#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr) #else #define dbg(x) ((void)0) #define dbgif(cond, x) ((void)0) #endif template struct shortest_path { static constexpr T INF = T(1e18); int V, E; bool single_positive_weight; T wmin, wmax; std::vector> tos; std::vector head; std::vector> edges; void build_() { if (int(tos.size()) == E and int(head.size()) == V + 1) return; tos.resize(E); head.assign(V + 1, 0); for (const auto &e : edges) ++head[std::get<0>(e) + 1]; for (int i = 0; i < V; ++i) head[i + 1] += head[i]; auto cur = head; for (const auto &e : edges) { tos[cur[std::get<0>(e)]++] = std::make_pair(std::get<1>(e), std::get<2>(e)); } } shortest_path(int V = 0) : V(V), E(0), single_positive_weight(true), wmin(0), wmax(0) {} void add_edge(int s, int t, T w) { assert(0 <= s and s < V); assert(0 <= t and t < V); edges.emplace_back(s, t, w); ++E; if (w > 0 and wmax > 0 and wmax != w) single_positive_weight = false; wmin = std::min(wmin, w); wmax = std::max(wmax, w); } void add_bi_edge(int u, int v, T w) { add_edge(u, v, w); add_edge(v, u, w); } std::vector dist; std::vector prev; // Dijkstra algorithm // - Requirement: wmin >= 0 // - Complexity: O(E log E) using Pque = std::priority_queue, std::vector>, std::greater>>; template void dijkstra(int s, int t = INVALID) { assert(0 <= s and s < V); build_(); dist.assign(V, INF); prev.assign(V, INVALID); dist[s] = 0; Heap pq; pq.emplace(0, s); while (!pq.empty()) { T d; int v; std::tie(d, v) = pq.top(); pq.pop(); if (t == v) return; if (dist[v] < d) continue; for (int e = head[v]; e < head[v + 1]; ++e) { const auto &nx = tos[e]; T dnx = d + nx.second; if (dist[nx.first] > dnx) { dist[nx.first] = dnx, prev[nx.first] = v; pq.emplace(dnx, nx.first); } } } } // Dijkstra algorithm // - Requirement: wmin >= 0 // - Complexity: O(V^2 + E) void dijkstra_vquad(int s, int t = INVALID) { assert(0 <= s and s < V); build_(); dist.assign(V, INF); prev.assign(V, INVALID); dist[s] = 0; std::vector fixed(V, false); while (true) { int r = INVALID; T dr = INF; for (int i = 0; i < V; i++) { if (!fixed[i] and dist[i] < dr) r = i, dr = dist[i]; } if (r == INVALID or r == t) break; fixed[r] = true; int nxt; T dx; for (int e = head[r]; e < head[r + 1]; ++e) { std::tie(nxt, dx) = tos[e]; if (dist[nxt] > dist[r] + dx) dist[nxt] = dist[r] + dx, prev[nxt] = r; } } } // Bellman-Ford algorithm // - Requirement: no negative loop // - Complexity: O(VE) bool bellman_ford(int s, int nb_loop) { assert(0 <= s and s < V); build_(); dist.assign(V, INF), prev.assign(V, INVALID); dist[s] = 0; for (int l = 0; l < nb_loop; l++) { bool upd = false; for (int v = 0; v < V; v++) { if (dist[v] == INF) continue; for (int e = head[v]; e < head[v + 1]; ++e) { const auto &nx = tos[e]; T dnx = dist[v] + nx.second; if (dist[nx.first] > dnx) dist[nx.first] = dnx, prev[nx.first] = v, upd = true; } } if (!upd) return true; } return false; } // Bellman-ford algorithm using deque // - Requirement: no negative loop // - Complexity: O(VE) void spfa(int s) { assert(0 <= s and s < V); build_(); dist.assign(V, INF); prev.assign(V, INVALID); dist[s] = 0; std::deque q; std::vector in_queue(V); q.push_back(s), in_queue[s] = 1; while (!q.empty()) { int now = q.front(); q.pop_front(), in_queue[now] = 0; for (int e = head[now]; e < head[now + 1]; ++e) { const auto &nx = tos[e]; T dnx = dist[now] + nx.second; int nxt = nx.first; if (dist[nxt] > dnx) { dist[nxt] = dnx; if (!in_queue[nxt]) { if (q.size() and dnx < dist[q.front()]) { // Small label first optimization q.push_front(nxt); } else { q.push_back(nxt); } prev[nxt] = now, in_queue[nxt] = 1; } } } } } // 01-BFS // - Requirement: all weights must be 0 or w (positive constant). // - Complexity: O(V + E) void zero_one_bfs(int s, int t = INVALID) { assert(0 <= s and s < V); build_(); dist.assign(V, INF), prev.assign(V, INVALID); dist[s] = 0; std::vector q(V * 4); int ql = V * 2, qr = V * 2; q[qr++] = s; while (ql < qr) { int v = q[ql++]; if (v == t) return; for (int e = head[v]; e < head[v + 1]; ++e) { const auto &nx = tos[e]; T dnx = dist[v] + nx.second; if (dist[nx.first] > dnx) { dist[nx.first] = dnx, prev[nx.first] = v; if (nx.second) { q[qr++] = nx.first; } else { q[--ql] = nx.first; } } } } } // Dial's algorithm // - Requirement: wmin >= 0 // - Complexity: O(wmax * V + E) void dial(int s, int t = INVALID) { assert(0 <= s and s < V); build_(); dist.assign(V, INF), prev.assign(V, INVALID); dist[s] = 0; std::vector>> q(wmax + 1); q[0].emplace_back(s, dist[s]); int ninq = 1; int cur = 0; T dcur = 0; for (; ninq; ++cur, ++dcur) { if (cur == wmax + 1) cur = 0; while (!q[cur].empty()) { int v = q[cur].back().first; T dnow = q[cur].back().second; q[cur].pop_back(), --ninq; if (v == t) return; if (dist[v] < dnow) continue; for (int e = head[v]; e < head[v + 1]; ++e) { const auto &nx = tos[e]; T dnx = dist[v] + nx.second; if (dist[nx.first] > dnx) { dist[nx.first] = dnx, prev[nx.first] = v; int nxtcur = cur + int(nx.second); if (nxtcur >= int(q.size())) nxtcur -= q.size(); q[nxtcur].emplace_back(nx.first, dnx), ++ninq; } } } } } // Solver for DAG // - Requirement: graph is DAG // - Complexity: O(V + E) bool dag_solver(int s) { assert(0 <= s and s < V); build_(); dist.assign(V, INF), prev.assign(V, INVALID); dist[s] = 0; std::vector indeg(V, 0); std::vector q(V * 2); int ql = 0, qr = 0; q[qr++] = s; while (ql < qr) { int now = q[ql++]; for (int e = head[now]; e < head[now + 1]; ++e) { const auto &nx = tos[e]; ++indeg[nx.first]; if (indeg[nx.first] == 1) q[qr++] = nx.first; } } ql = qr = 0; q[qr++] = s; while (ql < qr) { int now = q[ql++]; for (int e = head[now]; e < head[now + 1]; ++e) { const auto &nx = tos[e]; --indeg[nx.first]; if (dist[nx.first] > dist[now] + nx.second) dist[nx.first] = dist[now] + nx.second, prev[nx.first] = now; if (indeg[nx.first] == 0) q[qr++] = nx.first; } } return *max_element(indeg.begin(), indeg.end()) == 0; } // Retrieve a sequence of vertex ids that represents shortest path [s, ..., goal] // If not reachable to goal, return {} std::vector retrieve_path(int goal) const { assert(int(prev.size()) == V); assert(0 <= goal and goal < V); if (dist[goal] == INF) return {}; std::vector ret{goal}; while (prev[goal] != INVALID) { goal = prev[goal]; ret.push_back(goal); } std::reverse(ret.begin(), ret.end()); return ret; } void solve(int s, int t = INVALID) { if (wmin >= 0) { if (single_positive_weight) { zero_one_bfs(s, t); } else if (wmax <= 10) { dial(s, t); } else { if ((long long)V * V < (E << 4)) { dijkstra_vquad(s, t); } else { dijkstra(s, t); } } } else { bellman_ford(s, V); } } // Warshall-Floyd algorithm // - Requirement: no negative loop // - Complexity: O(E + V^3) std::vector> floyd_warshall() { build_(); std::vector> dist2d(V, std::vector(V, INF)); for (int i = 0; i < V; i++) { dist2d[i][i] = 0; for (const auto &e : edges) { int s = std::get<0>(e), t = std::get<1>(e); dist2d[s][t] = std::min(dist2d[s][t], std::get<2>(e)); } } for (int k = 0; k < V; k++) { for (int i = 0; i < V; i++) { if (dist2d[i][k] == INF) continue; for (int j = 0; j < V; j++) { if (dist2d[k][j] == INF) continue; dist2d[i][j] = std::min(dist2d[i][j], dist2d[i][k] + dist2d[k][j]); } } } return dist2d; } void to_dot(std::string filename = "shortest_path") const { std::ofstream ss(filename + ".DOT"); ss << "digraph{\n"; build_(); for (int i = 0; i < V; i++) { for (int e = head[i]; e < head[i + 1]; ++e) { ss << i << "->" << tos[e].first << "[label=" << tos[e].second << "];\n"; } } ss << "}\n"; ss.close(); return; } }; #include #include #include #include #include #include #include #include template struct Point2d { static T_P EPS; static void set_eps(T_P e) { EPS = e; } T_P x, y; Point2d() : x(0), y(0) {} Point2d(T_P x, T_P y) : x(x), y(y) {} Point2d(const std::pair &p) : x(p.first), y(p.second) {} Point2d(const