Problem p00771 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)

using namespace std;

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;

struct Point {
  double x, y;
  Point() {}
  Point(double x, double y) : 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 k) { return Point(x * k, y * k); }
  Point operator/(double k) { return Point(x / k, y / k); }
  double norm() { return x * x + y * y; }
  double abs() { return sqrt(norm()); }

  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;
  }
};
typedef Point Vector;
typedef vector<Point> Polygon;

struct Segment {
  Point p1, p2;
  Segment() {}
  Segment(Point p1, Point p2) : p1(p1), p2(p2) {}
};
typedef Segment Line;

struct Circle {
  Point c;
  double r;
  Circle() {}
  Circle(Point c, double r) : c(c), r(r) {}
};

double norm(Vector a) { return a.x * a.x + a.y * a.y; }
double abs(Vector a) { return sqrt(norm(a)); }
double dot(Vector a, Vector b) { return a.x * b.x + a.y * b.y; }
double cross(Vector a, Vector b) { return a.x * b.y - a.y * b.x; }

bool isOrthogonal(Vector a, Vector b) { return equals(dot(a, b), 0.0); }

bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
  return isOrthogonal(a1 - a2, b1 - b2);
}

bool isOrthogonal(Segment s1, Segment s2) {
  return equals(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}

bool isParallel(Vector a, Vector b) { return equals(cross(a, b), 0.0); }

bool isParallel(Point a1, Point a2, Point b1, Point b2) {
  return isParallel(a1 - a2, b1 - b2);
}

bool isParallel(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) / norm(base);
  return s.p1 + base * r;
}

Point reflect(Segment s, Point p) { return p + (project(s, p) - p) * 2.0; }

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 (a.norm() < b.norm())
    return ONLINE_FRONT;
  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);
}

double getDistanceLP(Line l, Point p) {
  return abs(cross(l.p2 - l.p1, p - l.p1) / abs(l.p2 - l.p1));
}

double getDistanceSP(Segment s, Point p) {
  if (dot(s.p2 - s.p1, p - s.p1) < 0.0)
    return abs(p - s.p1);
  if (dot(s.p1 - s.p2, p - s.p2) < 0.0)
    return abs(p - s.p2);
  return getDistanceLP(s, p);
}

double getDistance(Segment s1, Segment s2) {
  if (intersect(s1, s2))
    return 0.0;
  return min(min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)),
             min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)));
}

Point getCrossPoint(Segment s1, Segment s2) {
  Vector base = s2.p2 - s2.p1;
  double d1 = abs(cross(base, s1.p1 - s2.p1));
  double d2 = abs(cross(base, s1.p2 - s2.p1));
  double t = d1 / (d1 + d2);
  return s1.p1 + (s1.p2 - s1.p1) * t;
}

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);
}

double arg(Vector p) { return atan2(p.y, p.x); }

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(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));
}

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 (fabs(cross(a, b)) < EPS && dot(a, b) < EPS)
      return 1;
    if (a.y > b.y)
      swap(a, b);
    if (a.y < EPS && EPS < b.y && cross(a, b) > EPS)
      x = !x;
  }
  return (x ? 2 : 0);
}

Polygon andrewScan(Polygon s) {
  Polygon u, l;
  if (s.size() < 3)
    return s;
  sort(s.begin(), s.end());
  u.push_back(s[0]);
  u.push_back(s[1]);
  l.push_back(s[s.size() - 1]);
  l.push_back(s[s.size() - 2]);
  for (int i = 2; i < (int)s.size(); i++) {
    for (int n = u.size(); n >= 2 && ccw(u[n - 2], u[n - 1], s[i]) != CLOCKWISE;
         n--) {
      u.pop_back();
    }
    u.push_back(s[i]);
  }
  for (int i = s.size() - 3; i >= 0; i--) {
    for (int n = l.size(); n >= 2 && ccw(l[n - 2], l[n - 1], s[i]) != CLOCKWISE;
         n--) {
      l.pop_back();
    }
    l.push_back(s[i]);
  }
  reverse(l.begin(), l.end());
  for (int i = u.size() - 2; i >= 1; i--)
    l.push_back(u[i]);
  return l;
}

double area(Polygon s) {
  double res = 0;
  for (int i = 0; i < (int)s.size(); i++) {
    res += cross(s[i], s[(i + 1) % s.size()]) / 2.0;
  }
  return abs(res);
}

