Problem p01626 (C++) — buggy submission, verdict: Memory 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 COUNTER_CLOCKWISE 1
#define CLOCKWISE -1
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0
#define equals(a, b) (fabs((a) - (b)) < EPS)

using namespace std;

const int IINF = INT_MAX;
// template - 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 : 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 &p) const {
    return (p.p1 == p1 && p.p2 == p2) || (p.p1 == p2 && p.p2 == p1);
  }
  bool operator<(const Segment &s) const {
    if (!(p1 == s.p1))
      return p1 < s.p1;
    return p2 < s.p2;
  }
};

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)); }

// rad は角度をラジアンで持たせること
Point rotate(Point a, double rad) {
  return Point(cos(rad) * a.x - sin(rad) * a.y,
               sin(rad) * a.x + cos(rad) * a.y);
}

// 度をラジアンに変換
double toRad(double agl) { return agl * M_PI / 180.0; }

// a => prev, b => cur, c=> next
// prev から cur へ行って next へ行く際の角度を求める
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);
}
// template - end

// ccw - begin
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;
}
// ccw - end

// intersect - begin
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)));
}
bool DEBUG = false;
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());
    // while(DEBUG);
    cerr << l << " ! " << m << endl;
    assert(vec[1] == vec[2]); // 同じセグメントかもよ
    return vec[1];
  }
  if (abs(A) < EPS)
    assert(false);
  return m.p1 + (m.p2 - m.p1) * (B / A);
}
// intersect - end

// 　点の内包判定 - begin
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);
}
bool collinear(Point p, Point q, Point r) {
  return fabs(cross3p(p, q, r)) < EPS;
}
bool ccwtest(Point p, Point q, Point r) { return cross3p(p, q, r) > 0; }
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)));
}

// 多角形poly内（線分上も含む）に点pが存在するかどうは判定する
bool inPolygon(Polygon poly, Point p) {
  if ((int)poly.size() == 0)
    return false;

  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;
    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);
}
// 点の内包判定 - end

// 線分の内包判定 - begin
bool inPolygon(const Polygon &poly, Segment seg) {
  vector<Point> vp;
  vp.push_back(seg.p1);
  vp.push_back(seg.p2);
  rep(i, (int)poly.size()) {
    Segment edge = Segment(poly[i], poly[(i + 1) % (int)poly.size()]);
    if (equals(cross(seg.p1 - seg.p2, edge.p1 - edge.p2), 0.0)) { // 後で変更
      if (onSegment(seg.p1, seg.p2, edge.p1))
        vp.push_back(edge.p1);
      if (onSegment(seg.p1, seg.p2, edge.p2))
        vp.push_back(edge.p2);
    } else {
      DEBUG = true;
      if (intersectSS(seg, edge))
        vp.push_back(crosspoint(seg, edge));
      DEBUG = false;
    }
  }
  sort(vp.begin(), vp.end());
  vp.erase(unique(vp.begin(), vp.end()), vp.end());
  rep(i, (int)vp.size() - 1) {
    Point middle_point = (vp[i] + vp[i + 1]) / 2.0;
    if (!inPolygon(poly, middle_point))
      return false;
  }
  return true;
}
// 線分の内包判定 - end

struct Node {
  int cur;
  double weight;
  bool operator<(const Node &node) const { return weight > node.weight; }
};

struct Edge {
  int from, to;
  double cost;
  Edge(int from = IINF, int to = IINF, double cost = IINF)
      : from(from), to(to), cost(cost) {}
  bool operator<(const Edge &a) const { return cost < a.cost; }
};

const string NO = "impossible";
const int MAX_N = 110;
const int MAX_V = 100000;
int N;
Polygon polies[MAX_N];
Point sp, ep;
Line mirror;
double mindist[MAX_V];

