Problem p02132 (C++) — buggy submission, verdict: Time Limit Exceeded

#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
const int INF = 1e9;
const ll LINF = 1e18;
template <class S, class T>
ostream &operator<<(ostream &out, const pair<S, T> &o) {
  out << "(" << o.first << "," << o.second << ")";
  return out;
}
template <class T> ostream &operator<<(ostream &out, const vector<T> V) {
  for (int i = 0; i < V.size(); i++) {
    out << V[i];
    if (i != V.size() - 1)
      out << " ";
  }
  return out;
}
template <class T>
ostream &operator<<(ostream &out, const vector<vector<T>> Mat) {
  for (int i = 0; i < Mat.size(); i++) {
    if (i != 0)
      out << endl;
    out << Mat[i];
  }
  return out;
}
template <class S, class T>
ostream &operator<<(ostream &out, const map<S, T> mp) {
  out << "{ ";
  for (auto it = mp.begin(); it != mp.end(); it++) {
    out << it->first << ":" << it->second;
    if (mp.size() - 1 != distance(mp.begin(), it))
      out << ", ";
  }
  out << " }";
  return out;
}

typedef long double ld;
typedef complex<ld> Point;

const ld eps = 1e-9, pi = acos(-1.0);
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);
} // 点の入力
bool eq(ld a, ld b) { return (abs(a - b) < eps); } // 誤差つき等号判定
ld dot(Point a, Point b) { return real(conj(a) * b); }   // 内積
ld cross(Point a, Point b) { return imag(conj(a) * b); } // 外積

// 直線の定義
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) {
    if (_num == 0)
      return a;
    else if (_num == 1)
      return b;
    else
      assert(false);
  }
};

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

// 垂線の足
Point proj(Line l, 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);
}

// CCW
int ccw(Point a, Point b, Point c) {
  b -= a;
  c -= a;
  if (cross(b, c) > eps)
    return 1; // a,b,cが反時計周りの順に並ぶ
  if (cross(b, c) < -eps)
    return -1; // a,b,cが時計周りの順に並ぶ
  if (dot(b, c) < 0)
    return 2; // c,a,bの順に直線に並ぶ
  if (norm(b) < norm(c))
    return -2; // a,b,cの順に直線に並ぶ
  return 0;    // a,c,bの順に直線に並ぶ
}

/* 交差判定 */
// 直線と直線の交差判定
bool isis_ll(Line l, Line m) { return !eq(cross(l.b - l.a, m.b - m.a), 0); }
// 直線と線分の交差判定
bool isis_ls(Line l, 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);
}
// 線分と線分の交差判定
bool isis_ss(Line s, 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;
}
// 点の直線上判定
bool isis_lp(Line l, Point p) { return (abs(cross(l.b - p, l.a - p)) < eps); }
// 点の線分上判定
bool isis_sp(Line s, Point p) {
  return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);
}

/* 距離 */
// 直線と直線の交点
Point is_ll(Line s, 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);
}

// 直線と点の距離
ld dist_lp(Line l, Point p) { return abs(p - proj(l, p)); }

// 直線と直線の距離
ld dist_ll(Line l, Line m) { return isis_ll(l, m) ? 0 : dist_lp(l, m.a); }

// 直線と線分の距離
ld dist_ls(Line l, Line s) {
  return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}

// 線分と点の距離
ld dist_sp(Line s, Point p) {
  Point r = proj(s, p);
  return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p));
}

// 線分と線分の距離
ld dist_ss(Line s, 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)});
}

/* 円 */
// 円と円の交点
vector<Point> is_cc(Circle c1, 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;
}
// 円と直線の交点
vector<Point> is_lc(Circle c, 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;
}
// 円と線分の距離
vector<Point> is_sc(Circle c, 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;
}
// 円と点の接線
vector<Line> tangent_cp(Circle c, 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;
}
// 円と円の接線
vector<Line> tangent_cc(Circle c1, 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(), nret.begin(), nret.end());
  } 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;
}

