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 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 6 ms / 2,000 ms |
| コード長 | 16,122 bytes |
| コンパイル時間 | 3,969 ms |
| コンパイル使用メモリ | 223,264 KB |
| 最終ジャッジ日時 | 2025-01-10 04:07:28 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 37 |
ソースコード
#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;}