Problem p01363 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>

#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;

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) {
  os << "(" << a.x << "," << a.y << ")";
}

ostream &operator<<(ostream &os, const Segment &a) {
  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)); }

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;
}

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);
}

// 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)));
}

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, bool flag = true) {
  if ((int)poly.size() == 0)
    return false;
  if (flag)
    rep(i, 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);
}

enum { OUT, ON, IN };
int contains(Polygon &P, Point &p) {
  bool in = false;
  for (int i = 0; i < P.size(); ++i) {
    Point a = P[i] - p, b = P[(i + 1) % P.size()] - p;
    if (a.y > b.y)
      swap(a, b);
    if (a.y <= 0 && 0 < b.y)
      if (cross(a, b) < 0)
        in = !in;
    if (cross(a, b) == 0 && dot(a, b) <= 0)
      return ON;
  }
  return in ? IN : OUT;
}
// -------------------

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

bool DEBUG = false;

struct Data {
  Point cur;
  double weight;
  int a, b;
  bool operator<(const Data &data) const { return LT(data.weight, weight); }
};

const double DINF = 1e30;
int N;
Point bomb;
vector<Polygon> polies;
vector<vector<double>> mindist;
vector<vector<bool>> goals;

bool isValidMove(Point src, Point dst) {

  Segment ururu_beam = Segment(src, dst);
  Point mp = (src + dst) * 0.5; // $
  rep(i, N) {
    int M = polies[i].size();
    bool in = false;
    bool on = false;
    rep(j, M) {
      Segment seg = Segment(polies[i][j], polies[i][(j + 1) % M]);

      Point a = polies[i][j] - mp, b = polies[i][(j + 1) % M] - mp;
      if (a.y > b.y)
        swap(a, b);
      if (a.y <= 0 && 0 < b.y)
        if (cross(a, b) < 0)
          in = !in;
      if (cross(a, b) == 0 && dot(a, b) <= 0)
        on = true;

      // ????????????????????¨??????????????§????????°???????§??????¶?????§?????£????????£???????§????
      if (equals(cross(ururu_beam.p1 - ururu_beam.p2, seg.p1 - seg.p2), 0.0))
        continue;
      seg = Segment(polies[i][j], polies[i][(j - 1 + M) % M]);
      if (equals(cross(ururu_beam.p1 - ururu_beam.p2, seg.p1 - seg.p2), 0.0))
        continue;
      seg = Segment(polies[i][j], polies[i][(j + 1) % M]);

      if (!intersectSS(ururu_beam, seg))
        continue;

      Point cp = crosspoint(ururu_beam, seg);

      //????????? src or dst ??§????????´???????????£???????§????
      if (cp == ururu_beam.p1 || cp == ururu_beam.p2)
        continue;

      if (cp == seg.p1 || cp == seg.p2) {

        // p0 -> p1 ->p2, p0 -> p1 -> p3 ???????????§???????????¨????????? (
        // ?????§continue??????????????? )
        Point p0 = src;
        Point p1 = cp;
        Point p2 = polies[i][(j + 1) % M];
        Point p3 = polies[i][(j - 1 + M) % M];
        if (cp == p2 || cp == p3)
          continue;
        int ccw_res1 = ccw(p0, p1, p2);
        int ccw_res2 = ccw(p0, p1, p3);
        if (ccw_res1 != ccw_res2)
          return false;
      } else
        return false;
    }
    if (!(src == bomb || dst == bomb) && !on && in)
      return false;
  }

  /*
  if( !( src == bomb || dst == bomb ) ) {
    Point mp = ( src + dst ) / 2.0;
    //rep(i,N) if( inPolygon(polies[i],mp,false) ) return false;
    rep(i,N) if( contains(polies[i],mp) == IN ) return false;
  }
  */

  return true;
}

double temper;
void dijkstra() {
  temper = DINF;
  priority_queue<Data> Q;
  Q.push((Data){(Point){0, 0}, 0, -1, -1});
  while (!Q.empty()) {
    Data data = Q.top();
    Q.pop();
    if (data.a != -1 && LT(mindist[data.a][data.b], data.weight))
      continue;
    if (data.a != -1 && goals[data.a][data.b]) {
      temper = data.weight;
      return;
    }
    rep(i, N) rep(j, polies[i].size()) {
      Point next = polies[i][j];
      if (data.cur == next)
        continue;
      if (!isValidMove(data.cur, next))
        continue;
      double next_weight = data.weight + abs(next - data.cur);
      if (LT(next_weight, mindist[i][j])) {
        mindist[i][j] = next_weight;
        Q.push((Data){next, next_weight, i, j});
      }
    }
  }
}