/* 多角形 */
typedef vector<Point> Polygon;
// 面積
ld area(const Polygon &p) {
  ld res = 0;
  int n = (int)p.size();
  for (int j = 0; j < n; j++)
    res += cross(p[j], p[(j + 1) % n]);
  return res / 2;
}
// 多角形の回転方向
bool is_counter_clockwise(const Polygon &poly) {
  ld angle = 0;
  int n = (int)poly.size();
  for (int i = 0; i < n; i++) {
    Point a = poly[i], b = poly[(i + 1) % n], c = poly[(i + 2) % n];
    angle += arg((c - b) / (b - a));
  }
  return angle > eps;
}
// 凸性判定
bool isConvex(const Polygon &poly) {
  int n = (int)poly.size();
  if (n < 3)
    return false;
  int s = -3;
  for (int i = 0; i < n; i++) {
    int r = ccw(poly[(i + n - 1) % n], poly[i % n], poly[(i + 1) % n]);
    if (r == 1 && s == -3)
      s = r;
    if (s * r == -1)
      return false;
  }
  return true;
}
// 円の内外判定
//  2 => out : 0 => on : 1 => in
int is_in_polygon(const Polygon &poly, Point p) {
  ld angle = 0;
  int n = (int)poly.size();
  for (int i = 0; i < n; i++) {
    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;
}
// 凸包 : 凸多角形のある一辺上にある点も含む
Polygon convex_hull(vector<Point> ps) {
  int n = (int)ps.size();
  if (n < 3)
    return ps;
  sort(ps.begin(), ps.end());
  Polygon u = {ps[0], ps[1]}, l = {ps[n - 1], ps[n - 2]};
  for (int i = 2; i < n; i++) {
    for (int j = (int)u.size(); j >= 2 && ccw(u[j - 2], u[j - 1], ps[i]) >= 0;
         j--)
      u.pop_back();
    u.push_back(ps[i]);
  }
  for (int i = n - 3; i >= 0; i--) {
    for (int j = (int)l.size(); j >= 2 && ccw(l[j - 2], l[j - 1], ps[i]) >= 0;
         j--)
      l.pop_back();
    l.push_back(ps[i]);
  }
  reverse(l.begin(), l.end());
  for (int i = (int)u.size() - 2; i >= 1; i--)
    l.push_back(u[i]);
  return l;
}
// 凸包 : 凸多角形のある一辺上にある点を含まない
/*
 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;
 }
 */
// 凸多角形の直径
ld convex_diameter(const Polygon &poly) {
  int n = (int)poly.size();
  int ii = 0, jj = 0;
  for (int i = 1; i < n; i++) {
    if (poly[i].imag() > poly[ii].imag())
      ii = i;
    if (poly[i].imag() < poly[jj].imag())
      jj = i;
  }
  ld res = abs(poly[ii] - poly[jj]);

  int i, maxi, j, maxj;
  i = maxi = ii;
  j = maxj = jj;
  do {
    if (cross(poly[(i + 1) % n] - poly[i], poly[(j + 1) % n] - poly[j]) >= 0)
      j = (j + 1) % n;
    else
      i = (i + 1) % n;
    if (abs(poly[i] - poly[j]) > res) {
      res = abs(poly[i] - poly[j]);
      maxi = i;
      maxj = j;
    }
  } while (i != ii || j != jj);
  return res;
}
// 凸カット
Polygon convex_cut(const Polygon &ps, Line l) {
  int n = (int)ps.size();
  Polygon Q;
  for (int i = 0; i < n; i++) {
    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) * ccw(l.a, l.b, B) < 0 && isis_ll(l, m))
      Q.push_back(is_ll(l, m));
  }
  return Q;
}

// 円と多角形の共通部分
double area_of_polygon_and_circle(const Polygon &poly, const Circle c) {
  int n = (int)poly.size();
  ld r = 0;
  for (int i = n - 1, j = 0; j < n; i = j++) {
    Point v = abs(poly[j] - poly[i]) / (poly[j] - poly[i]);
    if (poly[j] == poly[i])
      continue;
    assert(poly[j] != poly[i]);
    Point a = (poly[i] - c.p) * v, b = (poly[j] - c.p) * v;
    ld d = norm(c.r) - norm(a.imag());
    if (abs(a.imag()) < eps)
      continue;
    if (d < 0)
      d = 0;
    d = sqrt(d);
    double l, m;
    r += norm(c.r) * ((l = atan2(b.imag(), min(b.real(), -d)) -
                           atan2(a.imag(), min(a.real(), -d))) +
                      (m = atan2(b.imag(), max(b.real(), d)) -
                           atan2(a.imag(), max(a.real(), d)))) +
         a.imag() * (min(d, max(a.real(), -d)) - max(-d, min(b.real(), d)));
    assert(-pi < l && -pi < m && l < pi && m < pi);
  }
  return r / 2;
}

