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#include "geo/convex_layers.hpp"
#include "geo/dynamicupperhull.hpp" // https://codeforces.com/contest/1599/problem/D // 出力は反時計回りである vvc<int> convex_layers(vc<Point<ll>> points) { int N = len(points); DynamicUpperHull<Point<ll>> DUH(points, 1); FOR(i, N) points[i] = -points[i]; DynamicUpperHull<Point<ll>> DLH(points, 1); vvc<int> ANS; int done = 0; int k = 0; while (done < N) { ++k; auto A = DLH.get(); auto B = DUH.get(); if (len(A) >= 2) { POP(A), POP(B); A.insert(A.end(), all(B)); reverse(all(A)); } ANS.eb(A); for (auto&& i: A) { ++done; DUH.erase(i); DLH.erase(i); } } return ANS; }
#line 2 "geo/base.hpp" template <typename T> struct Point { T x, y; Point() : x(0), y(0) {} template <typename A, typename B> Point(A x, B y) : x(x), y(y) {} template <typename A, typename B> Point(pair<A, B> p) : x(p.fi), y(p.se) {} 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+(Point p) const { return {x + p.x, y + p.y}; } Point operator-(Point p) const { return {x - p.x, y - p.y}; } bool operator==(Point p) const { return x == p.x && y == p.y; } bool operator!=(Point p) const { return x != p.x || y != p.y; } Point operator-() const { return {-x, -y}; } Point operator*(T t) const { return {x * t, y * t}; } Point operator/(T t) const { return {x / t, y / t}; } bool operator<(Point p) const { if (x != p.x) return x < p.x; return y < p.y; } T dot(Point other) { return x * other.x + y * other.y; } T det(Point other) { return x * other.y - y * other.x; } double norm() { return sqrtl(x * x + y * y); } double angle() { return atan2(y, x); } Point rotate(double theta) { static_assert(!is_integral<T>::value); double c = cos(theta), s = sin(theta); return Point{c * x - s * y, s * x + c * y}; } }; #ifdef FASTIO template <typename T> void rd(Point<T> &p) { fastio::rd(p.x), fastio::rd(p.y); } template <typename T> void wt(Point<T> &p) { fastio::wt(p.x); fastio::wt(' '); fastio::wt(p.y); } #endif // A -> B -> C と進むときに、左に曲がるならば +1、右に曲がるならば -1 template <typename T> int ccw(Point<T> A, Point<T> B, Point<T> C) { T x = (B - A).det(C - A); if (x > 0) return 1; if (x < 0) return -1; return 0; } template <typename REAL, typename T, typename U> REAL dist(Point<T> A, Point<U> B) { REAL dx = REAL(A.x) - REAL(B.x); REAL dy = REAL(A.y) - REAL(B.y); return sqrt(dx * dx + dy * dy); } // ax+by+c template <typename T> struct Line { T a, b, c; Line(T a, T b, T c) : a(a), b(b), c(c) {} Line(Point<T> A, Point<T> B) { a = A.y - B.y, b = B.x - A.x, c = A.x * B.y - A.y * B.x; } Line(T x1, T y1, T x2, T y2) : Line(Point<T>(x1, y1), Point<T>(x2, y2)) {} template <typename U> U eval(Point<U> P) { return a * P.x + b * P.y + c; } template <typename U> T eval(U x, U y) { return a * x + b * y + c; } // 同じ直線が同じ a,b,c で表現されるようにする void normalize() { static_assert(is_same_v<T, int> || is_same_v<T, long long>); T g = gcd(gcd(abs(a), abs(b)), abs(c)); a /= g, b /= g, c /= g; if (b < 0) { a = -a, b = -b, c = -c; } if (b == 0 && a < 0) { a = -a, b = -b, c = -c; } } bool is_parallel(Line other) { return a * other.b - b * other.a == 0; } bool is_orthogonal(Line other) { return a * other.a + b * other.b == 0; } }; template <typename T> struct Segment { Point<T> A, B; Segment(Point<T> A, Point<T> B) : A(A), B(B) {} Segment(T x1, T y1, T x2, T y2) : Segment(Point<T>(x1, y1), Point<T>(x2, y2)) {} bool contain(Point<T> C) { T det = (C - A).det(B - A); if (det != 0) return 0; return (C - A).dot(B - A) >= 0 && (C - B).dot(A - B) >= 0; } Line<T> to_Line() { return Line(A, B); } }; template <typename REAL> struct Circle { Point<REAL> O; REAL r; Circle(Point<REAL> O, REAL r) : O(O), r(r) {} Circle(REAL x, REAL y, REAL r) : O(x, y), r(r) {} template <typename T> bool contain(Point<T> p) { REAL dx = p.x - O.x, dy = p.y - O.y; return dx * dx + dy * dy <= r * r; } }; #line 2 "geo/dynamicupperhull.hpp" /* https://codeforces.com/blog/entry/75929 動的凸包。 