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

// Point pを含む多角形のインデックスを返す,存在しない場合は-1
int selectGraph(Point p) {
  rep(i, N) if (inPolygon(polies[i], p)) return i;
  return -1;
}

void dijkstra(const vector<vector<Edge>> &G, const vector<Point> &ps) {
  priority_queue<Node> Q;
  int start = -1, goal = -1, V = ps.size();
  assert(V < MAX_V);
  rep(i, V) {
    if (start == -1 && ps[i] == sp)
      start = i;
    if (goal == -1 && ps[i] == ep)
      goal = i;
    if (start != -1 && goal != -1)
      break;
  }
  // assert( start != -1 && goal != -1 );
  rep(i, V) mindist[i] = 1e20;
  Q.push((Node){start, 0});
  mindist[start] = 0;
  while (!Q.empty()) {
    Node node = Q.top();
    Q.pop();
    int cur = node.cur;
    double weight = node.weight;

    if (cur == goal) {
      printf("%.12lf\\n", weight);
      return;
    }

    if (LT(mindist[cur], weight))
      continue;
    rep(i, G[cur].size()) {
      int to = G[cur][i].to;
      double new_weight = weight + G[cur][i].cost;
      if (LT(new_weight, mindist[to])) {
        mindist[to] = new_weight;
        Q.push((Node){to, mindist[to]});
      }
    }
  }
  puts(NO.c_str());
}

void compute() {
  int indices[4] = {selectGraph(sp), selectGraph(ep),
                    selectGraph(reflection(mirror, sp)),
                    selectGraph(reflection(mirror, ep))};

  bool failed = false;
  rep(i, 4) if (indices[i] == -1) {
    failed = true;
    break;
  }
  if (indices[0] != indices[1] || indices[2] != indices[3])
    failed = true;
  if (failed) {
    puts(NO.c_str());
    return;
  }
  rep(i, N) if (i != indices[0] && i != indices[2]) polies[i].clear();

  Polygon Real = polies[indices[0]];
  Polygon Mirr = polies[indices[2]];
  Polygon Mixi = Real;
  rep(i, (int)Mirr.size()) Mixi.push_back(reflection(mirror, Mirr[i]));
  Mixi.push_back(sp), Mixi.push_back(ep);
  sort(Mixi.begin(), Mixi.end());
  Mixi.erase(unique(Mixi.begin(), Mixi.end()), Mixi.end());

  vector<Segment> segment_buffer;
  rep(i, (int)Mixi.size()) REP(j, i + 1, (int)Mixi.size()) {
    Line line = Segment(Mixi[i], Mixi[j]);
    vector<Point> vp;
    vp.push_back(Mixi[i]);
    vp.push_back(Mixi[j]);
    rep(k, Real.size()) {
      Segment s = Segment(Real[k], Real[(k + 1) % Real.size()]);
      if (equals(cross(s.p1 - s.p2, line.p1 - line.p2), 0.0)) {
        if (onSegment(line.p1, line.p2, s.p1))
          vp.push_back(s.p1);
        if (onSegment(line.p1, line.p2, s.p2))
          vp.push_back(s.p2);
      } else {
        if (intersectLS(line, s))
          vp.push_back(crosspoint(line, s));
      }
    }
    sort(vp.begin(), vp.end());
    vp.erase(unique(vp.begin(), vp.end()), vp.end());
    rep(k, (int)vp.size() - 1) {
      Segment s = Segment(vp[k], vp[k + 1]);
      Segment rs = Segment(reflection(mirror, s.p1), reflection(mirror, s.p2));
      if (inPolygon(Real, s) && inPolygon(Mirr, rs))
        segment_buffer.push_back(s);
    }
  }

  sort(segment_buffer.begin(), segment_buffer.end());
  segment_buffer.erase(unique(segment_buffer.begin(), segment_buffer.end()),
                       segment_buffer.end());
  int dex = 0;
  map<Point, int> mp;
  vector<Point> ps;
  rep(i, segment_buffer.size()) {
    if (!mp.count(segment_buffer[i].p1)) {
      mp[segment_buffer[i].p1] = dex++;
      ps.push_back(segment_buffer[i].p1);
    }
    if (!mp.count(segment_buffer[i].p2)) {
      mp[segment_buffer[i].p2] = dex++;
      ps.push_back(segment_buffer[i].p2);
    }
  }

  vector<vector<Edge>> G(dex, vector<Edge>());
  rep(i, segment_buffer.size()) {
    G[mp[segment_buffer[i].p1]].push_back(
        Edge(mp[segment_buffer[i].p1], mp[segment_buffer[i].p2],
             abs(segment_buffer[i].p1 - segment_buffer[i].p2)));
    G[mp[segment_buffer[i].p2]].push_back(
        Edge(mp[segment_buffer[i].p2], mp[segment_buffer[i].p1],
             abs(segment_buffer[i].p1 - segment_buffer[i].p2)));
  }
  dijkstra(G, ps);
}