//???????????¶?´??????????ururu_beam??¨seg???????????§???????????¨?????????
bool isGoal(Point p) {
  Segment ururu_beam = Segment(bomb, p);
  rep(i, N) {
    int M = polies[i].size();
    rep(j, M) {
      Segment seg = Segment(polies[i][j], polies[i][(j + 1) % M]);
      if (!intersectSS(ururu_beam, seg))
        continue;
      Point cp = crosspoint(ururu_beam, seg);

      if (!(cp == p))
        return true;
      else if (cp == seg.p1 || cp == seg.p2) {
        int k = (cp == seg.p1 ? j : (j + 1) % M);
        int c1 = ccw(bomb, p, polies[i][(k - 1 + M) % M]);
        int c2 = ccw(bomb, p, polies[i][(k + 1) % M]);
        assert(!(p == polies[i][(k - 1 + M) % M]));
        assert(!(p == polies[i][(k + 1) % M]));
        assert(c1 == COUNTER_CLOCKWISE || c1 == CLOCKWISE);
        assert(c2 == COUNTER_CLOCKWISE || c2 == CLOCKWISE);
        if (c1 == c2)
          return true;
      }
    }
  }
  return false;
}

//????????¨?????????????????§??????????????¨???????¨????????????????
Point getOnSegmentPoint(Point p) {
  Segment ururu_beam = Segment(bomb, p);
  Vector e =
      (ururu_beam.p2 - ururu_beam.p1) / abs(ururu_beam.p2 - ururu_beam.p1);
  ururu_beam.p2 = bomb + e * 1000000;
  Point ret = Point(-DINF, -DINF);
  rep(i, N) {
    int M = polies[i].size();
    rep(j, M) {
      Segment seg = Segment(polies[i][j], polies[i][(j + 1) % M]);
      if (!intersectSS(ururu_beam, seg))
        continue;
      Point cp = crosspoint(ururu_beam, seg);
      if (cp == p)
        continue;
      if (ret == Point(-DINF, -DINF))
        ret = cp;
      else if (LT(abs(cp - bomb), abs(ret - bomb)))
        ret = cp;
    }
  }
  return ret;
}

Point vir;
bool comp_dist(const Point &p, const Point &q) {
  return LT(abs(vir - p), abs(vir - q));
}

void compute() {

  if (isGoal(Point(0, 0))) {
    printf("%.10f\\n", 0.0);
    return;
  }

  rep(i, N) rep(j, polies[i].size()) goals[i][j] = isGoal(polies[i][j]);

  // dijkstra ??§??????????????????????????¢????±???????
  dijkstra();

  // rep(i,N) rep(j,polies[i].size()) goals[i][j] = isGoal(polies[i][j]);
  // double answer = DINF;
  double answer = temper;
  rep(i, N)
      rep(j, polies[i].size()) if (goals[i][j] && LT(mindist[i][j], answer)) {
    answer = mindist[i][j];
  }

  // ??´????????¨??????????£?????????????
  // ???????????????????????´??????????????´????????§????????°????°?????????´??°??????
  rep(i, N) {
    int M = polies[i].size();
    rep(j, M) {
      Point p0 = bomb;
      Point p1 = polies[i][j];
      Point p2 = polies[i][(j + 1) % M];
      Point p3 = polies[i][(j - 1 + M) % M];
      int ccw_res1 = ccw(p0, p1, p2);
      int ccw_res2 = ccw(p0, p1, p3);
      if ((ccw_res1 == COUNTER_CLOCKWISE || ccw_res1 == CLOCKWISE) &&
          (ccw_res2 == COUNTER_CLOCKWISE || ccw_res2 == CLOCKWISE) &&
          ccw_res1 != ccw_res2) {
        continue;
      }

      //?????????????§???¢????§?????????????????????¶?????????????????????
      //?????????
      Point p = getOnSegmentPoint(polies[i][j]);
      if (p.x != -DINF && p.y != -DINF) {
        // if( !( LT(abs(p),answer) ) )
        if (isGoal(p)) {
          if (LT(abs(p), answer) && isValidMove(Point(0, 0), p)) {
            answer = min(answer, abs(p));
          } else {
            double mini = DINF;
            rep(k, N)
                rep(l, polies[k].size()) if (LT(mindist[k][l] +
                                                    abs(polies[k][l] - p),
                                                min(answer, mini)) &&
                                             isValidMove(polies[k][l], p)) {
              mini = min(mini, mindist[k][l] + abs(polies[k][l] - p));
            }
            answer = min(answer, mini);
          }
        }
      }

