Problem p01800 (C++) — buggy submission, verdict: Runtime Error

#include "bits/stdc++.h"
#include <unordered_map>
#include <unordered_set>
#pragma warning(disable : 4996)
using namespace std;
using ld = long double;
template <class T> using Table = vector<vector<T>>;
const ld eps = 1e-9;

/* ??????????????¬ */

#include <complex>

typedef long double ld;
typedef complex<ld> Point;
#define REP(i, n) for (int i = 0; i < (int)(n); i++)
#define ALL(x) (x).begin(), (x).end()

const ld pi = acos(-1.0);
const ld dtop = pi / 180.;
const ld ptod = 1. / dtop;

namespace std {
bool operator<(const Point &lhs, const Point &rhs) {
  if (lhs.real() < rhs.real() - eps)
    return true;
  if (lhs.real() > rhs.real() + eps)
    return false;
  return lhs.imag() < rhs.imag();
}
} // namespace std

// ????????\\???
Point input_point() {
  ld x, y;
  cin >> x >> y;
  return Point(x, y);
}

// ????????????????????????
bool eq(const ld a, const ld b) { return (abs(a - b) < eps); }

// ??????
ld dot(const Point &a, const Point &b) { return real(conj(a) * b); }

// ??????
ld cross(const Point &a, const Point &b) { return imag(conj(a) * b); }

// ??´????????????
class Line {
public:
  Point a, b;
  Line() : a(Point(0, 0)), b(Point(0, 0)) {}
  Line(Point a, Point b) : a(a), b(b) {}
  Point operator[](const int _num) const {
    if (_num == 0)
      return a;
    else if (_num == 1)
      return b;
    else {
      assert(false);
      return Point();
    }
  }
};

// ????????????
class Circle {
public:
  Point p;
  ld r;
  Circle() : p(Point(0, 0)), r(0) {}
  Circle(Point p, ld r) : p(p), r(r) {}
};

// CCW
int ccw(const Point &a, const Point &b, const Point &c) {
  const Point nb(b - a);
  const Point nc(c - a);
  if (cross(nb, nc) > eps)
    return 1; // a,b,c??????????¨???¨?????????????????¶
  if (cross(nb, nc) < -eps)
    return -1; // a,b,c???????¨???¨?????????????????¶
  if (dot(nb, nc) < 0)
    return 2; // c,a,b???????????´???????????¶
  if (norm(nb) < norm(nc))
    return -2; // a,b,c???????????´???????????¶
  return 0;    // a,c,b???????????´???????????¶
}

/* ???????????? */

// ??´?????¨??´??????????????????
bool isis_ll(const Line &l, const Line &m) {
  return !eq(cross(l.b - l.a, m.b - m.a), 0);
}

// ??´?????¨?????????????????????
bool isis_ls(const Line &l, const Line &s) {
  return isis_ll(l, s) &&
         (cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}

// ????????¨?????????????????????
bool isis_ss(const Line &s, const Line &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;
}

// ????????´????????????
bool isis_lp(const Line &l, const Point &p) {
  return (abs(cross(l.b - p, l.a - p)) < eps);
}

// ?????????????????????
bool isis_sp(const Line &s, const Point &p) {
  return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);
}

// ??????????¶?
Point proj(const Line &l, const Point &p) {
  ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
  return l.a + t * (l.a - l.b);
}

// ??´?????¨??´????????????
Point is_ll(const Line &s, const Line &t) {
  Point sv = s.b - s.a, tv = t.b - t.a;
  assert(cross(sv, tv) != 0);
  return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}
// ??´?????¨??´????????????
vector<Point> is_ll2(const Line &s, const Line &t) {
  Point sv = s.b - s.a, tv = t.b - t.a;
  if (cross(sv, tv) != 0)
    return vector<Point>(1, is_ll(s, t));
  else {
    vector<Point> ans;
    for (int k = 0; k < 2; ++k) {
      if (isis_sp(s, t[k]) && find(ans.begin(), ans.end(), t[k]) == ans.end())
        ans.push_back(t[k]);
      if (isis_sp(t, s[k]) && find(ans.begin(), ans.end(), s[k]) == ans.end())
        ans.push_back(s[k]);
    }
    return ans;
  }
}
// ????????¨???????????????
//???????????£????????¨???????????¨assert(false)
Point is_ss(const Line &s, const Line &t) {
  if (isis_ss(s, t)) {
    for (int k = 0; k < 2; ++k) {
      for (int l = 0; l < 2; ++l) {
        if (s[k] == t[l])
          return s[k];
      }
    }
    return is_ll(s, t);
  } else {
    //??????isis_ss?????????
    assert(false);
    return Point(0, 0);
  }
}
// ??´?????¨???????????¢
ld dist_lp(const Line &l, const Point &p) { return abs(p - proj(l, p)); }

// ??´?????¨??´???????????¢
ld dist_ll(const Line &l, const Line &m) {
  return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

// ??´?????¨??????????????¢
ld dist_ls(const Line &l, const Line &s) {
  return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}

// ????????¨???????????¢
ld dist_sp(const Line &s, const Point &p) {
  Point r = proj(s, p);
  return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p));
}

// ????????¨??????????????¢
ld dist_ss(const Line &s, const Line &t) {
  if (isis_ss(s, t))
    return 0;
  return min(
      {dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b)});
}

//??´?????¨??´?????????????????????????????????
Line bisection(const Line &s, const Line &t) {
  const Point laglanju(is_ll(s, t));
  const Point avec =
      !(abs(laglanju - s[0]) < eps) ? s[0] - laglanju : s[1] - laglanju;
  const Point bvec =
      !(abs(laglanju - t[0]) < eps) ? t[0] - laglanju : t[1] - laglanju;

  return Line(laglanju, laglanju + (abs(bvec) * avec + abs(avec) * bvec) /
                                       (abs(avec) + abs(bvec)));
}