Point getCrossPointLL(Line l1, Line l2) {
  double a = cross(l1.p2 - l1.p1, l2.p2 - l2.p1);
  double b = cross(l1.p2 - l1.p1, l1.p2 - l2.p1);
  if (abs(a) < EPS && abs(b) < EPS)
    return l2.p1;
  return l2.p1 + (l2.p2 - l2.p1) * (b / a);
}

Polygon convexCut(Polygon p, Line l) {
  Polygon q;
  for (int i = 0; i < (int)p.size(); i++) {
    Point a = p[i], b = p[(i + 1) % p.size()];
    if (ccw(l.p1, l.p2, a) != -1)
      q.push_back(a);
    if (ccw(l.p1, l.p2, a) * ccw(l.p1, l.p2, b) < 0)
      q.push_back(getCrossPointLL(Line(a, b), l));
  }
  return q;
}

Line bisector(Point p1, Point p2) {
  Circle c1 = Circle(p1, abs(p1 - p2)), c2 = Circle(p2, abs(p1 - p2));
  pair<Point, Point> p = getCrossPoints(c1, c2);
  if (cross(p2 - p1, p.first - p1) > 0)
    swap(p.first, p.second);
  return Line(p.first, p.second);
}

int main() {
  int n;
  while (cin >> n, n) {
    Polygon p(n);
    double ll[n];
    for (int i = 0; i < n; i++)
      cin >> p[i].x >> p[i].y >> ll[i];
    double l = 0, r = 400;
    for (int i = 0; i < 500; i++) {
      double m = (l + r) / 2;
      bool f = 1;
      Circle c[n];
      for (int j = 0; j < n; j++) {
        if (m > ll[j]) {
          f = 0;
          break;
        }
        c[j] = Circle(p[j], sqrt(ll[j] * ll[j] - m * m));
      }

      for (int j = 0; j < n; j++)
        for (int k = j + 1; k < n; k++)
          f &= abs(c[j].c - c[k].c) <= (c[j].r + c[k].r);

      //*
      for (int j = 0; j < n; j++) {
        for (int k = j + 1; k < n; k++) {
          for (int a = k + 1; a < n; a++) {
            bool ff = 0;
            pair<Point, Point> pp;
            pp = getCrossPoints(c[j], c[k]);
            ff |= abs(c[a].c - pp.first) <= c[a].r;
            ff |= abs(c[a].c - pp.second) <= c[a].r;
            pp = getCrossPoints(c[k], c[a]);
            ff |= abs(c[j].c - pp.first) <= c[j].r;
            ff |= abs(c[j].c - pp.second) <= c[j].r;
            pp = getCrossPoints(c[a], c[j]);
            ff |= abs(c[k].c - pp.first) <= c[k].r;
            ff |= abs(c[k].c - pp.second) <= c[k].r;
            // if(!ff) cout<<j<<" "<<k<<" "<<a<<endl;
            ff |= abs(c[j].c - c[k].c) + c[j].r < c[k].r;
            ff |= abs(c[j].c - c[k].c) + c[k].r < c[j].r;
            ff |= abs(c[k].c - c[a].c) + c[k].r < c[a].r;
            ff |= abs(c[k].c - c[a].c) + c[a].r < c[k].r;
            ff |= abs(c[a].c - c[j].c) + c[a].r < c[j].r;
            ff |= abs(c[a].c - c[j].c) + c[j].r < c[a].r;
            f &= ff;
            if (!f)
              break;
          }
        }
      }
      //*/

      if (f)
        l = m;
      else
        r = m;
    }
    printf("%.12lf\\n", l);
  }
  return 0;
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)

using namespace std;