/*
 <url:>
 問題文============================================================

 =================================================================

 解説=============================================================

 ================================================================
 */
typedef Point P;
template <class iter>
std::pair<P, ld> min_ball(iter left, iter right, int seed = 1333) {
  const int n = right - left;

  assert(n >= 1);
  if (n == 1) {
    return {*left, ld(0)};
  }

  std::mt19937 mt(seed);
  std::shuffle(left, right, mt);
  // std::random_shuffle(left, right); // simple but deprecated

  iter ps = left;
  using circle = std::pair<P, ld>;

  auto make_circle_3 = [](const P &a, const P &b, const P &c) -> circle {
    ld A = std::norm(b - c), B = std::norm(c - a), C = std::norm(a - b),
       S = cross(b - a, c - a);
    P p = (A * (B + C - A) * a + B * (C + A - B) * b + C * (A + B - C) * c) /
          (4 * S * S);
    ld r2 = std::norm(p - a);
    return {p, r2};
  };

  auto make_circle_2 = [](const P &a, const P &b) -> circle {
    P c = (a + b) / (ld)2;
    ld r2 = std::norm(a - c);
    return {c, r2};
  };

  auto in_circle = [](const P &a, const circle &c) -> bool {
    return std::norm(a - c.first) <= c.second + eps;
  };

  circle c = make_circle_2(ps[0], ps[1]);

  // MiniDisc
  for (int i = 2; i < n; ++i) {
    if (!in_circle(ps[i], c)) {
      // MiniDiscWithPoint
      c = make_circle_2(ps[0], ps[i]);
      for (int j = 1; j < i; ++j) {
        if (!in_circle(ps[j], c)) {
          // MiniDiscWith2Points
          c = make_circle_2(ps[i], ps[j]);
          for (int k = 0; k < j; ++k) {
            if (!in_circle(ps[k], c)) {
              c = make_circle_3(ps[i], ps[j], ps[k]);
            }
          }
        }
      }
    }
  }
  return c;
}

#define MAX_N 15
#define MAX_M 15
ll N, M;
Point p[MAX_N];

// dp[S][cnt] := 死んでいる勇者がSでcnt回爆発を行なっている時の最小半径
ld dp[1 << MAX_N][MAX_M];

vector<pair<ld, ll>> St;
void init() {
  for (int i = 0; i < (1 << MAX_N); i++)
    for (int j = 0; j < MAX_M; j++)
      dp[i][j] = -1;
}

ld rec(ll S, ll cnt, int p) {
  ld &res = dp[S][cnt];
  if (S == ((1 << N) - 1))
    return 0;
  if (cnt == M)
    return LINF;
  if (!(res < 0))
    return res;
  res = LINF;
  for (int i = p; i < St.size(); i++) {
    if (S == (S | St[i].second))
      continue;
    res = min(res, max(St[i].first, rec(S | St[i].second, cnt + 1, i + 1)));
  }
  return res;
}

int main(void) {
  cin.tie(0);
  ios::sync_with_stdio(false);
  init();
  cin >> N >> M;
  for (int i = 0; i < N; i++)
    p[i] = input_point();

  // 最小包含円
  for (int i = 1; i < (1 << N); i++) {
    vector<P> tp;
    for (int j = 0; j < N; j++) {
      if ((i >> j) & 1) {
        tp.push_back(p[j]);
      }
    }
    auto c = min_ball(tp.begin(), tp.end());
    //        cout << bitset<10>(i) << " " << c << endl;
    St.push_back({sqrt(c.second), i});
  }

  cout << fixed << setprecision(12) << rec(0, 0, 0) << endl;
  return 0;
}


Error: TLE

Fixed submission:

#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
const int INF = 1e9;
const ll LINF = 1e18;
template <class S, class T>
ostream &operator<<(ostream &out, const pair<S, T> &o) {
  out << "(" << o.first << "," << o.second << ")";
  return out;
}
template <class T> ostream &operator<<(ostream &out, const vector<T> V) {
  for (int i = 0; i < V.size(); i++) {
    out << V[i];
    if (i != V.size() - 1)
      out << " ";
  }
  return out;
}
template <class T>
ostream &operator<<(ostream &out, const vector<vector<T>> Mat) {
  for (int i = 0; i < Mat.size(); i++) {
    if (i != 0)
      out << endl;
    out << Mat[i];
  }
  return out;
}
template <class S, class T>
ostream &operator<<(ostream &out, const map<S, T> mp) {
  out << "{ ";
  for (auto it = mp.begin(); it != mp.end(); it++) {
    out << it->first << ":" << it->second;
    if (mp.size() - 1 != distance(mp.begin(), it))
      out << ", ";
  }
  out << " }";
  return out;
}

typedef long double ld;
typedef complex<ld> Point;

const ld eps = 1e-9, pi = acos(-1.0);
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);
} // 点の入力
bool eq(ld a, ld b) { return (abs(a - b) < eps); } // 誤差つき等号判定
ld dot(Point a, Point b) { return real(conj(a) * b); }   // 内積
ld cross(Point a, Point b) { return imag(conj(a) * b); } // 外積

// 直線の定義
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) {
    if (_num == 0)
      return a;
    else if (_num == 1)
      return b;
    else
      assert(false);
  }
};

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

// 垂線の足
Point proj(Line l, 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);
}

// CCW
int ccw(Point a, Point b, Point c) {
  b -= a;
  c -= a;
  if (cross(b, c) > eps)
    return 1; // a,b,cが反時計周りの順に並ぶ
  if (cross(b, c) < -eps)
    return -1; // a,b,cが時計周りの順に並ぶ
  if (dot(b, c) < 0)
    return 2; // c,a,bの順に直線に並ぶ
  if (norm(b) < norm(c))
    return -2; // a,b,cの順に直線に並ぶ
  return 0;    // a,c,bの順に直線に並ぶ
}

/* 交差判定 */
// 直線と直線の交差判定
bool isis_ll(Line l, Line m) { return !eq(cross(l.b - l.a, m.b - m.a), 0); }
// 直線と線分の交差判定
bool isis_ls(Line l, 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);
}
// 線分と線分の交差判定
bool isis_ss(Line s, 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;
}
// 点の直線上判定
bool isis_lp(Line l, Point p) { return (abs(cross(l.b - p, l.a - p)) < eps); }
// 点の線分上判定
bool isis_sp(Line s, Point p) {
  return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);
}

/* 距離 */
// 直線と直線の交点
Point is_ll(Line s, 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);
}

// 直線と点の距離
ld dist_lp(Line l, Point p) { return abs(p - proj(l, p)); }

// 直線と直線の距離
ld dist_ll(Line l, Line m) { return isis_ll(l, m) ? 0 : dist_lp(l, m.a); }

// 直線と線分の距離
ld dist_ls(Line l, Line s) {
  return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}

// 線分と点の距離
ld dist_sp(Line s, Point p) {
  Point r = proj(s, p);
  return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p));
}

// 線分と線分の距離
ld dist_ss(Line s, 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)});
}

/* 円 */
// 円と円の交点
vector<Point> is_cc(Circle c1, 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;
}
// 円と直線の交点
vector<Point> is_lc(Circle c, 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;
}
// 円と線分の距離
vector<Point> is_sc(Circle c, 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;
}
// 円と点の接線
vector<Line> tangent_cp(Circle c, 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;
}
// 円と円の接線
vector<Line> tangent_cc(Circle c1, 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(), nret.begin(), nret.end());
  } 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;
}