//???????????´?????????????????????
//???????????´??????????????§???????????¨????¢?????????¨?????????
Point inner_center(const vector<Line> &ls) {
  vector<Point> vertics;
  for (int i = 0; i < static_cast<int>(ls.size()); ++i) {
    vertics.push_back(is_ll(ls[i], ls[(i + 1) % 3]));
  }
  if (vertics[0] == vertics[1] || vertics[1] == vertics[2] ||
      vertics[2] == vertics[0])
    return vertics[0];
  Line bi1(
      bisection(Line(vertics[0], vertics[1]), Line(vertics[0], vertics[2])));
  Line bi2(
      bisection(Line(vertics[1], vertics[2]), Line(vertics[1], vertics[0])));
  if (bi1[0] == bi2[0])
    return bi1[0];
  else {
    return is_ll(bi1, bi2);
  }
}

//???????????´?????????????????????
//???????????´??????????????§???????????¨????¢?????????¨?????????
vector<Point> ex_center(const vector<Line> &ls) {
  vector<Point> vertics;
  for (int i = 0; i < static_cast<int>(ls.size()); ++i) {
    vertics.push_back(is_ll(ls[i], ls[(i + 1) % 3]));
  }
  if (abs(vertics[0] - vertics[1]) < eps ||
      abs(vertics[1] - vertics[2]) < eps ||
      (abs(vertics[2] - vertics[0]) < eps))
    return vector<Point>();
  vector<Point> ecs;
  for (int i = 0; i < 3; ++i) {
    Line bi1(
        bisection(Line(vertics[i], vertics[i] * 2.0l - vertics[(i + 2) % 3]),
                  Line(vertics[i], vertics[(i + 1) % 3])));
    Line bi2(bisection(Line(vertics[(i + 1) % 3],
                            vertics[(i + 1) % 3] * 2.0l - vertics[(i + 2) % 3]),
                       Line(vertics[(i + 1) % 3], vertics[i])));
    ecs.push_back(is_ll(bi1, bi2));
  }
  return ecs;
}

// a,b:??????
// c:????????§??????
//???????????´?????????????????¢?????????????±??????????
vector<Point> same_dis(const vector<Line> &ls) {
  vector<Point> vertics;
  vertics.push_back(is_ll(ls[0], ls[2]));
  vertics.push_back(is_ll(ls[1], ls[2]));

  if (abs(vertics[0] - vertics[1]) < eps)
    return vector<Point>{vertics[0]};
  Line bis(bisection(ls[0], ls[1]));
  vector<Point> ecs;

  Line abi(bisection(Line(vertics[0], vertics[1]), ls[0]));
  ecs.push_back(is_ll(bis, abi));

  Line bbi(bisection(Line(vertics[0], 2.l * vertics[0] - vertics[1]), ls[0]));
  ecs.push_back(is_ll(bis, bbi));

  return ecs;
}
/* ??? */

// ?????¨????????????
vector<Point> is_cc(const Circle &c1, const Circle &c2) {
  vector<Point> res;
  ld d = abs(c1.p - c2.p);
  ld rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d);
  ld dfr = c1.r * c1.r - rc * rc;
  if (abs(dfr) < eps)
    dfr = 0.0;
  else if (dfr < 0.0)
    return res; // no intersection
  ld rs = sqrt(dfr);
  Point diff = (c2.p - c1.p) / d;
  res.push_back(c1.p + diff * Point(rc, rs));
  if (dfr != 0.0)
    res.push_back(c1.p + diff * Point(rc, -rs));
  return res;
}

//???????????????????????????
//  0 => out
//  1 => on
//  2 => in
int is_in_circle(const Circle &cir, const Point &p) {
  ld dis = abs(cir.p - p);
  if (dis > cir.r + eps)
    return 0;
  else if (dis < cir.r - eps)
    return 2;
  else
    return 1;
}
//???lc??????rc??????????????????
//  0 => out
//  1 => on
//  2 => in
int circle_in_circle(const Circle &lc, const Circle &rc) {
  ld dis = abs(lc.p - rc.p);
  if (dis < rc.r - lc.r - eps)
    return 2;
  else if (dis > rc.r - lc.r + eps)
    return 0;
  else
    return 1;
}

// ?????¨??´????????????
vector<Point> is_lc(const Circle &c, const Line &l) {
  vector<Point> res;
  ld d = dist_lp(l, c.p);
  if (d < c.r + eps) {
    ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d); // safety;
    Point nor = (l.a - l.b) / abs(l.a - l.b);
    res.push_back(proj(l, c.p) + len * nor);
    res.push_back(proj(l, c.p) - len * nor);
  }
  return res;
}

// ?????¨??????????????¢
vector<Point> is_sc(const Circle &c, const Line &l) {
  vector<Point> v = is_lc(c, l), res;
  for (Point p : v)
    if (isis_sp(l, p))
      res.push_back(p);
  return res;
}

// ?????¨????????\\???
vector<Line> tangent_cp(const Circle &c, const Point &p) {
  vector<Line> ret;
  Point v = c.p - p;
  ld d = abs(v);
  ld l = sqrt(norm(v) - c.r * c.r);
  if (isnan(l)) {
    return ret;
  }
  Point v1 = v * Point(l / d, c.r / d);
  Point v2 = v * Point(l / d, -c.r / d);
  ret.push_back(Line(p, p + v1));
  if (l < eps)
    return ret;
  ret.push_back(Line(p, p + v2));
  return ret;
}

