NOI十连测 第六测 T3
思路:考试的时候我非常地**，写了圆并，然后还TM写了半平面交和三角剖分，虽然只有30分。。但是看在我写了500行的份上还是挂着吧。。
#include<cstdio>
#include<cmath>
#include<cstring>
#include<iostream>
#include<algorithm>
const double Pi=acos(-);
const double eps=1e-;
int n,m,cnt,tot,num;
bool pd[],check;
int read(){
int t=,f=;char ch=getchar();
while (ch<''||ch>'') {if (ch=='-') f=-;ch=getchar();}
while (''<=ch&&ch<='') {t=t*+ch-'';ch=getchar();}
return t*f;
}
struct node{
double l,r;
}L[];
struct Point{
double x,y;
Point(){}
Point(double x0,double y0):x(x0),y(y0){}
}p[],c[],d[];
struct Line{
Point s,e;
double slop;
Line(){}
Line(Point s0,Point e0):s(s0),e(e0){}
}l[],q[];
struct Circle{
Point p;
double r;
Circle(){}
Circle(double x0,double y0,double r0):p(Point(x0,y0)),r(r0){}
}a[];
bool cmp2(node a,node b){
if (fabs(a.l-b.l)<eps) return a.r<b.r;
else return (a.l<b.l);
}
int sgn(double x){if (x>eps) return ;if (x<-eps) return -;return ;}
double operator *(Point p1,Point p2){return p1.x*p2.y-p1.y*p2.x;}
double operator /(Point p1,Point p2){return p1.x*p2.x+p1.y*p2.y;}
Point operator -(Point p1,Point p2){return Point(p1.x-p2.x,p1.y-p2.y);}
Point operator +(Point p1,Point p2){return Point(p1.x+p2.x,p1.y+p2.y);}
Point operator *(Point p1,double x){return Point(p1.x*x,p1.y*x);}
Point operator /(Point p1,double x){return Point(p1.x/x,p1.y/x);}
double sqr(double x){return x*x;}
double llen(Point p1){return sqrt(sqr(p1.x)+sqr(p1.y)); }
double dis(Point p1,Point p2){return llen(p1-p2);}
double dis(Point p1){return llen(p1);}
Point evector(Point p1){double t=llen(p1);if (t<eps) return Point(,);else return p1/t;}
bool cmp3(Line p1,Line p2){
if (p1.slop!=p2.slop) return p1.slop<p2.slop;
else return (p1.e-p1.s)*(p2.e-p1.s)>;
}
bool cmp(Point p1,Point p2){
double t=(p1-p[])*(p2-p[]);
if (fabs(t)<eps) return dis(p[],p1)<dis(p[],p2);
return t>;
}
bool conclude(Circle p1,Circle p2){
double Len=dis(p1.p,p2.p);
if (fabs(p1.r-p2.r)>=Len) return ;
return ;
}
bool intersect(Circle p1,Circle p2){
double Len=dis(p1.p,p2.p);
if (fabs(p1.r-p2.r)<=Len&&Len<=p1.r+p2.r) return ;
return ;
}
double dist_line(Line p){
double A,B,C,dist;
A=p.s.y-p.e.y;
B=p.s.x-p.e.x;
C=p.s.x*p.e.y-p.s.y*p.e.x;
dist=fabs(C)/sqrt(sqr(A)+sqr(B));
return dist;
}
double dist_line(Point p1,Line p){
p.s.x-=p1.x;
p.e.x-=p1.x;
p.s.y-=p1.y;
p.e.y-=p1.y;
return dist_line(p);
}
double get_cos(double a,double b,double c){
return (b*b+c*c-a*a)/(*b*c);
}
double get_angle(Point p1,Point p2){
