Problem p02300 (C++) — buggy submission, verdict: Runtime Error

#include <bits/stdc++.h>
#define range(i, a, b) for (int i = (a); i < (b); i++)
#define rep(i, b) for (int i = 0; i < (b); i++)
#define all(a) (a).begin(), (a).end()
#define show(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \\
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \\
       << " " << __FILE__ << endl;
const int INF = 2000000000;
using namespace std;

typedef complex<double> Point;
typedef Point Vector;
//???????????¨????§???????
struct Segment {
  Point p1, p2;
};
//??´????????¨????§???????
typedef Segment Line;
//????§???¢?????¨????§???????
typedef vector<Point> Polygon;

namespace std {
bool operator<(const Point &a, const Point &b) {
  return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
}
bool operator==(const Point &a, const Point &b) {
  return a.real() == b.real() && a.imag() == b.imag();
}
} // namespace std

class Circle {
public:
  Point c;
  double r;
  Circle(Point c = Point(), double r = 0.0) : c(c), r(r) {}
};

// ?¨±???????????????
#define EPS (1e-10)

// ????????????a?????¶??????????±???????
// double length = abs(a);

// 2???a,b???????????¢????±???????
// double distance = abs(a-b);

/*
// ????????????a?????????????????????????±???????
Point b = a / abs(a);

// ????????????a?????????????????????n1,n2????±???????
Point n1 = a * Point(0, 1);
Point n2 = a * Point(0, -1);
*/

int ccw(Point, Point, Point);

// 2??????????????????????????????????????????
bool EQ(double a, double b) { return (abs(a - b) < EPS); }

// 2??????????????????????????????????????????
bool EQV(Vector a, Vector b) {
  return (EQ(a.real(), b.real()) && EQ(a.imag(), b.imag()));
}

// ?????? (dot product) : a???b = |a||b|cos??
double dot(Point a, Point b) {
  return (a.real() * b.real() + a.imag() * b.imag());
}

// ?????? (cross product) : a??b = |a||b|sin??
double cross(Point a, Point b) {
  return (a.real() * b.imag() - a.imag() * b.real());
}

// 2??´????????´????????? : a??\\b <=> dot(a, b) = 0
bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
  return EQ(dot(a1 - a2, b1 - b2), 0.0);
}
bool isOrthogonal(Line s1, Line s2) {
  return isOrthogonal(s1.p1, s1.p2, s2.p1, s2.p2);
}

// 2??´?????????????????? : a//b <=> cross(a, b) = 0
bool isParallel(Point a1, Point a2, Point b1, Point b2) {
  return EQ(cross(a1 - a2, b1 - b2), 0.0);
}
bool isParallel(Line s1, Line s2) {
  return isParallel(s1.p1, s1.p2, s2.p1, s2.p2);
}

// ???c?????´???a,b????????????????????????
bool isPointOnLine(Point a, Point b, Point c) {
  return EQ(cross(b - a, c - a), 0.0);
}
bool isPointOnLine(Line s, Point c) { return isPointOnLine(s.p1, s.p2, c); }

// ???a,b???????????´?????¨???c??¨????????¢
double distanceLPoint(Point a, Point b, Point c) {
  return abs(cross(b - a, c - a)) / abs(b - a);
}
double distanceLPoint(Line s, Point c) { return distanceLPoint(s.p1, s.p2, c); }

// ???a,b???????????¨??????????????¨???c??¨????????¢
double distanceLsPoint(Point a, Point b, Point c) {
  if (dot(b - a, c - a) < EPS)
    return abs(c - a);
  if (dot(a - b, c - b) < EPS)
    return abs(c - b);
  return abs(cross(b - a, c - a)) / abs(b - a);
}
double distanceLsPoint(Segment s, Point c) {
  return distanceLsPoint(s.p1, s.p2, c);
}

// a1,a2???????????¨??????????????¨b1,b2???????????¨???????????????????????????
bool isIntersectedLs(Point a1, Point a2, Point b1, Point b2) {
  return (ccw(a1, a2, b1) * ccw(a1, a2, b2) <= 0 &&
          ccw(b1, b2, a1) * ccw(b1, b2, a2) <= 0);
}
bool isIntersectedLs(Segment s1, Segment s2) {
  return isIntersectedLs(s1.p1, s1.p2, s2.p1, s2.p2);
}

