Problem p00738 (C++) — buggy submission, verdict: Runtime Error

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cctype>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <functional>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <vector>
using namespace std;

#define dump(a) (cerr << (#a) << " = " << (a) << endl)
#define FOR(it, c)                                                             \\
  for (__typeof((c).begin()) it = (c).begin(); it != (c).end(); ++it)
#define RFOR(it, c)                                                            \\
  for (__typeof((c).rbegin()) it = (c).rbegin(); it != (c).rend(); ++it)
#define exist(c, v) (find((c).begin(), (c).end(), (v)) != (c).end())

template <class T> inline void chmax(T &a, const T &b) {
  if (b > a)
    a = b;
}
template <class T> inline void chmin(T &a, const T &b) {
  if (b < a)
    a = b;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << '(' << p.first << ", " << p.second << ')';
  return os;
}

template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) {
  copy(v.begin(), v.end(), ostream_iterator<T>(os, " "));
  return os;
}

const double EPS = 1e-9;

struct point {
  double x, y;
  point() : x(0), y(0) {}
  point(double x, double y) : x(x), y(y) {}
  point(const point &p) : x(p.x), y(p.y) {}

  point operator+(const point &p) const { return point(x + p.x, y + p.y); }

  point operator-(const point &p) const { return point(x - p.x, y - p.y); }

  point operator*(const double s) const { return point(x * s, y * s); }

  point operator*(const point &p) const {
    return point(x * p.x - y * p.y, x * p.y + y * p.x);
  }

  point operator/(const double s) const { return point(x / s, y / s); }

  bool operator<(const point &p) const {
    return x + EPS < p.x || abs(x - p.x) < EPS && y + EPS < p.y;
  }

  bool operator==(const point &p) const {
    return abs(x - p.x) < EPS && abs(y - p.y) < EPS;
  }
};

inline point rotate90(const point &p) { return point(-p.y, p.x); }

inline point rotate(const point &p, const double theta) {
  const double s = sin(theta), c = cos(theta);
  return point(c * p.x - s * p.y, s * p.x + c * p.y);
}

inline double angle(const point &p) { return atan2(p.y, p.x); }

inline double abs(const point &p) { return sqrt(p.x * p.x + p.y * p.y); }

inline double norm(const point &p) { return p.x * p.x + p.y * p.y; }

inline double dot(const point &l, const point &r) {
  return l.x * r.x + l.y * r.y;
}

inline double cross(const point &l, const point &r) {
  return l.x * r.y - l.y * r.x;
}

struct line {
  point a, b;
  line(point a, point b) : a(a), b(b) {}
};

struct segment {
  point a, b;
  segment(point a, point b) : a(a), b(b) {}
};

struct circle {
  point c;
  double r;
  circle(point c, double r) : c(c), r(r) {}
};

typedef vector<point> polygon;

inline int ccw(const point &a, point b, point c) {
  b = b - a;
  c = c - a;
  const double tmp = cross(b, c);
  if (tmp > EPS)
    return 1; // ccw
  if (tmp < -EPS)
    return -1; // cw
  if (dot(b, c) < 0)
    return 2; // c, a, b 順に一直線上
  if (norm(b) < norm(c))
    return -2; // a, b, c 順に一直線上
  return 0;    // a, c, b 順で一直線上
}

inline point projection(const line &l, const point &p) {
  const point dif = l.b - l.a;
  const double tmp = dot(p - l.a, dif) / norm(dif);
  return l.a + dif * tmp;
}

inline bool intersect(const line &l, const line &m) {
  return abs(cross(l.b - l.a, m.b - m.a)) > EPS ||
         abs(cross(l.b - l.a, m.b - l.a)) < EPS;
}

inline bool intersect(const line &l, const segment &s) {
  return cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < EPS;
}

inline bool intersect(const line &l, const point &p) {
  return abs(ccw(l.a, l.b, p)) != -1;
}

inline bool intersect(const segment &s, const segment &t) {
  return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 &&
         ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}

inline bool intersect(const segment &s, const point &p) {
  return ccw(s.a, s.b, p) == 0;
}

inline bool intersect(const circle &c, const point &p) {
  return abs(c.c - p) <= c.r + EPS;
}

