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| #include <cstdio>
#include <cmath>
#include <algorithm>
using namespace std;
const int N = 1e6 + 10;
const double pi = acos(-1), eps = 1e-8;
int cmp(double a, double b)
{
if (a - b > eps)
return 1;
if (b - a > eps)
return -1;
return 0;
}
int sign(double a)
{
return cmp(a, 0);
}
struct Point
{
double x, y;
void input()
{
scanf("%lf%lf", &x, &y);
}
bool operator<(const Point &_) const
{
int t = cmp(x, _.x);
if (t == 1)
return false;
if (t == -1)
return true;
return y < _.y;
}
Point operator+(const Point &_) const
{
return (Point){x + _.x, y + _.y};
}
Point operator-(const Point &_) const
{
return (Point){x - _.x, y - _.y};
}
Point operator*(const double &t) const
{
return (Point){x * t, y * t};
}
Point operator/(const double &t) const
{
return (Point){x / t, y / t};
}
};
double dot(Point a, Point b)
{
return a.x * b.x + a.y * b.y;
}
double cross(Point x, Point y)
{
return x.x * y.y - y.x * x.y;
}
double area(Point a, Point b, Point c)
{
return cross(b - a, c - a);
}
double Len(Point a)
{
return sqrt(dot(a, a));
}
double Angle(Point a, Point b)
{
return acos(dot(a, b) / Len(a) / Len(b));
}
double Distance(Point a, Point b)
{
double dx = a.x - b.x, dy = a.y - b.y;
return sqrt(dx * dx + dy * dy);
}
Point rotate(Point a, double theta)
{
return (Point){a.x * cos(theta) - a.y * sin(theta), a.x * sin(theta) + a.y * cos(theta)};
}
struct Segment
{
Point x, y;
void input()
{
x.input(), y.input();
}
double Angle()
{
return atan2(y.y - x.y, y.x - x.x);
}
bool operator<(Segment &_)
{
double a = Angle(), b = _.Angle();
if (!cmp(a, b))
return sign(area(x, y, _.y)) == -1;
return a < b;
}
int onSegment(Point p)
{
return -sign(area(x, y, p));
}
double DistanceToLine(Point p)
{
Point u = y - x, v = p - x;
return abs(cross(v, u) / Len(v));
}
double DistanceToSegment(Point p)
{
if (!cmp(x.x, y.x) && cmp(x.y, y.y))
return Len(p - x);
Point u = y - x, v = p - x, w = p - y;
if (sign(dot(u, v)) == -1)
return Len(v);
if (sign(dot(v, w)) == 1)
return Len(u);
return DistanceToLine(p);
}
Point Projection(Point p)
{
Point u = y - x;
return x + u * (dot(u, p - x) / dot(u, u));
}
};
Segment Vertical(Point a, Point b)
{
return (Segment){(a + b) / 2, rotate(b - a, pi / 2)};
}
Point Intersection(Segment a, Segment b)
{
Point u = a.x - b.x;
double t = cross(b.y, u) / cross(a.y, b.y);
return a.x + a.y * t;
}
bool ExistIntersection(Segment a, Segment b)
{
return sign(cross(a.y - a.x, b.x - a.x)) * sign(cross(a.y - a.x, b.y - a.x)) <= 0 && sign(cross(b.y - b.x, a.x - b.x)) * sign(cross(b.y - b.x, a.y - b.x)) <= 0;
}
struct Circle
{
Point p;
double r;
};
Circle circle(Point a, Point b, Point c)
{
Segment u = Vertical(a, b), v = Vertical(a, c);
Point p = Intersection(u, v);
return {p, Distance(p, a)};
}
struct Polygon
{
int n;
Point p[N];
void input()
{
scanf("%d", &n);
for (int i = 0; i < n; i++)
p[i].input();
}
void insert(Point a)
{
p[n++] = a;
}
double PolygonArea()
{
double res = 0;
for (int i = 1; i < n; i++)
res += area(p[0], p[i], p[i + 1]);
return res / 2;
}
double PolygonCircumference()
{
double res = 0;
for (int i = 0; i + 1 < n; i++)
res += Distance(p[i], p[i + 1]);
return res;
}
void ConvexHull(int &cnt, Point *ans)
{
static bool vis[N];
sort(p, p + n);
static int top = 0, stk[N];
stk[++top] = 0, stk[++top] = 1;
for (int i = 2; i < n; i++)
{
while (top >= 2)
{
int t = sign(area(p[stk[top]], p[stk[top - 1]], p[i]));
if (t == -1)
vis[stk[top--]] = false;
else if (t == 0)
top--;
else
break;
}
vis[stk[++top] = i] = true;
}
vis[0] = false;
for (int i = n - 1; i >= 0; i--)
{
if (vis[i])
continue;
while (top >= 2 && sign(area(p[stk[top]], p[stk[top - 1]], p[i])) == -1)
top--;
vis[stk[++top] = i] = true;
}
cnt = 0;
for (int i = 1; i < top; i++)
ans[cnt++] = p[stk[i]];
}
Circle cover()
{
random_shuffle(p, p + n);
Circle c;
c.p = p[0];
c.r = 0;
for (int i = 1; i < n; i++)
{
if (cmp(c.r, Distance(c.p, p[i])) >= 0)
continue;
c.p = p[i];
c.r = 0;
for (int j = 0; j < i; j++)
{
if (cmp(c.r, Distance(c.p, p[j])) >= 0)
continue;
c.p = (p[i] + p[j]) / 2;
c.r = Distance(p[i], p[j]) / 2;
for (int k = 0; k < j; k++)
{
if (cmp(c.r, Distance(c.p, p[k])) >= 0)
continue;
c = circle(p[i], p[j], p[k]);
}
}
}
return c;
}
};
void HalfPlaneIntersection(int idx, Segment *l, int &cnt, Point *ans)
{
sort(l, l + idx);
static int hd = 0, tl = -1, q[N];
for (int i = 0; i < idx; i++)
{
if (i && !cmp(l[i].Angle(), l[i - 1].Angle()))
continue;
while (hd + 1 <= tl && l[i].onSegment(Intersection(l[q[tl - 1]], l[q[tl]])) >= 0)
tl--;
while (hd + 1 <= tl && l[i].onSegment(Intersection(l[q[hd + 1]], l[q[hd]])) >= 0)
hd++;
q[++tl] = i;
}
while (hd + 1 <= tl && l[q[hd]].onSegment(Intersection(l[q[tl - 1]], l[q[tl]])) >= 0)
tl--;
while (hd + 1 <= tl && l[q[tl]].onSegment(Intersection(l[q[hd + 1]], l[q[hd]])) >= 0)
hd++;
q[++tl] = q[hd];
for (int i = hd; i < tl; i++)
ans[cnt++] = Intersection(l[q[i]], l[q[i + 1]]);
}
int main()
{
Polygon p;
p.input();
Circle c = p.cover();
printf("%.2lf %.2lf %.2lf", c.p.x, c.p.y, c.r);
return 0;
}
|