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#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/1198" #include"../../template/template.hpp" #include"../../geometry/Partition_by_Circles.hpp" using namespace lib; int main(){ while (true){ int n, m; cin >> n >> m; if (n == 0 && m == 0) break; Partition_by_Circles pc; while (n--){ ld x, y, r; cin >> x >> y >> r; pc.add_circle(circle({vec(x,y),r})); } pc.build_graph(100000); string ans = ""; while (m--){ ld px, py, qx, qy; cin >> px >> py >> qx >> qy; int ip = pc.get_area_idx(vec(px,py)); int iq = pc.get_area_idx(vec(qx,qy)); ans += (ip == iq ? "YES" : "NO"); ans += (m == 0 ? '\n' : ' '); } cout << ans; } }
#line 1 "test/geometry/aoj_1198.test.cpp" #define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/1198" #line 2 "template/template.hpp" #include <bits/stdc++.h> #define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++) #define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--) #define all(v) v.begin(), v.end() using ll = long long; using ld = long double; using ull = unsigned long long; template <typename T> bool chmin(T &a, const T &b) { if (a <= b) return false; a = b; return true; } template <typename T> bool chmax(T &a, const T &b) { if (a >= b) return false; a = b; return true; } namespace lib { using namespace std; } // namespace lib // using namespace lib; #line 4 "test/geometry/aoj_1198.test.cpp" #line 2 "geometry/Partition_by_Circles.hpp" #line 2 "geometry/base_ld.hpp" #line 4 "geometry/base_ld.hpp" namespace lib { using vec = complex<ld>; const ld PI = acos(-1); void ldout(int len = 20) { cout << fixed << setprecision(len); } int sgn(ld a, const ld eps = 1e-7) { return (a < -eps) ? -1 : (a > eps) ? 1 : 0; } bool same_vec(vec a, vec b) { a -= b; return sgn(a.real()) == 0 && sgn(a.imag()) == 0; } ld dot(const vec &a, const vec &b) { return (conj(a) * b).real(); } ld cross(const vec &a, const vec &b) { return (conj(a) * b).imag(); } int isp(const vec &a, const vec &b, const vec &c) { int cross_sgn = sgn(cross(b - a, c - a)); if (cross_sgn == 0) { if (sgn(dot(b - a, c - a)) < 0) return -2; if (sgn(dot(a - b, c - b)) < 0) return 2; } return cross_sgn; } vec rot90(const vec &a) { return {-a.imag(), a.real()}; } vec rot(const vec &a, ld rad) { return a * vec(cosl(rad), sinl(rad)); } bool comp_for_argument_sort(const vec &lhs, const vec &rhs) { // if (abs(arg(lhs)-arg(rhs)) < eps) return false; // need ? return arg(lhs) < arg(rhs); } } // namespace lib #line 2 "data_structure/dsu.hpp" #line 4 "data_structure/dsu.hpp" namespace lib { struct dsu { public: dsu(int n = 0) : _n(n), data(n, -1) {} int leader(int a) { if (data[a] < 0) return a; return data[a] = leader(data[a]); } int merge(int a, int b) { int x = leader(a), y = leader(b); if (x == y) return x; if (-data[x] < -data[y]) swap(x, y); data[x] += data[y]; data[y] = x; return x; } bool same(int a, int b) { return leader(a) == leader(b); } int size(int a) { return -data[leader(a)]; } private: int _n; vector<int> data; }; } // namespace lib #line 6 "geometry/Partition_by_Circles.hpp" namespace lib{ struct circle { vec c; ld r; }; // c1 != c2 vector<ld> cross_point_x(const circle &c1, const circle &c2){ assert(sgn(abs(c1.r - c2.r)) != 0 || sgn(abs(c1.c - c2.c)) != 0); ld d = abs(c1.c - c2.c); // 円が離れすぎている if (sgn(d - c1.r - c2.r) > 0) return {}; // 円が近すぎる if (sgn(abs(c1.r - c2.r) - d) > 0) return {}; // 外接している if (sgn(d - c1.r - c2.r) == 0){ return {(c1.r*c2.c.real() + c2.r*c1.c.real()) / (c1.r + c2.r)}; } // 内接している if (sgn(abs(c1.r - c2.r) - d) == 0){ return {(c1.r * c2.c.real() - c2.r * c1.c.real()) / (c1.r - c2.r)}; } // 2 点を共有する ld e = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d); vec p = c1.c + (c2.c - c1.c) * e / d; vec v((c1.c - c2.c).imag(),(c2.c - c1.c).real()); v *= sqrtl(max(c1.r * c1.r - e * e, ld(0))) / abs(v); return {(p+v).real(),(p-v).real()}; } vector<ld> cross_point_y(const