Problem p00249 (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 equals(a, b) (fabs((a) - (b)) < EPS)
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0

using namespace std;

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 : (!equals(y, p.y) && 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 &s) const {
    return (p2 == s.p2) ? p1 < s.p1 : p2 < s.p2;
  }
  bool operator==(const Segment &s) const {
    return (s.p1 == p1 && s.p2 == p2) || (s.p1 == p2 && s.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 ????§???????????????¢?????§?????????????????¨
Point rotate(Point a, double rad) {
  return Point(cos(rad) * a.x - sin(rad) * a.y,
               sin(rad) * a.x + cos(rad) * a.y);
}

// ??????????????¢????????????
double toRad(double agl) { return agl * M_PI / 180.0; }

// a => prev, b => cur, c=> next
// prev ?????? cur ????????£??? next ????????????????§????????±???????
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);
}

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;
}

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);
}

double getArea(vector<Point> &vec) {
  double sum = 0;
  for (int i = 0; i < vec.size(); i++)
    sum += cross(vec[i], vec[(i + 1) % vec.size()]);
  return fabs(sum) / 2.0;
}

// 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; // can be modified to accept collinear points
}

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)));
}

Point getCentroidOfConvex(Polygon &poly) {
  double area = getArea(poly);
  int V = poly.size();
  assert(!equals(area, 0.0));
  double x = 0, y = 0;
  rep(i, (int)poly.size()) {
    x += (poly[i].x + poly[(i + 1) % V].x) *
         (poly[i].x * poly[(i + 1) % V].y - poly[(i + 1) % V].x * poly[i].y);
    y += (poly[i].y + poly[(i + 1) % V].y) *
         (poly[i].x * poly[(i + 1) % V].y - poly[(i + 1) % V].x * poly[i].y);
  }
  return Point(x / (6.0 * area), y / (6.0 * area));
}

// --------------------------

/*
  360???????????£??¨?????? <= ?????????
  or
  ???????????§?±±???????????????,?????????????????§??????
  360????????????????????£????????£?????????

  ???????????§?????? ????????????(?????<)
  ?????´????????§????????¨?????????????????????

 */

bool DEBUG = 0;

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

int V;
double d, vol;
Polygon poly;
Point ps[110];

double lets_compute_arg(int L, int R) {
  assert(L != R);
  Point lp = poly[L], rp = poly[R];
  // cout << lp << " " << rp << " ---" << endl;
  rp = rp - lp;
  lp = Point(0, 0);
  // cout << lp << " " << rp << " ---" << endl;
  Vector e = rp / abs(rp);
  e = e * 100000;
  e = rotate(e, toRad(90.0));

  Line line = Line(e, e * -1);

  // cout << "heikou? " << line.p1-line.p2 << " " << poly[L]-poly[R] << " :: "
  // << cross(line.p1-line.p2,poly[L]-poly[R]) << endl;
  assert(intersectLL(line, Line(poly[L], poly[R])));
  Point cp = crosspoint(line, Line(poly[L], poly[R]));
  // cout << "cp = " << cp << endl;
  double ret = getArg(Point(0, -1000), Point(0, 0), cp);
  // if( LT(ret,toRad(90.0)) ) ret = toRad(180.0) - ret;
  /*
  cout << "ret arg = " << ret * 180.0 / M_PI << endl;
  cout << rotate(cp,toRad(180.0)+ret) << endl;
  cout << rotate(poly[L],toRad(180.0)+ret) << endl;
  cout << rotate(poly[R],toRad(180.0)+ret) << endl;
  */
  return ret + toRad(180.0);
}

double getNewVolume(double h) {
  Segment cut_line = Segment(Point(-20000, h), Point(20000, h));
  int nV = 0;
  // ps[0] = poly[0];

  int index = 0;
  int cross_ps[2];

  // cout << "cut_line = " << cut_line << endl;
  rep(i, V) {
    Segment seg = Segment(poly[i], poly[(i + 1) % V]);
    if (intersectSS(cut_line, seg)) { // ???????????´????????????
      Point cp = crosspoint(cut_line, seg);
      if (!(cp == seg.p1 || cp == seg.p2)) {
        ps[nV++] = cp;
      }
    }
    ps[nV++] = poly[(i + 1) % V];
  }

  rep(i, nV) if (equals(cut_line.p2.y, ps[i].y)) { cross_ps[index++] = i; }

  /*
  cout << "H = " << h << endl;
  cout << "cutted poly = " << endl;
  rep(i,nV) {
    cout << ps[i] << endl;
  } puts("");

  cout << "index = " << index << endl;
  */

  assert(index == 2);

  int sp = -1;
  double maxi_h = -1e30;
  rep(i, nV) maxi_h = max(maxi_h, ps[i].y);
  rep(i, nV) if (equals(maxi_h, ps[i].y)) {
    sp = i;
    break;
  }
  assert(sp != -1);

