题链
#include<bits/stdc++.h>//O(n),最小圆覆盖
#define eps 1e-12
using namespace std;
int n,m;
struct node {
double x, y;
} s[500005];
node o;//圆心坐标
double ri;//半径
double dis(node a, node b) {
return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
}
void getr(node p1, node p2, node p3) {//三个点求三角形圆心坐标和半径
double a, b, c, d, e, f;
a = p2.y - p1.y;
b = p3.y - p1.y;
c = p2.x - p1.x;
d = p3.x - p1.x;
f = p3.x * p3.x + p3.y * p3.y - p1.x * p1.x - p1.y * p1.y;
e = p2.x * p2.x + p2.y * p2.y - p1.x * p1.x - p1.y * p1.y;
o.x = (a * f - b * e) / (2 * a * d - 2 * b * c);
o.y = (d * e - c * f) / (2 * a * d - 2 * b * c);
ri = dis(o, p1);
}
int main() {
ios::sync_with_stdio(false);
scanf("%d",&n);
for (int i = 1; i <= n; i++) {
scanf("%lf %lf",&s[i].x,&s[i].y);
}
random_shuffle(s + 1, s + n + 1);
o = s[1];
ri = 0;
for (int i = 2; i <= n; i++) {
if (dis(s[i], o) > ri + eps) {
o = s[i];
ri = 0;//第一个点为圆心
for (int j = 1; j < i; j++) {
if (dis(o, s[j]) > ri + eps) {
o.x = (s[i].x + s[j].x) / 2;
o.y = (s[i].y + s[j].y) / 2;
ri = dis(o, s[j]);//第一个点和第二个点中点为圆心,距离为直径
for (int k = 1; k < j; k++) {
if (dis(o, s[k]) > ri + eps) {
getr(s[i], s[j], s[k]);//三点定圆
}
}
}
}
}
}
printf("%.10f\n",ri);
printf("%.10f %.10f\n",o.x,o.y);
return 0;
}