int main() {
  while (cin >> N, N) {
    rep(i, N) {
      int M;
      cin >> M;
      polies[i].resize(M);
      rep(j, M) cin >> polies[i][j].x >> polies[i][j].y;
    }
    cin >> sp.x >> sp.y >> ep.x >> ep.y;
    cin >> mirror.p1.x >> mirror.p1.y >> mirror.p2.x >> mirror.p2.y;
    compute();
  }
  return 0;
}
/*
スタートとゴールがある多角形を選ぶ
鏡の向こうの多角形も１つ選ぶ
鏡に対称にして多角形を移動する
鏡の向こうの選ばれし多角形を鏡を基準に折りたたむ
こうしてできたものの各線分で移動可能なものをつめこみグラフ化する
できあがったグラフをつかってdijkstra
 */

Error: MLE

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-9)
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0
#define equals(a, b) (fabs((a) - (b)) < EPS)

using namespace std;

const int IINF = INT_MAX;
// template - 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 : 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 &p) const {
    return (p.p1 == p1 && p.p2 == p2) || (p.p1 == p2 && p.p2 == p1);
  }
  bool operator<(const Segment &s) const {
    if (!(p1 == s.p1))
      return p1 < s.p1;
    return p2 < s.p2;
  }
};

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)); }

// rad は角度をラジアンで持たせること
Point rotate(Point a, double rad) {
  return Point(cos(rad) * a.x - sin(rad) * a.y,
               sin(rad) * a.x + cos(rad) * a.y);
}

// 度をラジアンに変換
double toRad(double agl) { return agl * M_PI / 180.0; }

// a => prev, b => cur, c=> next
// prev から cur へ行って next へ行く際の角度を求める
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);
}
// template - end

// ccw - begin
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;
}
// ccw - end

// intersect - begin
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)));
}
bool DEBUG = false;
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());
    // while(DEBUG);
    assert(vec[1] == vec[2]); // 同じセグメントかもよ
    return vec[1];
  }
  if (abs(A) < EPS)
    assert(false);
  return m.p1 + (m.p2 - m.p1) * (B / A);
}
// intersect - end

// 　点の内包判定 - begin
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);
}
bool collinear(Point p, Point q, Point r) {
  return fabs(cross3p(p, q, r)) < EPS;
}
bool ccwtest(Point p, Point q, Point r) { return cross3p(p, q, r) > 0; }
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)));
}

// 多角形poly内（線分上も含む）に点pが存在するかどうは判定する
bool inPolygon(Polygon poly, Point p) {
  if ((int)poly.size() == 0)
    return false;

  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;
    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()]);
  }
  return (fabs(sum - 2 * M_PI) < EPS || fabs(sum + 2 * M_PI) < EPS);
}
// 点の内包判定 - end

// 線分の内包判定 - begin
bool inPolygon(const Polygon &poly, Segment seg) {
  vector<Point> vp;
  vp.push_back(seg.p1);
  vp.push_back(seg.p2);
  rep(i, (int)poly.size()) {
    Segment edge = Segment(poly[i], poly[(i + 1) % (int)poly.size()]);
    if (equals(cross(seg.p1 - seg.p2, edge.p1 - edge.p2), 0.0)) { // 後で変更
      if (onSegment(seg.p1, seg.p2, edge.p1))
        vp.push_back(edge.p1);
      if (onSegment(seg.p1, seg.p2, edge.p2))
        vp.push_back(edge.p2);
    } else {
      DEBUG = true;
      if (intersectSS(seg, edge))
        vp.push_back(crosspoint(seg, edge));
      DEBUG = false;
    }
  }
  sort(vp.begin(), vp.end());
  vp.erase(unique(vp.begin(), vp.end()), vp.end());
  rep(i, (int)vp.size() - 1) {
    Point middle_point = (vp[i] + vp[i + 1]) / 2.0;
    if (!inPolygon(poly, middle_point))
      return false;
  }
  return true;
}
// 線分の内包判定 - end

