Problem p00068 (C++)

Buggy submission (status: Runtime Error):
#include "bits/stdc++.h"
using namespace std;

// #define int long long
#define DBG 1
#define dump(o)                                                                \
  if (DBG) {                                                                   \
    cerr << #o << " " << (o) << endl;                                          \
  }
#define dumpc(o)                                                               \
  if (DBG) {                                                                   \
    cerr << #o;                                                                \
    for (auto &e : (o))                                                        \
      cerr << " " << e;                                                        \
    cerr << endl;                                                              \
  }
#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define rrep(i, a, b) for (int i = (b)-1; i >= (a); i--)
#define all(c) begin(c), end(c)
const int INF =
    sizeof(int) == sizeof(long long) ? 0x3f3f3f3f3f3f3f3fLL : 0x3f3f3f3f;
const int MOD = (int)(1e9 + 7);

#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)

// 0?¬?
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); }
  bool operator<(const Point &p) const { return 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;
  }

  double abs() { return sqrt(norm()); }
  double norm() { return x * x + y * y; }

  // Vector????????¢
  Point rotate(double rad) {
    return Point(x * cos(rad) - y * sin(rad), x * sin(rad) + y * cos(rad));
  }
};
inline ostream &operator<<(ostream &os, const Point &p) {
  os << p.x << " " << p.y;
  return os;
}
inline istream &operator>>(istream &is, Point &p) {
  double x, y;
  is >> x >> y;
  p = Point(x, y);
  return is;
}

// 1?¬?
using Vector = Point;

class Segment {
public:
  Point p1, p2;
  Segment(Point p1 = Point(), Point p2 = Point(1, 1)) : p1(p1), p2(p2) {}
  Vector vec() { return p2 - p1; }
};
using Line = Segment;

// 2?¬?
class Circle {
public:
  Point c;  // center
  double r; // radius
  Circle(Point c = Point(), double r = 0.0) : c(c), r(r) {}
};
using Polygon = vector<Point>;

//?????? dot product
double dot(Vector a, Vector b) { return a.x * b.x + a.y * b.y; }
//?????? cross product
double cross(Vector a, Vector b) { return a.x * b.y - a.y * b.x; }

//????????¢??? radian ??? ??? degree
double rad(double deg) { return acos(-1) * deg / 180; }
//????§? argument
double arg(Vector p) { return atan2(p.y, p.x); }
//?\???¢??? polar form
Vector polar(double r, double a) { return Point(cos(a) * r, sin(a) * r); }

//??´?????????
bool is_orthogonal(Vector a, Vector b) { return equals(dot(a, b), 0.0); }
bool is_orthogonal(Point a1, Point a2, Point b1, Point b2) {
  return is_orthogonal(a1 - a2, b1 - b2);
}
bool is_orthogonal(Segment s1, Segment s2) {
  return equals(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}

//????????????
bool is_parallel(Vector a, Vector b) { return equals(cross(a, b), 0.0); }
bool is_parallel(Point a1, Point a2, Point b1, Point b2) {
  return is_parallel(a1 - a2, b1 - b2);
}
bool is_parallel(Segment s1, Segment s2) {
  return equals(cross(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}

//?°???±
Point project(Segment s, Point p) {
  Vector base = s.p2 - s.p1;
  double r = dot(p - s.p1, base) / base.norm();
  return s.p1 + base * r;
}
//????°?
Point reflect(Segment s, Point p) { return p + (project(s, p) - p) * 2.0; }

//??????(p0,p1)????????????p2???????????¢???
enum {
  ONLINE_FRONT = -2,
  CLOCKWISE,
  ON_SEGMENT,
  COUNTER_CLOCKWISE,
  ONLINE_BACK
};
int ccw(Point p0, Point p1, Point p2) {
  Vector a = p1 - p0, 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; // p2 p0 p1
  if (a.norm() < b.norm())
    return ONLINE_FRONT; // p0 p1 p2
  return ON_SEGMENT;
}

//??´?????¨??´??????????????????
bool intersect(Point p1, Point p2, Point p3, Point p4) {
  return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 &&
          ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);
}
bool intersect(Segment s1, Segment s2) {
  return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}
//(?????????????¶????)

