Problem p01927 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <algorithm>
#include <cassert>
#include <climits>
#include <complex>
#include <cstdio>
#include <cstring>
#include <deque>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <unordered_set>
#include <vector>

#define REP(i, s, n) for (int i = s; i < n; i++)
#define rep(i, n) REP(i, 0, n)
#define EPS (1e-8)
#define equals(a, b) (fabs((a) - (b)) < EPS)
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0

using namespace std;

// -- BEGIN --
class Point {
public:
  double x, y;

  Point(double x = 0, double y = 0) : x(x), y(y) {}

  Point operator+(Point p) { return Point(x + p.x, y + p.y); }
  Point operator-(Point p) { return Point(x - p.x, y - p.y); }
  Point operator*(double a) { return Point(a * x, a * y); }
  Point operator/(double a) { return Point(x / a, y / a); }
  Point operator*(Point a) {
    return Point(x * a.x - y * a.y, x * a.y + y * a.x);
  }

  bool operator<(const Point &p) const {
    return !equals(x, p.x) ? x < p.x : (!equals(y, p.y) && y < p.y);
  }

  bool operator==(const Point &p) const {
    return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
  }
};

struct Segment {
  Point p1, p2;
  Segment(Point p1 = Point(), Point p2 = Point()) : p1(p1), p2(p2) {}
  bool operator<(const Segment &s) const {
    return (p2 == s.p2) ? p1 < s.p1 : p2 < s.p2;
  }
  bool operator==(const Segment &s) const {
    return (s.p1 == p1 && s.p2 == p2) || (s.p1 == p2 && s.p2 == p1);
  }
};

typedef Point Vector;
typedef Segment Line;
typedef vector<Point> Polygon;

ostream &operator<<(ostream &os, const Point &a) {
  return os << "(" << a.x << "," << a.y << ")";
}

ostream &operator<<(ostream &os, const Segment &a) {
  return os << "( " << a.p1 << " , " << a.p2 << " )";
}

double dot(Point a, Point b) { return a.x * b.x + a.y * b.y; }

double cross(Point a, Point b) { return a.x * b.y - a.y * b.x; }

double norm(Point a) { return a.x * a.x + a.y * a.y; }

double abs(Point a) { return sqrt(norm(a)); }

// rad ????§???????????????¢?????§?????????????????¨
Point rotate(Point a, double rad) {
  return Point(cos(rad) * a.x - sin(rad) * a.y,
               sin(rad) * a.x + cos(rad) * a.y);
}

// ??????????????¢????????????
double toRad(double agl) { return agl * M_PI / 180.0; }

// a => prev, b => cur, c=> next
// prev ?????? cur ????????£??? next ????????????????§????????±???????
double getArg(Point a, Point b, Point c) {
  double arg1 = atan2(b.y - a.y, b.x - a.x);
  double arg2 = atan2(c.y - b.y, c.x - b.x);
  double arg = fabs(arg1 - arg2);
  while (arg > M_PI)
    arg -= 2.0 * M_PI;
  return fabs(arg);
}

int ccw(Point p0, Point p1, Point p2) {
  Point a = p1 - p0;
  Point b = p2 - p0;
  if (cross(a, b) > EPS)
    return COUNTER_CLOCKWISE;
  if (cross(a, b) < -EPS)
    return CLOCKWISE;
  if (dot(a, b) < -EPS)
    return ONLINE_BACK;
  if (norm(a) < norm(b))
    return ONLINE_FRONT;
  return ON_SEGMENT;
}

Polygon andrewScan(Polygon s) {
  Polygon u, l;
  if ((int)s.size() < 3)
    return s;

  sort(s.begin(), s.end());

  u.push_back(s[0]);
  u.push_back(s[1]);
  l.push_back(s[s.size() - 1]);
  l.push_back(s[s.size() - 2]);

  for (int i = 2; i < (int)s.size(); i++) {
    for (int n = (int)u.size();
         n >= 2 && ccw(u[n - 2], u[n - 1], s[i]) != CLOCKWISE; n--)
      u.pop_back();
    u.push_back(s[i]);
  }

  for (int i = (int)s.size() - 3; i >= 0; i--) {
    for (int n = (int)l.size();
         n >= 2 && ccw(l[n - 2], l[n - 1], s[i]) != CLOCKWISE; n--)
      l.pop_back();
    l.push_back(s[i]);
  }

  reverse(l.begin(), l.end());

  for (int i = (int)u.size() - 2; i >= 1; i--)
    l.push_back(u[i]);

  return l;
}

// cross product of pq and pr
double cross3p(Point p, Point q, Point r) {
  return (r.x - q.x) * (p.y - q.y) - (r.y - q.y) * (p.x - q.x);
}