inline bool intersect(const circle &c, const circle &d) {
  return abs(c.c - d.c) <= c.r + d.r && abs(c.c - d.c) >= abs(c.r - d.r);
}

inline double dist(const line &l, const point &p) {
  return abs(cross((l.b - l.a), (p - l.a))) / abs(l.b - l.a);
  //	return abs(p - projection(l, p));
}

inline double dist(const line &l, const line &m) {
  return intersect(l, m) ? 0 : dist(l, m.a);
}

inline double dist(const line &l, const segment &s) {
  return intersect(l, s) ? 0 : min(dist(l, s.a), dist(l, s.b));
}

inline double dist(const segment &s, const point &p) {
  if (dot((s.b - s.a), (p - s.a)) < 0)
    return abs(p - s.a);
  if (dot((s.a - s.b), (p - s.b)) < 0)
    return abs(p - s.b);
  return dist(line(s.a, s.b), p);

  //	const point tmp = projection(line(s.a, s.b), p);
  //	return intersect(s, tmp) ? abs(tmp - p) : min(abs(s.a - p), abs(s.b -
  //p));
}

inline double dist(const segment &s, const segment &t) {
  if (intersect(s, t))
    return 0;
  return min(min(dist(s, t.a), dist(s, t.b)), min(dist(t, s.a), dist(t, s.b)));
}

inline double dist(const point &a, const point &b) { return abs(a - b); }

inline point crosspoint(const line &l, const line &m) {
  const double tmp = cross(l.b - l.a, m.b - m.a);
  if (abs(tmp) < EPS) // 平行
    return l.a;
  return m.a + (m.b - m.a) * cross(l.b - l.a, l.a - m.a) * (1.0 / tmp);
}

inline point crosspoint(const segment &s, const segment &t) {
  if (!intersect(s, t)) // 交点を持たない
    return s.a;         // 用改善

  const double tmp = cross(s.b - s.a, t.b - t.a);
  if (abs(tmp) < EPS) { // 一直線上
    if (intersect(s, t.a))
      return t.a;
    if (intersect(s, t.b))
      return t.b;
    if (intersect(t, s.a))
      return s.a;
    return s.b;
  }

  return t.a + (t.b - t.a) * cross(s.b - s.a, s.b - t.a) * (1.0 / tmp);
}

// 先に，intersectを用いて交差判定を行うこと
inline vector<point> crosspoint(const circle &c, const circle &d) {
  vector<point> res;
  if (abs(c.c - d.c) < EPS) // 中心の座標が同じ
    return res;

  const double tmp = abs(c.c - d.c);
  const double rc = (tmp * tmp + c.r * c.r - d.r * d.r) / (tmp + tmp);
  const double rs = sqrt(c.r * c.r - rc * rc);
  const point diff = (d.c - c.c) / tmp;
  res.push_back(point(c.c + diff * point(rc, rs)));
  res.push_back(point(c.c + diff * point(rc, -rs)));
  return res;
}

inline vector<point> crosspoint(const circle &c, const line &l) {
  vector<point> res;
  const point h = projection(l, c.c);
  const double d = abs(h - c.c);
  if (d > c.r - EPS) {
    res.push_back(h);
  } else if (d <= c.r - EPS) {
    point v = l.b - l.a;
    v = v * sqrt(c.r * c.r - d * d) / abs(v);
    res.push_back(h + v);
    res.push_back(h - v);
  }

  return res;
}

inline vector<point> crosspoint(const circle &c, const segment &s) {
  vector<point> res;
  vector<point> tmp = crosspoint(c, line(s.a, s.b));
  for (int i = 0; i < tmp.size(); ++i)
    if (intersect(s, tmp[i]))
      res.push_back(tmp[i]);

  return res;
}

inline double areaTriangle(point a, point b, const point &c) {
  a = a - c;
  b = b - c;
  return fabs(a.x * b.y - b.x * a.y) / 2.0;
}

inline double area(const polygon &p) {
  const int num = p.size();
  if (num < 3)
    return 0;

  if (num == 3)
    return areaTriangle(p[0], p[1], p[2]);

  double res = cross(p[num - 1], p[0]);
  for (int i = 1; i < num; ++i)
    res += cross(p[i - 1], p[i]);

  return res * 0.5;
}

// L.aからL.bの方向を見た場合に，点aが左側に来る．
inline line bisector(const point &a, const point &b) {
  return line(
      point((a.x - a.y + b.x + b.y) / 2.0, (a.y + a.x + b.y - b.x) / 2.0),
      point((a.x + a.y + b.x - b.y) / 2.0, (a.y - a.x + b.y + b.x) / 2.0));
}