// a1,a2???????????¨??????????????¨b1,b2???????????¨??????????????????????¨????
Point intersectionLs(Point a1, Point a2, Point b1, Point b2) {
  Vector base = b2 - b1;
  double d1 = abs(cross(base, a1 - b1));
  double d2 = abs(cross(base, a2 - b1));
  double t = d1 / (d1 + d2);

  return Point(a1 + (a2 - a1) * t);
}
Point intersectionLs(Segment s1, Segment s2) {
  return intersectionLs(s1.p1, s1.p2, s2.p1, s2.p2);
}

// a1,a2???????????´?????¨b1,b2???????????´??????????????????
bool isIntersectedL(Point a1, Point a2, Point b1, Point b2) {
  return !EQ(cross(a1 - a2, b1 - b2), 0.0);
}
bool isIntersectedL(Line l1, Line l2) {
  return isIntersectedL(l1.p1, l1.p2, l2.p1, l2.p2);
}

// a1,a2???????????´?????¨b1,b2???????????´?????????????¨????
Point intersectionL(Point a1, Point a2, Point b1, Point b2) {
  Point a = a2 - a1;
  Point b = b2 - b1;
  return a1 + a * cross(b, b1 - a1) / cross(b, a);
}
Point intersectionL(Line l1, Line l2) {
  return intersectionL(l1.p1, l1.p2, l2.p1, l2.p2);
}

// ??????s1??¨??????s2????????¢
double distanceLL(Segment s1, Segment s2) {
  if (isIntersectedLs(s1.p1, s1.p2, s2.p1, s2.p2))
    return 0.0;
  return min(min(distanceLsPoint(s1.p1, s1.p2, s2.p1),
                 distanceLsPoint(s1.p1, s1.p2, s2.p2)),
             min(distanceLsPoint(s2.p1, s2.p2, s1.p1),
                 distanceLsPoint(s2.p1, s2.p2, s1.p2)));
}

// ??????s???????????????p????°???±
Point project(Segment s, Point p) {
  Vector base = s.p2 - s.p1;
  double r = dot(p - s.p1, base) / norm(base);
  return Point(s.p1 + base * r);
}

//??????s???????±??????¨?????????p??????????§°??????
Point reflect(Segment s, Point p) {
  return Point(p + (project(s, p) - p) * 2.0);
}

//???p???angle?????????????¨???????????????¢
Point rotation(Point p, double angle) {
  double x, y;
  x = p.real() * cos(angle) - p.imag() * sin(angle);
  y = p.real() * sin(angle) + p.imag() * cos(angle);
  return Point(x, y);
}

//???c??¨??????l?????????
pair<Point, Point> getCrossPoints(Circle c, Line l) {
  Vector pr = project(l, c.c);
  Vector e = (l.p2 - l.p1) / abs(l.p2 - l.p1);
  double base = sqrt(c.r * c.r - norm(pr - c.c));
  return make_pair(pr + e * base, pr - e * base);
}

//???c1??¨???c2?????????
double arg(Vector p) { return atan2(p.imag(), p.real()); }
Vector polar(double a, double r) { return Point(cos(r) * a, sin(r) * a); }

pair<Point, Point> getCrossPoints(Circle c1, Circle c2) {
  double d = abs(c1.c - c2.c);
  double a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
  double t = arg(c2.c - c1.c);
  return make_pair(Point(c1.c + polar(c1.r, t + a)),
                   Point(c1.c + polar(c1.r, t - a)));
}

//????????????
static const int IN = 2;
static const int ON = 1;
static const int OUT = 0;

int contains(Polygon g, Point p) {
  int n = g.size();
  bool x = false;
  rep(i, n) {
    Point a = g[i] - p, b = g[(i + 1) % n] - p;
    if (abs(cross(a, b)) < EPS && dot(a, b) < EPS)
      return ON;
    if (a.imag() > b.imag())
      swap(a, b);
    if (a.imag() < EPS && EPS < b.imag() && cross(a, b) > EPS)
      x = not x;
  }
  return (x ? IN : OUT);
}

//???????????????????????????
static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;
static const int ONLINE_FRONT = -2;
static const int ON_SEGMENT = 0;

int ccw(Point p0, Point p1, Point p2) {
  Vector a = p1 - p0;
  Vector 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 (abs(a) < abs(b))
    return ONLINE_FRONT;

  return ON_SEGMENT;
}

//??????
Polygon andrewScan(Polygon s) {
  Polygon u;
  if (s.size() < 3)
    return s;
  sort(s.begin(), s.end());

