一坨计算几何的板子
一个辣鸡抄板选手。
//Achen
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<vector>
#include<cstdio>
#include<queue>
#include<cmath>
typedef long long LL;
typedef double db;
const int N=1e5+7;
const db eps=1e-10;
using namespace std;
template<typename T>void read(T &x) {
char ch=getchar(); x=0; T f=1;
while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
if(ch=='-') f=-1,ch=getchar();
for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}
struct pt {
db x,y;
pt(db x=0,db y=0):x(x),y(y){}
}p[N],q[N];
typedef pt vc;
vc operator + (vc A,vc B) { return vc(A.x+B.x,A.y+B.y);}
vc operator - (vc A,vc B) { return vc(A.x-B.x,A.y-B.y);}
vc operator * (vc A,db p) { return vc(A.x*p,A.y*p);}
vc operator / (vc A,db p) { return vc(A.x/p,A.y/p);}
bool operator <(const vc&A,const vc&B) { return A.x<B.x||(A.x==B.x&&A.y<B.y);}
int dcmp(double x) { if(fabs(x)<eps) return 0; else return x<0?-1:1;}
bool operator == (const vc&A,const vc&B) { return dcmp(A.x-B.x)==0&&dcmp(A.y-B.y)==0; }
db dot(vc A,vc B) { return A.x*B.x+A.y*B.y; }
db length(vc A) { return sqrt(dot(A,A)); }
db angle(vc A,vc B) { return acos(dot(A,B)/length(A)/length(B)); }
db cross(vc A,vc B) { return A.x*B.y-A.y*B.x; }
db area2(pt A,pt B,pt C) { return cross(B-A,C-A);}
struct ln {
pt a,b; db slop;
friend bool operator <(const ln&A,const ln&B) {
return A.slop==B.slop?cross(A.b-A.a,B.b-A.a)>0:A.slop<B.slop;
}
}L[N],a[N],que[N];
//绕起点顺时逆时针a弧度
vc rotate(vc A,db rad) { return vc(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));}
//计算向量单位法线。需要先确保不是零向量
vc nomal(vc A) { db L=length(A); return vc(-A.y/L,A.x/L); }
//cross(v,w)!=0
pt getlinejd(pt p,vc v,pt q,vc w) {
vc u=p-q;
db t=cross(w,u)/cross(v,w);
return p+v*t;
}
db distoline(pt P,pt A,pt B) {
vc v1=B-A,v2=P-A;
return fabs(cross(v1,v2)/length(v1));
}
db distoseg(pt P,pt A,pt B) {
if(A==B) return length(P-A);
vc v1=B-A,v2=P-A,v3=P-B;
if(dcmp(dot(v1,v2))<0) return length(v2);
else if(dcmp(dot(v1,v3))<0) return length(v3);
else return fabs(cross(v1,v2))/length(v1);
}
pt getlinety(pt P,pt A,pt B) {
vc v=B-A;
return A+v*(dot(v,P-A)/dot(v,v));
}
bool segxj(pt p1,pt p2,pt p3,pt p4) {
if(!(max(p1.x,p2.x)>=min(p3.x,p4.x)+eps&&max(p3.x,p4.x)>min(p1.x,p2.x)+eps)
&&(max(p1.y,p2.y)>=min(p3.y,p4.y)+eps&&max(p3.y,p4.y)>min(p1.y,p2.y)+eps)) return 0;
if(cross(p3-p1,p2-p1)*cross(p4-p1,p2-p1)>eps) return 0;
if(cross(p1-p3,p4-p3)*cross(p2-p3,p4-p3)>eps) return 0;
return 1;
}
db polygonArea(pt p[],int n) {
db res=0;
for(int i=1;i<n-1;i++)
res+=cross(p[i]-p[0],p[i+1]-p[0]);
return res/2;
}
int main() {
return 0;
}
//Achen
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<vector>
#include<cstdio>
#include<queue>
#include<cmath>
typedef long long LL;
typedef double db;
const db eps=1e-10;
const int N=50007;
using namespace std;
int n;
