#473624 (C++17) No.1041 直線大学

提出ソース

結果

問題	No.1041 直線大学
ユーザー	👑 emthrm
提出日時	2020-05-01 21:24:30
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	4 ms / 2,000 ms
コード長	16,122 bytes
コンパイル時間	2,703 ms
コンパイル使用メモリ	229,528 KB
実行使用メモリ	5,248 KB
最終ジャッジ日時	2024-11-16 07:43:02
合計ジャッジ時間	3,686 ms
ジャッジサーバーID （参考情報）	judge5 / judge2

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	1 ms 5,248 KB
testcase_01	AC	2 ms 5,248 KB
testcase_02	AC	2 ms 5,248 KB
testcase_03	AC	1 ms 5,248 KB
testcase_04	AC	2 ms 5,248 KB
testcase_05	AC	2 ms 5,248 KB
testcase_06	AC	1 ms 5,248 KB
testcase_07	AC	2 ms 5,248 KB
testcase_08	AC	1 ms 5,248 KB
testcase_09	AC	1 ms 5,248 KB
testcase_10	AC	3 ms 5,248 KB
testcase_11	AC	2 ms 5,248 KB
testcase_12	AC	2 ms 5,248 KB
testcase_13	AC	2 ms 5,248 KB
testcase_14	AC	3 ms 5,248 KB
testcase_15	AC	2 ms 5,248 KB
testcase_16	AC	2 ms 5,248 KB
testcase_17	AC	2 ms 5,248 KB
testcase_18	AC	2 ms 5,248 KB
testcase_19	AC	3 ms 5,248 KB
testcase_20	AC	2 ms 5,248 KB
testcase_21	AC	2 ms 5,248 KB
testcase_22	AC	1 ms 5,248 KB
testcase_23	AC	4 ms 5,248 KB
testcase_24	AC	2 ms 5,248 KB
testcase_25	AC	2 ms 5,248 KB
testcase_26	AC	2 ms 5,248 KB
testcase_27	AC	2 ms 5,248 KB
testcase_28	AC	2 ms 5,248 KB
testcase_29	AC	2 ms 5,248 KB
testcase_30	AC	2 ms 5,248 KB
testcase_31	AC	2 ms 5,248 KB
testcase_32	AC	2 ms 5,248 KB
testcase_33	AC	2 ms 5,248 KB
testcase_34	AC	1 ms 5,248 KB
testcase_35	AC	2 ms 5,248 KB
testcase_36	AC	2 ms 5,248 KB
testcase_37	AC	2 ms 5,248 KB
testcase_38	AC	4 ms 5,248 KB
testcase_39	AC	2 ms 5,248 KB

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ソースコード

raw source code

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
const int INF = 0x3f3f3f3f;
const ll LINF = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-8;
const int MOD = 1000000007;
// const int MOD = 998244353;
const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
const int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  }
} iosetup;

namespace Geometry {
  using Real = double;

  int sgn(Real x) { return x > EPS ? 1 : x < -EPS ? -1 : 0; }

  Real degree_to_radian(Real d) { return d * M_PI / 180; }
  Real radian_to_degree(Real r) { return r * 180 / M_PI; }

  struct Point {
    Real x, y;
    Point(Real x = 0, Real y = 0) : x(x), y(y) {}
    Real abs() const { return sqrt(norm()); }
    Real arg() const { Real res = atan2(y, x); return res < 0 ? res + M_PI * 2 : res; }
    Real norm() const { return x * x + y * y; }
    Point rotate(Real angle) const { Real cs = cos(angle), sn = sin(angle); return Point(x * cs - y * sn, x * sn + y * cs); }
    Point unit_vector() const { Real a = abs(); return Point(x / a, y / a); }
    pair<Point, Point> normal_unit_vector() const { Point p = unit_vector(); return {Point(-p.y, p.x), Point(p.y, -p.x)}; }
    Point &operator+=(const Point &p) { x += p.x; y += p.y; return *this; }
    Point &operator-=(const Point &p) { x -= p.x; y -= p.y; return *this; }
    Point &operator*=(Real k) { x *= k; y *= k; return *this; }
    Point &operator/=(Real k) { x /= k; y /= k; return *this; }
    bool operator<(const Point &p) const { int x_sgn = sgn(p.x - x); return x_sgn != 0 ? x_sgn == 1 : sgn(p.y - y) == 1; }
    bool operator<=(const Point &p) const { return !(p < *this); }
    bool operator>(const Point &p) const { return p < *this; }
    bool operator>=(const Point &p) const { return !(*this < p); }
    Point operator+() const { return *this; }
    Point operator-() const { return Point(-x, -y); }
    Point operator+(const Point &p) const { return Point(*this) += p; }
    Point operator-(const Point &p) const { return Point(*this) -= p; }
    Point operator*(Real k) const { return Point(*this) *= k; }
    Point operator/(Real k) const { return Point(*this) /= k; }
    friend ostream &operator<<(ostream &os, const Point &p) { return os << '(' << p.x << ", " << p.y << ')'; }
    friend istream &operator>>(istream &is, Point &p) { Real x, y; is >> x >> y; p = Point(x, y); return is; }
  };

