Problem p01508 (C++) — buggy submission, verdict: Runtime Error

#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));
  }
};

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)));
}

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);
}

// intersect - end

// onSegment - being

// 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; }

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) {
  // cout << "@" << p << endl;
  if ((int)poly.size() == 0)
    return false;

  rep(i, poly.size()) if (onSegment(poly[i], poly[(i + 1) % poly.size()],
                                    p)) return true;
  rep(i, poly.size()) if (poly[i] == 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( p == Point(5.2777777777777778,10) ) cout << "angle " <<
    // angle(p,poly[i],poly[(i+1)%poly.size()]) << " " << sum << endl;
    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-6;
  return (fabs(sum - 2 * M_PI) < eps || fabs(sum + 2 * M_PI) < eps);
}

// onSegment - end

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 - edge.p1, seg.p2 - edge.p2), 0.0)) {
      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 {
      if (intersectSS(seg, edge))
        vp.push_back(crosspoint(seg, edge));
    }
  }
  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;
}

const int MAX_N = 110;
int N;
Point ps[MAX_N];

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

void compute() {

  vector<Point> poly;
  rep(i, N) poly.push_back(ps[i]);
  vector<Segment> segs;
  rep(i, N) segs.push_back(Segment(ps[i], ps[(i + 1) % N]));

  double ans = 0;
  rep(i, N) REP(j, i + 1, N) {
    // if( !( i == 18 && j == 20 ) ) continue;
    // cout << ps[i] << " " << ps[j] << endl;

    bool DEBUG = false;
    if (DEBUG) {
      cout << endl;
      cout << ps[i] << "," << ps[j] << " + " << abs(ps[i] - ps[j]) << endl;
    }

    Line line = Line(ps[i], ps[j]);
    // if( intersectLS(line,Segment(ps[0],ps[16])) )cout << "cpcpc" <<
    // crosspoint(Segment(ps[0],ps[16]),line) << endl;

    vector<Point> cand;
    cand.push_back(line.p1);
    cand.push_back(line.p2);
    rep(k, N) {
      Segment seg = Segment(ps[k], ps[(k + 1) % N]);
      if (!(line == seg) && intersectLS(line, seg) &&
          !equals(cross(line.p1 - line.p2, seg.p1 - seg.p2), 0.0)) {
        cand.push_back(crosspoint(line, seg));
      }
    }
    sort(cand.begin(), cand.end());
    cand.erase(unique(cand.begin(), cand.end()), cand.end());
    sort(cand.begin(), cand.end());

    // if( DEBUG )rep(k,cand.size()) cout << k << "-th : " << cand[k] << endl;
    DEBUG = false;

    line.p1 = ps[i], line.p2 = ps[j];
    rep(k, (int)cand.size()) if (cand[k] == line.p1) {
      int pos = k;
      while (pos - 1 >= 0 && inPolygon(poly, (line.p1 + cand[pos - 1]) / 2.0)) {
        line.p1 = cand[--pos];
      }
      // cout << cand[pos-1] << " A A A " << (line.p1+cand[pos-1])/2.0 << " " <<
      // inPolygon(poly,(line.p1+cand[pos-1])/2) << endl;
      break;
    }

    rep(k, (int)cand.size()) if (cand[k] == line.p2) {
      int pos = k;
      while (pos + 1 < cand.size() &&
             inPolygon(poly, (line.p2 + cand[pos + 1]) / 2.0)) {
        line.p2 = cand[++pos];
      }
      break;
    }

    DEBUG = true;
    // if( DEBUG ) cout << "renew : " << line << endl;
    DEBUG = false;