/* 多角形 */
typedef vector<Point> Polygon;
// 面積
ld area(const Polygon &p) {
  ld res = 0;
  int n = (int)p.size();
  for (int j = 0; j < n; j++)
    res += cross(p[j], p[(j + 1) % n]);
  return res / 2;
}
// 多角形の回転方向
bool is_counter_clockwise(const Polygon &poly) {
  ld angle = 0;
  int n = (int)poly.size();
  for (int i = 0; i < n; i++) {
    Point a = poly[i], b = poly[(i + 1) % n], c = poly[(i + 2) % n];
    angle += arg((c - b) / (b - a));
  }
  return angle > eps;
}
// 凸性判定
bool isConvex(const Polygon &poly) {
  int n = (int)poly.size();
  if (n < 3)
    return false;
  int s = -3;
  for (int i = 0; i < n; i++) {
    int r = ccw(poly[(i + n - 1) % n], poly[i % n], poly[(i + 1) % n]);
    if (r == 1 && s == -3)
      s = r;
    if (s * r == -1)
      return false;
  }
  return true;
}
// 円の内外判定
//  2 => out : 0 => on : 1 => in
int is_in_polygon(const Polygon &poly, Point p) {
  ld angle = 0;
  int n = (int)poly.size();
  for (int i = 0; i < n; i++) {
    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;
}
// 凸包 : 凸多角形のある一辺上にある点も含む
Polygon convex_hull(vector<Point> ps) {
  int n = (int)ps.size();
  if (n < 3)
    return ps;
  sort(ps.begin(), ps.end());
  Polygon u = {ps[0], ps[1]}, l = {ps[n - 1], ps[n - 2]};
  for (int i = 2; i < n; i++) {
    for (int j = (int)u.size(); j >= 2 && ccw(u[j - 2], u[j - 1], ps[i]) >= 0;
         j--)
      u.pop_back();
    u.push_back(ps[i]);
  }
  for (int i = n - 3; i >= 0; i--) {
    for (int j = (int)l.size(); j >= 2 && ccw(l[j - 2], l[j - 1], ps[i]) >= 0;
         j--)
      l.pop_back();
    l.push_back(ps[i]);
  }
  reverse(l.begin(), l.end());
  for (int i = (int)u.size() - 2; i >= 1; i--)
    l.push_back(u[i]);
  return l;
}
// 凸包 : 凸多角形のある一辺上にある点を含まない
/*
 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;
 }
 */
// 凸多角形の直径
ld convex_diameter(const Polygon &poly) {
  int n = (int)poly.size();
  int ii = 0, jj = 0;
  for (int i = 1; i < n; i++) {
    if (poly[i].imag() > poly[ii].imag())
      ii = i;
    if (poly[i].imag() < poly[jj].imag())
      jj = i;
  }
  ld res = abs(poly[ii] - poly[jj]);

  int i, maxi, j, maxj;
  i = maxi = ii;
  j = maxj = jj;
  do {
    if (cross(poly[(i + 1) % n] - poly[i], poly[(j + 1) % n] - poly[j]) >= 0)
      j = (j + 1) % n;
    else
      i = (i + 1) % n;
    if (abs(poly[i] - poly[j]) > res) {
      res = abs(poly[i] - poly[j]);
      maxi = i;
      maxj = j;
    }
  } while (i != ii || j != jj);
  return res;
}
// 凸カット
Polygon convex_cut(const Polygon &ps, Line l) {
  int n = (int)ps.size();
  Polygon Q;
  for (int i = 0; i < n; i++) {
    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) * ccw(l.a, l.b, B) < 0 && isis_ll(l, m))
      Q.push_back(is_ll(l, m));
  }
  return Q;
}

// 円と多角形の共通部分
double area_of_polygon_and_circle(const Polygon &poly, const Circle c) {
  int n = (int)poly.size();
  ld r = 0;
  for (int i = n - 1, j = 0; j < n; i = j++) {
    Point v = abs(poly[j] - poly[i]) / (poly[j] - poly[i]);
    if (poly[j] == poly[i])
      continue;
    assert(poly[j] != poly[i]);
    Point a = (poly[i] - c.p) * v, b = (poly[j] - c.p) * v;
    ld d = norm(c.r) - norm(a.imag());
    if (abs(a.imag()) < eps)
      continue;
    if (d < 0)
      d = 0;
    d = sqrt(d);
    double l, m;
    r += norm(c.r) * ((l = atan2(b.imag(), min(b.real(), -d)) -
                           atan2(a.imag(), min(a.real(), -d))) +
                      (m = atan2(b.imag(), max(b.real(), d)) -
                           atan2(a.imag(), max(a.real(), d)))) +
         a.imag() * (min(d, max(a.real(), -d)) - max(-d, min(b.real(), d)));
    assert(-pi < l && -pi < m && l < pi && m < pi);
  }
  return r / 2;
}