if (!sgn(dis(p1))||!sgn(dis(p2))) return 0.0;
double A,B,C;
A=dis(p1);
B=dis(p2);
C=dis(p1,p2);
if (C<=eps) return 0.0;
return fabs(acos(get_cos(C,A,B)));
}
Point get_point(Point p){
double T=sqr(p.x)+sqr(p.y);
return Point(sgn(p.x)*sqrt(sqr(p.x)/T),sgn(p.y)*sqrt(sqr(p.y)/T));
}
bool bigconclude(Circle p1,Circle p2,Point p){
Point e1=p2.p-p1.p;
Point e2=p-p1.p;
if (sgn(e1/e2)<) return ;
else return ;
}
double S(Point p1,Point p2,Point p3){
return fabs((p2-p1)*(p3-p1))/;
}
double work(Point p1,Point p2,double R){
Point O=Point(,);
double f=sgn(p1*p2),res=;
if (!sgn(f)||!sgn(dis(p1))||!sgn(dis(p2))) return 0.0;
double l=dist_line(Line(p1,p2));
double a=dis(p1);
double b=dis(p2);
double c=dis(p1,p2);
if (a<=R&&b<=R){
return fabs(p1*p2)/2.0*f;
}
if (a>=R&&b>=R&&l>=R){
double ang=get_angle(p1,p2);
return fabs((ang/(2.0))*(R*R))*f;
}
if (a>=R&&b>=R&&l<=R&&(get_cos(a,b,c)<=||get_cos(b,a,c)<=)){
double ang=get_angle(p1,p2);
return fabs((ang/(2.0))*(R*R))*f;
}
if (a>=R&&b>=R&&l<=R&&(get_cos(a,b,c)>&&get_cos(b,a,c)>)){
double dist=dist_line(Line(p1,p2));
double len=sqrt(sqr(R)-sqr(dist))*2.0;
double ang1=get_angle(p1,p2);
double cos2=get_cos(len,R,R);
res+=fabs(len*dist/2.0);
double ang2=ang1-acos(cos2);
res+=fabs((ang2/())*(R*R));
return res*f;
}
if ((a>=R&&b<R)||(a<R&&b>=R)){
if (b>a) std::swap(a,b),std::swap(p1,p2);
double T=sqr(p1.x-p2.x)+sqr(p1.y-p2.y);
Point u=Point(sgn(p1.x-p2.x)*sqrt(sqr(p1.x-p2.x)/T),sgn(p1.y-p2.y)*sqrt(sqr(p1.y-p2.y)/T));
double dist=dist_line(Line(p1,p2));
double len=sqrt(R*R-dist*dist);
double len2=sqrt(sqr(dis(p2))-sqr(dist));
if (fabs(dis(p2+u*len2)-dist)<=eps) len+=len2;
else len-=len2;
Point p=p2+u*len;
res+=S(O,p2,p);
double ang=get_angle(p1,p);
res+=fabs((ang/2.0)*R*R);
return res*f;
}
return ;
}
Point inter(Line p1,Line p2){
double t1=(p2.e-p1.s)*(p1.e-p1.s);
double t2=(p1.e-p1.s)*(p2.s-p1.s);
if (fabs(t1+t2)<eps) check=;
double k=t1/(t1+t2);
Point p;
p.x=p2.e.x+(p2.s.x-p2.e.x)*k;
p.y=p2.e.y+(p2.s.y-p2.e.y)*k;
return p;
}
bool jud(Line p1,Line p2,Line p3){
Point p=inter(p1,p2);
return (p3.e-p3.s)*(p-p3.s)<;
}
double inter(Circle P){
double res=;p[n+]=p[];
for (int i=;i<=n+;i++)
c[i].x=p[i].x-P.p.x,c[i].y=p[i].y-P.p.y;
for (int i=;i<=n;i++)
res+=work(c[i],c[i+],P.r);
return res;
}
void hpi(){
int L=,R=;tot=;
for (int i=;i<=cnt;i++){
if (l[i].slop!=l[i-].slop) tot++;
l[tot]=l[i];
}
q[++R]=l[];q[++R]=l[];
int all=tot;
for (int i=;i<=all;i++){