// L.aからL.bを向いた時の左側を残して切断する．
inline polygon convex_cut(const polygon &p, const line &l) {
  const int num = p.size();
  polygon res;
  for (int i = 0; i < num; ++i) {
    const int next = (i + 1) % num;
    const int tmp = ccw(l.a, l.b, p[i]);
    if (tmp != -1)
      res.push_back(p[i]);

    if (tmp * ccw(l.a, l.b, p[next]) < 0)
      res.push_back(crosspoint(l, line(p[i], p[next])));
  }

  return res;
}

vector<point> tangent(const circle &c, const point &p) {
  const double x = norm(p - c.c);
  double d = x - c.r * c.r;
  if (d < -EPS)
    return vector<point>();
  d = max(d, 0.0);
  const point q1 = (p - c.c) * (c.r * c.r / x);
  const point q2 = rotate90((p - c.c) * (-c.r * sqrt(d) / x));
  vector<point> res;
  res.push_back(c.c + q1 - q2);
  res.push_back(c.c + q1 + q2);
  return res;
}

vector<line> tangent(const circle &a, const circle &b) {
  vector<line> res;
  if (abs(a.r - b.r) < EPS) {
    point dir = b.c - a.c;
    dir = rotate90(dir * (a.r / abs(dir)));
    res.push_back(line(a.c + dir, b.c + dir));
    res.push_back(line(a.c - dir, b.c - dir));
  } else {
    point p = a.c * (-b.r) + b.c * a.r;
    p = p * (1.0 / (a.r - b.r));
    vector<point> ps = tangent(a, p), qs = tangent(b, p);
    for (int i = 0; i < min<int>(ps.size(), qs.size()); ++i)
      res.push_back(line(ps[i], qs[i]));
  }

  point p = a.c * b.r + b.c * a.r;
  p = p * (1.0 / (a.r + b.r));
  vector<point> ps = tangent(a, p), qs = tangent(b, p);
  for (int i = 0; i < min<int>(ps.size(), qs.size()); ++i)
    res.push_back(line(ps[i], qs[i]));

  return res;
}

const int MAX_N = 50;
const double INF = 2000;
int n;
double d[MAX_N];
int h[MAX_N];

double square(double x) { return x * x; }

bool check(double r) {
  for (int i = 0; i < n; ++i) {
    if (d[i] < sqrt(square(r) - square(r - min<double>(r, h[i]))))
      return false;

    continue;

    if (h[i] >= r) {
      if (d[i] < r)
        return false;
    }

    else {
      const double a = r - h[i];
      if (d[i] * d[i] + a * a < r * r)
        return false;
    }
  }

  return true;
}

int main() {
  while (scanf("%d", &n), n) {
    int sx, sy, ex, ey;
    scanf("%d %d %d %d", &sx, &sy, &ex, &ey);

    segment course(point(sx, sy), point(ex, ey));

    fill(d, d + n, INF);
    bool on = false;
    for (int i = 0; i < n; ++i) {
      int minX, minY, maxX, maxY;
      scanf("%d %d %d %d %d", &minX, &minY, &maxX, &maxY, &h[i]);

      vector<point> points;
      points.reserve(4);
      points.push_back(point(minX, minY));
      points.push_back(point(minX, maxY));
      points.push_back(point(maxX, maxY));
      points.push_back(point(maxX, minY));

      if (minX <= sx && sx <= maxX && minY <= sy && sy <= maxY ||
          minX <= ex && ex <= maxX && minY <= ey && ey <= maxY) {
        on = true;
        continue;
      }

      for (int j = 0; j < 4; ++j) {
        const segment edge(points[j], points[(j + 1) % 4]);
        if (intersect(course, edge)) {
          on = true;
          break;
        }

        chmin(d[i], dist(course, edge));
      }
    }

    if (on) {
      puts("0.0000");
      continue;
    }

    double low = 0.0, high = 1000.0;
    for (int i = 0; i < 100; ++i) {
      const double mid = (low + high) / 2;
      if (check(mid))
        low = mid;

      else
        high = mid;
    }

    printf("%.4lf\\n", low);
  }

  return EXIT_SUCCESS;
}

Error: WA

Fixed submission:

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cctype>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <functional>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <vector>
using namespace std;

#define dump(a) (cerr << (#a) << " = " << (a) << endl)
#define FOR(it, c)                                                             \\
  for (__typeof((c).begin()) it = (c).begin(); it != (c).end(); ++it)
#define RFOR(it, c)                                                            \\
  for (__typeof((c).rbegin()) it = (c).rbegin(); it != (c).rend(); ++it)
#define exist(c, v) (find((c).begin(), (c).end(), (v)) != (c).end())

template <class T> inline void chmax(T &a, const T &b) {
  if (b > a)
    a = b;
}
template <class T> inline void chmin(T &a, const T &b) {
  if (b < a)
    a = b;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << '(' << p.first << ", " << p.second << ')';
  return os;
}

template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) {
  copy(v.begin(), v.end(), ostream_iterator<T>(os, " "));
  return os;
}

const double EPS = 1e-9;

struct point {
  double x, y;
  point() : x(0), y(0) {}
  point(double x, double y) : x(x), y(y) {}
  point(const point &p) : x(p.x), y(p.y) {}

  point operator+(const point &p) const { return point(x + p.x, y + p.y); }

  point operator-(const point &p) const { return point(x - p.x, y - p.y); }

  point operator*(const double s) const { return point(x * s, y * s); }

  point operator*(const point &p) const {
    return point(x * p.x - y * p.y, x * p.y + y * p.x);
  }

  point operator/(const double s) const { return point(x / s, y / s); }

  bool operator<(const point &p) const {
    return x + EPS < p.x || abs(x - p.x) < EPS && y + EPS < p.y;
  }

  bool operator==(const point &p) const {
    return abs(x - p.x) < EPS && abs(y - p.y) < EPS;
  }
};

inline point rotate90(const point &p) { return point(-p.y, p.x); }

inline point rotate(const point &p, const double theta) {
  const double s = sin(theta), c = cos(theta);
  return point(c * p.x - s * p.y, s * p.x + c * p.y);
}

inline double angle(const point &p) { return atan2(p.y, p.x); }

inline double abs(const point &p) { return sqrt(p.x * p.x + p.y * p.y); }

inline double norm(const point &p) { return p.x * p.x + p.y * p.y; }

inline double dot(const point &l, const point &r) {
  return l.x * r.x + l.y * r.y;
}

inline double cross(const point &l, const point &r) {
  return l.x * r.y - l.y * r.x;
}

struct line {
  point a, b;
  line(point a, point b) : a(a), b(b) {}
};

struct segment {
  point a, b;
  segment(point a, point b) : a(a), b(b) {}
};

struct circle {
  point c;
  double r;
  circle(point c, double r) : c(c), r(r) {}
};

typedef vector<point> polygon;

inline int ccw(const point &a, point b, point c) {
  b = b - a;
  c = c - a;
  const double tmp = cross(b, c);
  if (tmp > EPS)
    return 1; // ccw
  if (tmp < -EPS)
    return -1; // cw
  if (dot(b, c) < 0)
    return 2; // c, a, b 順に一直線上
  if (norm(b) < norm(c))
    return -2; // a, b, c 順に一直線上
  return 0;    // a, c, b 順で一直線上
}

inline point projection(const line &l, const point &p) {
  const point dif = l.b - l.a;
  const double tmp = dot(p - l.a, dif) / norm(dif);
  return l.a + dif * tmp;
}

inline bool intersect(const line &l, const line &m) {
  return abs(cross(l.b - l.a, m.b - m.a)) > EPS ||
         abs(cross(l.b - l.a, m.b - l.a)) < EPS;
}

inline bool intersect(const line &l, const segment &s) {
  return cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < EPS;
}

inline bool intersect(const line &l, const point &p) {
  return abs(ccw(l.a, l.b, p)) != -1;
}

inline bool intersect(const segment &s, const segment &t) {
  return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 &&
         ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}

inline bool intersect(const segment &s, const point &p) {
  return ccw(s.a, s.b, p) == 0;
}

