library
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test/aoj/geometry/2454.test.cpp
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- Last update: 2020-10-26 15:08:18+09:00
- Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2454
Depends on
Code
// verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2454
// verification-helper: ERROR 1e-6
#include<bits/stdc++.h>
using namespace std;
#define call_from_test
#include "../../../geometry/geometry.cpp"
#undef call_from_test
// segmentArrangement
signed main(){
int n,m;
cin>>n>>m;
vector<Segment> ss(n);
Polygon ps(m);
for(int i=0;i<n;i++) cin>>ss[i];
for(int i=0;i<m;i++) cin>>ps[i];
map<Point, int> mp;
for(int i=0;i<m;i++) mp[ps[i]]=i;
Point s,g;
cin>>s>>g;
ps.emplace_back(s);
ps.emplace_back(g);
auto H=segmentArrangement(ss,ps);
vector< vector< pair<int, double> > > G(H.size());
for(int i=0;i<(int)H.size();i++)
for(int j:H[i]) G[i].emplace_back(j,abs(ps[i]-ps[j]));
double ans=0,tmp=0;
for(int i=0;i<n;i++) ans+=abs(ss[i].p1-ss[i].p2);
vector<int> used(G.size(),0);
queue<int> q;
for(int i=0;i<(int)G.size();i++)
if(ps[i]==g) {used[i]=1;q.emplace(i);}
while(!q.empty()){
int v=q.front();q.pop();
if(ps[v]==s){
cout<<(int)-1<<endl;
return 0;
}
if(mp.count(ps[v])) continue;
for(int u:H[v]){
if(!used[u]){
used[u]=1;
q.emplace(u);
}
}
}
for(int i=0;i<(int)G.size();i++)
if(ps[i]==s) q.emplace(i);
while(!q.empty()){
int v=q.front();q.pop();
for(auto &e:G[v]){
int u=e.first;
double &c=e.second;
if(used[v]&&used[u]) continue;
if(c==0) continue;
tmp+=c;c=0;
q.emplace(u);
}
}
tmp/=2;
cout<<fixed<<setprecision(12)<<ans-tmp<<endl;
return 0;
}#line 1 "test/aoj/geometry/2454.test.cpp"
// verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2454
// verification-helper: ERROR 1e-6
#include<bits/stdc++.h>
using namespace std;
#define call_from_test
#line 1 "geometry/geometry.cpp"
#line 3 "geometry/geometry.cpp"
using namespace std;
#endif
//BEGIN CUT HERE
#define equals(a,b) (fabs((a)-(b))<EPS)
namespace geometry {
const double EPS = 1e-10;
const double PI = asinl(1) * 2;
struct Point{
double x,y;
Point(){}
Point(double x,double y):x(x),y(y){}
Point operator+(Point p) {return Point(x+p.x,y+p.y);}
Point operator-(Point p) {return Point(x-p.x,y-p.y);}
Point operator*(double k){return Point(x*k,y*k);}
Point operator/(double k){return Point(x/k,y/k);}
double norm(){return x*x+y*y;}
double abs(){return sqrt(norm());}
bool operator<(const Point &p) const{
return x!=p.x?x<p.x:y<p.y;
//grid-point only
//return !equals(x,p.x)?x<p.x:!equals(y,p.y)?y<p.y:0;
}
bool operator==(const Point &p) const{
return fabs(x-p.x)<EPS and fabs(y-p.y)<EPS;
}
};
bool sort_x(Point a,Point b){
return a.x!=b.x?a.x<b.x:a.y<b.y;
}
bool sort_y(Point a,Point b){