  // cout << sp << " = " << cross_ps[0] << " or " << cross_ps[1] << endl;
  // cout << ps[sp] << endl;
  assert((cross_ps[0] != sp && cross_ps[1] != sp));
  bool found = false;
  int cur = sp;
  vector<Point> npoly;
  rep(i, nV) {
    bool same_point = (cross_ps[0] == cur || cross_ps[1] == cur);
    if (same_point && found) {
      npoly.push_back(ps[cur]);
      break;
    }
    if (same_point)
      found = true;
    if (found)
      npoly.push_back(ps[cur]);
    cur = (cur + 1) % nV;
  }

  if (DEBUG) {

    cout << "added polygon" << endl;
    rep(i, nV) { cout << ps[i] << endl; }
    cout << endl;

    cout << "cutted polygon" << endl;
    rep(i, npoly.size()) { cout << npoly[i] << endl; }
  }

  double area = getArea(npoly);
  return area * d;
}

void compute() {

  bool full = false;
  {
    double area = getArea(poly) * d;
    if (equals(area, vol))
      full = true;
  }

  double maxi = 0;
  Point centroid = getCentroidOfConvex(poly);
  // cout << "centroid = " << centroid << endl;
  rep(i, V) poly[i] = poly[i] - centroid;
  centroid = Point(0, 0);

  if (DEBUG) {
    cout << "moved polygon" << endl;
    rep(i, V) { cout << poly[i] << endl; }
    puts("");
  }

  rep(_, V) {

    if (DEBUG) {
      cout << "let's try" << endl;
      rep(i, V) { cout << poly[i] << endl; }
      puts("");
    }

    double maxi_y = -1e30, mini_y = 1e30;
    rep(i, V) maxi_y = max(maxi_y, poly[i].y), mini_y = min(mini_y, poly[i].y);
    double low_y = mini_y, high_y = maxi_y;

    if (!full) {
      rep(__, 60) {
        double mid_y = (low_y + high_y) / 2.0;

        double new_volume = getNewVolume(mid_y);

        if (equals(new_volume, vol)) {
          maxi = max(maxi, fabs(mid_y - mini_y));
          break;
        }
        if (LT(new_volume, vol))
          low_y = mid_y;
        else
          high_y = mid_y;
      }
    } else {
      rep(j, V) maxi = max(maxi, abs(mini_y - poly[j].y));
    }

    int left_p = -1, right_p = -1;
    rep(i, V) if (equals(mini_y, poly[i].y)) {
      if (left_p == -1)
        left_p = i;
      if (right_p == -1)
        right_p = i;
      if (LT(poly[i].x, poly[left_p].x))
        left_p = i;
      if (LT(poly[right_p].x, poly[i].x))
        right_p = i;
    }

    /*
    rep(i,V){
      cout << poly[i] << "!" << endl;
    }
    */

    assert(left_p != right_p);
    assert(left_p != -1 && right_p != -1);
    // cout << poly[left_p] << " => " << centroid << " => " << poly[right_p] <<
    // endl;
    (left_p += 1) %= V;
    (right_p += 1) %= V;
    double rad = lets_compute_arg(left_p, right_p);
    // cout << "rad = " << rad * 180.0 / M_PI << endl;
    // assert( LT(rad * 180.0 / M_PI,180.0) );
    // rad = toRad(360.0) - rad;
    // cout << "rad = " << rad * 180.0 / M_PI << endl;
    rep(i, V) poly[i] = rotate(poly[i], rad);
  }
  printf("%.10f\\n", maxi);
}

void fix() {
  bool update = true;
  while (update) {
    update = false;
    rep(i, poly.size()) {
      int j = (i + 1) % poly.size();
      int k = (i + 2) % poly.size();
      if (equals(cross(poly[j] - poly[i], poly[k] - poly[i]), 0.0)) {
        update = true;
        poly.erase(poly.begin() + j);
        goto Skip;
      }
    }
  Skip:;
  }
  V = poly.size();
}

int main() {

  // ????????????????????±?????????????????????????????????????????¨

  int a, b, c;
  while (scanf("%d %d %d", &a, &b, &c), a | b | c) {
    V = a, d = b, vol = c;
    poly.clear();
    poly.resize(V);
    rep(i, V) scanf("%lf %lf", &poly[i].x, &poly[i].y);
    fix();
    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 equals(a, b) (fabs((a) - (b)) < EPS)
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0

using namespace std;