  range(i, 0, s.size()) {
    //==
    //COUNTER_CLOCKWISE?????¨????§????180??\\???????????´?????????????????§????????????????????¨????????°?????????
    //!=
    //!CLOCKWISE?????¨????§????180??????????????´????????????????????°????????????
    for (int n = u.size();
         n >= 2 && ccw(u[n - 2], u[n - 1], s[i]) == COUNTER_CLOCKWISE; n--) {
      u.pop_back();
    }
    u.emplace_back(s[i]);
  }

  for (int i = s.size() - 2; i >= 0; i--) {
    //????????? == ??¨ != ????????´??????
    for (int n = u.size();
         n >= 2 && ccw(u[n - 2], u[n - 1], s[i]) == COUNTER_CLOCKWISE; n--) {
      u.pop_back();
    }
    u.emplace_back(s[i]);
  }

  reverse(u.begin(), u.end());
  u.pop_back();

  int i = 0;
  while (i < u.size() - 1) {
    if (u[i].imag() > u[i + 1].imag()) {
      u.emplace_back(u[i]);
      u.erase(u.begin());
      continue;
    } else if (u[i].imag() == u[i + 1].imag() &&
               u[i].real() > u[i + 1].real()) {
      u.emplace_back(u[i]);
      u.erase(u.begin());
      continue;
    }
    break;
  }

  return u;
}

double AreaOfTriangle(Point a, Point b, Point c) {
  double w, x, y, z;
  w = b.real() - a.real();
  x = b.imag() - a.imag();
  y = c.real() - a.real();
  z = c.imag() - a.imag();
  return abs((w * z - x * y) / 2);
}

double areaOfPolygon(Polygon g) {
  int n = g.size();
  double ret = 0.0;
  rep(i, n) ret += cross(g[i], g[(i + 1) % n]);
  return abs(ret) / 2.0;
}

//???????§???¢?????????????????????
bool isConvex(Polygon g) {
  int n = g.size();
  rep(i, n) {
    if (ccw(g[i], g[(i + 1) % n], g[(i + 2) % n]) == CLOCKWISE)
      return false;
  }
  return true;
}

int main() {
  int n;
  cin >> n;

  Polygon g, l;
  rep(i, n) {
    double a, b;
    cin >> a >> b;
    g.emplace_back(Point{a, b});
  }
  l = andrewScan(g);
  cout << l.size() << endl;
  for (auto it : l)
    cout << it.real() << ' ' << it.imag() << endl;
}

Error: 0
u[i].imag() = 0


Fixed submission:

#include <bits/stdc++.h>
#define range(i, a, b) for (int i = (a); i < (b); i++)
#define rep(i, b) for (int i = 0; i < (b); i++)
#define all(a) (a).begin(), (a).end()
#define show(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \\
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \\
       << " " << __FILE__ << endl;
const int INF = 2000000000;
using namespace std;

typedef complex<double> Point;
typedef Point Vector;
//???????????¨????§???????
struct Segment {
  Point p1, p2;
};
//??´????????¨????§???????
typedef Segment Line;
//????§???¢?????¨????§???????
typedef vector<Point> Polygon;

namespace std {
bool operator<(const Point &a, const Point &b) {
  return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
}
bool operator==(const Point &a, const Point &b) {
  return a.real() == b.real() && a.imag() == b.imag();
}
} // namespace std

class Circle {
public:
  Point c;
  double r;
  Circle(Point c = Point(), double r = 0.0) : c(c), r(r) {}
};

// ?¨±???????????????
#define EPS (1e-10)

// ????????????a?????¶??????????±???????
// double length = abs(a);

// 2???a,b???????????¢????±???????
// double distance = abs(a-b);

/*
// ????????????a?????????????????????????±???????
Point b = a / abs(a);

// ????????????a?????????????????????n1,n2????±???????
Point n1 = a * Point(0, 1);
Point n2 = a * Point(0, -1);
*/

int ccw(Point, Point, Point);

// 2??????????????????????????????????????????
bool EQ(double a, double b) { return (abs(a - b) < EPS); }

// 2??????????????????????????????????????????
bool EQV(Vector a, Vector b) {
  return (EQ(a.real(), b.real()) && EQ(a.imag(), b.imag()));
}

// ?????? (dot product) : a???b = |a||b|cos??
double dot(Point a, Point b) {
  return (a.real() * b.real() + a.imag() * b.imag());
}

// ?????? (cross product) : a??b = |a||b|sin??
double cross(Point a, Point b) {
  return (a.real() * b.imag() - a.imag() * b.real());
}

// 2??´????????´????????? : a??\\b <=> dot(a, b) = 0
bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
  return EQ(dot(a1 - a2, b1 - b2), 0.0);
}
bool isOrthogonal(Line s1, Line s2) {
  return isOrthogonal(s1.p1, s1.p2, s2.p1, s2.p2);
}