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;

struct Point {
  double x, y;
  Point() {}
  Point(double x, double y) : 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 k) { return Point(x * k, y * k); }
  Point operator/(double k) { return Point(x / k, y / k); }
  double norm() { return x * x + y * y; }
  double abs() { return sqrt(norm()); }

  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;
  }
};
typedef Point Vector;
typedef vector<Point> Polygon;

struct Segment {
  Point p1, p2;
  Segment() {}
  Segment(Point p1, Point p2) : p1(p1), p2(p2) {}
};
typedef Segment Line;

struct Circle {
  Point c;
  double r;
  Circle() {}
  Circle(Point c, double r) : c(c), r(r) {}
};

double norm(Vector a) { return a.x * a.x + a.y * a.y; }
double abs(Vector a) { return sqrt(norm(a)); }
double dot(Vector a, Vector b) { return a.x * b.x + a.y * b.y; }
double cross(Vector a, Vector b) { return a.x * b.y - a.y * b.x; }

bool isOrthogonal(Vector a, Vector b) { return equals(dot(a, b), 0.0); }

bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
  return isOrthogonal(a1 - a2, b1 - b2);
}

bool isOrthogonal(Segment s1, Segment s2) {
  return equals(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}

bool isParallel(Vector a, Vector b) { return equals(cross(a, b), 0.0); }

bool isParallel(Point a1, Point a2, Point b1, Point b2) {
  return isParallel(a1 - a2, b1 - b2);
}

bool isParallel(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) / norm(base);
  return s.p1 + base * r;
}

Point reflect(Segment s, Point p) { return p + (project(s, p) - p) * 2.0; }

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 (a.norm() < b.norm())
    return ONLINE_FRONT;
  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);
}

double getDistanceLP(Line l, Point p) {
  return abs(cross(l.p2 - l.p1, p - l.p1) / abs(l.p2 - l.p1));
}

double getDistanceSP(Segment s, Point p) {
  if (dot(s.p2 - s.p1, p - s.p1) < 0.0)
    return abs(p - s.p1);
  if (dot(s.p1 - s.p2, p - s.p2) < 0.0)
    return abs(p - s.p2);
  return getDistanceLP(s, p);
}

double getDistance(Segment s1, Segment s2) {
  if (intersect(s1, s2))
    return 0.0;
  return min(min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)),
             min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)));
}

Point getCrossPoint(Segment s1, Segment s2) {
  Vector base = s2.p2 - s2.p1;
  double d1 = abs(cross(base, s1.p1 - s2.p1));
  double d2 = abs(cross(base, s1.p2 - s2.p1));
  double t = d1 / (d1 + d2);
  return s1.p1 + (s1.p2 - s1.p1) * t;
}

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);
}

double arg(Vector p) { return atan2(p.y, p.x); }

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(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));
}

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 (fabs(cross(a, b)) < EPS && dot(a, b) < EPS)
      return 1;
    if (a.y > b.y)
      swap(a, b);
    if (a.y < EPS && EPS < b.y && cross(a, b) > EPS)
      x = !x;
  }
  return (x ? 2 : 0);
}

Polygon andrewScan(Polygon s) {
  Polygon u, l;
  if (s.size() < 3)
    return s;
  sort(s.begin(), s.end());
  u.push_back(s[0]);
  u.push_back(s[1]);
  l.push_back(s[s.size() - 1]);
  l.push_back(s[s.size() - 2]);
  for (int i = 2; i < (int)s.size(); i++) {
    for (int n = u.size(); n >= 2 && ccw(u[n - 2], u[n - 1], s[i]) != CLOCKWISE;
         n--) {
      u.pop_back();
    }
    u.push_back(s[i]);
  }
  for (int i = s.size() - 3; i >= 0; i--) {
    for (int n = l.size(); n >= 2 && ccw(l[n - 2], l[n - 1], s[i]) != CLOCKWISE;
         n--) {
      l.pop_back();
    }
    l.push_back(s[i]);
  }
  reverse(l.begin(), l.end());
  for (int i = u.size() - 2; i >= 1; i--)
    l.push_back(u[i]);
  return l;
}

double area(Polygon s) {
  double res = 0;
  for (int i = 0; i < (int)s.size(); i++) {
    res += cross(s[i], s[(i + 1) % s.size()]) / 2.0;
  }
  return abs(res);
}

