#1182147 (C++23) No.3675 偏光板

• 問題: No.3675 偏光板
• ユーザー: TKTYI
• 提出日時: 2026-09-03 01:34:38
• 言語: C++23 (gcc 15.3.0 + boost 1.92.0)
• 結果: WA
• 実行時間: -
• コード長: 10,467 bytes
• コンパイル時間: 2,288 ms
• コンパイル使用メモリ: 253,996 KB
• 実行使用メモリ: 39,072 KB
• 最終ジャッジ日時: 2026-09-04 23:11:06
• 合計ジャッジ時間: 5,664 ms
• ジャッジサーバーID （参考情報）: judge2_0 / judge6_1

ファイルパターン	結果
sample	AC * 6
other	AC * 48 WA * 6

ソースコード

#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <random>
#include <map>

using namespace std;

struct Point2D { double x, y; };
struct Circle { double x, y, r; };
struct Point3D {
  double x, y, z;
  int id;
  
  Point3D operator-(const Point3D& p) const {
    return {x - p.x, y - p.y, z - p.z, id};
  }
};
struct Face {
    int i, j, k;
    bool visible = true;
    vector<int> pts;
};

vector<Point2D> clip_polygon_halfplane(const vector<Point2D>& poly, double a, double b, double c) {
  vector<Point2D> res;
  int n = poly.size();
  if (n == 0) return res;

  for (int i = 0; i < n; i++) {
    Point2D p1 = poly[i];
    Point2D p2 = poly[(i + 1) % n];
    double d1 = a * p1.x + b * p1.y + c;
    double d2 = a * p2.x + b * p2.y + c;

    if (d1 >= -1e-9) {
      res.push_back(p1);
      if (d2 < -1e-9) {
        double t = d1 / (d1 - d2);
        t = max(0.0, min(1.0, t));
        res.push_back({p1.x + t * (p2.x - p1.x), p1.y + t * (p2.y - p1.y)});
      }
    } else if (d2 >= -1e-9) {
      double t = d1 / (d1 - d2);
      t = max(0.0, min(1.0, t));
      res.push_back({p1.x + t * (p2.x - p1.x), p1.y + t * (p2.y - p1.y)});
    }
  }
  return res;
}

vector<Point2D> clip_to_rect(vector<Point2D> poly, double X, double Y) {
  poly = clip_polygon_halfplane(poly, 1.0, 0.0, 0.0);
  poly = clip_polygon_halfplane(poly, -1.0, 0.0, X);
  poly = clip_polygon_halfplane(poly, 0.0, 1.0, 0.0);
  poly = clip_polygon_halfplane(poly, 0.0, -1.0, Y);
  return poly;
}

double circle_polygon_area(double cx, double cy, double R, vector<Point2D> poly) {
  int n = poly.size();
  if (n < 3) return 0.0;
  double area = 0.0;
  double R2 = R * R;
  for (int i = 0; i < n; i++) {
    Point2D p1 = poly[i];
    Point2D p2 = poly[(i + 1) % n];
    double x1 = p1.x - cx, y1 = p1.y - cy;
    double x2 = p2.x - cx, y2 = p2.y - cy;
    double dx = x2 - x1, dy = y2 - y1;
    double a = dx * dx + dy * dy;
    double b = 2.0 * (x1 * dx + y1 * dy);
    double c = x1 * x1 + y1 * y1 - R2;
    vector<double> ts = {0.0, 1.0};
    if (abs(a) > 1e-12) {
      double disc = b * b - 4 * a * c;
      if (disc > 0) {
        double sq = sqrt(disc);
        double t1 = (-b - sq) / (2 * a);
        double t2 = (-b + sq) / (2 * a);
        if (t1 > 0 && t1 < 1) ts.push_back(t1);
        if (t2 > 0 && t2 < 1) ts.push_back(t2);
      }
    }
    sort(ts.begin(), ts.end());
    for (size_t j = 0; j < ts.size() - 1; j++) {
      double ta = ts[j], tb = ts[j + 1];
      if (tb - ta < 1e-12) continue;
      Point2D sub_p1 = {x1 + ta * dx, y1 + ta * dy};
      Point2D sub_p2 = {x1 + tb * dx, y1 + tb * dy};
      double mx = (sub_p1.x + sub_p2.x) / 2.0;
      double my = (sub_p1.y + sub_p2.y) / 2.0;
      if (mx * mx + my * my <= R2 + 1e-9) {
        area += 0.5 * (sub_p1.x * sub_p2.y - sub_p1.y * sub_p2.x);
      } else {
        double ang1 = atan2(sub_p1.y, sub_p1.x);
        double ang2 = atan2(sub_p2.y, sub_p2.x);
        double dtheta = atan2(sin(ang2 - ang1), cos(ang2 - ang1));
        area += 0.5 * R2 * dtheta;
      }
    }
  }
  return abs(area);
}