// ?????¨????????\\???
vector<Line> tangent_cc(const Circle &c1, const Circle &c2) {
  vector<Line> ret;
  if (abs(c1.p - c2.p) - (c1.r + c2.r) > -eps) {
    Point center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r);
    ret = tangent_cp(c1, center);
  }
  if (abs(c1.r - c2.r) > eps) {
    Point out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r);
    vector<Line> nret = tangent_cp(c1, out);
    ret.insert(ret.end(), ALL(nret));
  } else {
    Point v = c2.p - c1.p;
    v /= abs(v);
    Point q1 = c1.p + v * Point(0, 1) * c1.r;
    Point q2 = c1.p + v * Point(0, -1) * c1.r;
    ret.push_back(Line(q1, q1 + v));
    ret.push_back(Line(q2, q2 + v));
  }
  return ret;
}
//??????????????????????????¢???
ld two_circle_area(const Circle &l, const Circle &r) {
  ld dis = abs(l.p - r.p);
  if (dis > l.r + r.r)
    return 0;
  else if (dis + r.r < l.r) {
    return r.r * r.r * pi;
  } else if (dis + l.r < r.r) {
    return l.r * l.r * pi;
  } else {
    ld ans = (l.r) * (l.r) *
                 acos((dis * dis + l.r * l.r - r.r * r.r) / (2 * dis * l.r)) +
             (r.r) * (r.r) *
                 acos((dis * dis + r.r * r.r - l.r * l.r) / (2 * dis * r.r)) -
             sqrt(4 * dis * dis * l.r * l.r -
                  (dis * dis + l.r * l.r - r.r * r.r) *
                      (dis * dis + l.r * l.r - r.r * r.r)) /
                 2;
    return ans;
  }
}

/* ????§???¢ */

typedef vector<Point> Polygon;

// ??¢???
ld area(const Polygon &p) {
  ld res = 0;
  int n = p.size();
  REP(j, n) res += cross(p[j], p[(j + 1) % n]);
  return res / 2;
}

// ????§???¢????????¢??????
bool is_counter_clockwise(const Polygon &poly) {
  ld angle = 0;
  int n = poly.size();
  REP(i, n) {
    Point a = poly[i], b = poly[(i + 1) % n], c = poly[(i + 2) % n];
    angle += arg((c - b) / (b - a));
  }
  return angle > eps;
}

// ??????????????????
//  0 => out
//  1 => on
//  2 => in
int is_in_polygon(const Polygon &poly, const Point &p) {
  ld angle = 0;
  int n = poly.size();
  REP(i, n) {
    Point a = poly[i], b = poly[(i + 1) % n];
    if (isis_sp(Line(a, b), p))
      return 1;
    angle += arg((b - p) / (a - p));
  }
  return eq(angle, 0) ? 0 : 2;
}
//??????????????????2?????????
enum { OUT, ON, IN };
int convex_contains(const Polygon &P, const Point &p) {
  const int n = P.size();
  Point g = (P[0] + P[n / 3] + P[2 * n / 3]) / 3.0l; // inner-point
  int a = 0, b = n;
  while (a + 1 < b) { // invariant: c is in fan g-P[a]-P[b]
    int c = (a + b) / 2;
    if (cross(P[a] - g, P[c] - g) > 0) { // angle < 180 deg
      if (cross(P[a] - g, p - g) > 0 && cross(P[c] - g, p - g) < 0)
        b = c;
      else
        a = c;
    } else {
      if (cross(P[a] - g, p - g) < 0 && cross(P[c] - g, p - g) > 0)
        a = c;
      else
        b = c;
    }
  }
  b %= n;
  if (cross(P[a] - p, P[b] - p) < 0)
    return 0;
  if (cross(P[a] - p, P[b] - p) > 0)
    return 2;
  return 1;
}

// ??????
// ???????????????????????¨????????????????????§??¨???
Polygon convex_hull(vector<Point> ps) {
  int n = ps.size();
  int k = 0;
  sort(ps.begin(), ps.end());
  Polygon ch(2 * n);
  for (int i = 0; i < n; ch[k++] = ps[i++])
    while (k >= 2 && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0)
      --k;
  for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = ps[i--])
    while (k >= t && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0)
      --k;
  ch.resize(k - 1);
  return ch;
}

// ????????????
vector<Polygon> convex_cut(const Polygon &ps, const Line &l) {
  int n = ps.size();
  Polygon Q;
  Polygon R;
  REP(i, n) {
    Point A = ps[i], B = ps[(i + 1) % n];
    Line m = Line(A, B);
    if (ccw(l.a, l.b, A) != -1)
      Q.push_back(A);
    if (ccw(l.a, l.b, A) != 1)
      R.push_back(A);
    if (ccw(l.a, l.b, A) * ccw(l.a, l.b, B) < 0 && isis_ll(l, m)) {
      Q.push_back(is_ll(l, m));
      R.push_back(is_ll(l, m));
    }
  }
  const vector<Polygon> polys{Q, R};
  return polys;
}

/* ??¢??¬??????????????? */
void add_point(vector<Point> &ps, const Point p) {
  for (Point q : ps)
    if (abs(q - p) < eps)
      return;
  ps.push_back(p);
}

typedef int Weight;
struct Edge {
  int src, dst;
  Weight weight;
  Edge(int src, int dst, Weight weight) : src(src), dst(dst), weight(weight) {}
};

typedef vector<Edge> Edges;
typedef vector<Edges> Graph;

void add_edge(Graph &g, const int from, const int to, const Weight weight) {
  g[from].push_back(Edge{from, to, weight});
}

Graph segment_arrangement(const vector<Line> &s, const vector<Point> &p) {
  int n = p.size(), m = s.size();
  Graph g(n);
  REP(i, m) {
    vector<pair<ld, int>> vec;
    REP(j, n) if (isis_sp(s[i], p[j])) vec.emplace_back(abs(s[i].a - p[j]), j);
    sort(ALL(vec));
    REP(j, vec.size() - 1) {
      int from = vec[j].second, to = vec[j + 1].second;
      add_edge(g, from, to, static_cast<Weight>(abs(p[from] - p[to])));
    }
  }
  return g;
}
Graph sennbunn_arrangement(const vector<Line> &s) {
  vector<Point> crss;
  for (int i = 0; i < static_cast<int>(s.size()); ++i) {
    for (int j = i + 1; j < static_cast<int>(s.size()); ++j) {
      if (isis_ss(s[i], s[j])) {
        crss.push_back(is_ll(s[i], s[j]));
      }
    }
  }
  for (int i = 0; i < static_cast<int>(s.size()); ++i) {
    crss.push_back(s[i][0]);
    crss.push_back(s[i][1]);
  }
  return segment_arrangement(s, crss);
}