/*
 <url:>
 問題文============================================================

 =================================================================

 解説=============================================================

 ================================================================
 */
typedef Point P;
template <class iter>
std::pair<P, ld> min_ball(iter left, iter right, int seed = 1333) {
  const int n = right - left;

  assert(n >= 1);
  if (n == 1) {
    return {*left, ld(0)};
  }

  std::mt19937 mt(seed);
  std::shuffle(left, right, mt);
  // std::random_shuffle(left, right); // simple but deprecated

  iter ps = left;
  using circle = std::pair<P, ld>;

  auto make_circle_3 = [](const P &a, const P &b, const P &c) -> circle {
    ld A = std::norm(b - c), B = std::norm(c - a), C = std::norm(a - b),
       S = cross(b - a, c - a);
    P p = (A * (B + C - A) * a + B * (C + A - B) * b + C * (A + B - C) * c) /
          (4 * S * S);
    ld r2 = std::norm(p - a);
    return {p, r2};
  };

  auto make_circle_2 = [](const P &a, const P &b) -> circle {
    P c = (a + b) / (ld)2;
    ld r2 = std::norm(a - c);
    return {c, r2};
  };

  auto in_circle = [](const P &a, const circle &c) -> bool {
    return std::norm(a - c.first) <= c.second + eps;
  };

  circle c = make_circle_2(ps[0], ps[1]);

  // MiniDisc
  for (int i = 2; i < n; ++i) {
    if (!in_circle(ps[i], c)) {
      // MiniDiscWithPoint
      c = make_circle_2(ps[0], ps[i]);
      for (int j = 1; j < i; ++j) {
        if (!in_circle(ps[j], c)) {
          // MiniDiscWith2Points
          c = make_circle_2(ps[i], ps[j]);
          for (int k = 0; k < j; ++k) {
            if (!in_circle(ps[k], c)) {
              c = make_circle_3(ps[i], ps[j], ps[k]);
            }
          }
        }
      }
    }
  }
  return c;
}

#define MAX_N 15
#define MAX_M 15
ll N, M;
Point p[MAX_N];

// dp[S][cnt] := 死んでいる勇者がSでcnt回爆発を行なっている時の最小半径
ld dp[1 << MAX_N][MAX_M];

vector<pair<ld, ll>> St;
void init() {
  for (int i = 0; i < (1 << MAX_N); i++)
    for (int j = 0; j < MAX_M; j++)
      dp[i][j] = -1;
}

ld rec(ll S, ll cnt) {
  ld &res = dp[S][cnt];
  if (S == ((1 << N) - 1))
    return 0;
  if (cnt == M)
    return LINF;
  if (!(res < 0))
    return res;
  res = LINF;
  for (int i = 0; i < St.size(); i++) {
    if (S == (S | St[i].second))
      continue;
    res = min(res, max(St[i].first, rec(S | St[i].second, cnt + 1)));
  }
  return res;
}

int main(void) {
  cin.tie(0);
  ios::sync_with_stdio(false);
  init();
  cin >> N >> M;
  for (int i = 0; i < N; i++)
    p[i] = input_point();

  // 最小包含円
  for (int i = 1; i < (1 << N); i++) {
    vector<P> tp;
    for (int j = 0; j < N; j++) {
      if ((i >> j) & 1) {
        tp.push_back(p[j]);
      }
    }
    auto c = min_ball(tp.begin(), tp.end());
    //        cout << bitset<10>(i) << " " << c << endl;
    St.push_back({sqrt(c.second), i});
  }

  cout << fixed << setprecision(12) << rec(0, 0) << endl;
  return 0;
}