// returns true if point r is on the same line as the line pq
bool collinear(Point p, Point q, Point r) {
  return fabs(cross3p(p, q, r)) < EPS;
}

// returns true if point t is on the left side of line pq
bool ccwtest(Point p, Point q, Point r) {
  return cross3p(p, q, r) > 0; // can be modified to accept collinear points
}

bool onSegment(Point p, Point q, Point r) {
  return collinear(p, q, r) &&
         equals(sqrt(pow(p.x - r.x, 2) + pow(p.y - r.y, 2)) +
                    sqrt(pow(r.x - q.x, 2) + pow(r.y - q.y, 2)),
                sqrt(pow(p.x - q.x, 2) + pow(p.y - q.y, 2)));
}

bool isConvex(vector<Point> p) {
  int sz = (int)p.size();
  if (sz < 3)
    return false; // boundary case, we treat a point or a line as not convex
  bool isLeft = ccwtest(p[0], p[1], p[2]);
  for (int i = 1; i < (int)p.size(); i++)
    if (ccwtest(p[i], p[(i + 1) % sz], p[(i + 2) % sz]) != isLeft)
      return false;
  return true;
}

double angle(Point a, Point b, Point c) {
  double ux = b.x - a.x, uy = b.y - a.y;
  double vx = c.x - a.x, vy = c.y - a.y;
  return acos((ux * vx + uy * vy) /
              sqrt((ux * ux + uy * uy) * (vx * vx + vy * vy)));
}

//????§???¢poly?????????????????????????????????p????????¨??????????????????????????????
bool inPolygon(Polygon &poly, Point p) {
  if ((int)poly.size() == 0)
    return false;
  rep(i, (int)poly.size()) if (onSegment(poly[i], poly[(i + 1) % poly.size()],
                                         p)) return true;
  double sum = 0;
  for (int i = 0; i < (int)poly.size(); i++) {
    if (equals(cross(poly[i] - p, poly[(i + 1) % poly.size()] - p), 0.0))
      continue; // ????????????????????¨angle???nan?????????sum???nan??????????????¬
    if (cross3p(p, poly[i], poly[(i + 1) % poly.size()]) < 0)
      sum -= angle(p, poly[i], poly[(i + 1) % poly.size()]);
    else
      sum += angle(p, poly[i], poly[(i + 1) % poly.size()]);
  }
  // ?????????????????????????????????????????¨?????????????????§??\\?????????????????????
  const double eps = 1e-5;
  return (fabs(sum - 2 * M_PI) < eps || fabs(sum + 2 * M_PI) < eps);
}

bool intersectLL(Line l, Line m) {
  return abs(cross(l.p2 - l.p1, m.p2 - m.p1)) > EPS || // non-parallel
         abs(cross(l.p2 - l.p1, m.p1 - l.p1)) < EPS;   // same line
}
bool intersectLS(Line l, Line s) {
  return cross(l.p2 - l.p1, s.p1 - l.p1) * // s[0] is left of l
             cross(l.p2 - l.p1, s.p2 - l.p1) <
         EPS; // s[1] is right of l
}
bool intersectLP(Line l, Point p) {
  return abs(cross(l.p2 - p, l.p1 - p)) < EPS;
}
bool intersectSS(Line s, Line t) {
  return ccw(s.p1, s.p2, t.p1) * ccw(s.p1, s.p2, t.p2) <= 0 &&
         ccw(t.p1, t.p2, s.p1) * ccw(t.p1, t.p2, s.p2) <= 0;
}
bool intersectSP(Line s, Point p) {
  return abs(s.p1 - p) + abs(s.p2 - p) - abs(s.p2 - s.p1) <
         EPS; // triangle inequality
}

Point projection(Line l, Point p) {
  double t = dot(p - l.p1, l.p1 - l.p2) / norm(l.p1 - l.p2);
  return l.p1 + (l.p1 - l.p2) * t;
}
Point reflection(Line l, Point p) { return p + (projection(l, p) - p) * 2; }
double distanceLP(Line l, Point p) { return abs(p - projection(l, p)); }
double distanceLL(Line l, Line m) {
  return intersectLL(l, m) ? 0 : distanceLP(l, m.p1);
}

double distanceLS(Line l, Line s) {
  if (intersectLS(l, s))
    return 0;
  return min(distanceLP(l, s.p1), distanceLP(l, s.p2));
}
double distanceSP(Line s, Point p) {
  Point r = projection(s, p);
  if (intersectSP(s, r))
    return abs(r - p);
  return min(abs(s.p1 - p), abs(s.p2 - p));
}

double distanceSS(Line s, Line t) {
  if (intersectSS(s, t))
    return 0;
  return min(min(distanceSP(s, t.p1), distanceSP(s, t.p2)),
             min(distanceSP(t, s.p1), distanceSP(t, s.p2)));
}