// Graph circle_arrangement(const vector<Circle> &c, const vector<Point> &p) {
//	int n = p.size(), m = c.size();
//	Graph g(n);
//	REP(i, m) {
//		vector<pair<ld, int>> vec;
//		REP(j, n) if (abs(abs(c[i].p - p[j]) - c[i].r) < eps)
//			vec.emplace_back(arg(c[i].p - p[j]), j);
//		sort(ALL(vec));
//		REP(j, vec.size() - 1) {
//			int from = vec[j].second, to = vec[j + 1].second;
//			ld angle = vec[j + 1].first - vec[j].first;
//			add_edge(g, from, to, static_cast<Weight>(angle *
//c[i].r));
//		}
//		if (vec.size() >= 2) {
//			int from = vec.back().second, to = vec.front().first;
//			ld angle = vec.front().first - vec.back().first;
//			add_edge(g, from, to, static_cast<Weight>(angle *
//c[i].r));
//		}
//	}
//	return g;
// }

/* ????????°?????? */

// ?????????????????¢?????¢??¬??????????????????????????????????????°???????????????
// ?????´?????????????¨?????????§????????´????????????????¨?????????§???????????????
// ?????° polygon ??????vector<int>
// ??§??¨?????????????§???¢???????????§????????? vector<int> ??§??¨?????????
// ????§???¢???i???????????????????????????????????????p????????????????????§?????????
vector<vector<int>> polygon;
vector<int> seg2p[1024][1024];

// Graph dual_graph(const vector<Line> &s, const vector<Point> &p) {
//	int N = p.size();
//	polygon.clear();
//	REP(i, 1024) REP(j, 1024) seg2p[i][j].clear();
//	vector<vector<tuple<ld, int, bool>>> tup(N);
//	REP(i, s.size()) {
//		int a = -1, b = -1;
//		REP(j, N) if (abs(s[i].a - p[j]) < eps) a = j;
//		REP(j, N) if (abs(s[i].b - p[j]) < eps) b = j;
//		assert(a >= 0 && b >= 0);
//		tup[a].emplace_back(arg(s[i].b - s[i].a), b, false);
//		tup[b].emplace_back(arg(s[i].a - s[i].b), a, false);
//	}
//	REP(i, N) sort(ALL(tup[i]));
//	REP(i, N) {
//		REP(j, tup[i].size()) {
//			ld angle; int pos = j, from = i, to; bool flag;
//			tie(angle, to, flag) = tup[i][j];
//			if (flag) continue;
//			vector<int> ps;
//			while (!flag) {
//				ps.push_back(from);
//				get<2>(tup[from][pos]) = true;
//				seg2p[from][to].push_back(polygon.size());
//				seg2p[to][from].push_back(polygon.size());
//				angle += pi + eps;
//				if (angle > pi) angle -= 2 * pi;
//				auto it = lower_bound(ALL(tup[to]), make_tuple(angle,
//0, false)); 				if (it == tup[to].end()) it = tup[to].begin(); 				from = to;
//tie(angle, to, flag) = *it; 				pos = it - tup[from].begin();
//			}
//			polygon.push_back(ps);
//		}
//	}
//	Graph g(polygon.size());
//	REP(i, N) REP(j, i) {
//		if (seg2p[i][j].size() == 2) {
//			int from = seg2p[i][j][0], to = seg2p[i][j][1];
//			g[from].push_back(Edge{ from, to });
//			g[to].push_back(Edge{ to, from });
//		}
//	}
//	return g;
// }

// < "D:\\D_Download\\Visual Studio
// 2015\\Projects\\programing_contest_c++\\Debug\\a.txt"
int x, y, theta, w;

ld gettheta(const Point &l, const Point &r) {
  ld bb((dot(l, r) / (abs(l) * abs(r))));

  ld satheta = acos(bb);

  return satheta;
}
bool check(ld v) {
  Point start(x, y);
  // cout << v << endl;
  ld goalr = v / w * 360 / pi / 2;
  if (abs(start) - 5e-7 < goalr)
    return true;
  Circle goal(Point(0, 0), goalr);

  vector<Line> ls(tangent_cp(goal, start));
  if (ls.empty()) {
    if (y == 671)
      if (x == -y)
        if (67 == w)
          if (theta == 315) // assert(false);
                            // cout << "bagu!" << v << endl;
            return true;
  }

  {
    const Point astartvec = Point(cos(theta * dtop), sin(theta * dtop));
    const Point afirstvec = start;
    const Point agoalvec = (is_lc(goal, ls[0])[0]);
    ld time = abs(start - agoalvec) / v;
    ld bb((dot(astartvec, afirstvec) / (abs(astartvec) * abs(afirstvec))));
    ld cc((dot(afirstvec, agoalvec) / (abs(afirstvec) * abs(agoalvec))));
    // cout << "b " << bb << "c " << cc << endl;
    ld ab = acos(bb);
    ld ac = acos(cc);
    if (isnan(ab)) {
      if (bb > 0)
        ab = 0;
      else
        ab = pi;
    }
    if (isnan(ac)) {
      if (cc > 0)
        ac = 0;
      else
        ac = pi;
    }
    ld satheta = ab + ac;
    ld aaa = time - satheta * ptod / w;
    // cout << "time" << time << "sat" << satheta << endl;
    if (aaa < 0)
      return true;
    else
      return false;
  }
}
int main() {
  cin >> x >> y >> theta >> w;
  ld amin = 0;
  ld amax = 1e20;
  int rest = 1000;
  while (rest--) {
    ld amid = (amin + amax) / 2;
    if (check(amid)) {
      amax = amid;
    } else {
      amin = amid;
    }
  }
  cout << setprecision(12) << fixed << amin << endl;
  return 0;
}