std::complex &p) : x(p.real()), y(p.imag()) {} std::complex to_complex() const noexcept { return {x, y}; } Point2d operator+(const Point2d &p) const noexcept { return Point2d(x + p.x, y + p.y); } Point2d operator-(const Point2d &p) const noexcept { return Point2d(x - p.x, y - p.y); } Point2d operator*(const Point2d &p) const noexcept { static_assert(std::is_floating_point::value == true); return Point2d(x * p.x - y * p.y, x * p.y + y * p.x); } Point2d operator*(T_P d) const noexcept { return Point2d(x * d, y * d); } Point2d operator/(T_P d) const noexcept { static_assert(std::is_floating_point::value == true); return Point2d(x / d, y / d); } Point2d inv() const { static_assert(std::is_floating_point::value == true); return conj() / norm2(); } Point2d operator/(const Point2d &p) const { return (*this) * p.inv(); } bool operator<(const Point2d &r) const noexcept { return x != r.x ? x < r.x : y < r.y; } bool operator==(const Point2d &r) const noexcept { return x == r.x and y == r.y; } bool operator!=(const Point2d &r) const noexcept { return !((*this) == r); } T_P dot(Point2d p) const noexcept { return x * p.x + y * p.y; } T_P det(Point2d p) const noexcept { return x * p.y - y * p.x; } T_P absdet(Point2d p) const noexcept { return std::abs(det(p)); } T_P norm() const noexcept { static_assert(std::is_floating_point::value == true); return std::sqrt(x * x + y * y); } T_P norm2() const noexcept { return x * x + y * y; } T_P arg() const noexcept { return std::atan2(y, x); } // rotate point/vector by rad Point2d rotate(T_P rad) const noexcept { static_assert(std::is_floating_point::value == true); return Point2d(x * std::cos(rad) - y * std::sin(rad), x * std::sin(rad) + y * std::cos(rad)); } Point2d normalized() const { static_assert(std::is_floating_point::value == true); return (*this) / this->norm(); } Point2d conj() const noexcept { return Point2d(x, -y); } template friend IStream &operator>>(IStream &is, Point2d &p) { T_P x, y; is >> x >> y; p = Point2d(x, y); return is; } template friend OStream &operator<<(OStream &os, const Point2d &p) { return os << '(' << p.x << ',' << p.y << ')'; } }; template <> double Point2d::EPS = 1e-9; template <> long double Point2d::EPS = 1e-12; template <> long long Point2d::EPS = 0; // Whether two segments s1t1 & s2t2 intersect or not (endpoints not included) // Google Code Jam 2013 Round 3 - Rural Planning // Google Code Jam 2021 Round 3 - Fence Design template bool intersect_open_segments(Point2d s1, Point2d t1, Point2d s2, Point2d t2) { if (s1 == t1 or s2 == t2) return false; // Not segment but point int nbad = 0; for (int t = 0; t < 2; t++) { Point2d v1 = t1 - s1, v2 = t2 - s2; T den = v2.det(v1); if (den == 0) { if (s1.det(v1) == s2.det(v1)) { auto L1 = s1.dot(v1), R1 = t1.dot(v1); auto L2 = s2.dot(v1), R2 = t2.dot(v1); if (L1 > R1) std::swap(L1, R1); if (L2 > R2) std::swap(L2, R2); if (L1 > L2) std::swap(L1, L2), std::swap(R1, R2); return R1 > L2; } else { return false; } } else { auto num = v2.det(s2 - s1); if ((0 < num and num < den) or (den < num and num < 0)) nbad++; } std::swap(s1, s2); std::swap(t1, t2); } return nbad == 2; } using Pt = Point2d; int main() { int N, M; cin >> N >> M; vector pts(N * 2); for (auto &v : pts) cin >> v; shortest_path graph(N * 2); auto f = [&](int i, int d) { return i * 2 + d; }; REP(i, N) REP(d, 2) REP(j, N) REP(e, 2) { const int s = f(i, d), t = f(j, e); if (s > t) continue; bool good = true; REP(u, N * 2) FOR(v, u + 1, N * 2) { if (s == u or s == v or t == u or t == v) continue; if (intersect_open_segments(pts[s], pts[t], pts[u], pts[v])) good = false; } if (good) graph.add_bi_edge(s, t, (pts[s] - pts[t]).norm()); } vector> dists; REP(i, N * 2) { graph.dijkstra_vquad(i); dists.push_back(graph.dist); } while (M--) { int i, d, j, e; cin >> i >> d >> j >> e; --i, --d, --j, --e; cout << dists.at(f(i, d)).at(f(j, e)) << '\n'; } }