while (L<R&&jud(q[R],q[R-],l[i])) R--;
while (L<R&&jud(q[L],q[L+],l[i])) L++;
q[++R]=l[i];
}
while (L<R&&jud(q[R],q[R-],q[L])) R--;
while (L<R&&jud(q[L],q[L+],q[R])) L++;
tot=;
for (int i=L;i<R;i++)
d[++tot]=inter(q[i],q[i+]);
}
bool judge(Point p1,Point p2){
return (fabs(p1.x-p2.x)<eps&&fabs(p1.y-p2.y)<eps);
}
double gworking1(Point c1,Point c2,Point p1,Point p2){
double rev=sgn(c1*c2);
if (fabs(rev)<eps) return ;
num=;
Point O=Point(,);
if ((c1*c2)<) std::swap(c1,c2);
l[++num].s=O,l[num].e=c1;if (judge(l[num].s,l[num].e)) num--;
l[++num].s=c1,l[num].e=c2;if (judge(l[num].s,l[num].e)) num--;
l[++num].s=c2,l[num].e=O;if (judge(l[num].s,l[num].e)) num--;
if ((p1*p2)<) std::swap(p1,p2);
l[++num].s=O,l[num].e=p1;if (judge(l[num].s,l[num].e)) num--;
l[++num].s=p1,l[num].e=p2;if (judge(l[num].s,l[num].e)) num--;
l[++num].s=p2,l[num].e=O;if (judge(l[num].s,l[num].e)) num--;
for (int i=;i<=num;i++)
l[i].slop=atan2(l[i].e.y-l[i].s.y,l[i].e.x-l[i].s.x);
std::sort(l+,l++num,cmp3);
check=;
hpi();
if (check) return ;
d[tot+]=d[];
double res=;
for (int i=;i<=tot;i++)
res+=(d[i]*d[i+])/2.0;
return fabs(res)*rev;
}
double Gworking1(double a1,double a2,Circle w){
double r=w.r;
Point p1=Point(r*cos(a1),r*sin(a1));
Point p2=Point(r*cos(a2),r*sin(a2));
p[n+]=p[];
for (int i=;i<=n+;i++)
c[i]=Point(p[i].x-w.p.x,p[i].y-w.p.y);
double res=;
for (int i=;i<=n;i++)
res+=gworking1(c[i],c[i+],p1,p2);
return res;
}
Point inter(Circle p,Line l,Point p1){
double Dist=dist_line(l);
double dis1=llen(p1);
double len=sqrt(sqr(dis1)-sqr(Dist));
Point e=evector(l.e-l.s);
Point sx=p1;
double R=p.r;
double len2=sqrt(sqr(R)-sqr(Dist));
sx=sx-e*len;
sx=sx+e*len2;
return sx;
}
double gworking2(Point c1,Point c2,Point p1,Point p2,double R){
double rev=sgn(c1*c2),res=;Point O=Point(,);
if ((p1*p2)<) std::swap(p1,p2);
if ((c1*c2)<) std::swap(c1,c2);
if (fabs(rev)<eps) return ;
if (!sgn(dis(p1))||!sgn(dis(p2))) return 0.0;
double l=dist_line(Line(p1,p2));
double a=dis(p1);
double b=dis(p2);
double c=dis(p1,p2);
if (a<=R&&b<=R){
res=fabs(p1*p2)/2.0;
}
else
if (a>=R&&b>=R&&l>=R){
double ang=get_angle(p1,p2);
res=abs((ang/(2.0))*(R*R));
}
else
if (a>=R&&b>=R&&l<=R&&(get_cos(a,b,c)<=||get_cos(b,a,c)<=)){
double ang=get_angle(p1,p2);
res=fabs((ang/(2.0))*(R*R));
}
else
if (a>=R&&b>=R&&l<=R&&(get_cos(a,b,c)>&&get_cos(b,a,c)>)){
double dist=dist_line(Line(p1,p2));
double len=sqrt(sqr(R)-sqr(dist))*2.0;
double ang1=get_angle(p1,p2);