// 2??????????????¢
double get_distance(Point a, Point b) { return (a - b).abs(); }
//??´?????¨???????????¢
double get_distance_LP(Line l, Point p) {
  return abs(cross(l.p2 - l.p1, p - l.p1) / (l.p2 - l.p1).abs());
}
//????????¨???????????¢
double get_distance_SP(Segment s, Point p) {
  if (dot(s.p2 - s.p1, p - s.p1) < 0.0)
    return (p - s.p1).abs();
  if (dot(s.p1 - s.p2, p - s.p2) < 0.0)
    return (p - s.p2).abs();
  return get_distance_LP(s, p);
}
//????????¨??????????????¢
double get_distance(Segment s1, Segment s2) {
  if (intersect(s1, s2))
    return 0.0;
  return min(min(get_distance_SP(s1, s2.p1), get_distance_SP(s1, s2.p2)),
             min(get_distance_SP(s2, s1.p1), get_distance_SP(s2, s1.p2)));
}

//?????¨??´??????????????????
bool intersect(Circle c, Line l) { return get_distance_LP(l, c.c) <= c.r; }
//?????¨?????????????????? ??±?????\????????°
int intersect(Circle c1, Circle c2) {
  double d = get_distance(c1.c, c2.c);
  if (d > c1.r + c2.r)
    return 4;
  if (d == c1.r + c2.r)
    return 3;
  if (d + c1.r == c2.r || d + c2.r == c1.r)
    return 1;
  if (d + c1.r < c2.r || d + c2.r < c1.r)
    return 0;
  return 2;
}

//????????¨???????????????
Point get_cross_point(Segment s1, Segment s2) {
  assert(intersect(s1, s2));
  Vector base = s2.p2 - s2.p1;
  double a1 = abs(cross(base, s1.p1 - s2.p1)); // area1
  double a2 = abs(cross(base, s1.p2 - s2.p1)); // area2
  double t = a1 / (a1 + a2);
  return s1.p1 + (s1.p2 - s1.p1) * t;
}
//??´?????¨??´????????????
// Point getCrossPointLL(Line l1, Line l2) {}

//?????¨??´????????????
pair<Point, Point> get_cross_points(Circle c, Line l) {
  assert(intersect(c, l));
  Vector pr = project(l, c.c);
  Vector e = (l.p2 - l.p1) / (l.p2 - l.p1).abs();
  double base = sqrt(c.r * c.r - (pr - c.c).norm());
  return make_pair(pr + e * base, pr - e * base);
}
//?????¨????????????
pair<Point, Point> get_cross_points(Circle c1, Circle c2) {
  int m = intersect(c1, c2);
  assert(m != 4 && m != 0);
  double d = (c1.c - c2.c).abs();
  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(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));
}

//????????????
enum { OUT = 0, ON, IN };
int contains(Polygon g, Point p) {
  int n = g.size();
  bool x = false;
  for (int i = 0; i < n; i++) {
    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.y > b.y)
      swap(a, b);
    if (a.y < EPS && EPS < b.y && cross(a, b) > EPS)
      x = !x;
  }
  return (x ? IN : OUT);
}

//????§???¢?????¢???
double area(Polygon g) {
  double a = 0;
  for (size_t i = 0; i < g.size(); i++)
    a += cross(g[i], g[(i + 1) % g.size()]);
  return a / 2.0;
}

//?????§????????????????¨??????????
bool is_convex(Polygon g) {
  for (size_t i = 0; i < g.size(); i++)
    if (ccw(g[i], g[(i + 1) % g.size()], g[(i + 2) % g.size()]) == CLOCKWISE)
      return false;
  return true;
}

// Graham scan
// https://en.wikipedia.org/wiki/Graham_scan
Polygon convex_hull(Polygon P) {
  sort(P.begin(), P.end());
  Polygon up;
  for (Point &p : P) {
    while (up.size() > 1 && ccw(up[up.size() - 2], up[up.size() - 1], p) > 0)
      up.pop_back();
    up.emplace_back(p);
  }
  Polygon down;
  for (Point &p : P) {
    while (down.size() > 1 &&
           ccw(down[down.size() - 2], down[down.size() - 1], p) < 0)
      down.pop_back();
    down.emplace_back(p);
  }
  down.insert(down.end(), up.begin() + 1, up.end() - 1); //???????¨??????????
  return down;
}

signed main() {
  for (int n; cin >> n && n;) {
    Polygon P(n);
    char c;
    rep(i, 0, n) cin >> P[i].x >> c >> P[i].y;
    Polygon CH = convex_hull(P);
    dumpc(CH);
    cout << (n - CH.size()) << endl;
  }
  return 0;
}