return a.y!=b.y?a.y<b.y:a.x<b.x;
}
typedef Point Vector;
typedef vector<Point> Polygon;
struct Segment{
Point p1,p2;
Segment(){}
Segment(Point p1, Point p2):p1(p1),p2(p2){}
};
typedef Segment Line;
struct Circle{
Point c;
double r;
Circle(){}
Circle(Point c,double r):c(c),r(r){}
};
double norm(Vector a){
return a.x*a.x+a.y*a.y;
}
double abs(Vector a){
return sqrt(norm(a));
}
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;
}
Point orth(Point p){return Point(-p.y,p.x);}
bool isOrthogonal(Vector a,Vector b){
return equals(dot(a,b),0.0);
}
bool isOrthogonal(Point a1,Point a2,Point b1,Point b2){
return isOrthogonal(a1-a2,b1-b2);
}
bool isOrthogonal(Segment s1,Segment s2){
return equals(dot(s1.p2-s1.p1,s2.p2-s2.p1),0.0);
}
bool isParallel(Vector a,Vector b){
return equals(cross(a,b),0.0);
}
bool isParallel(Point a1,Point a2,Point b1,Point b2){
return isParallel(a1-a2,b1-b2);
}
bool isParallel(Segment s1,Segment s2){
return equals(cross(s1.p2-s1.p1,s2.p2-s2.p1),0.0);
}
Point project(Segment s,Point p){
Vector base=s.p2-s.p1;
double r=dot(p-s.p1,base)/norm(base);
return s.p1+base*r;
}
Point reflect(Segment s,Point p){
return p+(project(s,p)-p)*2.0;
}
double arg(Vector p){
return atan2(p.y,p.x);
}
Vector polar(double a,double r){
return Point(cos(r)*a,sin(r)*a);
}
// COUNTER CLOCKWISE
static const int CCW_COUNTER_CLOCKWISE = 1;
static const int CCW_CLOCKWISE = -1;
static const int CCW_ONLINE_BACK = 2;
static const int CCW_ONLINE_FRONT = -2;
static const int CCW_ON_SEGMENT = 0;
int ccw(Point p0,Point p1,Point p2){
Vector a = p1-p0;
Vector b = p2-p0;
if(cross(a,b) > EPS) return CCW_COUNTER_CLOCKWISE;
if(cross(a,b) < -EPS) return CCW_CLOCKWISE;
if(dot(a,b) < -EPS) return CCW_ONLINE_BACK;
if(a.norm()<b.norm()) return CCW_ONLINE_FRONT;
return CCW_ON_SEGMENT;
}
bool intersectSS(Point p1,Point p2,Point p3,Point p4){
return (ccw(p1,p2,p3)*ccw(p1,p2,p4) <= 0 and
ccw(p3,p4,p1)*ccw(p3,p4,p2) <= 0 );
}
bool intersectSS(Segment s1,Segment s2){
return intersectSS(s1.p1,s1.p2,s2.p1,s2.p2);
}
bool intersectPS(Polygon p,Segment l){
int n=p.size();
for(int i=0;i<n;i++)
if(intersectSS(Segment(p[i],p[(i+1)%n]),l)) return 1;
return 0;
}
double getDistanceLP(Line l,Point p){
return fabs(cross(l.p2-l.p1,p-l.p1)/abs(l.p2-l.p1));
}
double getDistanceSP(Segment s,Point p){
if(dot(s.p2-s.p1,p-s.p1) < 0.0 ) return abs(p-s.p1);
if(dot(s.p1-s.p2,p-s.p2) < 0.0 ) return abs(p-s.p2);
return getDistanceLP(s,p);
}
double getDistanceSS(Segment s1,Segment s2){
if(intersectSS(s1,s2)) return 0.0;
return min(min(getDistanceSP(s1,s2.p1),getDistanceSP(s1,s2.p2)),
min(getDistanceSP(s2,s1.p1),getDistanceSP(s2,s1.p2)));
}
// intercsect of circles
static const int ICC_SEPERATE = 4;