      //?????´
      p = projection(Segment(bomb, polies[i][j]), Point(0, 0));

      // if( !( LT(abs(p),answer) ) )
      if (isGoal(p)) {
        if (isValidMove(Point(0, 0), p)) {
          answer = min(answer, abs(p));
        } else {
          bool success = true;
          Segment ururu_beam = Segment(p, Point(0, 0));
          rep(k, N) {
            int M2 = polies[k].size();
            rep(l, M2) {
              Segment seg = Segment(polies[k][l], polies[k][(l + 1) % M2]);
              if (!intersectSS(ururu_beam, seg))
                continue;
              if (equals(cross(ururu_beam.p1 - ururu_beam.p2, seg.p1 - seg.p2),
                         0.0))
                continue;
              Point cp = crosspoint(ururu_beam, seg);
              if (cp == seg.p1 || cp == seg.p2 || cp == ururu_beam.p1 ||
                  cp == ururu_beam.p2)
                continue;
              success = false;
              break;
            }
            if (!success)
              break;
          }
          if (success) {
            double mini = DINF;
            rep(k, N) rep(l, polies[k].size()) if (goals[k][l]) {
              mini =
                  min(mini, mindist[k][l] + abs(ururu_beam.p1 - ururu_beam.p2));
            }
          }
        }
      }
    }
  }

  printf("%.10f\\n", answer);
}

int main() {
  while (scanf("%d", &N), N) {
    polies.clear(), mindist.clear();
    goals.clear();
    polies.resize(N), mindist.resize(N), goals.resize(N);
    // cin >> bomb.x >> bomb.y;
    scanf("%lf %lf", &bomb.x, &bomb.y);
    rep(i, N) {
      int m;
      scanf("%d", &m);
      polies[i].resize(m), mindist[i].resize(m, DINF),
          goals[i].resize(m, false);
      rep(j, m)
          scanf("%lf %lf", &polies[i][j].x,
                &polies[i][j].y); // cin >> polies[i][j].x >> polies[i][j].y;
    }
    compute();
  }
  return 0;
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>

#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;

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) {
  os << "(" << a.x << "," << a.y << ")";
}

ostream &operator<<(ostream &os, const Segment &a) {
  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)); }

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;
}

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);
}

// 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)));
}

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, bool flag = true) {
  if ((int)poly.size() == 0)
    return false;
  if (flag)
    rep(i, 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);
}

enum { OUT, ON, IN };
int contains(Polygon &P, Point &p) {
  bool in = false;
  for (int i = 0; i < P.size(); ++i) {
    Point a = P[i] - p, b = P[(i + 1) % P.size()] - p;
    if (a.y > b.y)
      swap(a, b);
    if (a.y <= 0 && 0 < b.y)
      if (cross(a, b) < 0)
        in = !in;
    if (cross(a, b) == 0 && dot(a, b) <= 0)
      return ON;
  }
  return in ? IN : OUT;
}
// -------------------

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

bool DEBUG = false;

struct Data {
  Point cur;
  double weight;
  int a, b;
  bool operator<(const Data &data) const { return LT(data.weight, weight); }
};

const double DINF = 1e30;
int N;
Point bomb;
vector<Polygon> polies;
vector<vector<double>> mindist;
vector<vector<bool>> goals;

bool isValidMove(Point src, Point dst) {

  Segment ururu_beam = Segment(src, dst);
  Point mp = (src + dst) * 0.5; // $
  rep(i, N) {
    int M = polies[i].size();
    bool in = false;
    bool on = false;
    rep(j, M) {
      Segment seg = Segment(polies[i][j], polies[i][(j + 1) % M]);

      Point a = polies[i][j] - mp, b = polies[i][(j + 1) % M] - mp;
      if (a.y > b.y)
        swap(a, b);
      if (a.y <= 0 && 0 < b.y)
        if (cross(a, b) < 0)
          in = !in;
      if (cross(a, b) == 0 && dot(a, b) <= 0)
        on = true;