  struct Segment {
    Point s, t;
    Segment(const Point &s = {0, 0}, const Point &t = {0, 0}) : s(s), t(t) {}
  };
  struct Line : Segment {
    using Segment::Segment;
    Line(Real a, Real b, Real c) {
      if (sgn(a) == 0) {
        s = Point(0, -c / b); t = Point(1, s.y);
      } else if (sgn(b) == 0) {
        s = Point(-c / a, 0); t = Point(s.x, 1);
      } else if (sgn(c) == 0) {
        s = Point(0, 0); t = Point(1, -a / b);
      } else {
        s = Point(0, -c / b); t = Point(-c / a, 0);
      }
    }
  };

  struct Circle {
    Point p; Real r;
    Circle(const Point &p = {0, 0}, Real r = 0) : p(p), r(r) {}
  };

  Real cross(const Point &a, const Point &b) { return a.x * b.y - a.y * b.x; }
  Real dot(const Point &a, const Point &b) { return a.x * b.x + a.y * b.y; }

  int ccw(const Point &a, const Point &b, const Point &c) {
    Point ab = b - a, ac = c - a;
    int sign = sgn(cross(ab, ac));
    if (sign == 0) {
      if (sgn(dot(ab, ac)) == -1) return 2;
      if (sgn(ac.norm() - ab.norm()) == 1) return -2;
    }
    return sign;
  }

  Real get_angle(const Point &a, const Point &b, const Point &c) {
    Real ba_arg = (a - b).arg(), bc_arg = (c - b).arg();
    if (ba_arg > bc_arg) swap(ba_arg, bc_arg);
    return min(bc_arg - ba_arg, M_PI * 2 - (bc_arg - ba_arg));
  }

  Real closest_pair(vector<Point> ps) {
    int n = ps.size();
    assert(n > 1);
    sort(ALL(ps));
    function<Real(int, int)> rec = [&](int left, int right) {
      int mid = (left + right) >> 1;
      Real x_mid = ps[mid].x, d = LINF;
      if (left + 1 < mid) chmin(d, rec(left, mid));
      if (mid + 1 < right) chmin(d, rec(mid, right));
      inplace_merge(ps.begin() + left, ps.begin() + mid, ps.begin() + right, [&](const Point &a, const Point &b) { return sgn(b.y - a.y) == 1; });
      vector<Point> tmp;
      FOR(i, left, right) {
        if (sgn(abs(ps[i].x - x_mid) - d) == 1) continue;
        for (int j = static_cast<int>(tmp.size()) - 1; j >= 0; --j) {
          Point now = ps[i] - tmp[j];
          if (sgn(now.y - d) == 1) break;
          chmin(d, now.abs());
        }
        tmp.emplace_back(ps[i]);
      }
      return d;
    };
    return rec(0, n);
  }

  Point projection(const Segment &a, const Point &b) { return a.s + (a.t - a.s) * dot(a.t - a.s, b - a.s) / (a.t - a.s).norm(); }
  Point reflection(const Segment &a, const Point &b) { return projection(a, b) * 2 - b; }

  bool is_parallel(const Segment &a, const Segment &b) { return sgn(cross(a.t - a.s, b.t - b.s)) == 0; }
  bool is_orthogonal(const Segment &a, const Segment &b) { return sgn(dot(a.t - a.s, b.t - b.s)) == 0; }