static const int ICC_CIRCUMSCRIBE = 3;
static const int ICC_INTERSECT = 2;
static const int ICC_INSCRIBE = 1;
static const int ICC_CONTAIN = 0;
int intersectCC(Circle c1,Circle c2){
if(c1.r<c2.r) swap(c1,c2);
double d=abs(c1.c-c2.c);
double r=c1.r+c2.r;
if(equals(d,r)) return ICC_CIRCUMSCRIBE;
if(d>r) return ICC_SEPERATE;
if(equals(d+c2.r,c1.r)) return ICC_INSCRIBE;
if(d+c2.r<c1.r) return ICC_CONTAIN;
return ICC_INTERSECT;
}
bool intersectSC(Segment s,Circle c){
return getDistanceSP(s,c.c)<=c.r;
}
int intersectCS(Circle c,Segment s){
if(norm(project(s,c.c)-c.c)-c.r*c.r>EPS) return 0;
double d1=abs(c.c-s.p1),d2=abs(c.c-s.p2);
if(d1<c.r+EPS and d2<c.r+EPS) return 0;
if((d1<c.r-EPS and d2>c.r+EPS) or (d1>c.r+EPS and d2<c.r-EPS)) return 1;
Point h=project(s,c.c);
if(dot(s.p1-h,s.p2-h)<0) return 2;
return 0;
}
Point getCrossPointSS(Segment s1,Segment s2){
for(int k=0;k<2;k++){
if(getDistanceSP(s1,s2.p1)<EPS) return s2.p1;
if(getDistanceSP(s1,s2.p2)<EPS) return s2.p2;
swap(s1,s2);
}
Vector base=s2.p2-s2.p1;
double d1=fabs(cross(base,s1.p1-s2.p1));
double d2=fabs(cross(base,s1.p2-s2.p1));
double t=d1/(d1+d2);
return s1.p1+(s1.p2-s1.p1)*t;
}
Point getCrossPointLL(Line l1,Line l2){
double a=cross(l1.p2-l1.p1,l2.p2-l2.p1);
double b=cross(l1.p2-l1.p1,l1.p2-l2.p1);
if(fabs(a)<EPS and fabs(b)<EPS) return l2.p1;
return l2.p1+(l2.p2-l2.p1)*(b/a);
}
Polygon getCrossPointCL(Circle c,Line l){
Polygon ps;
Point pr=project(l,c.c);
Vector e=(l.p2-l.p1)/abs(l.p2-l.p1);
if(equals(getDistanceLP(l,c.c),c.r)){
ps.emplace_back(pr);
return ps;
}
double base=sqrt(c.r*c.r-norm(pr-c.c));
ps.emplace_back(pr+e*base);
ps.emplace_back(pr-e*base);
return ps;
}
Polygon getCrossPointCS(Circle c,Segment s){
Line l(s);
Polygon res=getCrossPointCL(c,l);
if(intersectCS(c,s)==2) return res;
if(res.size()>1u){
if(dot(l.p1-res[0],l.p2-res[0])>0) swap(res[0],res[1]);
res.pop_back();
}
return res;
}
Polygon getCrossPointCC(Circle c1,Circle c2){
Polygon p(2);
double d=abs(c1.c-c2.c);
double a=acos((c1.r*c1.r+d*d-c2.r*c2.r)/(2*c1.r*d));
double t=arg(c2.c-c1.c);
p[0]=c1.c+polar(c1.r,t+a);
p[1]=c1.c+polar(c1.r,t-a);
return p;
}
// IN:2 ON:1 OUT:0
int contains(Polygon g,Point p){
int n=g.size();
bool x=false;
for(int i=0;i<n;i++){
Point a=g[i]-p,b=g[(i+1)%n]-p;
if(fabs(cross(a,b)) < EPS and dot(a,b) < EPS) return 1;
if(a.y>b.y) swap(a,b);
if(a.y < EPS and EPS < b.y and cross(a,b) > EPS ) x = !x;
}
return (x?2:0);
}
Polygon andrewScan(Polygon s){
Polygon u,l;
if(s.size()<3) return s;
sort(s.begin(),s.end());
u.push_back(s[0]);
u.push_back(s[1]);
l.push_back(s[s.size()-1]);
l.push_back(s[s.size()-2]);
for(int i=2;i<(int)s.size();i++){
for(int n=u.size();
n>=2 and ccw(u[n-2],u[n-1],s[i])!=CCW_CLOCKWISE;
n--){
u.pop_back();