Point crosspoint(Line l, Line m) {
  double A = cross(l.p2 - l.p1, m.p2 - m.p1);
  double B = cross(l.p2 - l.p1, l.p2 - m.p1);
  if (abs(A) < EPS && abs(B) < EPS) {
    vector<Point> vec;
    vec.push_back(l.p1), vec.push_back(l.p2), vec.push_back(m.p1),
        vec.push_back(m.p2);
    sort(vec.begin(), vec.end());
    assert(vec[1] == vec[2]); //???????????°??????????????????
    return vec[1];
    // return m.p1;
  }
  if (abs(A) < EPS)
    assert(false);
  return m.p1 + (m.p2 - m.p1) * (B / A);
}

// -- END --

const bool debug = false;

struct Edge {
  int dst;
  double cost;
};

bool LT(double a, double b) { return !equals(a, b) && a < b; }
bool LTE(double a, double b) { return equals(a, b) || a < b; }

int N, VN[110];
double Hs[110];
Polygon polies[110];
Point ep[2];

bool check(Segment &seg, int skip1 = -1, int skip2 = -1) {
  rep(i, N) {
    if (i == skip1 || i == skip2)
      continue;
    rep(j, VN[i]) {
      Segment ururu_beam = Segment(polies[i][j], polies[i][(j + 1) % VN[i]]);
      if (equals(cross(seg.p1 - seg.p2, ururu_beam.p1 - ururu_beam.p2), 0))
        continue;
      if (intersectSS(seg, ururu_beam))
        return false;
    }
  }
  return true;
}

Segment nearestSS(Segment &seg1, Segment &seg2) {
  Segment seg = Segment(seg1.p1, seg2.p1);
  double mini = abs(seg1.p1 - seg2.p1);
  /*
  if( LT(abs(seg1.p1-seg2.p2),mini) ) {
    mini = abs(seg1.p1-seg2.p2);
    seg = Segment(seg1.p1,seg2.p2);
  }
  if( LT(abs(seg1.p2-seg2.p1),mini) ) {
    mini = abs(seg1.p2-seg2.p1);
    seg = Segment(seg1.p2,seg2.p1);
  }
  if( LT(abs(seg1.p2-seg2.p2),mini) ) {
    mini = abs(seg1.p2-seg2.p2);
    seg = Segment(seg1.p2,seg2.p2);
  }
  */
  Point proj = projection(seg2, seg1.p1);
  if (onSegment(seg2.p1, seg2.p2, proj) && LT(abs(seg1.p1 - proj), mini)) {
    mini = abs(seg1.p1 - proj);
    seg = Segment(seg1.p1, proj);
  }
  proj = projection(seg2, seg1.p2);
  if (onSegment(seg2.p1, seg2.p2, proj) && LT(abs(seg1.p2 - proj), mini)) {
    mini = abs(seg1.p2 - proj);
    seg = Segment(seg1.p2, proj);
  }
  proj = projection(seg1, seg2.p1);
  if (onSegment(seg1.p1, seg1.p2, proj) && LT(abs(seg2.p1 - proj), mini)) {
    mini = abs(seg2.p1 - proj);
    seg = Segment(seg2.p1, proj);
  }
  proj = projection(seg1, seg2.p2);
  if (onSegment(seg1.p1, seg1.p2, proj) && LT(abs(seg2.p2 - proj), mini)) {
    mini = abs(seg2.p2 - proj);
    seg = Segment(seg2.p2, proj);
  }
  return seg;
}

struct Data {
  int cur;
  double w;
  bool operator<(const Data &data) const {
    if (!equals(w, data.w))
      return LT(data.w, w);
    return cur > data.cur;
  }
};

vector<Edge> G[110];
double dijkstra(int V) {
  vector<double> mini(V, 1e8);
  mini[0] = 0;
  priority_queue<Data> Q;
  Q.push((Data){0, 0});
  while (!Q.empty()) {
    Data data = Q.top();
    Q.pop();
    if (data.cur == 1)
      return data.w;
    rep(i, (int)G[data.cur].size()) {
      Edge &e = G[data.cur][i];
      if (LT(data.w + e.cost, mini[e.dst])) {
        mini[e.dst] = data.w + e.cost;
        Q.push((Data){e.dst, mini[e.dst]});
      }
    }
  }
  return mini[1];
}

void compute(int N, double theta, double phi) {
  double ans = abs(ep[0] - ep[1]);
  // ??±?????????????????´????????????
  rep(i, N) {
    vector<Point> ps;
    Vector v = Vector(cos(theta), sin(theta));
    rep(j, VN[i]) {
      ps.push_back(polies[i][j]);
      ps.push_back(polies[i][j] - v * Hs[i] / tan(phi));
    }
    polies[i] = andrewScan(ps);
    VN[i] = (int)polies[i].size();

    if (debug) {
      puts("");
      cout << i << "-th polygon" << endl;
      rep(j, (int)polies[i].size()) { cout << polies[i][j] << endl; }
    }
  }