circle &c, const ld &x){ int cond = sgn(abs(c.c.real() - x) - c.r); if (cond > 0) return {}; if (cond == 0) return {c.c.imag()}; ld ydiff = sqrtl(max(c.r*c.r - (x - c.c.real()) * (x - c.c.real()),ld(0))); return {c.c.imag()+ydiff,c.c.imag()-ydiff}; } struct Partition_by_Circles { vector<circle> a; // 同じ円は与えられない void add_circle(circle c){ // x 座標で区切る場所が重ならないように 1 rad 回転しておく c.c = rot(c.c,1); a.emplace_back(c); } ld coordinate_width(){ ld res = 0.0; for (auto &c : a){ chmax(res,abs(c.c)+c.r); } return res; } vector<ld> x_coordinates(){ vector<ld> xs; for (auto &c : a){ xs.emplace_back(c.c.real()-c.r); xs.emplace_back(c.c.real()+c.r); } int siza = a.size(); for (int i = 0; i < siza-1; i++) for (int j = i+1; j < siza; j++){ for (auto x : cross_point_x(a[i],a[j])){ bool yet = true; for (auto testx : xs){ if (sgn(abs(x - testx)) == 0){ yet = false; break; } } if (yet) xs.emplace_back(x); } } sort(all(xs)); return xs; } using ylr = tuple<ld,int,int>; vector<ylr> y_coordinates(ld x){ vector<ylr> ys; auto add = [&](ld y, int l, int r){ bool yet = true; for (auto &[testy, testl, testr] : ys){ if (sgn(abs(y - testy)) == 0){ yet = false; testl += l; testr += r; break; } } if (yet) ys.push_back({y,l,r}); }; for (auto &c : a){ auto vecy = cross_point_y(c,x); if (vecy.empty()) continue; if ((int)(vecy.size()) == 2){ for (auto y : vecy) add(y,1,1); } else { if (c.c.real() < x){ add(vecy[0],2,0); } else { add(vecy[0],0,2); } } } sort(all(ys),[&](ylr lhs, ylr rhs){ return get<0>(lhs) < get<0>(rhs); }); return ys; } dsu d; vector<ld> xs; vector<int> lower_idx; map<int,int> mp; vector<vector<int>> build_graph(ld max_width = 0){ // 大きな円で全体を囲ってしまう if (sgn(max_width) == 0) max_width = coordinate_width()*2; a.push_back({vec(0,0),max_width}); // x 座標の列挙 xs = x_coordinates(); // 各 x について y 座標の列挙 vector<vector<ylr>> yss; yss.reserve(xs.size()); for (auto &x : xs) yss.push_back(y_coordinates(x)); // x で切って領域を舐める int idx = 0; vector<pair<int,int>> es, merge; vector<int> cur; for (int itr = 0; itr < (int)(xs.size())-1; itr++){ lower_idx.emplace_back(idx); vector<int> lid, rid; for (int l = 0; l < (int)(yss[itr].size()); l++){ for (int t = 0; t < get<2>(yss[itr][l]); t++){ lid.emplace_back(l); } } for (int r = 0; r < (int)(yss[itr+1].size()); r++){ for (int t = 0; t < get<1>(yss[itr+1][r]); t++){ rid.emplace_back(r); } } assert(lid.size() == rid.size()); int pre = 0; vector<int> nxt; for (int i = 0; i < (int)(lid.size())-1; i++){ for (int t = 0; t < rid[i+1]-rid[i]; t++){ nxt.emplace_back(idx); } if (i != 0){ es.emplace_back(idx-1,idx); } if (lid[i+1] - lid[i] != 0){ merge.emplace_back(cur[pre++],idx); } if (lid[i+1] - lid[i] == 2){ merge.emplace_back(cur[pre++],idx); } idx++; } swap(cur,nxt); } // グラフを構築 d = dsu(idx); for (auto &[u, v] : merge) d.merge(u,v); set<int> st; for (int i = 0; i < idx; i++) st.insert(d.leader(i)); int vid = 0; for (auto v : st) mp[v] = vid++; vector<vector<int>> graph(vid); for (auto [u, v] : es){ u = mp[d.leader(u)]; v = mp[d.leader(v)]; graph[u].emplace_back(v); graph[v].emplace_back(u); } return graph; } int get_area_idx(vec p){ p = rot(p,1); int xid = int(lower_bound(all(xs),p.real()) - xs.begin()) - 1; vector<ld> ys; for (auto &[y, l, r] : y_coordinates(p.real())) ys.emplace_back(y); int yid = int(lower_bound(all(ys),p.imag()) - ys.begin()) - 1; return mp[d.leader(lower_idx[xid] + yid)]; } }; } //namespace lib #line 6 "test/geometry/aoj_1198.test.cpp" using namespace lib; int main(){ while (true){ int n, m; cin >> n >> m; if (n == 0 && m == 0) break; Partition_by_Circles pc; while (n--){ ld x, y, r; cin >> x >> y >> r; pc.add_circle(circle({vec(x,y),r})); } pc.build_graph(100000); string ans = ""; while (m--){ ld px, py, qx, qy; cin >> px >> py >> qx >> qy; int ip = pc.get_area_idx(vec(px,py)); int iq = pc.get_area_idx(vec(qx,qy)); ans += (ip == iq ? "YES" : "NO"); ans += (m == 0 ? '\n' : ' '); } cout << ans; } }