Init

Luogu-P2533.cpp

@@ -0,0 +1,92 @@
+#include <algorithm>
+#include <cassert>
+#include <cmath>
+#include <cstdio>
+#include <random>
+const double EPS = 1e-7;
+struct point {
+  double x, y;
+  inline point operator+(point rhs) const {
+    return (point){x + rhs.x, y + rhs.y};
+  }
+  inline point operator-(point rhs) const {
+    return (point){x - rhs.x, y - rhs.y};
+  }
+  inline point operator*(double rhs) const { return (point){x * rhs, y * rhs}; }
+  inline double len() const { return sqrt(x * x + y * y); }
+};
+inline int sgn(double x) {
+  if (x < -EPS) return -1;
+  if (x > EPS) return 1;
+  return 0;
+}
+inline double det(point x, point y) { return x.x * y.y - x.y * y.x; }
+inline double dot(point x, point y) { return x.x * y.x + x.y * y.y; }
+inline double dis(point x, point y) { return (x - y).len(); }
+struct circle {
+  point c;
+  double r;
+};
+inline bool in_circle(point p, circle c) {
+  return sgn(c.r - (c.c - p).len()) >= 0;
+}
+inline circle make_circle(point x, point y) {
+  return (circle){(x + y) * 0.5, (x - y).len() * 0.5};
+}
+inline circle make_circle(point x, point y, point z) {
+  point p = y - x, q = z - x, s = (point){dot(p, p) * 0.5, dot(q, q) * 0.5};
+  double d = 1.0 / det(p, q);
+  p = (point){det(s, (point){p.y, q.y}), det((point){p.x, q.x}, s)} * d;
+  return (circle){x + p, p.len()};
+}
+inline circle get_circle(point x, point y, point z) {
+  if (sgn(det(y - x, z - x)) == 0) {
+    if ((x - y).len() >= (x - z).len()) {
+      if ((x - y).len() >= (y - z).len())
+        return make_circle(x, y);
+      else
+        return make_circle(y, z);
+    } else {
+      if ((x - z).len() >= (y - z).len())
+        return make_circle(x, z);
+      else
+        return make_circle(y, z);
+    }
+  } else
+    return make_circle(x, y, z);
+}
+using namespace std;
+const int maxn = 1e6 + 10;
+mt19937 rnd(random_device{}());
+inline int rand_less(int n) { return rnd() % n; }
+int n;
+point pnt[maxn];
+int main() {
+#ifdef local
+  freopen("pro.in", "r", stdin);
+#endif
+  scanf("%d", &n);
+  for (int i = 1; i <= n; i++) scanf("%lf%lf", &pnt[i].x, &pnt[i].y);
+  if (n == 2) {
+    printf("%.2lf %.2lf %.2lf\n", ((pnt[1] + pnt[2]) * 0.5).x,
+           ((pnt[1] + pnt[2]) * 0.5).x, dis(pnt[1], pnt[2]) / 2);
+    return 0;
+  }
+  random_shuffle(pnt + 1, pnt + 1 + n, rand_less);
+  circle cc = {pnt[1], 0};
+  // 注意：此处不要自作聪明地初始化，必须保证一定是真正的最小圆覆盖
+  for (int i = 2; i <= n; i++) {
+    if (in_circle(pnt[i], cc)) continue;
+    cc = make_circle(pnt[i], pnt[1]);
+    for (int j = 2; j <= i - 1; j++) {
+      if (in_circle(pnt[j], cc)) continue;
+      cc = make_circle(pnt[j], pnt[i]);
+      for (int k = 1; k <= j - 1; k++) {
+        if (in_circle(pnt[k], cc)) continue;
+        cc = get_circle(pnt[k], pnt[j], pnt[i]);
+      }
+    }
+  }
+  printf("%.2lf %.2lf %.2lf\n", cc.c.x, cc.c.y, cc.r);
+  return 0;
+}