      // ????????????????????¨??????????????§????????°???????§??????¶?????§?????£????????£???????§????
      if (equals(cross(ururu_beam.p1 - ururu_beam.p2, seg.p1 - seg.p2), 0.0))
        continue;
      seg = Segment(polies[i][j], polies[i][(j - 1 + M) % M]);
      if (equals(cross(ururu_beam.p1 - ururu_beam.p2, seg.p1 - seg.p2), 0.0))
        continue;
      seg = Segment(polies[i][j], polies[i][(j + 1) % M]);

      if (!intersectSS(ururu_beam, seg))
        continue;

      Point cp = crosspoint(ururu_beam, seg);

      //????????? src or dst ??§????????´???????????£???????§????
      if (cp == ururu_beam.p1 || cp == ururu_beam.p2)
        continue;

      if (cp == seg.p1 || cp == seg.p2) {

        // p0 -> p1 ->p2, p0 -> p1 -> p3 ???????????§???????????¨????????? (
        // ?????§continue??????????????? )
        Point p0 = src;
        Point p1 = cp;
        Point p2 = polies[i][(j + 1) % M];
        Point p3 = polies[i][(j - 1 + M) % M];
        if (cp == p2 || cp == p3)
          continue;
        int ccw_res1 = ccw(p0, p1, p2);
        int ccw_res2 = ccw(p0, p1, p3);
        if (ccw_res1 != ccw_res2)
          return false;
      } else
        return false;
    }
    if (!(src == bomb || dst == bomb) && !on && in)
      return false;
  }

  /*
  if( !( src == bomb || dst == bomb ) ) {
    Point mp = ( src + dst ) / 2.0;
    //rep(i,N) if( inPolygon(polies[i],mp,false) ) return false;
    rep(i,N) if( contains(polies[i],mp) == IN ) return false;
  }
  */

  return true;
}

void dijkstra() {
  priority_queue<Data> Q;
  Q.push((Data){(Point){0, 0}, 0, -1, -1});
  while (!Q.empty()) {
    Data data = Q.top();
    Q.pop();
    if (data.a != -1 && LT(mindist[data.a][data.b], data.weight))
      continue;
    rep(i, N) rep(j, polies[i].size()) {
      Point next = polies[i][j];
      if (data.cur == next)
        continue;
      if (!isValidMove(data.cur, next))
        continue;
      double next_weight = data.weight + abs(next - data.cur);
      if (LT(next_weight, mindist[i][j])) {
        mindist[i][j] = next_weight;
        Q.push((Data){next, next_weight, i, j});
      }
    }
  }
}

//???????????¶?´??????????ururu_beam??¨seg???????????§???????????¨?????????
bool isGoal(Point p) {
  Segment ururu_beam = Segment(bomb, p);
  rep(i, N) {
    int M = polies[i].size();
    rep(j, M) {
      Segment seg = Segment(polies[i][j], polies[i][(j + 1) % M]);
      if (!intersectSS(ururu_beam, seg))
        continue;
      Point cp = crosspoint(ururu_beam, seg);

      if (!(cp == p))
        return true;
      else if (cp == seg.p1 || cp == seg.p2) {
        int k = (cp == seg.p1 ? j : (j + 1) % M);
        int c1 = ccw(bomb, p, polies[i][(k - 1 + M) % M]);
        int c2 = ccw(bomb, p, polies[i][(k + 1) % M]);
        assert(!(p == polies[i][(k - 1 + M) % M]));
        assert(!(p == polies[i][(k + 1) % M]));
        assert(c1 == COUNTER_CLOCKWISE || c1 == CLOCKWISE);
        assert(c2 == COUNTER_CLOCKWISE || c2 == CLOCKWISE);
        if (c1 == c2)
          return true;
      }
    }
  }
  return false;
}

//????????¨?????????????????§??????????????¨???????¨????????????????
Point getOnSegmentPoint(Point p) {
  Segment ururu_beam = Segment(bomb, p);
  Vector e =
      (ururu_beam.p2 - ururu_beam.p1) / abs(ururu_beam.p2 - ururu_beam.p1);
  ururu_beam.p2 = bomb + e * 1000000;
  Point ret = Point(-DINF, -DINF);
  rep(i, N) {
    int M = polies[i].size();
    rep(j, M) {
      Segment seg = Segment(polies[i][j], polies[i][(j + 1) % M]);
      if (!intersectSS(ururu_beam, seg))
        continue;
      Point cp = crosspoint(ururu_beam, seg);
      if (cp == p)
        continue;
      if (ret == Point(-DINF, -DINF))
        ret = cp;
      else if (LT(abs(cp - bomb), abs(ret - bomb)))
        ret = cp;
    }
  }
  return ret;
}