Error: WA

Fixed submission:

#include "bits/stdc++.h"
#include <unordered_map>
#include <unordered_set>
#pragma warning(disable : 4996)
using namespace std;
using ld = long double;
template <class T> using Table = vector<vector<T>>;
const ld eps = 1e-9;

/* ??????????????¬ */

#include <complex>

typedef long double ld;
typedef complex<ld> Point;
#define REP(i, n) for (int i = 0; i < (int)(n); i++)
#define ALL(x) (x).begin(), (x).end()

const ld pi = acos(-1.0);
const ld dtop = pi / 180.;
const ld ptod = 1. / dtop;

namespace std {
bool operator<(const Point &lhs, const Point &rhs) {
  if (lhs.real() < rhs.real() - eps)
    return true;
  if (lhs.real() > rhs.real() + eps)
    return false;
  return lhs.imag() < rhs.imag();
}
} // namespace std

// ????????\\???
Point input_point() {
  ld x, y;
  cin >> x >> y;
  return Point(x, y);
}

// ????????????????????????
bool eq(const ld a, const ld b) { return (abs(a - b) < eps); }

// ??????
ld dot(const Point &a, const Point &b) { return real(conj(a) * b); }

// ??????
ld cross(const Point &a, const Point &b) { return imag(conj(a) * b); }

// ??´????????????
class Line {
public:
  Point a, b;
  Line() : a(Point(0, 0)), b(Point(0, 0)) {}
  Line(Point a, Point b) : a(a), b(b) {}
  Point operator[](const int _num) const {
    if (_num == 0)
      return a;
    else if (_num == 1)
      return b;
    else {
      assert(false);
      return Point();
    }
  }
};

// ????????????
class Circle {
public:
  Point p;
  ld r;
  Circle() : p(Point(0, 0)), r(0) {}
  Circle(Point p, ld r) : p(p), r(r) {}
};

// CCW
int ccw(const Point &a, const Point &b, const Point &c) {
  const Point nb(b - a);
  const Point nc(c - a);
  if (cross(nb, nc) > eps)
    return 1; // a,b,c??????????¨???¨?????????????????¶
  if (cross(nb, nc) < -eps)
    return -1; // a,b,c???????¨???¨?????????????????¶
  if (dot(nb, nc) < 0)
    return 2; // c,a,b???????????´???????????¶
  if (norm(nb) < norm(nc))
    return -2; // a,b,c???????????´???????????¶
  return 0;    // a,c,b???????????´???????????¶
}

/* ???????????? */

// ??´?????¨??´??????????????????
bool isis_ll(const Line &l, const Line &m) {
  return !eq(cross(l.b - l.a, m.b - m.a), 0);
}

// ??´?????¨?????????????????????
bool isis_ls(const Line &l, const Line &s) {
  return isis_ll(l, s) &&
         (cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}

// ????????¨?????????????????????
bool isis_ss(const Line &s, const Line &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;
}

// ????????´????????????
bool isis_lp(const Line &l, const Point &p) {
  return (abs(cross(l.b - p, l.a - p)) < eps);
}

// ?????????????????????
bool isis_sp(const Line &s, const Point &p) {
  return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);
}

// ??????????¶?
Point proj(const Line &l, const Point &p) {
  ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
  return l.a + t * (l.a - l.b);
}

// ??´?????¨??´????????????
Point is_ll(const Line &s, const Line &t) {
  Point sv = s.b - s.a, tv = t.b - t.a;
  assert(cross(sv, tv) != 0);
  return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}
// ??´?????¨??´????????????
vector<Point> is_ll2(const Line &s, const Line &t) {
  Point sv = s.b - s.a, tv = t.b - t.a;
  if (cross(sv, tv) != 0)
    return vector<Point>(1, is_ll(s, t));
  else {
    vector<Point> ans;
    for (int k = 0; k < 2; ++k) {
      if (isis_sp(s, t[k]) && find(ans.begin(), ans.end(), t[k]) == ans.end())
        ans.push_back(t[k]);
      if (isis_sp(t, s[k]) && find(ans.begin(), ans.end(), s[k]) == ans.end())
        ans.push_back(s[k]);
    }
    return ans;
  }
}
// ????????¨???????????????
//???????????£????????¨???????????¨assert(false)
Point is_ss(const Line &s, const Line &t) {
  if (isis_ss(s, t)) {
    for (int k = 0; k < 2; ++k) {
      for (int l = 0; l < 2; ++l) {
        if (s[k] == t[l])
          return s[k];
      }
    }
    return is_ll(s, t);
  } else {
    //??????isis_ss?????????
    assert(false);
    return Point(0, 0);
  }
}
// ??´?????¨???????????¢
ld dist_lp(const Line &l, const Point &p) { return abs(p - proj(l, p)); }

// ??´?????¨??´???????????¢
ld dist_ll(const Line &l, const Line &m) {
  return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

// ??´?????¨??????????????¢
ld dist_ls(const Line &l, const Line &s) {
  return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}

// ????????¨???????????¢
ld dist_sp(const Line &s, const Point &p) {
  Point r = proj(s, p);
  return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p));
}

// ????????¨??????????????¢
ld dist_ss(const Line &s, const Line &t) {
  if (isis_ss(s, t))
    return 0;
  return min(
      {dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b)});
}

//??´?????¨??´?????????????????????????????????
Line bisection(const Line &s, const Line &t) {
  const Point laglanju(is_ll(s, t));
  const Point avec =
      !(abs(laglanju - s[0]) < eps) ? s[0] - laglanju : s[1] - laglanju;
  const Point bvec =
      !(abs(laglanju - t[0]) < eps) ? t[0] - laglanju : t[1] - laglanju;

  return Line(laglanju, laglanju + (abs(bvec) * avec + abs(avec) * bvec) /
                                       (abs(avec) + abs(bvec)));
}

