Problem p01427 (C++) — buggy submission, verdict: Time Limit Exceeded

#include "bits/stdc++.h"
#include <unordered_map>
#pragma warning(disable : 4996)
using namespace std;

/* 幾何の基本 */

#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 eps = 1e-11, 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

// 点の入力
Point input_point() {
  ld x, y;
  cin >> x >> y;
  return Point(x, y);
}

// 誤差つき等号判定
bool eq(const ld a, const ld b) { return (abs(a - b) < eps); }

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

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

// 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) const {
    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) {}
};

// 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が反時計周りの順に並ぶ
  if (cross(nb, nc) < -eps)
    return -1; // a,b,cが時計周りの順に並ぶ
  if (dot(nb, nc) < 0)
    return 2; // c,a,bの順に直線に並ぶ
  if (norm(nb) < norm(nc))
    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(const Line &l, const 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(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);
}

// 線分と線分の交差判定
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;
}

// 点の直線上判定
bool isis_lp(const Line &l, const Point &p) {
  return (abs(cross(l.b - p, l.a - p)) < eps);
}

// 点の線分上判定
bool isis_sp(const Line &s, const Point &p) {
  return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);
}

// 垂線の足
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);
}

// 直線と直線の交点
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);
}

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

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

// 直線と線分の距離
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));
}

// 線分と点の距離
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));
}

// 線分と線分の距離
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)});
}

// 直線と直線の二等分線のベクトル
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)));
}

/* 円 */

// 円と円の交点
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;
}

// 円と直線の交点
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;
}

// 円と線分の距離
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;
}

// 円と点の接線
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;
}

// 円と円の接線
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;
}

/* 多角形 */

typedef vector<Point> Polygon;

// 面積
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;
}

// 多角形の回転方向
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;
}

// 円の内外判定
//  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;
}
// 円の内外判定2　高速
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;
}

// 凸包
// 点や線を返すことも有り得るので注意
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;
}

// 凸カット
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;
}

/* アレンジメント */
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 from, to;
  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, abs(p[from] - p[to]));
    }
  }
  return g;
}

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, 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, angle * c[i].r);
    }
  }
  return g;
}

/* 双対グラフ */

// 線分集合は既にアレンジメントされていなければならない．
// 内側の円は時計回りで，外側の円は反時計回りで得られる．
// 変数 polygon は，vector<int> で表される多角形の集合であり，
// vector<int> で表される
// 多角形のi番目は，その頂点の頂点集合pにおける番号である．
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;
// }

/* ビジュアライザ */
const ld zoom = 25;
const ld centerX = 6;
const ld centerY = 5;

void change_color(const int r, const int g, const int b) {
  fprintf(stderr, "c.strokeStyle = 'rgb(%d, %d, %d)';\\n", r, g, b);
}

int cordx(Point p) { return 400 + zoom * (p.real() - centerX); }
int cordy(Point p) { return 400 - zoom * (p.imag() - centerY); }

#define cord(p) cordx(p), cordy(p)

void draw_point(const Point &p) {
  fprintf(stderr, "circle(%d, %d, %d)\\n", cord(p), 2);
}

void draw_segment(const Line &l) {
  fprintf(stderr, "line(%d, %d, %d, %d)\\n", cord(l.a), cord(l.b));
}

void draw_line(const Line &l) {
  Point v = l.b - l.a;
  Line m(l.a - v * Point(1e4, 0), l.b + v * Point(1e4, 0));
  fprintf(stderr, "line(%d, %d, %d, %d)\\n", cord(m.a), cord(m.b));
}

void draw_polygon(const Polygon &p) {
  int n = p.size();
  REP(i, n) draw_segment(Line(p[i], p[(i + 1) % n]));
}

void draw_circle(const Circle c) {
  fprintf(stderr, "circle(%d, %d, %d)\\n", cord(c.p), (int)(zoom * c.r));
}

const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, 1, 0, -1};

int main() {
  int H, W;
  cin >> H >> W;
  vector<vector<bool>> fi(H + 2, vector<bool>(W + 2));
  for (int i = 0; i < H; ++i) {
    string st;
    cin >> st;
    for (int j = 0; j < W; ++j) {
      if (st[j] == '#') {
        fi[i + 1][j + 1] = true;
      }
    }
  }
  vector<Line> ls;
  vector<double> katas;
  vector<vector<bool>> tates(H + 2, vector<bool>(W + 1));
  vector<vector<bool>> yokos(H + 1, vector<bool>(W + 2));
  for (int y = 1; y < H + 1; ++y) {
    for (int x = 1; x < W + 1; ++x) {
      if (fi[y][x]) {
        for (int i = 0; i < 4; ++i) {
          Point ld(x, y + 1);
          Point lu(x, y);
          Point rd(x + 1, y + 1);
          Point ru(x + 1, y);
          if (!fi[y + dy[i]][x + dx[i]]) {
            if (i == 0) {
              tates[y][x - 1] = true;
              // ls.emplace_back(ld, lu);
            } else if (i == 1) {
              yokos[y][x] = true;
              // ls.emplace_back(rd, ld);
            } else if (i == 2) {
              tates[y][x] = true;
              // ls.emplace_back(ru, rd);
            } else {
              yokos[y - 1][x] = true;
              // ls.emplace_back(lu, ru);
            }
          }
        }
      }
    }
  }
  for (int x = 0; x < W + 1; ++x) {
    bool now = false;
    Point from;
    for (int y = 0; y < H + 2; ++y) {

