题意：给定三个点，及其半径，求一个点，到三个圆的范围尽可能近
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
const double eps=1e-5;
struct point
{
double x,y;
double r;
}p[3];
double dist(double x, double y,point tp){
return sqrt((x-tp.x)*(x-tp.x)+(y-tp.y)*(y-tp.y));
}
double cost(double x, double y){
double ang[3];
for(int i=0;i<3;++i){
ang[i]=dist(x,y,p[i])/p[i].r; //sin
}
double d[3];
for(int i=0;i<3;++i){
d[i]=ang[i]-ang[(i+1)%3]; //视角之间差值
}
double ans=0;
for(int i=0;i<3;++i){
ans+=d[i]*d[i] ; //类似方差
}
return ans;
}
main(){
for(int i=0;i<3;i++){
scanf("%lf%lf%lf",&p[i].x,&p[i].y,&p[i].r);
}
double x=0,y=0;
for (int i = 0; i < 3; ++i)
{
x+=p[i].x/3;y+=p[i].y/3; //在重心附件搜索
}
double t=1.0;
while(t>eps){
int kase=0;
double tp=cost(x,y);
if(cost(x+t,y)<tp){
x+=t;kase=1;
}else if(cost(x-t,y)<tp){
x-=t;kase=1;
}else if(cost(x,y-t)<tp){
y-=t;kase=1;
}else if(cost(x,y+t)<tp){
y+=t;kase=1;
}
if (!kase) //四周无更优解 缩小搜索范围
{
t/=2;
}
}
if(fabs(cost(x,y)<eps)){
printf("%lf %lf\n",x,y);
}
return 0;
}