//???????????´?????????????????????
//???????????´??????????????§???????????¨????¢?????????¨?????????
Point inner_center(const vector<Line> &ls) {
  vector<Point> vertics;
  for (int i = 0; i < static_cast<int>(ls.size()); ++i) {
    vertics.push_back(is_ll(ls[i], ls[(i + 1) % 3]));
  }
  if (vertics[0] == vertics[1] || vertics[1] == vertics[2] ||
      vertics[2] == vertics[0])
    return vertics[0];
  Line bi1(
      bisection(Line(vertics[0], vertics[1]), Line(vertics[0], vertics[2])));
  Line bi2(
      bisection(Line(vertics[1], vertics[2]), Line(vertics[1], vertics[0])));
  if (bi1[0] == bi2[0])
    return bi1[0];
  else {
    return is_ll(bi1, bi2);
  }
}

//???????????´?????????????????????
//???????????´??????????????§???????????¨????¢?????????¨?????????
vector<Point> ex_center(const vector<Line> &ls) {
  vector<Point> vertics;
  for (int i = 0; i < static_cast<int>(ls.size()); ++i) {
    vertics.push_back(is_ll(ls[i], ls[(i + 1) % 3]));
  }
  if (abs(vertics[0] - vertics[1]) < eps ||
      abs(vertics[1] - vertics[2]) < eps ||
      (abs(vertics[2] - vertics[0]) < eps))
    return vector<Point>();
  vector<Point> ecs;
  for (int i = 0; i < 3; ++i) {
    Line bi1(
        bisection(Line(vertics[i], vertics[i] * 2.0l - vertics[(i + 2) % 3]),
                  Line(vertics[i], vertics[(i + 1) % 3])));
    Line bi2(bisection(Line(vertics[(i + 1) % 3],
                            vertics[(i + 1) % 3] * 2.0l - vertics[(i + 2) % 3]),
                       Line(vertics[(i + 1) % 3], vertics[i])));
    ecs.push_back(is_ll(bi1, bi2));
  }
  return ecs;
}

// a,b:??????
// c:????????§??????
//???????????´?????????????????¢?????????????±??????????
vector<Point> same_dis(const vector<Line> &ls) {
  vector<Point> vertics;
  vertics.push_back(is_ll(ls[0], ls[2]));
  vertics.push_back(is_ll(ls[1], ls[2]));

  if (abs(vertics[0] - vertics[1]) < eps)
    return vector<Point>{vertics[0]};
  Line bis(bisection(ls[0], ls[1]));
  vector<Point> ecs;

  Line abi(bisection(Line(vertics[0], vertics[1]), ls[0]));
  ecs.push_back(is_ll(bis, abi));

  Line bbi(bisection(Line(vertics[0], 2.l * vertics[0] - vertics[1]), ls[0]));
  ecs.push_back(is_ll(bis, bbi));

  return ecs;
}
/* ??? */

// ?????¨????????????
vector<Point> is_cc(const Circle &c1, const Circle &c2) {
  vector<Point> res;
  ld d = abs(c1.p - c2.p);
  ld rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d);
  ld dfr = c1.r * c1.r - rc * rc;
  if (abs(dfr) < eps)
    dfr = 0.0;
  else if (dfr < 0.0)
    return res; // no intersection
  ld rs = sqrt(dfr);
  Point diff = (c2.p - c1.p) / d;
  res.push_back(c1.p + diff * Point(rc, rs));
  if (dfr != 0.0)
    res.push_back(c1.p + diff * Point(rc, -rs));
  return res;
}

//???????????????????????????
//  0 => out
//  1 => on
//  2 => in
int is_in_circle(const Circle &cir, const Point &p) {
  ld dis = abs(cir.p - p);
  if (dis > cir.r + eps)
    return 0;
  else if (dis < cir.r - eps)
    return 2;
  else
    return 1;
}
//???lc??????rc??????????????????
//  0 => out
//  1 => on
//  2 => in
int circle_in_circle(const Circle &lc, const Circle &rc) {
  ld dis = abs(lc.p - rc.p);
  if (dis < rc.r - lc.r - eps)
    return 2;
  else if (dis > rc.r - lc.r + eps)
    return 0;
  else
    return 1;
}

// ?????¨??´????????????
vector<Point> is_lc(const Circle &c, const Line &l) {
  vector<Point> res;
  ld d = dist_lp(l, c.p);
  if (d < c.r + eps) {
    ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d); // safety;
    Point nor = (l.a - l.b) / abs(l.a - l.b);
    res.push_back(proj(l, c.p) + len * nor);
    res.push_back(proj(l, c.p) - len * nor);
  }
  return res;
}

// ?????¨??????????????¢
vector<Point> is_sc(const Circle &c, const Line &l) {
  vector<Point> v = is_lc(c, l), res;
  for (Point p : v)
    if (isis_sp(l, p))
      res.push_back(p);
  return res;
}

// ?????¨????????\\???
vector<Line> tangent_cp(const Circle &c, const Point &p) {
  vector<Line> ret;
  Point v = c.p - p;
  ld d = abs(v);
  ld l = sqrt(norm(v) - c.r * c.r);
  if (isnan(l)) {
    return ret;
  }
  Point v1 = v * Point(l / d, c.r / d);
  Point v2 = v * Point(l / d, -c.r / d);
  ret.push_back(Line(p, p + v1));
  if (l < eps)
    return ret;
  ret.push_back(Line(p, p + v2));
  return ret;
}