double cos2=get_cos(len,R,R);
res+=fabs(len*dist/2.0);
double ang2=ang1-acos(cos2);
res+=fabs((ang2/())*(R*R));
}
else
if ((a>=R&&b<R)||(a<R&&b>=R)){
if (b>a) std::swap(a,b),std::swap(p1,p2);
double T=sqr(p1.x-p2.x)+sqr(p1.y-p2.y);
Point u=Point(sgn(p1.x-p2.x)*sqrt(sqr(p1.x-p2.x)/T),sgn(p1.y-p2.y)*sqrt(sqr(p1.y-p2.y)/T));
double dist=dist_line(Line(p1,p2));
double len=sqrt(R*R-dist*dist);
double len2=sqrt(sqr(dis(p2))-sqr(dist));
if (fabs(dis(p2+u*len2)-dist)<=eps) len+=len2;
else len-=len2;
Point p=p2+u*len;
res+=S(O,p2,p);
double ang=get_angle(p1,p);
res+=fabs((ang/2.0)*R*R);
}
int in1=((sgn(c1*p1)*sgn(p1*c2))>=);
int in2=((sgn(c1*p2)*sgn(p2*c2))>=);
if (in1&&in2) return res*rev;
if (!in1){
if (dis(p1)<=R){
Point sb=inter(Line(O,c1),Line(p1,p2));
double Di=dis(sb);
if (Di<=R) res-=S(O,sb,p1);
else{
Point sx=inter(Circle(,,R),Line(p1,p2),p1);
double ang=get_angle(c1,sx);
res-=fabs((ang/2.0)*R*R);
res-=S(O,sx,p1);
}
}else{
Point sb=inter(Line(O,c1),Line(p1,p2));
double Di=dis(sb);
if (Di>=R){
double ang=get_angle(c1,p1);
res-=fabs((ang/2.0)*R*R);
}else{
Point sx=inter(Circle(,,R),Line(p1,p2),p1);
double ang2=get_angle(p1,sx);
res-=fabs((ang2/2.0)*R*R);
res-=S(sb,sx,O);
}
}
}
if (!in2){
if (dis(p2)<=R){
Point sb=inter(Line(O,c2),Line(p1,p2));
double Di=dis(sb);
if (Di<=R) res-=S(O,sb,p2);
else{
Point sx=inter(Circle(,,R),Line(p2,p1),p2);
double ang=get_angle(c2,sx);
res-=fabs((ang/2.0)*R*R);
res-=S(O,sx,p2);
}
}else{
Point sb=inter(Line(O,c2),Line(p1,p2));
double Di=dis(sb);
if (Di>=R){
double ang=get_angle(c2,p2);
res-=fabs((ang/2.0)*R*R);
}else{
Point sx=inter(Circle(,,R),Line(p2,p1),p2);
double ang2=get_angle(p2,sx);
res-=fabs((ang2/2.0)*R*R);
res-=S(sb,sx,O);
}
}
}
return res*rev;
}
double Gworking2(double a1,double a2,Circle w){
double res=,r=w.r;
Point p1=Point(r*cos(a1),r*sin(a1));
Point p2=Point(r*cos(a2),r*sin(a2));
p[n+]=p[];
for (int i=;i<=n+;i++)
c[i]=Point(p[i].x-w.p.x,p[i].y-w.p.y);
for (int i=;i<=n;i++)
res+=gworking2(c[i],c[i+],p1,p2,r);
return res;
}
void graham(){
int k=;
for (int i=;i<=n;i++)
if (p[i].y<p[k].y||(p[i].x<p[k].x&&p[i].y==p[k].y)) k=i;
std::sort(p+,p++n,cmp);
int top=;c[top]=p[];
for (int i=;i<=n;i++){
while (top>&&(c[top]-c[top-])*(p[i]-c[top])<=) top--;
c[++top]=p[i];
}
n=top;
for (int i=;i<=top;i++)
p[i]=c[i];
}
void Work(Circle p1,Point a1,Point a2){
Point O=p1.p;double r=p1.r;
a1.x-=O.x;a2.x-=O.x;
a1.y-=O.y;a2.y-=O.y;
double x1=atan2(a1.y,a1.x),x2=atan2(a2.y,a2.x);