}
u.push_back(s[i]);
}
for(int i=s.size()-3;i>=0;i--){
for(int n=l.size();
n>=2 and ccw(l[n-2],l[n-1],s[i])!=CCW_CLOCKWISE;
n--){
l.pop_back();
}
l.push_back(s[i]);
}
reverse(l.begin(),l.end());
for(int i=u.size()-2;i>=1;i--) l.push_back(u[i]);
return l;
}
Polygon convex_hull(Polygon ps){
int n=ps.size();
sort(ps.begin(),ps.end(),sort_y);
int k=0;
Polygon qs(n*2);
for(int i=0;i<n;i++){
while(k>1 and cross(qs[k-1]-qs[k-2],ps[i]-qs[k-1])<0) k--;
qs[k++]=ps[i];
}
for(int i=n-2,t=k;i>=0;i--){
while(k>t and cross(qs[k-1]-qs[k-2],ps[i]-qs[k-1])<0) k--;
qs[k++]=ps[i];
}
qs.resize(k-1);
return qs;
}
double diameter(Polygon s){
Polygon p=s;
int n=p.size();
if(n==2) return abs(p[0]-p[1]);
int i=0,j=0;
for(int k=0;k<n;k++){
if(p[i]<p[k]) i=k;
if(!(p[j]<p[k])) j=k;
}
double res=0;
int si=i,sj=j;
while(i!=sj or j!=si){
res=max(res,abs(p[i]-p[j]));
if(cross(p[(i+1)%n]-p[i],p[(j+1)%n]-p[j])<0.0){
i=(i+1)%n;
}else{
j=(j+1)%n;
}
}
return res;
}
bool isConvex(Polygon p){
bool f=1;
int n=p.size();
for(int i=0;i<n;i++){
int t=ccw(p[(i+n-1)%n],p[i],p[(i+1)%n]);
f&=t!=CCW_CLOCKWISE;
}
return f;
}
double area(Polygon s){
double res=0;
for(int i=0;i<(int)s.size();i++){
res+=cross(s[i],s[(i+1)%s.size()])/2.0;
}
return res;
}
double area(Circle c1,Circle c2){
double d=abs(c1.c-c2.c);
if(c1.r+c2.r<=d+EPS) return 0;
if(d<=fabs(c1.r-c2.r)){
double r=min(c1.r,c2.r);
return PI*r*r;
}
double res=0;
for(int k=0;k<2;k++){
double rc=(d*d+c1.r*c1.r-c2.r*c2.r)/(2*d*c1.r);
double th=acosl(rc)*2;
res+=(th-sinl(th))*c1.r*c1.r/2;
swap(c1,c2);
}
return res;
}
Polygon convexCut(Polygon p,Line l){
Polygon q;
for(int i=0;i<(int)p.size();i++){
Point a=p[i],b=p[(i+1)%p.size()];
if(ccw(l.p1,l.p2,a)!=-1) q.push_back(a);
if(ccw(l.p1,l.p2,a)*ccw(l.p1,l.p2,b)<0)
q.push_back(getCrossPointLL(Line(a,b),l));
}
return q;
}
Line bisector(Point p1,Point p2){
Circle c1=Circle(p1,abs(p1-p2)),c2=Circle(p2,abs(p1-p2));
Polygon p=getCrossPointCC(c1,c2);
if(cross(p2-p1,p[0]-p1)>0) swap(p[0],p[1]);
return Line(p[0],p[1]);
}
Vector translate(Vector v,double theta){
Vector res;
res.x=cos(theta)*v.x-sin(theta)*v.y;
res.y=sin(theta)*v.x+cos(theta)*v.y;
return res;
}
vector<Line> corner(Line l1,Line l2){
vector<Line> res;
if(isParallel(l1,l2)){
double d=getDistanceLP(l1,l2.p1)/2.0;
Vector v1=l1.p2-l1.p1;
v1=v1/v1.abs()*d;
Point p=l2.p1+translate(v1,90.0*(PI/180.0));
double d1=getDistanceLP(l1,p);
double d2=getDistanceLP(l2,p);
if(fabs(d1-d2)>d){
p=l2.p1+translate(v1,-90.0*(PI/180.0));
}
res.push_back(Line(p,p+v1));
}else{
Point p=getCrossPointLL(l1,l2);
Vector v1=l1.p2-l1.p1,v2=l2.p2-l2.p1;
v1=v1/v1.abs();
v2=v2/v2.abs();
res.push_back(Line(p,p+(v1+v2)));
res.push_back(Line(p,p+translate(v1+v2,90.0*(PI/180.0))));
}
return res;
}