x 座標でソートして完全二分木のセグ木の形にしておく。 セグ木のマージ部分(次の bridge を求める)で二分探索する。 bridge 同士の 4 点での上側凸包を見れば、次に探索するべき区間対が分かる。 構築 O(NlogN)、更新 O(Nlog^2N) 座標 10^9 以下の整数を仮定 */ template <typename Point> struct DynamicUpperHull { struct node { int l, r; // 範囲 (-1 if no vertex) int bl, br; // bridge idx }; int N, sz; vc<Point> P; vc<node> seg; // 受け取ったインデックスとの対応 vc<int> to_original_idx, to_seg_idx; DynamicUpperHull(vc<Point> P) : DynamicUpperHull(P, 0) {} DynamicUpperHull(vc<Point> P, bool b) : DynamicUpperHull(P, vc<bool>(len(P), b)) {} DynamicUpperHull(vc<Point> _P, vc<bool> isin) : N(len(_P)), P(_P) { to_original_idx = argsort(P); sort(all(P)); sz = 1; while (sz < N) sz *= 2; to_seg_idx.resize(N); seg.assign(sz + sz, {-1, -1, -1, -1}); for (int i = 0; i < N; ++i) to_seg_idx[to_original_idx[i]] = i; for (int i = 0; i < N; ++i) if (isin[to_original_idx[i]]) { seg[sz + i] = {i, i + 1, i, i}; } FOR3_R(i, 1, sz) update(i); } void insert(int i) { i = to_seg_idx[i]; seg[sz + i] = {i, i + 1, i, i}; i = (sz + i) / 2; while (i) { update(i); i /= 2; } } void add(int i) { insert(i); } void erase(int i) { i = to_seg_idx[i]; seg[sz + i] = {-1, -1, -1, -1}; i = (sz + i) / 2; while (i) { update(i); i /= 2; } } void remove(int i) { insert(i); } inline bool exist(int i) { return seg[i].r != -1; } void update(int i) { if (!exist(2 * i + 0) && !exist(2 * i + 1)) { seg[i].r = -1; return; } if (!exist(2 * i + 0)) { seg[i] = seg[2 * i + 1]; return; } if (!exist(2 * i + 1)) { seg[i] = seg[2 * i + 0]; return; } int p = 2 * i, q = 2 * i + 1; ll X = P[seg[q].l].x; while (p < sz || q < sz) { if (p < sz && !exist(2 * p + 0)) { p = 2 * p + 1; continue; } if (p < sz && !exist(2 * p + 1)) { p = 2 * p + 0; continue; } if (q < sz && !exist(2 * q + 0)) { q = 2 * q + 1; continue; } if (q < sz && !exist(2 * q + 1)) { q = 2 * q + 0; continue; } int a = seg[p].bl, b = seg[p].br, c = seg[q].bl, d = seg[q].br; if (a != b && (P[b] - P[a]).det(P[c] - P[a]) > 0) p = p * 2 + 0; elif (c != d && (P[c] - P[b]).det(P[d] - P[b]) > 0) q = 2 * q + 1; elif (a == b) q = 2 * q + 0; elif (c == d) p = 2 * p + 1; else { i128 c1 = (P[b] - P[a]).det(P[c] - P[a]); i128 c2 = (P[a] - P[b]).det(P[d] - P[b]); if (c1 + c2 == 0 || c1 * P[d].x + c2 * P[c].x < X * (c1 + c2)) { p = 2 * p + 1; } else { q = 2 * q + 0; } } } seg[i].l = seg[2 * i].l, seg[i].r = seg[2 * i + 1].r; seg[i].bl = seg[p].l, seg[i].br = seg[q].l; } vc<int> get() { // output sensitive complexity vc<int> res; auto dfs = [&](auto self, int k, int l, int r) -> void { if (!exist(k) || l >= r) return; if (k >= sz) { res.eb(seg[k].l); return; } if (!exist(2 * k + 0)) return self(self, 2 * k + 1, l, r); if (!exist(2 * k + 1)) return self(self, 2 * k + 0, l, r); if (r <= seg[k].bl) return self(self, 2 * k + 0, l, r); if (seg[k].br <= l) return self(self, 2 * k + 1, l, r); self(self, 2 * k + 0, l, seg[k].bl + 1); self(self, 2 * k + 1, seg[k].br, r); }; dfs(dfs, 1, 0, N); for (auto&& i: res) i = to_original_idx[i]; return res; } void debug() { print("points"); FOR(i, len(P)) print(i, P[i].x, P[i].y); print("seg"); FOR(i, len(seg)) print(i, seg[i].l, seg[i].r, seg[i].bl, seg[i].br); print("get"); print(get()); } }; #line 2 "geo/convex_layers.hpp" // https://codeforces.com/contest/1599/problem/D // 出力は反時計回りである vvc<int> convex_layers(vc<Point<ll>> points) { int N = len(points); DynamicUpperHull<Point<ll>> DUH(points, 1); FOR(i, N) points[i] = -points[i]; DynamicUpperHull<Point<ll>> DLH(points, 1); vvc<int> ANS; int done = 0; int k = 0; while (done < N) { ++k; auto A = DLH.get(); auto B = DUH.get(); if (len(A) >= 2) { POP(A), POP(B); A.insert(A.end(), all(B)); reverse(all(A)); } ANS.eb(A); for (auto&& i: A) { ++done; DUH.erase(i); DLH.erase(i); } } return ANS; }