zoukankan      html  css  js  c++  java
  • HDU3982 Harry Potter and J.K.Rowling

    Harry Potter and J.K.Rowling

    In July 31st, last month, the author of the famous novel series J.K.Rowling celebrated her 46th birthday. Many friends gave their best wishes. They gathered together and shared one large beautiful cake.

    Rowling had lots of friends, and she had a knife to cut the cake into many pieces. On the cake there was a cherry. After several cuts, the piece with the cherry was left for Rowling. Before she enjoyed it, she wondered how large this piece was, i.e., she wondered how much percentage of the cake the piece with the only cherry has.

    (nleq 2000)

    题解

    半平面交+凸多边形与圆的面积交。

    然后被精度卡烂了。

    时间复杂度(O(nlog n))

    struct point {double x,y;};
    
    IN point operator+(CO point&a,CO point&b){
    	return (point){a.x+b.x,a.y+b.y};
    }
    IN point operator-(CO point&a,CO point&b){
    	return (point){a.x-b.x,a.y-b.y};
    }
    IN point operator*(CO point&a,double b){
    	return (point){a.x*b,a.y*b};
    }
    IN point operator/(CO point&a,double b){
    	return (point){a.x/b,a.y/b};
    }
    IN double dot(CO point&a,CO point&b){
    	return a.x*b.x+a.y*b.y;
    }
    IN double cross(CO point&a,CO point&b){
    	return a.x*b.y-a.y*b.x;
    }
    IN double len(CO point&a){
    	return sqrt(dot(a,a));
    }
    IN double angle(CO point&a,CO point&b){
    	double w=dot(a,b)/len(a)/len(b);
    	w=max(w,-1.0),w=min(w,1.0); // edit 3
    	return acos(w);
    }
    
    struct line {point x,y;};
    
    IN bool on_left(CO point&a,CO line&b){
    	return cross(a-b.x,b.y)<0;
    }
    IN int quad(CO point&a){
    	if(a.x>0 and a.y>=0) return 1;
    	else if(a.x<=0 and a.y>0) return 2;
    	else if(a.x<0 and a.y<=0) return 3;
    	else return 4;
    }
    IN bool operator<(CO line&a,CO line&b){
    	if(quad(a.y)!=quad(b.y)) return quad(a.y)<quad(b.y);
    	return cross(a.y,b.y)==0?on_left(a.x,b):cross(a.y,b.y)>0; // edit 2
    }
    IN point intersect(CO line&a,CO line&b){
    	return b.x+b.y*cross(b.x-a.x,a.y)/cross(a.y,b.y);
    }
    
    CO double pi=acos(-1),eps=1e-6;
    
    vector<point> seg_cross_circle(CO point&a,CO point&b,double r){
    	double dx=b.x-a.x,dy=b.y-a.y;
    	double A=dx*dx+dy*dy;
    	double B=2*dx*a.x+2*dy*a.y; // edit 1
    	double C=a.x*a.x+a.y*a.y-r*r;
    	double delta=B*B-4*A*C;
    	vector<point> ans;
    	if(delta<-eps) return ans; // edit 2
    	delta=sqrt(max(delta,0.0));
    	double t1=(-B+delta)/(2*A);
    	double t2=(-B-delta)/(2*A);
    	if(-t1<eps and t1-1<eps) // edit 3
    		ans.push_back((point){a.x+t1*dx,a.y+t1*dy});
    	if(-t2<eps and t2-1<eps)
    		ans.push_back((point){a.x+t2*dx,a.y+t2*dy});
    	return ans;
    }
    double triangle_cross_circle(point a,point b,double r){
    //	cerr<<"a="<<a.x<<" "<<a.y<<" b="<<b.x<<" "<<b.y<<endl;
    	bool AinC=dot(a,a)<r*r,BinC=dot(b,b)<r*r;
    	double sign=0.5*(cross(a,b)>0?1:-1),ans=0;
    	if(AinC and BinC) ans=abs(cross(a,b)); // edit 4
    	else if(AinC or BinC){
    		if(BinC) swap(a,b);
    		vector<point> tmp=seg_cross_circle(a,b,r);
    		ans=abs(cross(a,tmp[0]))+r*r*angle(tmp[0],b);
    	}
    	else{
    		vector<point> p=seg_cross_circle(a,b,r);
    		ans=r*r*angle(a,b);
    		if(p.size()==2){
    			ans-=r*r*angle(p[0],p[1]);
    			ans+=abs(cross(p[0],p[1]));
    		}
    	}
    //	cerr<<"ans="<<ans<<endl;
    	return ans*=sign;
    }
    
    CO int N=2e3+10;
    point p[N];
    line ln[N];
    
    int halfplane(int n){
    	sort(ln+1,ln+n+1);
    	int m=1;
    	for(int i=2;i<=n;++i){
    		if(cross(ln[i].y,ln[m].y)==0) continue;
    		ln[++m]=ln[i];
    	}
    	int l=1,r=1;
    	for(int i=2;i<=m;++i){
    		for(;l<r and !on_left(p[r],ln[i]);--r);
    		for(;l<r and !on_left(p[l+1],ln[i]);++l);
    		ln[++r]=ln[i];
    		if(l<r) p[r]=intersect(ln[r-1],ln[r]);
    	}
    	for(;l<r and !on_left(p[r],ln[l]);--r);
    	if(l<r) p[l]=p[r+1]=intersect(ln[l],ln[r]);
    	for(int i=1;i<=r-l+1;++i) p[i]=p[l+i-1];
    	return r-l+1;
    }
    void real_main(){
    	double r;scanf("%lf",&r);
    	int n=4+read<int>();
    	ln[1].x=(point){0,-r},ln[1].y=(point){1,0};
    	ln[2].x=(point){r,0},ln[2].y=(point){0,1};
    	ln[3].x=(point){0,r},ln[3].y=(point){-1,0};
    	ln[4].x=(point){-r,0},ln[4].y=(point){0,-1};
    	for(int i=5;i<=n;++i){
    		point a,b;scanf("%lf%lf%lf%lf",&a.x,&a.y,&b.x,&b.y);
    		ln[i].x=a,ln[i].y=b-a;
    	}
    	point o;scanf("%lf%lf",&o.x,&o.y);
    	for(int i=5;i<=n;++i)
    		if(!on_left(o,ln[i])) ln[i].y=ln[i].y*-1;
    	n=halfplane(n),p[n+1]=p[1];
    //	cerr<<"p=";
    //	for(int i=1;i<=n+1;++i)
    //		cerr<<" ("<<p[i].x<<","<<p[i].y<<")"<<endl;
    	double ans=0;
    	for(int i=1;i<=n;++i)
    		ans+=triangle_cross_circle(p[i],p[i+1],r);
    	ans=ans/(pi*r*r);
    	printf("%.5lf%%
    ",100*ans);
    }
    int main(){
    	int T=read<int>();
    	for(int i=1;i<=T;++i){
    		printf("Case %d: ",i);
    		real_main();
    	}
    	return 0;
    }
    
  • 相关阅读:
    从程序设计到软件工程
    必应词典客户端软件测试报告
    软工第二次阅读作业:软件开发的轻与重
    结对编程2:电梯调度程序的UI设计 心得文档
    [MVC]如何提升命名空间的优先级
    asp,net 实现treeview 选种父节点其子节点也选种
    asp.net jmail发送邮件代码
    mysql workbench建表时的字段选项含义
    C#/.NET中的委托与事件
    C# 处理日期时间
  • 原文地址:https://www.cnblogs.com/autoint/p/13185688.html
Copyright © 2011-2022 走看看