    // return;//////////////////

    bool failed = false;
    rep(k, N) {
      if (onSegment(line.p1, line.p2, segs[k].p1) ||
          onSegment(line.p1, line.p2, segs[k].p2))
        continue;
      if (collinear(line.p1, line.p2, segs[k].p1) &&
          collinear(line.p1, line.p2, segs[k].p2))
        continue;

      if (intersectSS(line, segs[k])) {
        Point cp = crosspoint(line, segs[k]);
        if (cp == line.p1 || cp == line.p2)
          continue;
        failed = true;
        break;
      }
    }
    if (failed)
      continue;
    if (!inPolygon(poly, line))
      continue;
    // cout << abs(line.p1-line.p2) << " :: " << line << " || " << ps[i] << ","
    // << ps[j] << endl;
    ans = max(ans, abs(line.p1 - line.p2));
  }
  // printf("%.12f\\n",ans);
  cout << setiosflags(ios::fixed) << setprecision(10) << ans << endl;
}

int main() {
  /*
  Segment seg1 = Segment(Point(0,0),Point(1,18));
  Segment seg2 = Segment(Point(10,10),Point(57,10));
  cout << crosspoint(seg1,seg2) << endl;*/
  int CNT = 1;
  while (/*scanf("%d",&N)*/ cin >> N, N) {
    rep(i, N) cin >> ps[i].x >> ps[i].y; // scanf("%lf %lf",&ps[i].x,&ps[i].y);
    /*
    Point p = Point(0.5555555556,10);
    Polygon pol;
    rep(i,N) pol.push_back(ps[i]);
    cout << p << " IN " << inPolygon(pol,p) << endl;
    cout << "____________" << endl;
    */
    // rep(i,N) ps[i].x += 300, ps[i].y += 300;
    // printf("Case %d: ",CNT++);
    cout << "Case " << CNT++ << ": ";
    compute();
  }
  return 0;
}

Error: WA

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 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));
  }
};

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)));
}

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);
}

// intersect - end

// arrangement - 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; }
};

void segmentArrangement(vector<Segment> vs, vector<Point> &ps) {

  rep(i, (int)vs.size()) ps.push_back(vs[i].p1);

  rep(i, (int)vs.size()) REP(j, i + 1, (int)vs.size()) {
    Line line = Line(vs[i].p1, vs[j].p1);
    rep(k, (int)vs.size()) {
      if (!(line == vs[k]) && intersectLS(line, vs[k]) &&
          !equals(cross(line.p1 - line.p2, vs[k].p1 - vs[k].p2), 0.0)) {
        ps.push_back(crosspoint(line, vs[k]));
      }
    }
  }

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

// arrangement - end

// onSegment - being

// 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; }

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)));
}

// onSegment - end

const int MAX_N = 110;
int N;
Point ps[MAX_N];

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

void compute() {

  //
  vector<Segment> segs;
  vector<Point> new_ps;
  rep(i, N) {
    new_ps.push_back(ps[i]);
    segs.push_back(Segment(ps[i], ps[(i + 1) % N]));
  }
  rep(i, N) REP(j, i + 1, N) {
    Line line = Line(ps[i], ps[j]);
    rep(k, N) {
      if (!(line == segs[k]) && intersectLS(line, segs[k]) &&
          !equals(cross(line.p1 - line.p2, segs[k].p1 - segs[k].p2), 0.0)) {
        new_ps.push_back(crosspoint(line, segs[k]));
      }
    }
  }

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

  assert((int)new_ps.size() < 5000);

  double ans = 0;
  rep(i, (int)new_ps.size()) REP(j, i + 1, (int)new_ps.size()) {
    Segment seg = Segment(new_ps[i], new_ps[j]);
    double dist = abs(seg.p1 - seg.p2);
    if (LTE(dist, ans))
      continue;
    bool failed = false;
    rep(k, (int)segs.size()) {
      if (onSegment(seg.p1, seg.p2, segs[k].p1) ||
          onSegment(seg.p1, seg.p2, segs[k].p2))
        continue;
      if (intersectSS(seg, segs[k])) {
        failed = true;
        break;
      }
    }
    if (failed)
      continue;
    ans = max(ans, dist);
  }
  printf("%.9lf\\n", ans);
}

int main() {
  int CNT = 1;
  while (scanf("%d", &N), N) {
    rep(i, N) scanf("%lf %lf", &ps[i].x, &ps[i].y);
    printf("Case %d: ", CNT++);
    compute();
  }
  return 0;
}