// 2??´?????????????????? : a//b <=> cross(a, b) = 0
bool isParallel(Point a1, Point a2, Point b1, Point b2) {
  return EQ(cross(a1 - a2, b1 - b2), 0.0);
}
bool isParallel(Line s1, Line s2) {
  return isParallel(s1.p1, s1.p2, s2.p1, s2.p2);
}

// ???c?????´???a,b????????????????????????
bool isPointOnLine(Point a, Point b, Point c) {
  return EQ(cross(b - a, c - a), 0.0);
}
bool isPointOnLine(Line s, Point c) { return isPointOnLine(s.p1, s.p2, c); }

// ???a,b???????????´?????¨???c??¨????????¢
double distanceLPoint(Point a, Point b, Point c) {
  return abs(cross(b - a, c - a)) / abs(b - a);
}
double distanceLPoint(Line s, Point c) { return distanceLPoint(s.p1, s.p2, c); }

// ???a,b???????????¨??????????????¨???c??¨????????¢
double distanceLsPoint(Point a, Point b, Point c) {
  if (dot(b - a, c - a) < EPS)
    return abs(c - a);
  if (dot(a - b, c - b) < EPS)
    return abs(c - b);
  return abs(cross(b - a, c - a)) / abs(b - a);
}
double distanceLsPoint(Segment s, Point c) {
  return distanceLsPoint(s.p1, s.p2, c);
}

// a1,a2???????????¨??????????????¨b1,b2???????????¨???????????????????????????
bool isIntersectedLs(Point a1, Point a2, Point b1, Point b2) {
  return (ccw(a1, a2, b1) * ccw(a1, a2, b2) <= 0 &&
          ccw(b1, b2, a1) * ccw(b1, b2, a2) <= 0);
}
bool isIntersectedLs(Segment s1, Segment s2) {
  return isIntersectedLs(s1.p1, s1.p2, s2.p1, s2.p2);
}

// a1,a2???????????¨??????????????¨b1,b2???????????¨??????????????????????¨????
Point intersectionLs(Point a1, Point a2, Point b1, Point b2) {
  Vector base = b2 - b1;
  double d1 = abs(cross(base, a1 - b1));
  double d2 = abs(cross(base, a2 - b1));
  double t = d1 / (d1 + d2);

  return Point(a1 + (a2 - a1) * t);
}
Point intersectionLs(Segment s1, Segment s2) {
  return intersectionLs(s1.p1, s1.p2, s2.p1, s2.p2);
}

// a1,a2???????????´?????¨b1,b2???????????´??????????????????
bool isIntersectedL(Point a1, Point a2, Point b1, Point b2) {
  return !EQ(cross(a1 - a2, b1 - b2), 0.0);
}
bool isIntersectedL(Line l1, Line l2) {
  return isIntersectedL(l1.p1, l1.p2, l2.p1, l2.p2);
}

// a1,a2???????????´?????¨b1,b2???????????´?????????????¨????
Point intersectionL(Point a1, Point a2, Point b1, Point b2) {
  Point a = a2 - a1;
  Point b = b2 - b1;
  return a1 + a * cross(b, b1 - a1) / cross(b, a);
}
Point intersectionL(Line l1, Line l2) {
  return intersectionL(l1.p1, l1.p2, l2.p1, l2.p2);
}

// ??????s1??¨??????s2????????¢
double distanceLL(Segment s1, Segment s2) {
  if (isIntersectedLs(s1.p1, s1.p2, s2.p1, s2.p2))
    return 0.0;
  return min(min(distanceLsPoint(s1.p1, s1.p2, s2.p1),
                 distanceLsPoint(s1.p1, s1.p2, s2.p2)),
             min(distanceLsPoint(s2.p1, s2.p2, s1.p1),
                 distanceLsPoint(s2.p1, s2.p2, s1.p2)));
}

// ??????s???????????????p????°???±
Point project(Segment s, Point p) {
  Vector base = s.p2 - s.p1;
  double r = dot(p - s.p1, base) / norm(base);
  return Point(s.p1 + base * r);
}

//??????s???????±??????¨?????????p??????????§°??????
Point reflect(Segment s, Point p) {
  return Point(p + (project(s, p) - p) * 2.0);
}

//???p???angle?????????????¨???????????????¢
Point rotation(Point p, double angle) {
  double x, y;
  x = p.real() * cos(angle) - p.imag() * sin(angle);
  y = p.real() * sin(angle) + p.imag() * cos(angle);
  return Point(x, y);
}