Fixed submission:
#include "bits/stdc++.h"
using namespace std;

// #define int long long
#define DBG 0
#define dump(o)                                                                \
  if (DBG) {                                                                   \
    cerr << #o << " " << (o) << endl;                                          \
  }
#define dumpc(o)                                                               \
  if (DBG) {                                                                   \
    cerr << #o;                                                                \
    for (auto &e : (o))                                                        \
      cerr << " " << e;                                                        \
    cerr << endl;                                                              \
  }
#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define rrep(i, a, b) for (int i = (b)-1; i >= (a); i--)
#define all(c) begin(c), end(c)
const int INF =
    sizeof(int) == sizeof(long long) ? 0x3f3f3f3f3f3f3f3fLL : 0x3f3f3f3f;
const int MOD = (int)(1e9 + 7);

#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)

// 0?¬?
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); }
  bool operator<(const Point &p) const { return 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;
  }

  double abs() { return sqrt(norm()); }
  double norm() { return x * x + y * y; }

  // Vector????????¢
  Point rotate(double rad) {
    return Point(x * cos(rad) - y * sin(rad), x * sin(rad) + y * cos(rad));
  }
};
inline ostream &operator<<(ostream &os, const Point &p) {
  os << p.x << " " << p.y;
  return os;
}
inline istream &operator>>(istream &is, Point &p) {
  double x, y;
  is >> x >> y;
  p = Point(x, y);
  return is;
}

// 1?¬?
using Vector = Point;

class Segment {
public:
  Point p1, p2;
  Segment(Point p1 = Point(), Point p2 = Point(1, 1)) : p1(p1), p2(p2) {}
  Vector vec() { return p2 - p1; }
};
using Line = Segment;

// 2?¬?
class Circle {
public:
  Point c;  // center
  double r; // radius
  Circle(Point c = Point(), double r = 0.0) : c(c), r(r) {}
};
using Polygon = vector<Point>;

//?????? dot product
double dot(Vector a, Vector b) { return a.x * b.x + a.y * b.y; }
//?????? cross product
double cross(Vector a, Vector b) { return a.x * b.y - a.y * b.x; }

//????????¢??? radian ??? ??? degree
double rad(double deg) { return acos(-1) * deg / 180; }
//????§? argument
double arg(Vector p) { return atan2(p.y, p.x); }
//?\???¢??? polar form
Vector polar(double r, double a) { return Point(cos(a) * r, sin(a) * r); }

//??´?????????
bool is_orthogonal(Vector a, Vector b) { return equals(dot(a, b), 0.0); }
bool is_orthogonal(Point a1, Point a2, Point b1, Point b2) {
  return is_orthogonal(a1 - a2, b1 - b2);
}
bool is_orthogonal(Segment s1, Segment s2) {
  return equals(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}

//????????????
bool is_parallel(Vector a, Vector b) { return equals(cross(a, b), 0.0); }
bool is_parallel(Point a1, Point a2, Point b1, Point b2) {
  return is_parallel(a1 - a2, b1 - b2);
}
bool is_parallel(Segment s1, Segment s2) {
  return equals(cross(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}

//?°???±
Point project(Segment s, Point p) {
  Vector base = s.p2 - s.p1;
  double r = dot(p - s.p1, base) / base.norm();
  return s.p1 + base * r;
}
//????°?
Point reflect(Segment s, Point p) { return p + (project(s, p) - p) * 2.0; }

//??????(p0,p1)????????????p2???????????¢???
enum {
  ONLINE_FRONT = -2,
  CLOCKWISE,
  ON_SEGMENT,
  COUNTER_CLOCKWISE,
  ONLINE_BACK
};
int ccw(Point p0, Point p1, Point p2) {
  Vector a = p1 - p0, 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; // p2 p0 p1
  if (a.norm() < b.norm())
    return ONLINE_FRONT; // p0 p1 p2
  return ON_SEGMENT;
}

//??´?????¨??´??????????????????
bool intersect(Point p1, Point p2, Point p3, Point p4) {
  return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 &&
          ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);
}
bool intersect(Segment s1, Segment s2) {
  return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}
//(?????????????¶????)