  // ?§??????????+??±?????????????????´?????????????????§?§??????§??????????????§??????????????±??????????????¢????±??????°?????????
  rep(i, N + 2) G[i].clear();
  rep(i, 2) { //?§??????????????????±??????????????´??????????????¢
    rep(j, N) {
      if (inPolygon(polies[j], ep[i])) {
        G[i].push_back((Edge){2 + j, 0});
        G[2 + j].push_back((Edge){i, 0});
      } else {
        double mini = 1e8;

        rep(k, VN[j]) {
          Segment seg = Segment(ep[i], polies[j][k]);
          if (LTE(ans, abs(seg.p1 - seg.p2)))
            continue;
          if (LT(abs(seg.p1 - seg.p2), mini) && check(seg, j)) {
            mini = abs(seg.p1 - seg.p2);
          }
        }
        rep(k, VN[j]) {
          Point p =
              projection(Line(polies[j][k], polies[j][(k + 1) % VN[j]]), ep[i]);
          if (!onSegment(polies[j][k], polies[j][(k + 1) % VN[j]], p))
            continue;
          Segment seg = Segment(ep[i], p);
          if (LTE(ans, abs(seg.p1 - seg.p2)))
            continue;
          if (LT(abs(seg.p1 - seg.p2), mini) && check(seg, j)) {
            mini = abs(seg.p1 - seg.p2);
          }
        }
        // if( !equals(mini,1e8) ) {
        if (LT(mini, ans)) {
          G[i].push_back((Edge){2 + j, mini});
          G[2 + j].push_back((Edge){i, mini});
        }
      }
    }
  }
  rep(i, N) { //??±??????????????´???i????????±??????????????´???j???????????¢
    REP(j, i + 1, N) {
      double mini = 1e8;

      rep(k, VN[i]) {
        Segment seg1 = Segment(polies[i][k], polies[i][(k + 1) % VN[i]]);
        rep(l, (int)polies[j].size()) {
          Segment seg2 = Segment(polies[j][l], polies[j][(l + 1) % VN[j]]);

          if (equals(cross(seg1.p1 - seg1.p2, seg2.p1 - seg2.p2), 0.0) &&
              (onSegment(seg1.p1, seg1.p2, seg2.p1) ||
               onSegment(seg1.p1, seg1.p2, seg2.p2))) {
            mini = 0;
            goto Skip;
          } else if (!equals(cross(seg1.p1 - seg1.p2, seg2.p1 - seg2.p2),
                             0.0) &&
                     intersectSS(seg1, seg2)) {
            mini = 0;
            goto Skip;
          } else {
            Segment seg = nearestSS(seg1, seg2);
            if (LTE(ans, abs(seg.p1 - seg.p2)))
              continue;
            if (LT(abs(seg.p1 - seg.p2), mini) && check(seg, i, j)) {
              mini = abs(seg.p1 - seg.p2);
            }
          }
        }
      }
    Skip:;
      // if( !equals(mini,1e8) ) {
      if (LT(mini, ans)) {
        G[2 + i].push_back((Edge){2 + j, mini});
        G[2 + j].push_back((Edge){2 + i, mini});
      }
    }
  }

  if (debug) {
    rep(i, 2 + N) {
      puts("");
      if (i < 2)
        cout << "(" << i << ")"
             << " From : " << ep[i] << endl;
      else
        cout << "(" << i << ")"
             << " From : "
             << "polygon " << i - 2 << " (" << polies[i - 2][0] << ")" << endl;
      rep(j, (int)G[i].size()) {
        cout << "  To : " << G[i][j].dst << ", Weight : " << G[i][j].cost
             << endl;
      }
    }
  }

  // dijkstra
  ans = min(ans, dijkstra(N + 2));
  printf("%.10f\\n", ans);
  // printf("%.10f\\n",dijkstra(N+2));
}

int main() {
  while (cin >> N, N) {
    rep(i, N) {
      cin >> VN[i] >> Hs[i];
      polies[i].resize(VN[i]);
      rep(j, VN[i]) cin >> polies[i][j].x >> polies[i][j].y;
    }
    double theta, phi;
    cin >> theta >> phi;
    rep(i, 2) cin >> ep[i].x >> ep[i].y;
    compute(N, toRad(theta), toRad(phi));
  }
  return 0;
}