Point3D cross(const Point3D& a, const Point3D& b) {
  return {
    a.y * b.z - a.z * b.y,
    a.z * b.x - a.x * b.z,
    a.x * b.y - a.y * b.x
  };
}

double dot(const Point3D& a, const Point3D& b) {
  return a.x * b.x + a.y * b.y + a.z * b.z;
}

double orient3d(const Point3D& a, const Point3D& b, const Point3D& c, const Point3D& d) {
  return dot(cross(b - a, c - a), d - a);
}

const double EPS = 1e-9;

vector<Face> get_convex_hull_3d(vector<Point3D> pts) {
  int n = pts.size();
  if (n < 4) return {};

  int p0 = 0, p1 = 1, p2 = -1, p3 = -1;
  while (p1 < n && abs(pts[p1].x - pts[p0].x) < EPS && 
                    abs(pts[p1].y - pts[p0].y) < EPS && 
                    abs(pts[p1].z - pts[p0].z) < EPS) {
    p1++;
  }
  if (p1 == n) return {};

  for (int i = p1 + 1; i < n; i++) {
    Point3D crs = cross(pts[p1] - pts[p0], pts[i] - pts[p0]);
    if (abs(crs.x) > EPS || abs(crs.y) > EPS || abs(crs.z) > EPS) {
      p2 = i;
      break;
    }
  }
  if (p2 == -1) return {};

  for (int i = p2 + 1; i < n; i++) {
    if (abs(orient3d(pts[p0], pts[p1], pts[p2], pts[i])) > EPS) {
      p3 = i;
      break;
    }
  }
  if (p3 == -1) return {};

  vector<int> remaining;
  for (int i = 0; i < n; i++) {
    if (i != p0 && i != p1 && i != p2 && i != p3) {
      remaining.push_back(i);
    }
  }
  mt19937 rng(1337);
  shuffle(remaining.begin(), remaining.end(), rng);

  vector<Face> faces;
  auto add_face = [&](int a, int b, int c) {
    faces.push_back({a, b, c, true, {}});
  };

  if (orient3d(pts[p0], pts[p1], pts[p2], pts[p3]) > 0) {
    add_face(p0, p2, p1);
    add_face(p0, p1, p3);
    add_face(p1, p2, p3);
    add_face(p2, p0, p3);
  } else {
    add_face(p0, p1, p2);
    add_face(p0, p3, p1);
    add_face(p1, p3, p2);
    add_face(p2, p3, p0);
  }

  for (int p_idx : remaining) {
    for (auto& f : faces) {
      if (orient3d(pts[f.i], pts[f.j], pts[f.k], pts[p_idx]) > EPS) {
        f.pts.push_back(p_idx);
        break;
      }
    }
  }

  for (int p_idx : remaining) {
    vector<int> vis_faces;
    for (int i = 0; i < (int)faces.size(); i++) {
      if (faces[i].visible && orient3d(pts[faces[i].i], pts[faces[i].j], pts[faces[i].k], pts[p_idx]) > EPS) {
        vis_faces.push_back(i);
      }
    }

    if (vis_faces.empty()) continue;

    map<pair<int, int>, int> edge_cnt;
    for (int f_idx : vis_faces) {
      const auto& f = faces[f_idx];
      edge_cnt[{f.i, f.j}]++;
      edge_cnt[{f.j, f.k}]++;
      edge_cnt[{f.k, f.i}]++;
    }

    vector<pair<int, int>> horizon;
    for (int f_idx : vis_faces) {
      const auto& f = faces[f_idx];
      pair<int, int> edges[3] = {{f.i, f.j}, {f.j, f.k}, {f.k, f.i}};
      for (auto& e : edges) {
        if (edge_cnt.find({e.second, e.first}) == edge_cnt.end()) {
          horizon.push_back(e);
        }
      }
    }

    vector<int> orphaned;
    for (int f_idx : vis_faces) {
      faces[f_idx].visible = false;
      for (int pt_i : faces[f_idx].pts) {
        if (pt_i != p_idx) {
          orphaned.push_back(pt_i);
        }
      }
    }
    sort(orphaned.begin(), orphaned.end());
    orphaned.erase(unique(orphaned.begin(), orphaned.end()), orphaned.end());

    int new_start_idx = faces.size();
    for (auto& e : horizon) {
      add_face(e.first, e.second, p_idx);
    }

    for (int pt_i : orphaned) {
      for (int i = new_start_idx; i < (int)faces.size(); i++) {
        if (orient3d(pts[faces[i].i], pts[faces[i].j], pts[faces[i].k], pts[pt_i]) > EPS) {
          faces[i].pts.push_back(pt_i);
          break;
        }
      }
    }
  }

  vector<Face> result;
  for (const auto& f : faces) {
    if (f.visible) {
      result.push_back(f);
    }
  }
  return result;
}

