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1118.cpp
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1118.cpp
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#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define PI (acos(-1))
#define ct cout<<
#define cn cin>>
#define spc <<" "<<
#define nl puts("")
#define _fl(x) puts("FLAG " #x),fflush(stdout);
#define _(x) cout<< #x <<" is "<< x <<endl;
#define fs first
#define sc second
#define pb push_back
#define all(v) (v).begin(), (v).end()
#define _109 (1000000000)
#define _0(arr) memset(arr,0,sizeof ( arr ) )
#define _1(arr) memset(arr,-1,sizeof ( arr ) )
#define _ninp(n,arr) for(int i=0; i<n;i++)cin>>arr[i];
#define _nout(n,arr) for(int i=0; i<n;i++)cout<<arr[i]<<" \n"[i==n-1];
double _eps=1e-6;
namespace Geometry{
// equation is in ax+by+c=0 form
typedef double myType;
int g(myType p,myType q){
return ((p>q) || fabs(p-q)<=_eps);
}
int l(myType p,myType q){
return ((p<q) || fabs(p-q)<=_eps);
}
struct pt{
myType x,y;
void in(){
cn x;
cn y;
}
void assign( myType _x,myType _y){
x=_x;
y=_y;
}
pt(){};
pt(myType _x,myType _y){
x=_x;
y=_y;
}
void out(){ct x spc y,nl;}
bool operator ==(const pt &a)const{
if(fabs(a.x-x)<=_eps && fabs(a.y-y)<=_eps)return true;
return false;
}
double to(pt a){
return sqrt((x-a.x)*(x-a.x)+(y-a.y)*(y-a.y));
}
vector<myType> eqn(pt p){
myType a,b,c;
a=(p.y- y);
b=-(p.x- x);
c= y*(p.x- x)- x*(p.y- y);
vector<myType> r;
r.pb(a);
r.pb(b);
r.pb(c);
return r;
}
vector<myType> eqn_by_slope(myType m){
myType a,b,c;
a=m;
b=-1;
c= y-m*x;
vector<myType> r;
r.pb(a);
r.pb(b);
r.pb(c);
return r;
}
int on_this_line(pt p1,pt p2){
vector<myType> v=p1.eqn(p2);
myType r=v[0]*x+v[1]*y+v[2];
if(fabs(r)<=_eps){
if(g(x,min(p1.x,p2.x)) && l(x,max(p1.x,p2.x)) && g(y,min(p1.y,p2.y)) && l(y,max(p1.y,p2.y)))
return 1;
}
return 0;
}
vector<myType> eqn_orthogonal_to(pt p, pt q){
vector<myType> v=p.eqn(q);
myType a=v[1];
myType b=-v[0];
myType c=-(a*x+b*y);
vector <myType> r;
r.pb(a);
r.pb(b);
r.pb(c);
return r;
}
};
pt solve_eqn(vector<myType> v,vector<myType> v1,ll INF){
v[2]=-v[2];
v1[2]=-v1[2];
myType ab=v[0]*v1[1]-(v1[0]*v[1]);
if(fabs(ab)<_eps){
pt r(INF,INF);
ct "IN/f";
return r;
}
myType x=(v[2]*v1[1]-(v1[2]*v[1]))/ab;
myType y=(v[0]*v1[2]-(v1[0]*v[2]))/ab;
pt r(x,y);
return r;
}
int orientation(pt a,pt b,pt c){
myType r=a.x*(b.y-c.y)+b.x*(c.y-a.y)+c.x*(a.y-b.y);
if(fabs(r)<=_eps)return 0;
else if(r<0) return -1;
return 1;
}
myType evaluate_x(vector<myType> &v,myType x){
return ((-v[2]-x*v[0])/v[1]);
}
myType evaluate_y(vector<myType> &v,myType y){
return ((-v[2]-y*v[1])/v[0]);
}
}
int main() {
int T;
cn T;
for(int caseno=1; caseno<=T ;caseno++){
ll x1,x2,y1,y2,r1,r2;
cn x1>>y1>>r1>>x2>>y2>>r2;
Geometry::pt a(x1,y1),b(x2,y2);
ll xdif=x1-x2;
ll ydif=y1-y2;
xdif*=xdif;
ydif*=ydif;
if(Geometry::l(r1+r2,a.to(b))){
printf("Case %d: 0\n",caseno);
continue;
}
else if(xdif+ydif-r2*r2<0 && Geometry::l(a.to(b)+r1,r2)){
printf("Case %d: %.10f\n",caseno,PI*r1*r1);
continue;
}
else if(xdif+ydif-r1*r1<0 && Geometry::l(a.to(b)+r2,r1)){
printf("Case %d: %.10f\n",caseno,PI*r2*r2);
continue;
}
vector<double>commonL;
ll aa=-2*x1+2*x2;
ll bb=-2*y1+2*y2;
ll cc=x1*x1-x2*x2+y1*y1-y2*y2-(r1*r1-r2*r2);
commonL.pb(aa);
commonL.pb(bb);
commonL.pb(cc);
Geometry::pt inter=Geometry::solve_eqn(commonL,a.eqn(b),1000000);
double c1d=a.to(inter);
double c1up=sqrt(r1*r1-c1d*c1d);
double c1Tarea=c1up*c1d;
double c2d=b.to(inter);
double c2up=sqrt(r2*r2-c2d*c2d);
double c2Tarea=c2d*c2up;
double c1angle=2*acos(c1d/r1);
double c2angle=2*acos(c2d/r2);
double c1Aarea=.5*r1*r1*c1angle;
double c2Aarea=.5*r2*r2*c2angle;
double total=c1Aarea+c2Aarea;
if(fabs(a.to(b)+b.to(inter)-a.to(inter))<=1e-6){
//c2 is inside c1 and the coomon line
//is after c2's center
double c2OuterArea=c2Aarea-c2Tarea-(c1Aarea-c1Tarea);
printf("Case %d: %.10f\n",caseno,PI*r2*r2-c2OuterArea);
}
else if(fabs(a.to(b)+a.to(inter)-b.to(inter))<=1e-6){
//c1 is inside c2
// common line is after c1's center
double c1OuterArea=c1Aarea-c1Tarea-(c2Aarea-c2Tarea);
printf("Case %d: %.10f\n",caseno,PI*r1*r1-c1OuterArea);
}
else printf("Case %d: %.10f\n",caseno,total-c1Tarea-c2Tarea);
}
return 0;
}