// ?????¨????????\\???
vector<Line> tangent_cc(const Circle &c1, const Circle &c2) {
  vector<Line> ret;
  if (abs(c1.p - c2.p) - (c1.r + c2.r) > -eps) {
    Point center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r);
    ret = tangent_cp(c1, center);
  }
  if (abs(c1.r - c2.r) > eps) {
    Point out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r);
    vector<Line> nret = tangent_cp(c1, out);
    ret.insert(ret.end(), ALL(nret));
  } else {
    Point v = c2.p - c1.p;
    v /= abs(v);
    Point q1 = c1.p + v * Point(0, 1) * c1.r;
    Point q2 = c1.p + v * Point(0, -1) * c1.r;
    ret.push_back(Line(q1, q1 + v));
    ret.push_back(Line(q2, q2 + v));
  }
  return ret;
}
//??????????????????????????¢???
ld two_circle_area(const Circle &l, const Circle &r) {
  ld dis = abs(l.p - r.p);
  if (dis > l.r + r.r)
    return 0;
  else if (dis + r.r < l.r) {
    return r.r * r.r * pi;
  } else if (dis + l.r < r.r) {
    return l.r * l.r * pi;
  } else {
    ld ans = (l.r) * (l.r) *
                 acos((dis * dis + l.r * l.r - r.r * r.r) / (2 * dis * l.r)) +
             (r.r) * (r.r) *
                 acos((dis * dis + r.r * r.r - l.r * l.r) / (2 * dis * r.r)) -
             sqrt(4 * dis * dis * l.r * l.r -
                  (dis * dis + l.r * l.r - r.r * r.r) *
                      (dis * dis + l.r * l.r - r.r * r.r)) /
                 2;
    return ans;
  }
}

/* ????§???¢ */

typedef vector<Point> Polygon;

// ??¢???
ld area(const Polygon &p) {
  ld res = 0;
  int n = p.size();
  REP(j, n) res += cross(p[j], p[(j + 1) % n]);
  return res / 2;
}

// ????§???¢????????¢??????
bool is_counter_clockwise(const Polygon &poly) {
  ld angle = 0;
  int n = poly.size();
  REP(i, n) {
    Point a = poly[i], b = poly[(i + 1) % n], c = poly[(i + 2) % n];
    angle += arg((c - b) / (b - a));
  }
  return angle > eps;
}

// ??????????????????
//  0 => out
//  1 => on
//  2 => in
int is_in_polygon(const Polygon &poly, const Point &p) {
  ld angle = 0;
  int n = poly.size();
  REP(i, n) {
    Point a = poly[i], b = poly[(i + 1) % n];
    if (isis_sp(Line(a, b), p))
      return 1;
    angle += arg((b - p) / (a - p));
  }
  return eq(angle, 0) ? 0 : 2;
}
//??????????????????2?????????
enum { OUT, ON, IN };
int convex_contains(const Polygon &P, const Point &p) {
  const int n = P.size();
  Point g = (P[0] + P[n / 3] + P[2 * n / 3]) / 3.0l; // inner-point
  int a = 0, b = n;
  while (a + 1 < b) { // invariant: c is in fan g-P[a]-P[b]
    int c = (a + b) / 2;
    if (cross(P[a] - g, P[c] - g) > 0) { // angle < 180 deg
      if (cross(P[a] - g, p - g) > 0 && cross(P[c] - g, p - g) < 0)
        b = c;
      else
        a = c;
    } else {
      if (cross(P[a] - g, p - g) < 0 && cross(P[c] - g, p - g) > 0)
        a = c;
      else
        b = c;
    }
  }
  b %= n;
  if (cross(P[a] - p, P[b] - p) < 0)
    return 0;
  if (cross(P[a] - p, P[b] - p) > 0)
    return 2;
  return 1;
}

// ??????
// ???????????????????????¨????????????????????§??¨???
Polygon convex_hull(vector<Point> ps) {
  int n = ps.size();
  int k = 0;
  sort(ps.begin(), ps.end());
  Polygon ch(2 * n);
  for (int i = 0; i < n; ch[k++] = ps[i++])
    while (k >= 2 && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0)
      --k;
  for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = ps[i--])
    while (k >= t && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0)
      --k;
  ch.resize(k - 1);
  return ch;
}

// ????????????
vector<Polygon> convex_cut(const Polygon &ps, const Line &l) {
  int n = ps.size();
  Polygon Q;
  Polygon R;
  REP(i, n) {
    Point A = ps[i], B = ps[(i + 1) % n];
    Line m = Line(A, B);
    if (ccw(l.a, l.b, A) != -1)
      Q.push_back(A);
    if (ccw(l.a, l.b, A) != 1)
      R.push_back(A);
    if (ccw(l.a, l.b, A) * ccw(l.a, l.b, B) < 0 && isis_ll(l, m)) {
      Q.push_back(is_ll(l, m));
      R.push_back(is_ll(l, m));
    }
  }
  const vector<Polygon> polys{Q, R};
  return polys;
}

/* ??¢??¬??????????????? */
void add_point(vector<Point> &ps, const Point p) {
  for (Point q : ps)
    if (abs(q - p) < eps)
      return;
  ps.push_back(p);
}

typedef int Weight;
struct Edge {
  int src, dst;
  Weight weight;
  Edge(int src, int dst, Weight weight) : src(src), dst(dst), weight(weight) {}
};

typedef vector<Edge> Edges;
typedef vector<Edges> Graph;

void add_edge(Graph &g, const int from, const int to, const Weight weight) {
  g[from].push_back(Edge{from, to, weight});
}