//???c??¨??????l?????????
pair<Point, Point> getCrossPoints(Circle c, Line l) {
  Vector pr = project(l, c.c);
  Vector e = (l.p2 - l.p1) / abs(l.p2 - l.p1);
  double base = sqrt(c.r * c.r - norm(pr - c.c));
  return make_pair(pr + e * base, pr - e * base);
}

//???c1??¨???c2?????????
double arg(Vector p) { return atan2(p.imag(), p.real()); }
Vector polar(double a, double r) { return Point(cos(r) * a, sin(r) * a); }

pair<Point, Point> getCrossPoints(Circle c1, Circle c2) {
  double d = abs(c1.c - c2.c);
  double a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
  double t = arg(c2.c - c1.c);
  return make_pair(Point(c1.c + polar(c1.r, t + a)),
                   Point(c1.c + polar(c1.r, t - a)));
}

//????????????
static const int IN = 2;
static const int ON = 1;
static const int OUT = 0;

int contains(Polygon g, Point p) {
  int n = g.size();
  bool x = false;
  rep(i, n) {
    Point a = g[i] - p, b = g[(i + 1) % n] - p;
    if (abs(cross(a, b)) < EPS && dot(a, b) < EPS)
      return ON;
    if (a.imag() > b.imag())
      swap(a, b);
    if (a.imag() < EPS && EPS < b.imag() && cross(a, b) > EPS)
      x = not x;
  }
  return (x ? IN : OUT);
}

//???????????????????????????
static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;
static const int ONLINE_FRONT = -2;
static const int ON_SEGMENT = 0;

int ccw(Point p0, Point p1, Point p2) {
  Vector a = p1 - p0;
  Vector 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 (abs(a) < abs(b))
    return ONLINE_FRONT;

  return ON_SEGMENT;
}

//??????
Polygon andrewScan(Polygon s) {
  Polygon u;
  if (s.size() < 3)
    return s;
  sort(s.begin(), s.end());

  range(i, 0, s.size()) {
    //==
    //COUNTER_CLOCKWISE?????¨????§????180??\\???????????´?????????????????§????????????????????¨????????°?????????
    //!=
    //!CLOCKWISE?????¨????§????180??????????????´????????????????????°????????????
    for (int n = u.size();
         n >= 2 && ccw(u[n - 2], u[n - 1], s[i]) == COUNTER_CLOCKWISE; n--) {
      u.pop_back();
    }
    u.emplace_back(s[i]);
  }

  for (int i = s.size() - 2; i >= 0; i--) {
    //????????? == ??¨ != ????????´??????
    for (int n = u.size();
         n >= 2 && ccw(u[n - 2], u[n - 1], s[i]) == COUNTER_CLOCKWISE; n--) {
      u.pop_back();
    }
    u.emplace_back(s[i]);
  }

  reverse(u.begin(), u.end());
  u.pop_back();

  int i = 0;
  while (i < u.size() - 1) {
    show(u[i].imag()) if (u[i].imag() > u[i + 1].imag()) {
      u.emplace_back(u[i]);
      u.erase(u.begin());
      continue;
    }
    else if (u[i].imag() == u[i + 1].imag() && u[i].real() > u[i + 1].real()) {
      u.emplace_back(u[i]);
      u.erase(u.begin());
      continue;
    }
    break;
  }

  return u;
}

double AreaOfTriangle(Point a, Point b, Point c) {
  double w, x, y, z;
  w = b.real() - a.real();
  x = b.imag() - a.imag();
  y = c.real() - a.real();
  z = c.imag() - a.imag();
  return abs((w * z - x * y) / 2);
}

double areaOfPolygon(Polygon g) {
  int n = g.size();
  double ret = 0.0;
  rep(i, n) ret += cross(g[i], g[(i + 1) % n]);
  return abs(ret) / 2.0;
}

//???????§???¢?????????????????????
bool isConvex(Polygon g) {
  int n = g.size();
  rep(i, n) {
    if (ccw(g[i], g[(i + 1) % n], g[(i + 2) % n]) == CLOCKWISE)
      return false;
  }
  return true;
}

int main() {
  int n;
  cin >> n;

  Polygon g, l;
  rep(i, n) {
    double a, b;
    cin >> a >> b;
    g.emplace_back(Point{a, b});
  }
  l = andrewScan(g);
  cout << l.size() << endl;
  for (auto it : l)
    cout << it.real() << ' ' << it.imag() << endl;
}