  Real distance(const Point&, const Point&);
  Real distance(const Segment&, const Point&);
  Real distance(const Line&, const Point&);
  int sizeof_common_tangent(const Circle&, const Circle&);
  bool has_intersected(const Segment &a, const Point &b) { return ccw(a.s, a.t, b) == 0; }
  bool has_intersected(const Segment &a, const Segment &b) { return ccw(a.s, a.t, b.s) * ccw(a.s, a.t, b.t) <= 0 && ccw(b.s, b.t, a.s) * ccw(b.s, b.t, a.t) <= 0; }
  bool has_intersected(const Line &a, const Point &b) { int c = ccw(a.s, a.t, b); return c != 1 && c != -1; }
  bool has_intersected(const Line &a, const Segment &b) { return ccw(a.s, a.t, b.s) * ccw(a.s, a.t, b.t) != 1; }
  bool has_intersected(const Line &a, const Line &b) { return sgn(cross(a.t - a.s, b.t - b.s)) != 0 || sgn(cross(a.t - a.s, b.s - a.s)) == 0; }
  bool has_intersected(const Circle &a, const Point &b) { return sgn(distance(a.p, b) - a.r) == 0; }
  bool has_intersected(const Circle &a, const Segment &b) { return sgn(a.r - distance(b, a.p)) != -1 && sgn(max(distance(a.p, b.s), distance(a.p, b.t)) - a.r) != -1; }
  bool has_intersected(const Circle &a, const Line &b) { return sgn(a.r - distance(b, a.p)) != -1; }
  bool has_intersected(const Circle &a, const Circle &b) { return sizeof_common_tangent(a, b) > 0; }

  Point intersection(const Line &a, const Line &b) {
    assert(has_intersected(a, b) && !is_parallel(a, b));
    return a.s + (a.t - a.s) * cross(b.t - b.s, b.s - a.s) / cross(b.t - b.s, a.t - a.s);
  }
  Point intersection(const Segment &a, const Segment &b) {
    assert(has_intersected(a, b));
    if (is_parallel(a, b)) {
      if (sgn(distance(a.s, b.s)) == 0) {
        assert(sgn(dot(a.t - a.s, b.t - a.s)) == -1);
        return a.s;
      } else if (sgn(distance(a.s, b.t)) == 0) {
        assert(sgn(dot(a.t - a.s, b.s - a.s)) == -1);
        return a.s;
      } else if (sgn(distance(a.t, b.s)) == 0) {
        assert(sgn(dot(a.s - a.t, b.t - a.t)) == -1);
        return a.t;
      } else if (sgn(distance(a.t, b.t)) == 0) {
        assert(sgn(dot(a.s - a.t, b.s - a.t)) == -1);
        return a.t;
      } else {
        assert(false);
      }
    } else {
      return intersection(Line(a.s, a.t), Line(b.s, b.t));
    }
  }
  Point intersection(const Line &a, const Segment &b) {
    assert(has_intersected(a, b));
    return intersection(a, Line(b.s, b.t));
  }
  vector<Point> intersection(const Circle &a, const Line &b) {
    Point pro = projection(b, a.p);
    Real nor = (a.p - pro).norm();
    int sign = sgn(a.r - sqrt(nor));
    if (sign == -1) return {};
    if (sign == 0) return {pro};
    Point v = (b.t - b.s).unit_vector() * sqrt(a.r * a.r - nor);
    return {pro + v, pro - v};
  }
  vector<Point> intersection(const Circle &a, const Segment &b) {
    if (!has_intersected(a, b)) return {};
    vector<Point> res = intersection(a, Line(b.s, b.t));
    if (sgn(distance(a.p, b.s) - a.r) != -1 && sgn(distance(a.p, b.t) - a.r) != -1) return res;
    return {sgn(dot(res[0] - b.s, res[0] - b.t)) == 1 ? res[1] : res[0]};
  }
  vector<Point> intersection(const Circle &a, const Circle &b) {
    int sz = sizeof_common_tangent(a, b);
    if (sz == 0 || sz == 4) return {};
    Real alpha = (b.p - a.p).arg();
    if (sz == 1 || sz == 3) return {Point(a.p.x + a.r * cos(alpha), a.p.y + a.r * sin(alpha))};
    Real dist = (b.p - a.p).norm(), beta = acos((dist + a.r * a.r - b.r * b.r) / (2 * sqrt(dist) * a.r));
    return {a.p + Point(a.r * cos(alpha + beta), a.r * sin(alpha + beta)), a.p + Point(a.r * cos(alpha - beta), a.r * sin(alpha - beta))};
  }