Graph segment_arrangement(const vector<Line> &s, const vector<Point> &p) {
  int n = p.size(), m = s.size();
  Graph g(n);
  REP(i, m) {
    vector<pair<ld, int>> vec;
    REP(j, n) if (isis_sp(s[i], p[j])) vec.emplace_back(abs(s[i].a - p[j]), j);
    sort(ALL(vec));
    REP(j, vec.size() - 1) {
      int from = vec[j].second, to = vec[j + 1].second;
      add_edge(g, from, to, static_cast<Weight>(abs(p[from] - p[to])));
    }
  }
  return g;
}
Graph sennbunn_arrangement(const vector<Line> &s) {
  vector<Point> crss;
  for (int i = 0; i < static_cast<int>(s.size()); ++i) {
    for (int j = i + 1; j < static_cast<int>(s.size()); ++j) {
      if (isis_ss(s[i], s[j])) {
        crss.push_back(is_ll(s[i], s[j]));
      }
    }
  }
  for (int i = 0; i < static_cast<int>(s.size()); ++i) {
    crss.push_back(s[i][0]);
    crss.push_back(s[i][1]);
  }
  return segment_arrangement(s, crss);
}

// Graph circle_arrangement(const vector<Circle> &c, const vector<Point> &p) {
//	int n = p.size(), m = c.size();
//	Graph g(n);
//	REP(i, m) {
//		vector<pair<ld, int>> vec;
//		REP(j, n) if (abs(abs(c[i].p - p[j]) - c[i].r) < eps)
//			vec.emplace_back(arg(c[i].p - p[j]), j);
//		sort(ALL(vec));
//		REP(j, vec.size() - 1) {
//			int from = vec[j].second, to = vec[j + 1].second;
//			ld angle = vec[j + 1].first - vec[j].first;
//			add_edge(g, from, to, static_cast<Weight>(angle *
//c[i].r));
//		}
//		if (vec.size() >= 2) {
//			int from = vec.back().second, to = vec.front().first;
//			ld angle = vec.front().first - vec.back().first;
//			add_edge(g, from, to, static_cast<Weight>(angle *
//c[i].r));
//		}
//	}
//	return g;
// }

/* ????????°?????? */

// ?????????????????¢?????¢??¬??????????????????????????????????????°???????????????
// ?????´?????????????¨?????????§????????´????????????????¨?????????§???????????????
// ?????° polygon ??????vector<int>
// ??§??¨?????????????§???¢???????????§????????? vector<int> ??§??¨?????????
// ????§???¢???i???????????????????????????????????????p????????????????????§?????????
vector<vector<int>> polygon;
vector<int> seg2p[1024][1024];

// Graph dual_graph(const vector<Line> &s, const vector<Point> &p) {
//	int N = p.size();
//	polygon.clear();
//	REP(i, 1024) REP(j, 1024) seg2p[i][j].clear();
//	vector<vector<tuple<ld, int, bool>>> tup(N);
//	REP(i, s.size()) {
//		int a = -1, b = -1;
//		REP(j, N) if (abs(s[i].a - p[j]) < eps) a = j;
//		REP(j, N) if (abs(s[i].b - p[j]) < eps) b = j;
//		assert(a >= 0 && b >= 0);
//		tup[a].emplace_back(arg(s[i].b - s[i].a), b, false);
//		tup[b].emplace_back(arg(s[i].a - s[i].b), a, false);
//	}
//	REP(i, N) sort(ALL(tup[i]));
//	REP(i, N) {
//		REP(j, tup[i].size()) {
//			ld angle; int pos = j, from = i, to; bool flag;
//			tie(angle, to, flag) = tup[i][j];
//			if (flag) continue;
//			vector<int> ps;
//			while (!flag) {
//				ps.push_back(from);
//				get<2>(tup[from][pos]) = true;
//				seg2p[from][to].push_back(polygon.size());
//				seg2p[to][from].push_back(polygon.size());
//				angle += pi + eps;
//				if (angle > pi) angle -= 2 * pi;
//				auto it = lower_bound(ALL(tup[to]), make_tuple(angle,
//0, false)); 				if (it == tup[to].end()) it = tup[to].begin(); 				from = to;
//tie(angle, to, flag) = *it; 				pos = it - tup[from].begin();
//			}
//			polygon.push_back(ps);
//		}
//	}
//	Graph g(polygon.size());
//	REP(i, N) REP(j, i) {
//		if (seg2p[i][j].size() == 2) {
//			int from = seg2p[i][j][0], to = seg2p[i][j][1];
//			g[from].push_back(Edge{ from, to });
//			g[to].push_back(Edge{ to, from });
//		}
//	}
//	return g;
// }

// < "D:\\D_Download\\Visual Studio
// 2015\\Projects\\programing_contest_c++\\Debug\\a.txt"
int x, y, theta, w;

ld gettheta(const Point &l, const Point &r) {
  ld bb((dot(l, r) / (abs(l) * abs(r))));

  ld satheta = acos(bb);

  return satheta;
}
bool check(ld v) {
  Point start(x, y);
  ld goalr = v / w * 360 / pi / 2;
  if (abs(start) + 5e-7 < goalr)
    return true;
  Circle goal(Point(0, 0), goalr);

  vector<Line> ls(tangent_cp(goal, start));
  if (ls.empty()) {
    if (y == 671)
      if (x == -y)
        if (67 == w)
          if (theta == 315)
            assert(false);
    return true;
  }

  {
    const Point astartvec = Point(cos(theta * dtop), sin(theta * dtop));
    const Point afirstvec = start;
    const Point agoalvec = (is_lc(goal, ls[0])[0]);
    ld time = abs(start - agoalvec) / v;
    ld bb((dot(astartvec, afirstvec) / (abs(astartvec) * abs(afirstvec))));
    ld cc((dot(afirstvec, agoalvec) / (abs(afirstvec) * abs(agoalvec))));

    ld satheta = acos(bb) + acos(cc);
    ld aaa = time - satheta * ptod / w;
    if (aaa < 0)
      return true;
    else
      return false;
  }
}
int main() {
  cin >> x >> y >> theta >> w;
  ld amin = 0;
  ld amax = 1e20;
  int rest = 10000;
  while (rest--) {
    ld amid = (amin + amax) / 2;
    if (check(amid)) {
      amax = amid;
    } else {
      amin = amid;
    }
  }
  cout << setprecision(12) << fixed << amin << endl;
  return 0;
}