Point vir;
bool comp_dist(const Point &p, const Point &q) {
  return LT(abs(vir - p), abs(vir - q));
}

void compute() {

  if (isGoal(Point(0, 0))) {
    printf("%.10f\\n", 0.0);
    return;
  }

  // dijkstra ??§??????????????????????????¢????±???????
  dijkstra();

  rep(i, N) rep(j, polies[i].size()) goals[i][j] = isGoal(polies[i][j]);

  double answer = DINF;
  rep(i, N)
      rep(j, polies[i].size()) if (goals[i][j] && LT(mindist[i][j], answer)) {
    answer = mindist[i][j];
  }

  // ??´????????¨??????????£?????????????
  // ???????????????????????´??????????????´????????§????????°????°?????????´??°??????
  rep(i, N) {
    int M = polies[i].size();
    rep(j, M) {
      Point p0 = bomb;
      Point p1 = polies[i][j];
      Point p2 = polies[i][(j + 1) % M];
      Point p3 = polies[i][(j - 1 + M) % M];
      int ccw_res1 = ccw(p0, p1, p2);
      int ccw_res2 = ccw(p0, p1, p3);
      if ((ccw_res1 == COUNTER_CLOCKWISE || ccw_res1 == CLOCKWISE) &&
          (ccw_res2 == COUNTER_CLOCKWISE || ccw_res2 == CLOCKWISE) &&
          ccw_res1 != ccw_res2) {
        continue;
      }

      //?????????????§???¢????§?????????????????????¶?????????????????????
      //?????????
      Point p = getOnSegmentPoint(polies[i][j]);
      if (p.x != -DINF && p.y != -DINF) {
        if (isGoal(p)) {
          if (LT(abs(p), answer) && isValidMove(Point(0, 0), p)) {
            answer = min(answer, abs(p));
          } else {
            double mini = DINF;
            rep(k, N)
                rep(l, polies[k].size()) if (LT(mindist[k][l] +
                                                    abs(polies[k][l] - p),
                                                min(answer, mini)) &&
                                             isValidMove(polies[k][l], p)) {
              mini = min(mini, mindist[k][l] + abs(polies[k][l] - p));
            }
            answer = min(answer, mini);
          }
        }
      }

      //?????´
      p = projection(Segment(bomb, polies[i][j]), Point(0, 0));

      if (isGoal(p)) {
        if (isValidMove(Point(0, 0), p)) {
          answer = min(answer, abs(p));
        } else {
          bool success = true;
          Segment ururu_beam = Segment(p, Point(0, 0));
          rep(k, N) {
            int M2 = polies[k].size();
            rep(l, M2) {
              Segment seg = Segment(polies[k][l], polies[k][(l + 1) % M2]);
              if (!intersectSS(ururu_beam, seg))
                continue;
              if (equals(cross(ururu_beam.p1 - ururu_beam.p2, seg.p1 - seg.p2),
                         0.0))
                continue;
              Point cp = crosspoint(ururu_beam, seg);
              if (cp == seg.p1 || cp == seg.p2 || cp == ururu_beam.p1 ||
                  cp == ururu_beam.p2)
                continue;
              success = false;
              break;
            }
            if (!success)
              break;
          }
          if (success) {
            double mini = DINF;
            rep(k, N) rep(l, polies[k].size()) if (goals[k][l]) {
              mini =
                  min(mini, mindist[k][l] + abs(ururu_beam.p1 - ururu_beam.p2));
            }
          }
        }
      }
    }
  }

  printf("%.10f\\n", answer);
}

int main() {
  while (scanf("%d", &N), N) {
    polies.clear(), mindist.clear();
    goals.clear();
    polies.resize(N), mindist.resize(N), goals.resize(N);
    // cin >> bomb.x >> bomb.y;
    scanf("%lf %lf", &bomb.x, &bomb.y);
    rep(i, N) {
      int m;
      scanf("%d", &m);
      polies[i].resize(m), mindist[i].resize(m, DINF),
          goals[i].resize(m, false);
      rep(j, m)
          scanf("%lf %lf", &polies[i][j].x,
                &polies[i][j].y); // cin >> polies[i][j].x >> polies[i][j].y;
    }
    compute();
  }
  return 0;
}