// 線分アレンジメント - begin
struct Edge {
  int from, to;
  double cost;
  Edge(int from = IINF, int to = IINF, double cost = IINF)
      : from(from), to(to), cost(cost) {}
  bool operator<(const Edge &a) const { return cost < a.cost; }
};

vector<vector<Edge>> segmentArrangement(vector<Segment> &vs,
                                        vector<Point> &ps) {
  rep(i, vs.size()) ps.push_back(vs[i].p1), ps.push_back(vs[i].p2);
  rep(i, vs.size()) REP(j, i + 1, vs.size()) if (intersectSS(vs[i], vs[j]))
      ps.push_back(Point(crosspoint(vs[i], vs[j])));

  sort(ps.begin(), ps.end());
  ps.erase(unique(ps.begin(), ps.end()), ps.end());

  vector<vector<Edge>> ret(ps.size());

  for (int i = 0; i < vs.size(); i++) {
    vector<pair<double, int>> list;
    rep(j, ps.size()) if (intersectSP(vs[i], ps[j]))
        list.push_back(pair<double, int>(norm(vs[i].p1 - ps[j]), j));

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

    for (int j = 0; j + 1 < list.size(); ++j) {
      int from = list[j].second, to = list[j + 1].second;
      double cost = abs(ps[from] - ps[to]);
      ret[from].push_back(Edge(from, to, cost));
      ret[to].push_back(Edge(to, from, cost));
    }
  }
  return ret;
}
// 線分アレンジメント - end

// 線分マージ - begin
bool merge_if_able(Segment &s, Segment t) {
  if (abs(cross(s.p2 - s.p1, t.p2 - t.p1)) > EPS)
    return false;
  if (ccw(s.p1, t.p1, s.p2) == +1 || ccw(s.p1, t.p1, s.p2) == -1)
    return false; // not on the same line
  if (ccw(s.p1, s.p2, t.p1) == -2 || ccw(t.p1, t.p2, s.p1) == -2)
    return false; // separated
  s = Segment(min(s.p1, t.p1), max(s.p2, t.p2));
  return true;
}
void merge_segments(vector<Segment> &segs) {
  for (int i = 0; i < segs.size(); ++i)
    if (segs[i].p2 < segs[i].p1)
      swap(segs[i].p2, segs[i].p1);
  for (int i = 0; i < segs.size(); ++i)
    for (int j = i + 1; j < segs.size(); ++j)
      if (merge_if_able(segs[i], segs[j]))
        segs[j--] = segs.back(), segs.pop_back();
}
// 線分マージ - end

struct Node {
  int cur;
  double weight;
  bool operator<(const Node &node) const { return weight > node.weight; }
};

const string NO = "impossible";
const int MAX_N = 110;
const int MAX_V = 7000;
int N;
Polygon polies[MAX_N];
Point sp, ep;
Line mirror;
double mindist[MAX_V];

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

// Point pを含む多角形のインデックスを返す,存在しない場合は-1
int selectGraph(Point p) {
  rep(i, N) if (inPolygon(polies[i], p)) return i;
  return -1;
}

void dijkstra(const vector<vector<Edge>> &G, const vector<Point> &ps) {
  priority_queue<Node> Q;
  int start = -1, goal = -1, V = ps.size();
  assert(V < MAX_V);
  rep(i, V) {
    if (start == -1 && ps[i] == sp)
      start = i;
    if (goal == -1 && ps[i] == ep)
      goal = i;
    if (start != -1 && goal != -1)
      break;
  }
  // assert( start != -1 && goal != -1 );
  rep(i, V) mindist[i] = 1e20;
  Q.push((Node){start, 0});
  mindist[start] = 0;
  while (!Q.empty()) {
    Node node = Q.top();
    Q.pop();
    int cur = node.cur;
    double weight = node.weight;

    if (cur == goal) {
      printf("%.12lf\\n", weight);
      return;
    }

    if (LT(mindist[cur], weight))
      continue;
    rep(i, G[cur].size()) {
      int to = G[cur][i].to;
      double new_weight = weight + G[cur][i].cost;
      if (LT(new_weight, mindist[to])) {
        mindist[to] = new_weight;
        Q.push((Node){to, mindist[to]});
      }
    }
  }
  puts(NO.c_str());
}