Error: TLE

Fixed submission:

#include <algorithm>
#include <cassert>
#include <climits>
#include <complex>
#include <cstdio>
#include <cstring>
#include <deque>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <unordered_set>
#include <vector>

#define REP(i, s, n) for (int i = s; i < n; i++)
#define rep(i, n) REP(i, 0, n)
#define EPS (1e-8)
#define equals(a, b) (fabs((a) - (b)) < EPS)
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0

using namespace std;

// -- BEGIN --
class Point {
public:
  double x, y;

  Point(double x = 0, double y = 0) : x(x), y(y) {}

  Point operator+(Point p) { return Point(x + p.x, y + p.y); }
  Point operator-(Point p) { return Point(x - p.x, y - p.y); }
  Point operator*(double a) { return Point(a * x, a * y); }
  Point operator/(double a) { return Point(x / a, y / a); }
  Point operator*(Point a) {
    return Point(x * a.x - y * a.y, x * a.y + y * a.x);
  }

  bool operator<(const Point &p) const {
    return !equals(x, p.x) ? x < p.x : (!equals(y, p.y) && y < p.y);
  }

  bool operator==(const Point &p) const {
    return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
  }
};

struct Segment {
  Point p1, p2;
  Segment(Point p1 = Point(), Point p2 = Point()) : p1(p1), p2(p2) {}
  bool operator<(const Segment &s) const {
    return (p2 == s.p2) ? p1 < s.p1 : p2 < s.p2;
  }
  bool operator==(const Segment &s) const {
    return (s.p1 == p1 && s.p2 == p2) || (s.p1 == p2 && s.p2 == p1);
  }
};

typedef Point Vector;
typedef Segment Line;
typedef vector<Point> Polygon;

ostream &operator<<(ostream &os, const Point &a) {
  return os << "(" << a.x << "," << a.y << ")";
}

ostream &operator<<(ostream &os, const Segment &a) {
  return os << "( " << a.p1 << " , " << a.p2 << " )";
}

double dot(Point a, Point b) { return a.x * b.x + a.y * b.y; }

double cross(Point a, Point b) { return a.x * b.y - a.y * b.x; }

double norm(Point a) { return a.x * a.x + a.y * a.y; }

double abs(Point a) { return sqrt(norm(a)); }

// rad ????§???????????????¢?????§?????????????????¨
Point rotate(Point a, double rad) {
  return Point(cos(rad) * a.x - sin(rad) * a.y,
               sin(rad) * a.x + cos(rad) * a.y);
}

// ??????????????¢????????????
double toRad(double agl) { return agl * M_PI / 180.0; }

// a => prev, b => cur, c=> next
// prev ?????? cur ????????£??? next ????????????????§????????±???????
double getArg(Point a, Point b, Point c) {
  double arg1 = atan2(b.y - a.y, b.x - a.x);
  double arg2 = atan2(c.y - b.y, c.x - b.x);
  double arg = fabs(arg1 - arg2);
  while (arg > M_PI)
    arg -= 2.0 * M_PI;
  return fabs(arg);
}

int ccw(Point p0, Point p1, Point p2) {
  Point a = p1 - p0;
  Point b = p2 - p0;
  if (cross(a, b) > EPS)
    return COUNTER_CLOCKWISE;
  if (cross(a, b) < -EPS)
    return CLOCKWISE;
  if (dot(a, b) < -EPS)
    return ONLINE_BACK;
  if (norm(a) < norm(b))
    return ONLINE_FRONT;
  return ON_SEGMENT;
}

Polygon andrewScan(Polygon s) {
  Polygon u, l;
  if ((int)s.size() < 3)
    return s;

  sort(s.begin(), s.end());

  u.push_back(s[0]);
  u.push_back(s[1]);
  l.push_back(s[s.size() - 1]);
  l.push_back(s[s.size() - 2]);

  for (int i = 2; i < (int)s.size(); i++) {
    for (int n = (int)u.size();
         n >= 2 && ccw(u[n - 2], u[n - 1], s[i]) != CLOCKWISE; n--)
      u.pop_back();
    u.push_back(s[i]);
  }

  for (int i = (int)s.size() - 3; i >= 0; i--) {
    for (int n = (int)l.size();
         n >= 2 && ccw(l[n - 2], l[n - 1], s[i]) != CLOCKWISE; n--)
      l.pop_back();
    l.push_back(s[i]);
  }

  reverse(l.begin(), l.end());

  for (int i = (int)u.size() - 2; i >= 1; i--)
    l.push_back(u[i]);

  return l;
}

// cross product of pq and pr
double cross3p(Point p, Point q, Point r) {
  return (r.x - q.x) * (p.y - q.y) - (r.y - q.y) * (p.x - q.x);
}