template<typename T>void read(T &x) {
char ch=getchar(); x=0; T f=1;
while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
if(ch=='-') f=-1,ch=getchar();
for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}
struct pt {
db x,y;
pt(db x=0,db y=0):x(x),y(y){}
}p[N],q[N];
typedef pt vc;
vc operator + (vc A,vc B) { return vc(A.x+B.x,A.y+B.y);}
vc operator - (vc A,vc B) { return vc(A.x-B.x,A.y-B.y);}
bool operator <(const vc&A,const vc&B) { return A.x<B.x||(A.x==B.x&&A.y<B.y);}
int dcmp(double x) { if(fabs(x)<eps) return 0; else return x<0?-1:1;}
bool operator == (const vc&A,const vc&B) { return dcmp(A.x-B.x)==0&&dcmp(A.y-B.y)==0; }
db dot(vc A,vc B) { return A.x*B.x+A.y*B.y; }
db length(vc A) { return dot(A,A); }
db cross(vc A,vc B) { return A.x*B.y-A.y*B.x; }
bool cmp(const pt &A,const pt&B) {
return dcmp(cross(A-p[1],B-p[1]))==0?length(A-p[1])<length(B-p[1]):cross(A-p[1],B-p[1])>0;
}
int top;
void graham() {
for(int i=2;i<=n;i++) if(p[i]<p[1]) swap(p[i],p[1]);
sort(p+2,p+n+1,cmp);
q[++top]=p[1]; q[++top]=p[2];
for(int i=3;i<=n;i++) {
while(top>1&&cross(q[top]-q[top-1],p[i]-q[top-1])<eps) top--;
q[++top]=p[i];
}
}
db RC() {
q[top+1]=q[1];
int now=2;
db res=0;
for(int i=1;i<=top;i++) {
while(cross(q[i+1]-q[i],q[now]-q[i])<cross(q[i+1]-q[i],q[now+1]-q[i])) {
now++; if(now==top+1) now=1;
}
res=max(res,length(q[now]-q[i]));
}
return res;
}
int main() {
read(n);
for(int i=1;i<=n;i++) { read(p[i].x); read(p[i].y); }
graham();
printf("%d\n",(int)RC());
return 0;
}
//Achen
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<vector>
#include<cstdio>
#include<queue>
#include<cmath>
typedef long long LL;
typedef double db;
const db eps=1e-10;
const int N=50007;
using namespace std;
int n,cnt,tot;
template<typename T>void read(T &x) {
char ch=getchar(); x=0; T f=1;
while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
if(ch=='-') f=-1,ch=getchar();
for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}
struct pt {
db x,y;
pt(db x=0,db y=0):x(x),y(y){}
}p[N];
typedef pt vc;
vc operator + (vc A,vc B) { return vc(A.x+B.x,A.y+B.y);}
vc operator - (vc A,vc B) { return vc(A.x-B.x,A.y-B.y);}
vc operator * (vc A,db p) { return vc(A.x*p,A.y*p);}
vc operator / (vc A,db p) { return vc(A.x/p,A.y/p);}
bool operator <(const vc&A,const vc&B) { return A.x<B.x||(A.x==B.x&&A.y<B.y);}
int dcmp(double x) { if(fabs(x)<eps) return 0; else return x<0?-1:1;}
bool operator == (const vc&A,const vc&B) { return dcmp(A.x-B.x)==0&&dcmp(A.y-B.y)==0; }
db dot(vc A,vc B) { return A.x*B.x+A.y*B.y; }
db length(vc A) { return dot(A,A); }
db cross(vc A,vc B) { return A.x*B.y-A.y*B.x; }
struct ln {
pt a,b; db slop;
friend bool operator <(const ln&A,const ln&B) {
return A.slop==B.slop?cross(A.b-A.a,B.b-A.a)>0:A.slop<B.slop;
}
}L[N],a[N],que[N];
db polygonArea(int n) {
if(n<3) return 0;
db res=0;