  Real distance(const Point &a, const Point &b) { return (b - a).abs(); }
  Real distance(const Segment &a, const Point &b) {
    Point foot = projection(a, b);
    return has_intersected(a, foot) ? distance(foot, b) : min(distance(a.s, b), distance(a.t, b));
  }
  Real distance(const Segment &a, const Segment &b) { return has_intersected(a, b) ? 0 : min({distance(a, b.s), distance(a, b.t), distance(b, a.s), distance(b, a.t)}); }
  Real distance(const Line &a, const Point &b) { return distance(projection(a, b), b); }
  Real distance(const Line &a, const Segment &b) { return has_intersected(a, b) ? 0 : min(distance(a, b.s), distance(a, b.t)); }
  Real distance(const Line &a, const Line &b) { return has_intersected(a, b) ? 0 : distance(a, b.s); }

  vector<Point> tangency(const Circle &a, const Point &b) {
    Real dist = distance(a.p, b);
    int sign = sgn(dist - a.r);
    if (sign == -1) return {};
    if (sign == 0) return {b};
    Real alpha = (b - a.p).arg(), beta = acos(a.r / dist);
    return {a.p + Point(a.r * cos(alpha + beta), a.r * sin(alpha + beta)), a.p + Point(a.r * cos(alpha - beta), a.r * sin(alpha - beta))};
  }
  int sizeof_common_tangent(const Circle &a, const Circle &b) {
    Real dist = distance(a.p, b.p);
    int sign = sgn(a.r + b.r - dist);
    if (sign == -1) return 4;
    if (sign == 0) return 3;
    sign = sgn((sgn(a.r - b.r) == -1 ? b.r - a.r : a.r - b.r) - dist);
    if (sign == -1) return 2;
    if (sign == 0) return 1;
    return 0;
  }
  vector<Line> common_tangent(const Circle &a, const Circle &b) {
    vector<Line> tangents;
    Real dist = distance(a.p, b.p), argument = (b.p - a.p).arg();
    int sign = sgn(a.r + b.r - dist);
    if (sign == -1) {
      Real ac = acos((a.r + b.r) / dist), alpha = argument + ac, cs = cos(alpha), sn = sin(alpha);
      tangents.emplace_back(a.p + Point(a.r * cs, a.r * sn), b.p + Point(-b.r * cs, -b.r * sn));
      alpha = argument - ac; cs = cos(alpha); sn = sin(alpha);
      tangents.emplace_back(a.p + Point(a.r * cs, a.r * sn), b.p + Point(-b.r * cs, -b.r * sn));
    } else if (sign == 0) {
      Point s = a.p + Point(a.r * cos(argument), a.r * sin(argument));
      tangents.emplace_back(s, s + (b.p - a.p).normal_unit_vector().first);
    }
    if (sgn(b.r - a.r) == -1) {
      sign = sgn(a.r - b.r - dist);
      if (sign == -1) {
        Real at = acos((a.r - b.r) / dist), alpha = argument + at, cs = cos(alpha), sn = sin(alpha);
        tangents.emplace_back(a.p + Point(a.r * cs, a.r * sn), b.p + Point(b.r * cs, b.r * sn));
        alpha = argument - at; cs = cos(alpha); sn = sin(alpha);
        tangents.emplace_back(a.p + Point(a.r * cs, a.r * sn), b.p + Point(b.r * cs, b.r * sn));
      } else if (sign == 0) {
        Point s = a.p + Point(a.r * cos(argument), a.r * sin(argument));
        tangents.emplace_back(s, s + (b.p - a.p).normal_unit_vector().first);
      }
    } else {
      sign = sgn(b.r - a.r - dist);
      if (sign == -1) {
        Real at = acos((b.r - a.r) / dist), alpha = argument - at, cs = cos(alpha), sn = sin(alpha);
        tangents.emplace_back(a.p + Point(-a.r * cs, -a.r * sn), b.p + Point(-b.r * cs, -b.r * sn));
        alpha = argument + at; cs = cos(alpha); sn = sin(alpha);
        tangents.emplace_back(a.p + Point(-a.r * cs, -a.r * sn), b.p + Point(-b.r * cs, -b.r * sn));
      } else if (sign == 0) {
        Point s = b.p + Point(-b.r * cos(argument), -b.r * sin(argument));
        tangents.emplace_back(s, s + (a.p - b.p).normal_unit_vector().first);
      }
    }
    return tangents;
  }