// returns true if point r is on the same line as the line pq
bool collinear(Point p, Point q, Point r) {
  return fabs(cross3p(p, q, r)) < EPS;
}

// returns true if point t is on the left side of line pq
bool ccwtest(Point p, Point q, Point r) {
  return cross3p(p, q, r) > 0; // can be modified to accept collinear points
}

bool onSegment(Point p, Point q, Point r) {
  return collinear(p, q, r) &&
         equals(sqrt(pow(p.x - r.x, 2) + pow(p.y - r.y, 2)) +
                    sqrt(pow(r.x - q.x, 2) + pow(r.y - q.y, 2)),
                sqrt(pow(p.x - q.x, 2) + pow(p.y - q.y, 2)));
}

bool isConvex(vector<Point> p) {
  int sz = (int)p.size();
  if (sz < 3)
    return false; // boundary case, we treat a point or a line as not convex
  bool isLeft = ccwtest(p[0], p[1], p[2]);
  for (int i = 1; i < (int)p.size(); i++)
    if (ccwtest(p[i], p[(i + 1) % sz], p[(i + 2) % sz]) != isLeft)
      return false;
  return true;
}

double angle(Point a, Point b, Point c) {
  double ux = b.x - a.x, uy = b.y - a.y;
  double vx = c.x - a.x, vy = c.y - a.y;
  return acos((ux * vx + uy * vy) /
              sqrt((ux * ux + uy * uy) * (vx * vx + vy * vy)));
}

//????§???¢poly?????????????????????????????????p????????¨??????????????????????????????
bool inPolygon(Polygon &poly, Point p) {
  if ((int)poly.size() == 0)
    return false;
  rep(i, (int)poly.size()) if (onSegment(poly[i], poly[(i + 1) % poly.size()],
                                         p)) return true;
  double sum = 0;
  for (int i = 0; i < (int)poly.size(); i++) {
    if (equals(cross(poly[i] - p, poly[(i + 1) % poly.size()] - p), 0.0))
      continue; // ????????????????????¨angle???nan?????????sum???nan??????????????¬
    if (cross3p(p, poly[i], poly[(i + 1) % poly.size()]) < 0)
      sum -= angle(p, poly[i], poly[(i + 1) % poly.size()]);
    else
      sum += angle(p, poly[i], poly[(i + 1) % poly.size()]);
  }
  // ?????????????????????????????????????????¨?????????????????§??\\?????????????????????
  const double eps = 1e-5;
  return (fabs(sum - 2 * M_PI) < eps || fabs(sum + 2 * M_PI) < eps);
}

bool intersectLL(Line l, Line m) {
  return abs(cross(l.p2 - l.p1, m.p2 - m.p1)) > EPS || // non-parallel
         abs(cross(l.p2 - l.p1, m.p1 - l.p1)) < EPS;   // same line
}
bool intersectLS(Line l, Line s) {
  return cross(l.p2 - l.p1, s.p1 - l.p1) * // s[0] is left of l
             cross(l.p2 - l.p1, s.p2 - l.p1) <
         EPS; // s[1] is right of l
}
bool intersectLP(Line l, Point p) {
  return abs(cross(l.p2 - p, l.p1 - p)) < EPS;
}
bool intersectSS(Line s, Line t) {
  return ccw(s.p1, s.p2, t.p1) * ccw(s.p1, s.p2, t.p2) <= 0 &&
         ccw(t.p1, t.p2, s.p1) * ccw(t.p1, t.p2, s.p2) <= 0;
}
bool intersectSP(Line s, Point p) {
  return abs(s.p1 - p) + abs(s.p2 - p) - abs(s.p2 - s.p1) <
         EPS; // triangle inequality
}

Point projection(Line l, Point p) {
  double t = dot(p - l.p1, l.p1 - l.p2) / norm(l.p1 - l.p2);
  return l.p1 + (l.p1 - l.p2) * t;
}
Point reflection(Line l, Point p) { return p + (projection(l, p) - p) * 2; }
double distanceLP(Line l, Point p) { return abs(p - projection(l, p)); }
double distanceLL(Line l, Line m) {
  return intersectLL(l, m) ? 0 : distanceLP(l, m.p1);
}

double distanceLS(Line l, Line s) {
  if (intersectLS(l, s))
    return 0;
  return min(distanceLP(l, s.p1), distanceLP(l, s.p2));
}
double distanceSP(Line s, Point p) {
  Point r = projection(s, p);
  if (intersectSP(s, r))
    return abs(r - p);
  return min(abs(s.p1 - p), abs(s.p2 - p));
}

double distanceSS(Line s, Line t) {
  if (intersectSS(s, t))
    return 0;
  return min(min(distanceSP(s, t.p1), distanceSP(s, t.p2)),
             min(distanceSP(t, s.p1), distanceSP(t, s.p2)));
}