Point getCrossPointLL(Line l1, Line l2) {
  double a = cross(l1.p2 - l1.p1, l2.p2 - l2.p1);
  double b = cross(l1.p2 - l1.p1, l1.p2 - l2.p1);
  if (abs(a) < EPS && abs(b) < EPS)
    return l2.p1;
  return l2.p1 + (l2.p2 - l2.p1) * (b / a);
}

Polygon convexCut(Polygon p, Line l) {
  Polygon q;
  for (int i = 0; i < (int)p.size(); i++) {
    Point a = p[i], b = p[(i + 1) % p.size()];
    if (ccw(l.p1, l.p2, a) != -1)
      q.push_back(a);
    if (ccw(l.p1, l.p2, a) * ccw(l.p1, l.p2, b) < 0)
      q.push_back(getCrossPointLL(Line(a, b), l));
  }
  return q;
}

Line bisector(Point p1, Point p2) {
  Circle c1 = Circle(p1, abs(p1 - p2)), c2 = Circle(p2, abs(p1 - p2));
  pair<Point, Point> p = getCrossPoints(c1, c2);
  if (cross(p2 - p1, p.first - p1) > 0)
    swap(p.first, p.second);
  return Line(p.first, p.second);
}

int main() {
  int n;
  while (cin >> n, n) {
    Polygon p(n);
    double ll[n];
    for (int i = 0; i < n; i++)
      cin >> p[i].x >> p[i].y >> ll[i];
    double l = 0, r = 400;
    for (int i = 0; i < 1000; i++) {
      double m = (l + r) / 2;
      bool f = 1;
      Circle c[n];
      for (int j = 0; j < n; j++) {
        if (m > ll[j]) {
          f = 0;
          break;
        }
        c[j] = Circle(p[j], sqrt(ll[j] * ll[j] - m * m));
      }

      for (int j = 0; j < n; j++)
        for (int k = j + 1; k < n; k++)
          f &= abs(c[j].c - c[k].c) <= (c[j].r + c[k].r);

      //*
      for (int j = 0; j < n; j++) {
        for (int k = j + 1; k < n; k++) {
          for (int a = k + 1; a < n; a++) {
            bool ff = 0;
            pair<Point, Point> pp;
            pp = getCrossPoints(c[j], c[k]);
            ff |= abs(c[a].c - pp.first) <= c[a].r;
            ff |= abs(c[a].c - pp.second) <= c[a].r;
            pp = getCrossPoints(c[k], c[a]);
            ff |= abs(c[j].c - pp.first) <= c[j].r;
            ff |= abs(c[j].c - pp.second) <= c[j].r;
            pp = getCrossPoints(c[a], c[j]);
            ff |= abs(c[k].c - pp.first) <= c[k].r;
            ff |= abs(c[k].c - pp.second) <= c[k].r;
            // if(!ff) cout<<j<<" "<<k<<" "<<a<<endl;
            ff |= abs(c[j].c - c[k].c) + c[j].r < c[k].r;
            ff |= abs(c[j].c - c[k].c) + c[k].r < c[j].r;
            ff |= abs(c[k].c - c[a].c) + c[k].r < c[a].r;
            ff |= abs(c[k].c - c[a].c) + c[a].r < c[k].r;
            ff |= abs(c[a].c - c[j].c) + c[a].r < c[j].r;
            ff |= abs(c[a].c - c[j].c) + c[j].r < c[a].r;
            f &= ff;
          }
        }
      }
      //*/

      if (f)
        l = m;
      else
        r = m;
    }
    printf("%.12lf\\n", l);
  }
  return 0;
}