for(int i=1;i<n-1;i++)
res+=cross(p[i]-p[0],p[i+1]-p[0]);
return fabs(res)/2;
}
pt inter(ln A,ln B) {
pt res;
db s1=cross(B.b-A.a,A.b-A.a);
db s2=cross(A.b-A.a,B.a-A.a);
db k=s1/(s1+s2);
res.x=B.b.x+(B.a.x-B.b.x)*k;
res.y=B.b.y+(B.a.y-B.b.y)*k;
return res;
}
bool ck(ln A,ln B,ln P) {
pt pp=inter(A,B);
return cross(P.b-P.a,pp-P.a)<0;
}
db solve() {
sort(L+1,L+cnt+1);
for(int i=1;i<=cnt;i++) {
if(L[i].slop!=L[i-1].slop) tot++;
a[tot]=L[i];
}
int ql=1,qr=0;
L[++qr]=a[1]; L[++qr]=a[2];
for(int i=3;i<=tot;i++) {
while(qr>ql&&ck(L[qr-1],L[qr],a[i])) qr--;
while(qr>ql&&ck(L[ql+1],L[ql],a[i])) ql++;
L[++qr]=a[i];
}
while(qr>ql&&ck(L[qr-1],L[qr],L[ql])) qr--;
while(qr>ql&&ck(L[ql+1],L[ql],L[qr])) ql++;
L[qr+1]=L[ql];
cnt=0;
for(int i=ql;i<=qr;i++)
p[cnt++]=inter(L[i],L[i+1]);
return polygonArea(cnt);
}
int main() {
read(n);
for(int i=1;i<=n;i++) {
int k;
read(k);
for(int j=1;j<=k;j++) { read(p[j].x);read(p[j].y); }
for(int j=1;j<k;j++) {
L[++cnt].a=p[j]; L[cnt].b=p[j+1];
}
L[++cnt].a=p[k]; L[cnt].b=p[1];
}
for(int i=1;i<=cnt;i++)
L[i].slop=atan2(L[i].b.y-L[i].a.y,L[i].b.x-L[i].a.x);
printf("%.3lf\n",solve());
return 0;
}
/*
2
6
-2 0
-1 -2
1 -2
2 0
1 2
-1 2
4
0 -3
1 -1
2 2
-1 0
*/
//Achen
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<vector>
#include<cstdio>
#include<queue>
#include<cmath>
const int N=507;
typedef long long LL;
typedef double db;
using namespace std;
const db eps=1e-10;
int n; db r;
template<typename T>void read(T &x) {
char ch=getchar(); x=0; T f=1;
while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
if(ch=='-') f=-1,ch=getchar();
for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}
struct pt {
db x,y;
pt(){}
pt(db x,db y):x(x),y(y){}
}p[N],c;
pt operator + (pt A,pt B) { return pt(A.x+B.x,A.y+B.y); }
pt operator - (pt A,pt B) { return pt(A.x-B.x,A.y-B.y); }
db dot(pt A,pt B) { return A.x*B.x+A.y*B.y; }
db length(pt A) { return sqrt(dot(A,A)); }
int dcmp(db x) { if(fabs(x)<eps) return 0; return x>0?1:-1; }
pt circle_center(pt a,pt b,pt c) {
pt res;
db a1=b.x-a.x,a2=c.x-a.x;
db b1=b.y-a.y,b2=c.y-a.y;
db c1=(a1*a1+b1*b1)/2.0;
db c2=(a2*a2+b2*b2)/2.0;
db d=a1*b2-a2*b1;
res.x=a.x+(b2*c1-b1*c2)/d;
res.y=a.y+(a1*c2-a2*c1)/d;
return res;
}
void min_circle_cover(pt p[],int n,pt &c,db &r) {
random_shuffle(p+1,p+n+1);
c=p[0]; r=0;
for(int i=2;i<=n;i++) {
if(dcmp(length(p[i]-c)-r)>0) {
c=p[i]; r=0;
for(int j=1;j<i;j++) {
if(dcmp(length(p[j]-c)-r)>0) {
c.x=(p[i].x+p[j].x)/2;
c.y=(p[i].y+p[j].y)/2;
r=length(p[i]-c);
for(int k=1;k<j;k++) {
if(dcmp(length(p[k]-c)-r)>0) {
c=circle_center(p[i],p[j],p[k]);
r=length(p[k]-c);
}
}
}
}
}
}
}
int main() {
srand(998244353);
for(;;) {
read(n);
if(!n) break;
for(int i=1;i<=n;i++)
scanf("%lf %lf",&p[i].x,&p[i].y);
min_circle_cover(p,n,c,r);
printf("%.2lf %.2lf %.2lf\n",c.x,c.y,r);
}
return 0;
}