Point crosspoint(Line l, Line m) {
  double A = cross(l.p2 - l.p1, m.p2 - m.p1);
  double B = cross(l.p2 - l.p1, l.p2 - m.p1);
  if (abs(A) < EPS && abs(B) < EPS) {
    vector<Point> vec;
    vec.push_back(l.p1), vec.push_back(l.p2), vec.push_back(m.p1),
        vec.push_back(m.p2);
    sort(vec.begin(), vec.end());
    assert(vec[1] == vec[2]); //???????????°??????????????????
    return vec[1];
    // return m.p1;
  }
  if (abs(A) < EPS)
    assert(false);
  return m.p1 + (m.p2 - m.p1) * (B / A);
}

// -- END --

const bool debug = false;

struct Edge {
  int dst;
  double cost;
};

bool LT(double a, double b) { return !equals(a, b) && a < b; }

int N, VN[110];
double Hs[110];
Polygon polies[110];
Point ep[2];

bool check(Segment &seg, int skip1 = -1, int skip2 = -1) {
  rep(i, N) {
    if (i == skip1 || i == skip2)
      continue;
    rep(j, VN[i]) {
      Segment ururu_beam = Segment(polies[i][j], polies[i][(j + 1) % VN[i]]);
      if (equals(cross(seg.p1 - seg.p2, ururu_beam.p1 - ururu_beam.p2), 0))
        continue;
      if (intersectSS(seg, ururu_beam))
        return false;
    }
  }
  return true;
}

Segment nearestSS(Segment &seg1, Segment &seg2) {
  Segment seg = Segment(seg1.p1, seg2.p1);
  double mini = abs(seg1.p1 - seg2.p1);
  /*
  if( LT(abs(seg1.p1-seg2.p2),mini) ) {
    mini = abs(seg1.p1-seg2.p2);
    seg = Segment(seg1.p1,seg2.p2);
  }
  if( LT(abs(seg1.p2-seg2.p1),mini) ) {
    mini = abs(seg1.p2-seg2.p1);
    seg = Segment(seg1.p2,seg2.p1);
  }
  if( LT(abs(seg1.p2-seg2.p2),mini) ) {
    mini = abs(seg1.p2-seg2.p2);
    seg = Segment(seg1.p2,seg2.p2);
  }
  */
  Point proj = projection(seg2, seg1.p1);
  if (onSegment(seg2.p1, seg2.p2, proj) && LT(abs(seg1.p1 - proj), mini)) {
    mini = abs(seg1.p1 - proj);
    seg = Segment(seg1.p1, proj);
  }
  proj = projection(seg2, seg1.p2);
  if (onSegment(seg2.p1, seg2.p2, proj) && LT(abs(seg1.p2 - proj), mini)) {
    mini = abs(seg1.p2 - proj);
    seg = Segment(seg1.p2, proj);
  }
  proj = projection(seg1, seg2.p1);
  if (onSegment(seg1.p1, seg1.p2, proj) && LT(abs(seg2.p1 - proj), mini)) {
    mini = abs(seg2.p1 - proj);
    seg = Segment(seg2.p1, proj);
  }
  proj = projection(seg1, seg2.p2);
  if (onSegment(seg1.p1, seg1.p2, proj) && LT(abs(seg2.p2 - proj), mini)) {
    mini = abs(seg2.p2 - proj);
    seg = Segment(seg2.p2, proj);
  }
  return seg;
}

struct Data {
  int cur;
  double w;
  bool operator<(const Data &data) const {
    if (!equals(w, data.w))
      return LT(data.w, w);
    return cur > data.cur;
  }
};

vector<Edge> G[110];
double dijkstra(int V) {
  vector<double> mini(V, 1e8);
  mini[0] = 0;
  priority_queue<Data> Q;
  Q.push((Data){0, 0});
  while (!Q.empty()) {
    Data data = Q.top();
    Q.pop();
    if (data.cur == 1)
      return data.w;
    rep(i, (int)G[data.cur].size()) {
      Edge &e = G[data.cur][i];
      if (LT(data.w + e.cost, mini[e.dst])) {
        mini[e.dst] = data.w + e.cost;
        Q.push((Data){e.dst, mini[e.dst]});
      }
    }
  }
  return mini[1];
}

