(cnt>1) m--;
    	
    	return m;
    }
    
    double PolygonArea(int m){
    	double area =0;
    	for(int i=1; i<m-1; i++)
    		area+=Cross(ch[i]-ch[0], ch[i+1]-ch[0]);
    	return area/2;
    }
    
    double torad(double x){
    	return x/180 * acos(-1);
    }
    
    int main() {
    	int T;
    	scanf("%d", &T);
    	while(T--){
    		int n;
    		cnt=0;
    		double s1=0, x, y, w, h, j, rad;
    		scanf("%d", &n);
    		for(int i=0; i<n; i++)
    		{
    			Point t;
    			scanf("%lf%lf%lf%lf%lf", &t.x, &t.y, &w, &h, &j);
    			rad=torad(j);
    			GetPoint(t, w, h, -rad);
    			s1+=w*h;
    		}
    		
    		int m=ConvexHull();
    		
    		double s=PolygonArea(m);
    		
    		double percenty=s1/s*100;
    		printf("%.1lf %\n", percenty);
    	}
    	return 0;
    }