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| #include <algorithm> | |
| #include <cstdio> | |
| #include <vector> | |
| #include <cmath> | |
| using namespace std; | |
| const double eps = 1e-8; | |
| int cmp(double x) { | |
| if (fabs(x) < eps) return 0; | |
| if (x > 0) return 1; | |
| return -1; | |
| } | |
| struct Point { | |
| double x, y; | |
| Point() {} | |
| Point(double a, double b): x(a), y(b) {} | |
| Point operator+(const Point &rhs) | |
| { | |
| return Point(x + rhs.x, y + rhs.y); | |
| } | |
| Point operator-(const Point &rhs) const | |
| { | |
| return Point(x - rhs.x, y - rhs.y); | |
| } | |
| bool operator==(const Point &rhs) const | |
| { | |
| return cmp(x - rhs.x) == 0 && cmp(y - rhs.y) == 0; | |
| } | |
| double operator^(const Point &rhs) const | |
| { | |
| return x * rhs.y - y * rhs.x; | |
| } | |
| }; | |
| class Solver { | |
| public: | |
| Solver(const vector<Point> &P): points(P) {} | |
| void run(void); | |
| private: | |
| double cross(const Point &O, const Point &A, const Point &B) | |
| { | |
| return (A.x - O.x) * (B.y - O.y) - (A.y - O.y) * (B.x - O.x); | |
| } | |
| double Area(void) | |
| { | |
| double sum = 0.0; | |
| for (int i = 0; i < points.size() - 1; ++i) { | |
| sum += (points[i] ^ points[i + 1]); | |
| } | |
| return sum / 2.0; | |
| } | |
| void ComputeConvexHull(void); | |
| Point ComputeCenter(void); | |
| vector<Point> points; | |
| }; | |
| bool ComparePoints(const Point &a, const Point &b) | |
| { | |
| return cmp(a.x - b.x) < 0 || (cmp(a.x - b.x) == 0 && a.y < b.y); | |
| } | |
| void Solver::ComputeConvexHull() | |
| { | |
| int n = points.size(); | |
| vector<Point> convex_hull(2 * n); | |
| sort(points.begin(), points.end(), ComparePoints); | |
| points.erase(unique(points.begin(), points.end()), points.end()); | |
| int k = 0; | |
| for (int i = 0; i < n; i++) { | |
| while (k >= 2 && cross(convex_hull[k - 2], | |
| convex_hull[k - 1], | |
| points[i]) <= eps) | |
| --k; | |
| convex_hull[k++] = points[i]; | |
| } | |
| int t = k + 1; | |
| for (int i = n - 2; i >= 0; i--) { | |
| while (k >= t && cross(convex_hull[k - 2], | |
| convex_hull[k - 1], | |
| points[i]) <= eps) | |
| --k; | |
| convex_hull[k++] = points[i]; | |
| } | |
| points.assign(convex_hull.begin(), convex_hull.begin() + k - 1); | |
| } | |
| Point Solver::ComputeCenter() | |
| { | |
| vector<Point> p(points); | |
| Point ans; | |
| double area = 0.0, tmp; | |
| ans.x = ans.y = 0.0; | |
| for (int i = 1; i < p.size() - 1; i++) | |
| { | |
| tmp = cross(p[i], p[0], p[i + 1]) / 2.0; | |
| ans.x += (p[0].x + p[i].x + p[i + 1].x) * tmp; | |
| ans.y += (p[0].y + p[i].y + p[i + 1].y) * tmp; | |
| area += tmp; | |
| } | |
| ans.x /= (3 * area); | |
| ans.y /= (3 * area); | |
| return ans; | |
| } | |
| void Solver::run() | |
| { | |
| ComputeConvexHull(); | |
| Point p = ComputeCenter(); | |
| printf("%.3lf %.3lf\n", p.x, p.y); | |
| } | |
| int main() | |
| { | |
| int N; | |
| while (scanf("%d", &N) && N >= 3) { | |
| vector<Point> p; | |
| double x, y; | |
| for (int i = 0; i < N; ++i) { | |
| scanf("%lf%lf", &x, &y); | |
| p.push_back(Point(x, y)); | |
| } | |
| Solver s(p); | |
| s.run(); | |
| } | |
| } |
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