if (x1<) x1+=*Pi;
if (x2<) x2+=*Pi;
if (x1<=x2){
cnt++;
L[cnt].l=x1;
L[cnt].r=x2;
}else{
cnt++;
L[cnt].l=x1;
L[cnt].r=*Pi;
cnt++;
L[cnt].l=0.0;
L[cnt].r=x2;
}
}
void add(Circle p1,Circle p2){
double x1=p1.p.x,x2=p2.p.x,y1=p1.p.y,y2=p2.p.y,r1=p1.r,r2=p2.r;
double A=-*(x1+x2),B=-*(y1+y2),C=sqr(x1)+sqr(x2)+sqr(y1)+sqr(y2)-sqr(r1)-sqr(r2);
Point S,E;
if (fabs(A)<eps){
S=Point(,(C)/B);
E=Point(,(C)/B);
}else
if (fabs(B)<eps){
S=Point((C)/A,);
E=Point((C)/A,);
}else{
S=Point(,(C-A)/B);
E=Point(,(C-*A)/B);
}
Line l=Line(S,E);
double Dist1=dist_line(p1.p,l);
double Dist2=llen(p1.p-S);
Point e=evector(E-S);
double Dist3=sqrt(sqr(Dist2)-sqr(Dist1));
e=e*Dist3;
Point a1,a2;
if (fabs(dis(S+e,p1.p)-Dist1)<eps){
S=S+e;
}
else S=S-e;
e=e/Dist3;
double Dist4=sqrt(sqr(p1.r)-sqr(llen(S-p1.p)));
e=e*Dist4;
a1=S+e;
a2=S-e;
if ((a1-p1.p)*(a2-p1.p)<) std::swap(a1,a2);
//a1放在a2的顺时针方向、
if (bigconclude(p1,p2,a1)) std::swap(a1,a2);
//a1到a2必须是逆时针。
Work(p1,a1,a2);
}
int main(){
freopen("aerolite.in","r",stdin);
freopen("aerolite.out","w",stdout);
scanf("%d",&m);
for (int i=;i<=m;i++){
scanf("%lf%lf%lf",&a[i].p.x,&a[i].p.y,&a[i].r);
}
scanf("%d",&n);
for (int i=;i<=n;i++){
scanf("%lf%lf",&p[i].x,&p[i].y);
}
graham();
for (int i=;i<=m;i++) pd[i]=;
for (int i=;i<=m;i++){
for (int j=;j<=m;j++)
if (i!=j){
if (conclude(a[i],a[j])) {pd[i]=;break;}
}
}
double ans=;
for (int i=;i<=m;i++)
if (pd[i]){
bool mark=;
for (int j=;j<=m;j++)
if (i!=j&&pd[j]){
if (intersect(a[i],a[j])) {mark=;break;}
}
if (!mark) ans+=inter(a[i]),pd[i]=;
}
int j=;
for (int i=;i<=m;i++)
if (pd[i]) a[++j]=a[i];
for (int i=;i<=m;i++) pd[i]=;
for (int i=;i<=m;i++){
cnt=;
for (int j=;j<=m;j++)
if (i!=j){
add(a[i],a[j]);
}
std::sort(L+,L++cnt,cmp2);
L[].r=0.0;
L[cnt+].l=*Pi;
double Reach=0.0,Last=0.0;
int ww=;
for (int j=;j<=cnt;j++)
if (L[j].l>Reach){
if (j==) ww++;
ans+=Gworking1(Last,Reach,a[i]);
Last=L[j].l;
ans+=Gworking2(Reach,L[j].l,a[i]);
Reach=L[j].r;
}else{
Reach=L[j].r;
}
if (fabs(Reach-*Pi)<eps){
ans+=Gworking1(Last,Reach,a[i]);
}else
if (fabs(Reach-*Pi)>=eps){
ans+=Gworking1(Last,Reach,a[i]);
ans+=Gworking2(Reach,*Pi,a[i]);
}
}
printf("%.8lf\n",ans);
return ;
}
NOI十连测 第六测 T3的更多相关文章
- NOI十连测 第六测 T1
思路: 用treap动态维护,记一个sum1,sum2,注意!,写treap如果有删除操作,千万不能把权值相同的分开来..,这在删除的时候会进入死循环,这是一个惨痛的教训... #include< ...
- <转>二十问全链路压测干货汇总(上)
本文转载自:微信公众号-数列科技<二十问全链路压测干货汇总(上)> 最近几年全链路压测无疑成为了一个热门话题,在各个技术峰会上都可以看到它的身影. 一些大型的互联网公司,比如阿里巴巴.京东 ...