  Real intersection_area(const Circle &a, const Circle &b) {
    Real nor = (b.p - a.p).norm(), dist = sqrt(nor);
    if (sgn(a.r + b.r - dist) != 1) return 0;
    if (sgn(abs(a.r - b.r) - dist) != -1) return min(a.r, b.r) * min(a.r, b.r) * M_PI;
    Real alpha = acos((nor + a.r * a.r - b.r * b.r) / (2 * dist * a.r)), beta = acos((nor + b.r * b.r - a.r * a.r) / (2 * dist * b.r));
    return (alpha - sin(alpha + alpha) * 0.5) * a.r * a.r + (beta - sin(beta + beta) * 0.5) * b.r * b.r;
  }

  using Polygon = vector<Point>;

  Real area(const Polygon &a) {
    int n = a.size();
    Real res = 0;
    REP(i, n) res += cross(a[i], a[(i + 1) % n]);
    return res * 0.5;
  }

  Point centroid(const Polygon &a) {
    Point res(0, 0);
    int n = a.size();
    Real den = 0;
    REP(i, n) {
      Real cro = cross(a[i], a[(i + 1) % n]);
      res += (a[i] + a[(i + 1) % n]) / 3 * cro;
      den += cro;
    }
    return res / den;
  }

  int is_contained(const Polygon &a, const Point &b) {
    int n = a.size();
    bool is_in = false;
    REP(i, n) {
      Point p = a[i] - b, q = a[(i + 1) % n] - b;
      if (sgn(q.y - p.y) == -1) swap(p, q);
      int sign = sgn(cross(p, q));
      if (sign == 1 && sgn(p.y) != 1 && sgn(q.y) == 1) is_in = !is_in;
      if (sign == 0 && sgn(dot(p, q)) != 1) return 1;
    }
    return is_in ? 2 : 0;
  }

  bool is_convex(const Polygon &a) {
    int n = a.size();
    REP(i, n) {
      if (ccw(a[(i - 1 + n) % n], a[i], a[(i + 1) % n]) == -1) return false;
    }
    return true;
  }

  Polygon monotone_chain(vector<Point> ps, bool tight = true) {
    sort(ALL(ps));
    int n = ps.size(), idx = 0;
    Polygon convex_hull(n << 1);
    for (int i = 0; i < n; convex_hull[idx++] = ps[i++]) {
      while (idx >= 2 && sgn(cross(convex_hull[idx - 1] - convex_hull[idx - 2], ps[i] - convex_hull[idx - 1])) < tight) --idx;
    }
    for (int i = n - 2, border = idx + 1; i >= 0; convex_hull[idx++] = ps[i--]) {
      while (idx >= border && sgn(cross(convex_hull[idx - 1] - convex_hull[idx - 2], ps[i] - convex_hull[idx - 1])) < tight) --idx;
    }
    convex_hull.resize(idx - 1);
    return convex_hull;
  }

  Polygon cut_convex(const Polygon &a, const Line &b) {
    int n = a.size();
    Polygon res;
    REP(i, n) {
      int c = ccw(b.s, b.t, a[i]);
      if (c != -1) res.emplace_back(a[i]);
      if (c * ccw(b.s, b.t, a[(i + 1) % n]) == -1) res.emplace_back(intersection(Line(a[i], a[(i + 1) % n]), b));
    }
    if (res.size() < 3) res.clear();
    return res;
  }

  pair<Point, Point> rotating_calipers(const Polygon &a) {
    int n = a.size(), high = 0, low = 0;
    if (n <= 2) {
      assert(n == 2);
      return {a[0], a[1]};
    }
    FOR(i, 1, n) {
      if (a[i].y > a[high].y) high = i;
      if (a[i].y < a[low].y) low = i;
    }
    Real max_norm = (a[high] - a[low]).norm();
    int i = high, j = low, max_i = i, max_j = j;
    do {
      ((sgn(cross(a[(i + 1) % n] - a[i], a[(j + 1) % n] - a[j])) != -1 ? j : i) += 1) %= n;
      Real tmp = (a[j] - a[i]).norm();
      if (sgn(tmp - max_norm) == 1) {
        max_norm = tmp;
        max_i = i; max_j = j;
      }
    } while (i != high || j != low);
    return {a[max_i], a[max_j]};
  }
}

using namespace Geometry;

int main() {
  int n; cin >> n;
  vector<Point> p(n); REP(i, n) cin >> p[i];
  int ans = 2;
  REP(i, n) FOR(j, i + 1, n) {
    Line line(p[i], p[j]);
    int cnt = 0;
    REP(k, n) cnt += has_intersected(line, p[k]);
    chmax(ans, cnt);
  }
  cout << ans << '\n';
  return 0;
}

yukicoder

結果

テストケース

ソースコード