vector<Face> get_lower_hull(const vector<Point3D>& pts) {
  auto all_faces = get_convex_hull_3d(pts);
  vector<Face> lower_faces;
  for (const auto& f : all_faces) {
    Point3D norm = cross(pts[f.j] - pts[f.i], pts[f.k] - pts[f.i]);
    if (norm.z < -EPS) {
      lower_faces.push_back(f);
    }
  }
  return lower_faces;
}

double f(int X, int Y, vector<Circle> C) {
  vector<Circle> unique_C;
  for (auto c : C) {
    bool dup = false;
    for (auto& uc : unique_C) {
      if (abs(c.x - uc.x) < 1e-7 && abs(c.y - uc.y) < 1e-7) {
        uc.r = max(uc.r, c.r);
        dup = true;
        break;
      }
    }
    if (!dup) unique_C.push_back(c);
  }
  C = unique_C;

  int N = C.size();
  if (N == 0) return 0.0;

  double min_x = 0, max_x = X, min_y = 0, max_y = Y;
  for (auto c : C) {
    min_x = min(min_x, c.x); max_x = max(max_x, c.x);
    min_y = min(min_y, c.y); max_y = max(max_y, c.y);
  }
  double CX = (min_x + max_x) / 2.0;
  double CY = (min_y + max_y) / 2.0;
  double M = max({max_x - min_x, max_y - min_y, (double)X, (double)Y, 100.0}) * 10.0;

  vector<Circle> C_ext = C;
  C_ext.push_back({CX - M, CY - M, 0.0});
  C_ext.push_back({CX + M, CY - M, 0.0});
  C_ext.push_back({CX + M, CY + M, 0.0});
  C_ext.push_back({CX - M, CY + M, 0.0});

  vector<Point3D> pts;
  for (auto c : C_ext) {
    pts.push_back({c.x, c.y, c.x * c.x + c.y * c.y - c.r * c.r});
  }

  vector<Face> lower = get_lower_hull(pts);
  vector<vector<Point2D>> circle_to_centers(C_ext.size());

  for (auto& face : lower) {
    Circle p_i = C_ext[face.i], p_j = C_ext[face.j], p_k = C_ext[face.k];
    
    double A = 2 * (p_j.x - p_i.x);
    double B_coef = 2 * (p_j.y - p_i.y);
    double E = pts[face.j].z - pts[face.i].z;
    
    double C_coef = 2 * (p_k.x - p_i.x);
    double D_coef = 2 * (p_k.y - p_i.y);
    double F = pts[face.k].z - pts[face.i].z;
    
    double det = A * D_coef - B_coef * C_coef;
    if (abs(det) < 1e-12) continue;
    
    double cx = (E * D_coef - B_coef * F) / det;
    double cy = (A * F - E * C_coef) / det;
    Point2D center = {cx, cy};

    circle_to_centers[face.i].push_back(center);
    circle_to_centers[face.j].push_back(center);
    circle_to_centers[face.k].push_back(center);
  }

  double area = 0.0;
  for (int i = 0; i < N; i++) {
    auto centers = circle_to_centers[i];
    if (centers.size() < 3) continue;

    vector<Point2D> unique_centers;
    for (auto c : centers) {
      bool dup = false;
      for (auto u : unique_centers) {
        if (hypot(c.x - u.x, c.y - u.y) < 1e-6) { dup = true; break; }
      }
      if (!dup) unique_centers.push_back(c);
    }
    if (unique_centers.size() < 3) continue;

    double gx = 0, gy = 0;
    for (auto p : unique_centers) gx += p.x, gy += p.y;
    gx /= unique_centers.size(); gy /= unique_centers.size();
    sort(unique_centers.begin(), unique_centers.end(), [&](const Point2D& a, const Point2D& b) {
      return atan2(a.y - gy, a.x - gx) < atan2(b.y - gy, b.x - gx);
    });

    vector<Point2D> clipped_poly = clip_to_rect(unique_centers, X, Y);

    if (clipped_poly.size() >= 3) {
      area += circle_polygon_area(C[i].x, C[i].y, C[i].r, clipped_poly);
    }
  }
  return area;
}

int main() {
  int X, Y, N;
  if (!(cin >> X >> Y >> N)) return 0;
  vector<Circle> v, h;
  mt19937 rnd(1337);
  uniform_real_distribution<double> dist(-1e-9, 1e-9);
  for (int i = 0; i < N; i++) {
    double x, y, r;
    char d;
    cin >> x >> y >> r >> d;
  
    x += dist(rnd);
    y += dist(rnd);
    r += abs(dist(rnd));
    
    (d == 'V' ? v : h).push_back({x, y, r});
  }
  double ans = (double) X * Y;
  ans -= f(X, Y, v) * 0.5;
  ans -= f(X, Y, h) * 0.5;
  printf("%.20lf\n", ans);
  return 0;
}