      if (tates[y][x]) {
        if (!now) {
          from = Point(x + 1, y);
        }
        now = true;
      } else {
        if (now) {
          ls.emplace_back(from, Point(x + 1, y));
        }
        now = false;
      }
    }
  }
  for (int y = 0; y < H + 1; ++y) {
    bool now = false;
    Point from;
    for (int x = 0; x < W + 2; ++x) {
      if (yokos[y][x]) {
        if (!now) {
          from = Point(x, y + 1);
        }
        now = true;
      } else {
        if (now) {
          ls.emplace_back(from, Point(x, y + 1));
        }
        now = false;
      }
    }
  }
  for (int y = 1; y < H + 1; ++y) {
    for (int x = 2; x < W + 2; ++x) {
      katas.push_back(double(y - (H + 1)) / (x - 1));
    }
  }
  katas.push_back(0);
  katas.push_back(-1000);
  sort(katas.begin(), katas.end());
  vector<double> newkatas;
  double now = 1;
  for (int i = 0; i < katas.size(); ++i) {
    if (abs(katas[i] - now) > 1e-10) {
      newkatas.push_back(katas[i]);
      now = (katas[i]);
    }
  }
  int ans = 0;

  map<double, int> mp;
  mp[0] = 0;
  mp[-1000] = 0;
  for (int j = 0; j < ls.size(); ++j) {
    if (ls[j][0] == Point(1, H + 1) || ls[j][1] == Point(1, H + 1))
      continue;
    double kataf = (ls[j][0].imag() - H - 1) / (ls[j][0].real() + eps - 1);
    double katat = (ls[j][1].imag() - H - 1) / (ls[j][1].real() + eps - 1);
    if (kataf < katat)
      swap(kataf, katat);
    assert(kataf >= katat);
    mp[kataf]--;
    mp[katat]++;
  }
  int anow = 0;
  for (auto &it : mp) {
    it.second += anow;
    anow = it.second;
  }

  for (int i = 0; i < newkatas.size() - 1; ++i) {
    double kata = (newkatas[i + 1] + newkatas[i]) / 2;
    Line l(Point(1, H + 1), Point(1 + 1, H + 1 + kata));
    int nans = 0;
    nans = prev(mp.lower_bound(kata))->second;
    if (fi[H][1])
      nans += 1;
    ans = max(ans, 1 + nans / 2);
  }
  cout << ans << endl;
  return 0;
}

Error: TLE

Fixed submission:

#include "bits/stdc++.h"
#include <unordered_map>
#pragma warning(disable : 4996)
using namespace std;

/* 幾何の基本 */

#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 eps = 1e-11, 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

// 点の入力
Point input_point() {
  ld x, y;
  cin >> x >> y;
  return Point(x, y);
}

// 誤差つき等号判定
bool eq(const ld a, const ld b) { return (abs(a - b) < eps); }

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

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

// 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) const {
    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) {}
};

// 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が反時計周りの順に並ぶ
  if (cross(nb, nc) < -eps)
    return -1; // a,b,cが時計周りの順に並ぶ
  if (dot(nb, nc) < 0)
    return 2; // c,a,bの順に直線に並ぶ
  if (norm(nb) < norm(nc))
    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(const Line &l, const 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(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);
}

// 線分と線分の交差判定
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;
}

// 点の直線上判定
bool isis_lp(const Line &l, const Point &p) {
  return (abs(cross(l.b - p, l.a - p)) < eps);
}

// 点の線分上判定
bool isis_sp(const Line &s, const Point &p) {
  return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);
}

// 垂線の足
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);
}

// 直線と直線の交点
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);
}

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

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

// 直線と線分の距離
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));
}

// 線分と点の距離
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));
}

// 線分と線分の距離
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)});
}

// 直線と直線の二等分線のベクトル
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)));
}

/* 円 */

// 円と円の交点
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;
}

// 円と直線の交点
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;
}

// 円と線分の距離
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;
}

// 円と点の接線
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;
}

// 円と円の接線
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;
}

/* 多角形 */

typedef vector<Point> Polygon;

// 面積
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;
}

// 多角形の回転方向
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;
}

// 円の内外判定
//  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;
}
// 円の内外判定2　高速
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;
}

// 凸包
// 点や線を返すことも有り得るので注意
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;
}

// 凸カット
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;
}

/* アレンジメント */
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 from, to;
  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, abs(p[from] - p[to]));
    }
  }
  return g;
}

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, 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, angle * c[i].r);
    }
  }
  return g;
}