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 : (!equals(y, p.y) && 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 &s) const {
    return (p2 == s.p2) ? p1 < s.p1 : p2 < s.p2;
  }
  bool operator==(const Segment &s) const {
    return (s.p1 == p1 && s.p2 == p2) || (s.p1 == p2 && s.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 ????§???????????????¢?????§?????????????????¨
Point rotate(Point a, double rad) {
  return Point(cos(rad) * a.x - sin(rad) * a.y,
               sin(rad) * a.x + cos(rad) * a.y);
}

// ??????????????¢????????????
double toRad(double agl) { return agl * M_PI / 180.0; }

// a => prev, b => cur, c=> next
// prev ?????? cur ????????£??? next ????????????????§????????±???????
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);
}

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;
}

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);
}

double getArea(vector<Point> &vec) {
  double sum = 0;
  for (int i = 0; i < vec.size(); i++)
    sum += cross(vec[i], vec[(i + 1) % vec.size()]);
  return fabs(sum) / 2.0;
}

// 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; // can be modified to accept collinear points
}

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)));
}

Point getCentroidOfConvex(Polygon &poly) {
  double area = getArea(poly);
  int V = poly.size();
  assert(!equals(area, 0.0));
  double x = 0, y = 0;
  rep(i, (int)poly.size()) {
    x += (poly[i].x + poly[(i + 1) % V].x) *
         (poly[i].x * poly[(i + 1) % V].y - poly[(i + 1) % V].x * poly[i].y);
    y += (poly[i].y + poly[(i + 1) % V].y) *
         (poly[i].x * poly[(i + 1) % V].y - poly[(i + 1) % V].x * poly[i].y);
  }
  return Point(x / (6.0 * area), y / (6.0 * area));
}

// --------------------------

/*
  360???????????£??¨?????? <= ?????????
  or
  ???????????§?±±???????????????,?????????????????§??????
  360????????????????????£????????£?????????

  ???????????§?????? ????????????(?????<)
  ?????´????????§????????¨?????????????????????

 */

bool DEBUG = 0;

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

int V;
double d, vol;
Polygon poly;
Point ps[110];

double lets_compute_arg(int L, int R) {
  assert(L != R);
  Point lp = poly[L], rp = poly[R];
  // cout << lp << " " << rp << " ---" << endl;
  rp = rp - lp;
  lp = Point(0, 0);
  // cout << lp << " " << rp << " ---" << endl;
  Vector e = rp / abs(rp);
  e = e * 100000;
  e = rotate(e, toRad(90.0));

  Line line = Line(e, e * -1);

  // cout << "heikou? " << line.p1-line.p2 << " " << poly[L]-poly[R] << " :: "
  // << cross(line.p1-line.p2,poly[L]-poly[R]) << endl;
  assert(intersectLL(line, Line(poly[L], poly[R])));
  Point cp = crosspoint(line, Line(poly[L], poly[R]));
  // cout << "cp = " << cp << endl;
  double ret = getArg(Point(0, -1000), Point(0, 0), cp);
  if (LT(ret, toRad(90.0)))
    ret = toRad(180.0) - ret;
  /*
  cout << "ret arg = " << ret * 180.0 / M_PI << endl;
  cout << rotate(cp,toRad(180.0)+ret) << endl;
  cout << rotate(poly[L],toRad(180.0)+ret) << endl;
  cout << rotate(poly[R],toRad(180.0)+ret) << endl;
  */
  return ret + toRad(180.0);
}

double getNewVolume(double h) {
  Segment cut_line = Segment(Point(-20000, h), Point(20000, h));
  int nV = 0;
  // ps[0] = poly[0];

  int index = 0;
  int cross_ps[2];

  // cout << "cut_line = " << cut_line << endl;
  rep(i, V) {
    Segment seg = Segment(poly[i], poly[(i + 1) % V]);
    if (intersectSS(cut_line, seg)) { // ???????????´????????????
      Point cp = crosspoint(cut_line, seg);
      if (!(cp == seg.p1 || cp == seg.p2)) {
        ps[nV++] = cp;
      }
    }
    ps[nV++] = poly[(i + 1) % V];
  }

  rep(i, nV) if (equals(cut_line.p2.y, ps[i].y)) { cross_ps[index++] = i; }

  /*
  cout << "H = " << h << endl;
  cout << "cutted poly = " << endl;
  rep(i,nV) {
    cout << ps[i] << endl;
  } puts("");

  cout << "index = " << index << endl;
  */

  assert(index == 2);

  int sp = -1;
  double maxi_h = -1e30;
  rep(i, nV) maxi_h = max(maxi_h, ps[i].y);
  rep(i, nV) if (equals(maxi_h, ps[i].y)) {
    sp = i;
    break;
  }
  assert(sp != -1);