void compute(int N, double theta, double phi) {
  // ??±?????????????????´????????????
  rep(i, N) {
    vector<Point> ps;
    Vector v = Vector(cos(theta), sin(theta));
    rep(j, VN[i]) {
      ps.push_back(polies[i][j]);
      ps.push_back(polies[i][j] - v * Hs[i] / tan(phi));
    }
    polies[i] = andrewScan(ps);
    VN[i] = (int)polies[i].size();

    if (debug) {
      puts("");
      cout << i << "-th polygon" << endl;
      rep(j, (int)polies[i].size()) { cout << polies[i][j] << endl; }
    }
  }

  // ?§??????????+??±?????????????????´?????????????????§?§??????§??????????????§??????????????±??????????????¢????±??????°?????????
  rep(i, N + 2) G[i].clear();
  rep(i, 2) { //?§??????????????????±??????????????´??????????????¢
    rep(j, N) {
      if (inPolygon(polies[j], ep[i])) {
        G[i].push_back((Edge){2 + j, 0});
        G[2 + j].push_back((Edge){i, 0});
      } else {
        double mini = 1e8;

        rep(k, VN[j]) {
          Segment seg = Segment(ep[i], polies[j][k]);
          if (LT(abs(seg.p1 - seg.p2), mini) && check(seg, j)) {
            mini = abs(seg.p1 - seg.p2);
          }
        }
        rep(k, VN[j]) {
          Point p =
              projection(Line(polies[j][k], polies[j][(k + 1) % VN[j]]), ep[i]);
          if (!onSegment(polies[j][k], polies[j][(k + 1) % VN[j]], p))
            continue;
          Segment seg = Segment(ep[i], p);
          if (LT(abs(seg.p1 - seg.p2), mini) && check(seg, j)) {
            mini = abs(seg.p1 - seg.p2);
          }
        }
        if (!equals(mini, 1e8)) {
          G[i].push_back((Edge){2 + j, mini});
          G[2 + j].push_back((Edge){i, mini});
        }
      }
    }
  }
  rep(i, N) { //??±??????????????´???i????????±??????????????´???j???????????¢
    REP(j, i + 1, N) {
      double mini = 1e8;

      rep(k, VN[i]) {
        Segment seg1 = Segment(polies[i][k], polies[i][(k + 1) % VN[i]]);
        rep(l, (int)polies[j].size()) {
          Segment seg2 = Segment(polies[j][l], polies[j][(l + 1) % VN[j]]);

          if (equals(cross(seg1.p1 - seg1.p2, seg2.p1 - seg2.p2), 0.0) &&
              (onSegment(seg1.p1, seg1.p2, seg2.p1) ||
               onSegment(seg1.p1, seg1.p2, seg2.p2))) {
            mini = 0;
            goto Skip;
          } else if (!equals(cross(seg1.p1 - seg1.p2, seg2.p1 - seg2.p2),
                             0.0) &&
                     intersectSS(seg1, seg2)) {
            mini = 0;
            goto Skip;
          } else {
            Segment seg = nearestSS(seg1, seg2);
            if (LT(abs(seg.p1 - seg.p2), mini) && check(seg, i, j)) {
              mini = abs(seg.p1 - seg.p2);
            }
          }
        }
      }
    Skip:;
      if (!equals(mini, 1e8)) {
        G[2 + i].push_back((Edge){2 + j, mini});
        G[2 + j].push_back((Edge){2 + i, mini});
      }
    }
  }

  if (debug) {
    rep(i, 2 + N) {
      puts("");
      if (i < 2)
        cout << "(" << i << ")"
             << " From : " << ep[i] << endl;
      else
        cout << "(" << i << ")"
             << " From : "
             << "polygon " << i - 2 << " (" << polies[i - 2][0] << ")" << endl;
      rep(j, (int)G[i].size()) {
        cout << "  To : " << G[i][j].dst << ", Weight : " << G[i][j].cost
             << endl;
      }
    }
  }

  // dijkstra
  printf("%.10f\\n", dijkstra(N + 2));
}

int main() {
  while (cin >> N, N) {
    rep(i, N) {
      cin >> VN[i] >> Hs[i];
      polies[i].resize(VN[i]);
      rep(j, VN[i]) cin >> polies[i][j].x >> polies[i][j].y;
    }
    double theta, phi;
    cin >> theta >> phi;
    rep(i, 2) cin >> ep[i].x >> ep[i].y;
    compute(N, toRad(theta), toRad(phi));
  }
  return 0;
}