Polygon tangent(Circle c1,Point p2){
Circle c2=Circle(p2,sqrt(norm(c1.c-p2)-c1.r*c1.r));
Polygon p=getCrossPointCC(c1,c2);
sort(p.begin(),p.end());
return p;
}
vector<Line> tangent(Circle c1,Circle c2){
vector<Line> ls;
if(c1.r<c2.r) swap(c1,c2);
double g=norm(c1.c-c2.c);
if(equals(g,0)) return ls;
Point u=(c2.c-c1.c)/sqrt(g);
Point v=orth(u);
for(int s=1;s>=-1;s-=2){
double h=(c1.r+s*c2.r)/sqrt(g);
if(equals(1-h*h,0)){
ls.emplace_back(c1.c+u*c1.r,c1.c+(u+v)*c1.r);
}else if(1-h*h>0){
Point uu=u*h,vv=v*sqrt(1-h*h);
ls.emplace_back(c1.c+(uu+vv)*c1.r,c2.c-(uu+vv)*c2.r*s);
ls.emplace_back(c1.c+(uu-vv)*c1.r,c2.c-(uu-vv)*c2.r*s);
}
}
return ls;
}
double closest_pair(Polygon &a,int l=0,int r=-1){
if(r<0){
r=a.size();
sort(a.begin(),a.end(),sort_x);
}
if(r-l<=1) return abs(a[0]-a[1]);
int m=(l+r)>>1;
double x=a[m].x;
double d=min(closest_pair(a,l,m),closest_pair(a,m,r));
inplace_merge(a.begin()+l,a.begin()+m,a.begin()+r,sort_y);
Polygon b;
for(int i=l;i<r;i++){
if(fabs(a[i].x-x)>=d) continue;
for(int j=0;j<(int)b.size();j++){
double dy=a[i].y-next(b.rbegin(),j)->y;
if(dy>=d) break;
d=min(d,abs(a[i]-*next(b.rbegin(),j)));
}
b.emplace_back(a[i]);
}
return d;
}
vector<vector<int>>
segmentArrangement(vector<Segment> &ss, Polygon &ps){
int n=ss.size();
for(int i=0;i<n;i++){
ps.emplace_back(ss[i].p1);
ps.emplace_back(ss[i].p2);
for(int j=i+1;j<n;j++)
if(intersectSS(ss[i],ss[j]))
ps.emplace_back(getCrossPointSS(ss[i],ss[j]));
}
sort(ps.begin(),ps.end());
ps.erase(unique(ps.begin(),ps.end()),ps.end());
vector<vector<int> > G(ps.size());
for(int i=0;i<n;i++){
vector<pair<double,int> > ls;
for(int j=0;j<(int)ps.size();j++)
if(getDistanceSP(ss[i],ps[j])<EPS)
ls.emplace_back(make_pair(norm(ss[i].p1-ps[j]),j));
sort(ls.begin(),ls.end());
for(int j=0;j+1<(int)ls.size();j++){
int a=ls[j].second,b=ls[j+1].second;
G[a].emplace_back(b);
G[b].emplace_back(a);
}
}
for(auto &v:G){
sort(v.begin(),v.end());
v.erase(unique(v.begin(),v.end()),v.end());
}
return G;
}
struct EndPoint{
Point p;
int seg,st;
EndPoint(){}
EndPoint(Point p,int seg,int st):p(p),seg(seg),st(st){}
bool operator<(const EndPoint &ep)const{
if(p.y==ep.p.y) return st<ep.st;
return p.y<ep.p.y;
}
};
int manhattan_intersection(vector<Segment> ss,const int INF){
const int BTM = 0;
const int LFT = 1;
const int RGH = 2;
const int TOP = 3;
int n=ss.size();
vector<EndPoint> ep;
for(int i=0;i<n;i++){
if(ss[i].p1.y==ss[i].p2.y){
if(ss[i].p1.x>ss[i].p2.x) swap(ss[i].p1,ss[i].p2);
ep.emplace_back(ss[i].p1,i,LFT);
ep.emplace_back(ss[i].p2,i,RGH);
}else{
if(ss[i].p1.y>ss[i].p2.y) swap(ss[i].p1,ss[i].p2);
ep.emplace_back(ss[i].p1,i,BTM);
ep.emplace_back(ss[i].p2,i,TOP);
}
}
sort(ep.begin(),ep.end());
set<int> bt;
bt.insert(INF);
int cnt=0;