  // cout << sp << " = " << cross_ps[0] << " or " << cross_ps[1] << endl;
  // cout << ps[sp] << endl;
  assert((cross_ps[0] != sp && cross_ps[1] != sp));
  bool found = false;
  int cur = sp;
  vector<Point> npoly;
  rep(i, nV) {
    bool same_point = (cross_ps[0] == cur || cross_ps[1] == cur);
    if (same_point && found) {
      npoly.push_back(ps[cur]);
      break;
    }
    if (same_point)
      found = true;
    if (found)
      npoly.push_back(ps[cur]);
    cur = (cur + 1) % nV;
  }

  if (DEBUG) {

    cout << "added polygon" << endl;
    rep(i, nV) { cout << ps[i] << endl; }
    cout << endl;

    cout << "cutted polygon" << endl;
    rep(i, npoly.size()) { cout << npoly[i] << endl; }
  }

  double area = getArea(npoly);
  return area * d;
}

void compute() {

  bool full = false;
  {
    double area = getArea(poly) * d;
    if (equals(area, vol))
      full = true;
  }

  double maxi = 0;
  Point centroid = getCentroidOfConvex(poly);
  // cout << "centroid = " << centroid << endl;
  rep(i, V) poly[i] = poly[i] - centroid;
  centroid = Point(0, 0);

  if (DEBUG) {
    cout << "moved polygon" << endl;
    rep(i, V) { cout << poly[i] << endl; }
    puts("");
  }

  rep(_, V) {

    if (DEBUG) {
      cout << "let's try" << endl;
      rep(i, V) { cout << poly[i] << endl; }
      puts("");
    }

    double maxi_y = -1e30, mini_y = 1e30;
    rep(i, V) maxi_y = max(maxi_y, poly[i].y), mini_y = min(mini_y, poly[i].y);
    double low_y = mini_y, high_y = maxi_y;

    if (!full) {
      rep(__, 60) {
        double mid_y = (low_y + high_y) / 2.0;

        double new_volume = getNewVolume(mid_y);

        if (equals(new_volume, vol)) {
          maxi = max(maxi, fabs(mid_y - mini_y));
          break;
        }
        if (LT(new_volume, vol))
          low_y = mid_y;
        else
          high_y = mid_y;
      }
    } else {
      rep(j, V) maxi = max(maxi, abs(mini_y - poly[j].y));
    }

    int left_p = -1, right_p = -1;
    rep(i, V) if (equals(mini_y, poly[i].y)) {
      if (left_p == -1)
        left_p = i;
      if (right_p == -1)
        right_p = i;
      if (LT(poly[i].x, poly[left_p].x))
        left_p = i;
      if (LT(poly[right_p].x, poly[i].x))
        right_p = i;
    }

    /*
    rep(i,V){
      cout << poly[i] << "!" << endl;
    }
    */

    assert(left_p != right_p);
    assert(left_p != -1 && right_p != -1);
    // cout << poly[left_p] << " => " << centroid << " => " << poly[right_p] <<
    // endl;
    (left_p += 1) %= V;
    (right_p += 1) %= V;
    double rad = lets_compute_arg(left_p, right_p);
    // cout << "rad = " << rad * 180.0 / M_PI << endl;
    // assert( LT(rad * 180.0 / M_PI,180.0) );
    // rad = toRad(360.0) - rad;
    // cout << "rad = " << rad * 180.0 / M_PI << endl;
    rep(i, V) poly[i] = rotate(poly[i], rad);
  }
  printf("%.10f\\n", maxi);
}

void fix() {
  bool update = true;
  while (update) {
    update = false;
    rep(i, poly.size()) {
      int j = (i + 1) % poly.size();
      int k = (i + 2) % poly.size();
      if (equals(cross(poly[j] - poly[i], poly[k] - poly[i]), 0.0)) {
        update = true;
        poly.erase(poly.begin() + j);
        goto Skip;
      }
    }
  Skip:;
  }
  V = poly.size();
}

int main() {

  // ????????????????????±?????????????????????????????????????????¨

  int a, b, c;
  while (scanf("%d %d %d", &a, &b, &c), a | b | c) {
    V = a, d = b, vol = c;
    poly.clear();
    poly.resize(V);
    rep(i, V) scanf("%lf %lf", &poly[i].x, &poly[i].y);
    fix();
    compute();
  }
  return 0;
}