inline bool intersect(const circle &c, const point &p) {
  return abs(c.c - p) <= c.r + EPS;
}

inline bool intersect(const circle &c, const circle &d) {
  return abs(c.c - d.c) <= c.r + d.r && abs(c.c - d.c) >= abs(c.r - d.r);
}

inline double dist(const line &l, const point &p) {
  return abs(p - projection(l, p));
}

inline double dist(const line &l, const line &m) {
  return intersect(l, m) ? 0 : dist(l, m.a);
}

inline double dist(const line &l, const segment &s) {
  return intersect(l, s) ? 0 : min(dist(l, s.a), dist(l, s.b));
}

inline double dist(const segment &s, const point &p) {
  const point tmp = projection(line(s.a, s.b), p);
  return intersect(s, tmp) ? abs(tmp - p) : min(abs(s.a - p), abs(s.b - p));
}

inline double dist(const segment &s, const segment &t) {
  if (intersect(s, t))
    return 0;
  return min(min(dist(s, t.a), dist(s, t.b)), min(dist(t, s.a), dist(t, s.b)));
}

inline double dist(const point &a, const point &b) { return abs(a - b); }

inline point crosspoint(const line &l, const line &m) {
  const double tmp = cross(l.b - l.a, m.b - m.a);
  if (abs(tmp) < EPS) // 平行
    return l.a;
  return m.a + (m.b - m.a) * cross(l.b - l.a, l.a - m.a) * (1.0 / tmp);
}

inline point crosspoint(const segment &s, const segment &t) {
  if (!intersect(s, t)) // 交点を持たない
    return s.a;         // 用改善

  const double tmp = cross(s.b - s.a, t.b - t.a);
  if (abs(tmp) < EPS) { // 一直線上
    if (intersect(s, t.a))
      return t.a;
    if (intersect(s, t.b))
      return t.b;
    if (intersect(t, s.a))
      return s.a;
    return s.b;
  }

  return t.a + (t.b - t.a) * cross(s.b - s.a, s.b - t.a) * (1.0 / tmp);
}

// 先に，intersectを用いて交差判定を行うこと
inline vector<point> crosspoint(const circle &c, const circle &d) {
  vector<point> res;
  if (abs(c.c - d.c) < EPS) // 中心の座標が同じ
    return res;

  const double tmp = abs(c.c - d.c);
  const double rc = (tmp * tmp + c.r * c.r - d.r * d.r) / (tmp + tmp);
  const double rs = sqrt(c.r * c.r - rc * rc);
  const point diff = (d.c - c.c) / tmp;
  res.push_back(point(c.c + diff * point(rc, rs)));
  res.push_back(point(c.c + diff * point(rc, -rs)));
  return res;
}

inline vector<point> crosspoint(const circle &c, const line &l) {
  vector<point> res;
  const point h = projection(l, c.c);
  const double d = abs(h - c.c);
  if (d > c.r - EPS) {
    res.push_back(h);
  } else if (d <= c.r - EPS) {
    point v = l.b - l.a;
    v = v * sqrt(c.r * c.r - d * d) / abs(v);
    res.push_back(h + v);
    res.push_back(h - v);
  }

  return res;
}

inline vector<point> crosspoint(const circle &c, const segment &s) {
  vector<point> res;
  vector<point> tmp = crosspoint(c, line(s.a, s.b));
  for (int i = 0; i < tmp.size(); ++i)
    if (intersect(s, tmp[i]))
      res.push_back(tmp[i]);

  return res;
}

inline double areaTriangle(point a, point b, const point &c) {
  a = a - c;
  b = b - c;
  return fabs(a.x * b.y - b.x * a.y) / 2.0;
}

inline double area(const polygon &p) {
  const int num = p.size();
  if (num < 3)
    return 0;

  if (num == 3)
    return areaTriangle(p[0], p[1], p[2]);

  double res = cross(p[num - 1], p[0]);
  for (int i = 1; i < num; ++i)
    res += cross(p[i - 1], p[i]);

  return res * 0.5;
}

// L.aからL.bの方向を見た場合に，点aが左側に来る．
inline line bisector(const point &a, const point &b) {
  return line(
      point((a.x - a.y + b.x + b.y) / 2.0, (a.y + a.x + b.y - b.x) / 2.0),
      point((a.x + a.y + b.x - b.y) / 2.0, (a.y - a.x + b.y + b.x) / 2.0));
}