void compute() {
  /*
  Segment A = Segment(Point(2,2),Point(6,2));
  Segment B = Segment(Point(5,2),Point(6,2));
  cout << merge_if_able(A,B) << endl;
  vector<Segment> aa;
  aa.push_back(A);
  aa.push_back(B);
  merge_segments(aa);
  rep(i,aa.size()) cout<< aa[i] << endl;
  */
  int indices[4] = {selectGraph(sp), selectGraph(ep),
                    selectGraph(reflection(mirror, sp)),
                    selectGraph(reflection(mirror, ep))};

  bool failed = false;
  rep(i, 4) if (indices[i] == -1) {
    failed = true;
    break;
  }
  if (indices[0] != indices[1] || indices[2] != indices[3])
    failed = true;
  if (failed) {
    puts(NO.c_str());
    return;
  }
  rep(i, N) if (i != indices[0] && i != indices[2]) polies[i].clear();

  Polygon Real = polies[indices[0]];
  Polygon Mirr = polies[indices[2]];
  Polygon Mixi = Real;
  rep(i, (int)Mirr.size()) Mixi.push_back(reflection(mirror, Mirr[i]));
  Mixi.push_back(sp), Mixi.push_back(ep);

  vector<Segment> segment_buffer;
  rep(i, (int)Mixi.size()) REP(j, i + 1, (int)Mixi.size()) {
    Segment seg = Segment(Mixi[i], Mixi[j]);
    segment_buffer.push_back(seg);
    /*
    vector<Point> vp;
    rep(k,Real.size()) {
      Segment s = Segment(Real[k],Real[(k+1)%Real.size()]);
      if( equals(cross(s.p1-s.p2,seg.p1-seg.p2),0.0) ) {
        if( onSegment(s.p1,s.p2,seg.p1) ) vp.push_back(seg.p1);
        if( onSegment(s.p1,s.p2,seg.p2) ) vp.push_back(seg.p2);
      } else {
        if( intersectSS(seg,s) )vp.push_back(crosspoint(seg,s));
      }
    }
    sort(vp.begin(),vp.end());
    vp.erase(unique(vp.begin(),vp.end()),vp.end());
    rep(k,(int)vp.size()-1) {
      Segment  s = Segment(vp[k],vp[k+1]);
      Segment rs = Segment(reflection(mirror,s.p1),reflection(mirror,s.p2));
      if( inPolygon(Real,s) && inPolygon(Mirr,rs) ) segment_buffer.push_back(s);
    }
    */
  }

  sort(segment_buffer.begin(), segment_buffer.end());
  segment_buffer.erase(unique(segment_buffer.begin(), segment_buffer.end()),
                       segment_buffer.end());
  merge_segments(segment_buffer);
  vector<Point> ps;
  vector<vector<Edge>> tmp = segmentArrangement(segment_buffer, ps);
  vector<vector<Edge>> G(ps.size());

  rep(i, (int)tmp.size()) rep(j, (int)tmp[i].size()) {
    Segment seg = Segment(ps[tmp[i][j].from], ps[tmp[i][j].to]);
    Segment rseg =
        Segment(reflection(mirror, seg.p1), reflection(mirror, seg.p2));
    if (inPolygon(Real, seg) && inPolygon(Mirr, rseg))
      G[i].push_back(tmp[i][j]);
  }
  Real.clear();
  Mirr.clear();
  Mixi.clear();
  segment_buffer.clear();
  tmp.clear();
  dijkstra(G, ps);
}

int main() {
  while (cin >> N, N) {
    rep(i, N) {
      int M;
      cin >> M;
      polies[i].resize(M);
      rep(j, M) cin >> polies[i][j].x >> polies[i][j].y;
    }
    cin >> sp.x >> sp.y >> ep.x >> ep.y;
    cin >> mirror.p1.x >> mirror.p1.y >> mirror.p2.x >> mirror.p2.y;
    compute();
  }
  return 0;
}
/*
スタートとゴールがある多角形を選ぶ
鏡の向こうの多角形も１つ選ぶ
鏡に対称にして多角形を移動する
鏡の向こうの選ばれし多角形を鏡を基準に折りたたむ
こうしてできたものの各線分で移動可能なものをつめこみグラフ化する
できあがったグラフをつかってdijkstra
 */