/* 双対グラフ */

// 線分集合は既にアレンジメントされていなければならない．
// 内側の円は時計回りで，外側の円は反時計回りで得られる．
// 変数 polygon は，vector<int> で表される多角形の集合であり，
// vector<int> で表される
// 多角形のi番目は，その頂点の頂点集合pにおける番号である．
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;
// }

/* ビジュアライザ */
const ld zoom = 25;
const ld centerX = 6;
const ld centerY = 5;

void change_color(const int r, const int g, const int b) {
  fprintf(stderr, "c.strokeStyle = 'rgb(%d, %d, %d)';\\n", r, g, b);
}

int cordx(Point p) { return 400 + zoom * (p.real() - centerX); }
int cordy(Point p) { return 400 - zoom * (p.imag() - centerY); }

#define cord(p) cordx(p), cordy(p)

void draw_point(const Point &p) {
  fprintf(stderr, "circle(%d, %d, %d)\\n", cord(p), 2);
}

void draw_segment(const Line &l) {
  fprintf(stderr, "line(%d, %d, %d, %d)\\n", cord(l.a), cord(l.b));
}

void draw_line(const Line &l) {
  Point v = l.b - l.a;
  Line m(l.a - v * Point(1e4, 0), l.b + v * Point(1e4, 0));
  fprintf(stderr, "line(%d, %d, %d, %d)\\n", cord(m.a), cord(m.b));
}

void draw_polygon(const Polygon &p) {
  int n = p.size();
  REP(i, n) draw_segment(Line(p[i], p[(i + 1) % n]));
}

void draw_circle(const Circle c) {
  fprintf(stderr, "circle(%d, %d, %d)\\n", cord(c.p), (int)(zoom * c.r));
}

const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, 1, 0, -1};

int main() {
  int H, W;
  cin >> H >> W;
  vector<vector<bool>> fi(H + 2, vector<bool>(W + 2));
  for (int i = 0; i < H; ++i) {
    string st;
    cin >> st;
    for (int j = 0; j < W; ++j) {
      if (st[j] == '#') {
        fi[i + 1][j + 1] = true;
      }
    }
  }
  vector<Line> ls;
  vector<double> katas;
  vector<vector<bool>> tates(H + 2, vector<bool>(W + 1));
  vector<vector<bool>> yokos(H + 1, vector<bool>(W + 2));
  for (int y = 1; y < H + 1; ++y) {
    for (int x = 1; x < W + 1; ++x) {
      if (fi[y][x]) {
        for (int i = 0; i < 4; ++i) {
          Point ld(x, y + 1);
          Point lu(x, y);
          Point rd(x + 1, y + 1);
          Point ru(x + 1, y);
          if (!fi[y + dy[i]][x + dx[i]]) {
            if (i == 0) {
              tates[y][x - 1] = true;
              // ls.emplace_back(ld, lu);
            } else if (i == 1) {
              yokos[y][x] = true;
              // ls.emplace_back(rd, ld);
            } else if (i == 2) {
              tates[y][x] = true;
              // ls.emplace_back(ru, rd);
            } else {
              yokos[y - 1][x] = true;
              // ls.emplace_back(lu, ru);
            }
          }
        }
      }
    }
  }
  for (int x = 0; x < W + 1; ++x) {
    bool now = false;
    Point from;
    for (int y = 0; y < H + 2; ++y) {

      if (tates[y][x]) {
        if (!now) {
          from = Point(x + 1, y);
        }
        now = true;
      } else {
        if (now) {
          ls.emplace_back(from, Point(x + 1, y));
        }
        now = false;
      }
    }
  }
  for (int y = 0; y < H + 1; ++y) {
    bool now = false;
    Point from;
    for (int x = 0; x < W + 2; ++x) {
      if (yokos[y][x]) {
        if (!now) {
          from = Point(x, y + 1);
        }
        now = true;
      } else {
        if (now) {
          ls.emplace_back(from, Point(x, y + 1));
        }
        now = false;
      }
    }
  }
  for (int y = 1; y < H + 1; ++y) {
    for (int x = 2; x < W + 2; ++x) {
      katas.push_back(double(y - (H + 1)) / (x - 1));
    }
  }
  katas.push_back(0);
  katas.push_back(-1000);
  sort(katas.begin(), katas.end());
  vector<double> newkatas;
  double now = 1;
  for (int i = 0; i < katas.size(); ++i) {
    if (abs(katas[i] - now) > 1e-10) {
      newkatas.push_back(katas[i]);
      now = (katas[i]);
    }
  }
  int ans = 0;
  for (int i = 0; i < newkatas.size() - 1; ++i) {
    double kata = (newkatas[i + 1] + newkatas[i]) / 2;
    Line l(Point(1, H + 1), Point(1 + 1, H + 1 + kata));
    int nans = 0;
    for (int j = 0; j < ls.size(); ++j) {
      if (isis_ls(l, ls[j])) {
        nans++;
      }
    }
    if (fi[H][1])
      nans--;
    ans = max(ans, 1 + nans / 2);
  }
  cout << ans << endl;
  return 0;
}