for(int i=0;i<n*2;i++){
if(ep[i].st==TOP){
bt.erase(ep[i].p.x);
}else if(ep[i].st==BTM){
bt.emplace(ep[i].p.x);
}else if(ep[i].st==LFT){
auto b=bt.lower_bound(ss[ep[i].seg].p1.x);
auto e=bt.upper_bound(ss[ep[i].seg].p2.x);
cnt+=distance(b,e);
}
}
return cnt;
}
double area(Polygon ps,Circle c){
if(ps.size()<3u) return 0;
function<double(Circle, Point, Point)> dfs=
[&](Circle c,Point a,Point b){
Vector va=c.c-a,vb=c.c-b;
double f=cross(va,vb),res=0;
if(equals(f,0.0)) return res;
if(max(abs(va),abs(vb))<c.r+EPS) return f;
Vector d(dot(va,vb),cross(va,vb));
if(getDistanceSP(Segment(a,b),c.c)>c.r-EPS)
return c.r*c.r*atan2(d.y,d.x);
auto u=getCrossPointCS(c,Segment(a,b));
if(u.empty()) return res;
if(u.size()>1u and dot(u[1]-u[0],a-u[0])>0) swap(u[0],u[1]);
u.emplace(u.begin(),a);
u.emplace_back(b);
for(int i=1;i<(int)u.size();i++)
res+=dfs(c,u[i-1],u[i]);
return res;
};
double res=0;
for(int i=0;i<(int)ps.size();i++)
res+=dfs(c,ps[i],ps[(i+1)%ps.size()]);
return res/2;
}
}
using namespace geometry;
namespace geometry{
istream &operator>>(istream &is,Point &p){
is>>p.x>>p.y;
return is;
}
istream &operator>>(istream &is,Polygon &p){
for(int i=0;i<(int)p.size();i++) is>>p[i];
return is;
}
istream &operator>>(istream &is,Segment &s){
is>>s.p1>>s.p2;
return is;
}
istream &operator>>(istream &is,Circle &c){
is>>c.c>>c.r;
return is;
}
ostream &operator<<(ostream &os,Point p){
os<<fixed<<setprecision(12)<<p.x<<" "<<p.y;
return os;
}
}
//END CUT HERE
#ifndef call_from_test
signed main(){
return 0;
}
#endif
#line 9 "test/aoj/geometry/2454.test.cpp"
#undef call_from_test
// segmentArrangement
signed main(){
int n,m;
cin>>n>>m;
vector<Segment> ss(n);
Polygon ps(m);
for(int i=0;i<n;i++) cin>>ss[i];
for(int i=0;i<m;i++) cin>>ps[i];
map<Point, int> mp;
for(int i=0;i<m;i++) mp[ps[i]]=i;
Point s,g;
cin>>s>>g;
ps.emplace_back(s);
ps.emplace_back(g);
auto H=segmentArrangement(ss,ps);
vector< vector< pair<int, double> > > G(H.size());
for(int i=0;i<(int)H.size();i++)
for(int j:H[i]) G[i].emplace_back(j,abs(ps[i]-ps[j]));
double ans=0,tmp=0;
for(int i=0;i<n;i++) ans+=abs(ss[i].p1-ss[i].p2);
vector<int> used(G.size(),0);
queue<int> q;
for(int i=0;i<(int)G.size();i++)
if(ps[i]==g) {used[i]=1;q.emplace(i);}
while(!q.empty()){
int v=q.front();q.pop();
if(ps[v]==s){
cout<<(int)-1<<endl;
return 0;
}
if(mp.count(ps[v])) continue;
for(int u:H[v]){
if(!used[u]){
used[u]=1;
q.emplace(u);
}
}
}
for(int i=0;i<(int)G.size();i++)
if(ps[i]==s) q.emplace(i);
while(!q.empty()){
int v=q.front();q.pop();
for(auto &e:G[v]){
int u=e.first;
double &c=e.second;
if(used[v]&&used[u]) continue;
if(c==0) continue;
tmp+=c;c=0;
q.emplace(u);
}
}
tmp/=2;
cout<<fixed<<setprecision(12)<<ans-tmp<<endl;
return 0;
}