- 「NOI十联测」深邃
「NOI十联测」深邃 要使得最大的连通块最小,显然先二分答案. 先固定1结点为根. 对于一个果实,显然是先处理子树中未分配的点,再向外延伸. 每个结点记录一个\(si[]\),表示子树中未分配的点数, ...
- 「NOI十联测」奥义商店
「NOI十联测」奥义商店 若lzz想花费最少的钱,那么显然要选择数目较少的颜色. 先考虑暴力的写法. 每次向两边统计,每个物品要求被买的概率可以由上一个物品推出. now=1;//now 被买概率 M ...
- 「NOI十联测」黑暗
「NOI十联测」黑暗 \(n\) 个点的无向图,每条边都可能存在,一个图的权值是连通块个数的 \(m\) 次方,求所有可能的图的权值和.(n≤30000,m≤15) 令\(ans[n][m]\)为n个 ...
- NOI十连测 第四测 T3
思路: 算法一:可以n^2找出每个点的权值,然后n^2做完,预计得分10 算法二:随机找点然后每次找最高..貌似只有10分?然而考试的时候煞笔了,边界设成inf.. 算法三:随机找几个点,然后随机爬山 ...
- NOI十连测 第五测 T2
思路:考虑建立可持久化线段树,第一层维护的是i这个位置的next位置,第二层,维护的是接下来走这个字符会到哪个节点. 感觉很巧妙啊,不愧是Claris #include<algorithm> ...
- NOI十连测 第五测 T1
#include<cstdio> #include<cstring> #include<cmath> #include<iostream> #inclu ...
- NOI十连测 第四测 T2
思路:线段树套可持久化treap,可持久化treap我还是第一次听说.. 改题的时候没看数据范围..乱开数组T_T #include<algorithm> #include<cstd ...
随机推荐
- Android自定义日历，可以点击、标注日期、节气、旧历等
1. [图片] 9A59974C-47D4-47E3-8136-3F873EB9BBDC.jpg 2. [图片] left_arrow_pre.png 3. [图片] left_arrow.png 4 ...
- 负载均衡 > 常见问题
证书管理相关问题 常用证书申请流程 1.本地生成私钥:openssl genrsa -out privateKey.pem 2048 其中privateKey.pem为您的私钥文件,请妥善保管. 2. ...
- 深入浅出Node.js (5) - 内存控制
5.1 V8的垃圾回收机制与内存限制 5.1.1 Node与V8 5.1.2 V8的内存限制 5.1.3 V8的对象分配 5.1.4 V8的垃圾回收机制 5.1.5 查看垃圾回收日志 5.2 高效使用 ...
- JAVASCRIPT实现XML分页
为了方便用户查看大批量数据,我们会用到动态分页,因此分页功能是我们在网站上见过的最普遍也是最常用的一个功能模块了.而以往的信息分页都是连接到数据库的,每一次点击都必须要后台数据库的支持.这样不但服务器 ...
- statfs函数说明
函数: statfs 功能描述: 查询文件系统相关的信息. 用法: #include <sys/vfs.h> /* 或者 <sys/statfs.h> ...
- 图论专题训练1-D(K步最短路,矩阵连乘)
题目链接 /* *题目大意: *求出从i到j,刚好经过k条边的最短路; * *矩阵乘法的应用之一(国家队论文): *矩阵乘法不满足交换律,矩阵乘法满足结合律; *给定一个有向图,问从A点恰好走k步(允 ...
- JSplitPane详解
摘自http://blog.163.com/xiexueyong1987@126/blog/static/1262673422010102711295541/ JSplitPane详解 pasting ...
- [转]Hulu 2013北京地区校招笔试题
填空题: 1.中序遍历二叉树,结果为ABCDEFGH,后序遍历结果为ABEDCHGF,逆序遍历结果为? 2.对字符串HELL0_HULU中的字符进行二进制编码,使得字符串的编码长度尽可能短,最短长度为 ...
- python list 中找连续的数字(由网友处学习)
# -*- coding: utf-8 -*- # python:2.x __author__ = 'Administrator' #学习这个要求的:http://wsky.org/archives/ ...
- jquery.validate详解一
jQuery校验 官网地址:http://bassistance.de/jquery-plugins/jquery-plugin-validation 一导入js库 <script src=&q ...