// 2??????????????¢
double get_distance(Point a, Point b) { return (a - b).abs(); }
//??´?????¨???????????¢
double get_distance_LP(Line l, Point p) {
  return abs(cross(l.p2 - l.p1, p - l.p1) / (l.p2 - l.p1).abs());
}
//????????¨???????????¢
double get_distance_SP(Segment s, Point p) {
  if (dot(s.p2 - s.p1, p - s.p1) < 0.0)
    return (p - s.p1).abs();
  if (dot(s.p1 - s.p2, p - s.p2) < 0.0)
    return (p - s.p2).abs();
  return get_distance_LP(s, p);
}
//????????¨??????????????¢
double get_distance(Segment s1, Segment s2) {
  if (intersect(s1, s2))
    return 0.0;
  return min(min(get_distance_SP(s1, s2.p1), get_distance_SP(s1, s2.p2)),
             min(get_distance_SP(s2, s1.p1), get_distance_SP(s2, s1.p2)));
}

//?????¨??´??????????????????
bool intersect(Circle c, Line l) { return get_distance_LP(l, c.c) <= c.r; }
//?????¨?????????????????? ??±?????\????????°
int intersect(Circle c1, Circle c2) {
  double d = get_distance(c1.c, c2.c);
  if (d > c1.r + c2.r)
    return 4;
  if (d == c1.r + c2.r)
    return 3;
  if (d + c1.r == c2.r || d + c2.r == c1.r)
    return 1;
  if (d + c1.r < c2.r || d + c2.r < c1.r)
    return 0;
  return 2;
}

//????????¨???????????????
Point get_cross_point(Segment s1, Segment s2) {
  assert(intersect(s1, s2));
  Vector base = s2.p2 - s2.p1;
  double a1 = abs(cross(base, s1.p1 - s2.p1)); // area1
  double a2 = abs(cross(base, s1.p2 - s2.p1)); // area2
  double t = a1 / (a1 + a2);
  return s1.p1 + (s1.p2 - s1.p1) * t;
}
//??´?????¨??´????????????
// Point getCrossPointLL(Line l1, Line l2) {}

//?????¨??´????????????
pair<Point, Point> get_cross_points(Circle c, Line l) {
  assert(intersect(c, l));
  Vector pr = project(l, c.c);
  Vector e = (l.p2 - l.p1) / (l.p2 - l.p1).abs();
  double base = sqrt(c.r * c.r - (pr - c.c).norm());
  return make_pair(pr + e * base, pr - e * base);
}
//?????¨????????????
pair<Point, Point> get_cross_points(Circle c1, Circle c2) {
  int m = intersect(c1, c2);
  assert(m != 4 && m != 0);
  double d = (c1.c - c2.c).abs();
  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(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));
}

//????????????
enum { OUT = 0, ON, IN };
int contains(Polygon g, Point p) {
  int n = g.size();
  bool x = false;
  for (int i = 0; i < n; i++) {
    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.y > b.y)
      swap(a, b);
    if (a.y < EPS && EPS < b.y && cross(a, b) > EPS)
      x = !x;
  }
  return (x ? IN : OUT);
}

//????§???¢?????¢???
double area(Polygon g) {
  double a = 0;
  for (size_t i = 0; i < g.size(); i++)
    a += cross(g[i], g[(i + 1) % g.size()]);
  return a / 2.0;
}

//?????§????????????????¨??????????
bool is_convex(Polygon g) {
  for (size_t i = 0; i < g.size(); i++)
    if (ccw(g[i], g[(i + 1) % g.size()], g[(i + 2) % g.size()]) == CLOCKWISE)
      return false;
  return true;
}

// Graham scan
// https://en.wikipedia.org/wiki/Graham_scan
Polygon convex_hull(Polygon P) {
  sort(P.begin(), P.end());
  Polygon up;
  for (Point &p : P) {
    while (up.size() > 1 && ccw(up[up.size() - 2], up[up.size() - 1], p) > 0)
      up.pop_back();
    up.emplace_back(p);
  }
  Polygon down;
  for (Point &p : P) {
    while (down.size() > 1 &&
           ccw(down[down.size() - 2], down[down.size() - 1], p) < 0)
      down.pop_back();
    down.emplace_back(p);
  }
  down.insert(down.end(), up.begin() + 1, up.end() - 1); //???????¨??????????
  return down;
}

signed main() {
  for (int n; cin >> n && n;) {
    Polygon P(n);
    char c;
    rep(i, 0, n) cin >> P[i].x >> c >> P[i].y;
    Polygon CH = convex_hull(P);
    dumpc(CH);
    cout << (n - CH.size()) << endl;
  }
  return 0;
}