// L.aからL.bを向いた時の左側を残して切断する．
inline polygon convex_cut(const polygon &p, const line &l) {
  const int num = p.size();
  polygon res;
  for (int i = 0; i < num; ++i) {
    const int next = (i + 1) % num;
    const int tmp = ccw(l.a, l.b, p[i]);
    if (tmp != -1)
      res.push_back(p[i]);

    if (tmp * ccw(l.a, l.b, p[next]) < 0)
      res.push_back(crosspoint(l, line(p[i], p[next])));
  }

  return res;
}

vector<point> tangent(const circle &c, const point &p) {
  const double x = norm(p - c.c);
  double d = x - c.r * c.r;
  if (d < -EPS)
    return vector<point>();
  d = max(d, 0.0);
  const point q1 = (p - c.c) * (c.r * c.r / x);
  const point q2 = rotate90((p - c.c) * (-c.r * sqrt(d) / x));
  vector<point> res;
  res.push_back(c.c + q1 - q2);
  res.push_back(c.c + q1 + q2);
  return res;
}

vector<line> tangent(const circle &a, const circle &b) {
  vector<line> res;
  if (abs(a.r - b.r) < EPS) {
    point dir = b.c - a.c;
    dir = rotate90(dir * (a.r / abs(dir)));
    res.push_back(line(a.c + dir, b.c + dir));
    res.push_back(line(a.c - dir, b.c - dir));
  } else {
    point p = a.c * (-b.r) + b.c * a.r;
    p = p * (1.0 / (a.r - b.r));
    vector<point> ps = tangent(a, p), qs = tangent(b, p);
    for (int i = 0; i < min<int>(ps.size(), qs.size()); ++i)
      res.push_back(line(ps[i], qs[i]));
  }

  point p = a.c * b.r + b.c * a.r;
  p = p * (1.0 / (a.r + b.r));
  vector<point> ps = tangent(a, p), qs = tangent(b, p);
  for (int i = 0; i < min<int>(ps.size(), qs.size()); ++i)
    res.push_back(line(ps[i], qs[i]));

  return res;
}

const int MAX_N = 50;
const double INF = 2000;
int n;
double d[MAX_N];
int h[MAX_N];

bool check(double r) {
  for (int i = 0; i < n; ++i) {
    if (h[i] >= r) {
      if (d[i] < r)
        return false;
    }

    else {
      const double a = r - h[i];
      if (d[i] * d[i] + a * a < r * r)
        return false;
    }
  }

  return true;
}

int main() {
  while (scanf("%d", &n), n) {
    int sx, sy, ex, ey;
    scanf("%d %d %d %d", &sx, &sy, &ex, &ey);

    segment course(point(sx, sy), point(ex, ey));

    fill(d, d + n, INF);
    bool on = false;
    for (int i = 0; i < n; ++i) {
      int minX, minY, maxX, maxY;
      scanf("%d %d %d %d %d", &minX, &minY, &maxX, &maxY, &h[i]);

      vector<point> points;
      points.reserve(4);
      points.push_back(point(minX, minY));
      points.push_back(point(minX, maxY));
      points.push_back(point(maxX, maxY));
      points.push_back(point(maxX, minY));

      if (minX <= sx && sx <= maxX && minY <= sy && sy <= maxY ||
          minX <= ex && ex <= maxX && minY <= ey && ey <= maxY) {
        on = true;
        break;
      }

      for (int j = 0; j < 4; ++j) {
        const segment edge(points[j], points[(j + 1) % 4]);
        if (intersect(course, edge)) {
          on = true;
          break;
        }

        chmin(d[i], dist(course, points[j]));
        chmin(d[i], dist(course, edge));
      }
    }

    if (on) {
      puts("0");
      continue;
    }

    double low = 0.0, high = 1000.0;
    for (int i = 0; i < 100; ++i) {
      const double mid = (low + high) / 2;
      if (check(mid))
        low = mid;

      else
        high = mid;
    }

    printf("%.15lf\\n", low);
  }

  return EXIT_SUCCESS;
}