#include #include #include #include #include /* struct Info { using V; using E; using Point; using Path; static Point rake(Point, Point); static Point id(); static Path to_path(V, Point); static Path compress(Path, E, Path); static Path reverse(Path); static Point to_point(E, Path); }; */ template class top_tree { using V = typename Info::V; using E = typename Info::E; using Point = typename Info::Point; using Path = typename Info::Path; struct node_type; using node_ptr = node_type*; struct vertex_node { V v; Path path; vertex_node(V v_, Path path_) : v(std::move(v_)), path(std::move(path_)) {} }; struct solid_edge_node { bool rev; E e; Path sum; solid_edge_node(E e_, Path sum_) : rev(false), e(std::move(e_)), sum(std::move(sum_)) {} }; struct dashed_edge_node { E e; Point point; Point sum; dashed_edge_node(E e_, Point point_, Point sum_) : e(std::move(e_)), point(std::move(point_)), sum(std::move(sum_)) {} }; using data_variant = std::variant; struct node_type { node_ptr p; std::array c; data_variant data; template node_type(Args &&... args) : p(nullptr), c({ nullptr, nullptr, nullptr }), data(std::forward(args)...) {} }; static void link_child(node_type& par, const node_ptr ch, const int dir) { par.c[dir] = ch; if (ch) { ch->p = ∥ } } static int get_dir(const node_type& node) { if (node.p) { for (int i = 0; i < 3; i++) { if (node.p->c[i] == &node) { return i; } } assert(false); } else { return 1; } } static void p_replace(node_type& prev, node_type& n) { if (prev.p) { prev.p->c[get_dir(prev)] = &n; n.p = prev.p; } else { n.p = nullptr; } } static Point get_sum_point(const node_ptr ptr) { if (ptr) { return std::get(ptr->data).sum; } else { return Info::id(); } } static const Path& get_sum_path(const node_type& node) { struct { const Path& operator()(const vertex_node& v) const { return v.path; } const Path& operator()(const solid_edge_node& s) const { return s.sum; } const Path& operator()(const dashed_edge_node&) const { throw "top_tree: internal error"; } } visitor{}; return std::visit(visitor, node.data); } static void update(node_type& node) { struct { node_type& node; void operator()(vertex_node&) const { throw "top_tree: internal error"; } void operator()(solid_edge_node& s) const { s.sum = Info::compress(get_sum_path(*node.c[0]), s.e, get_sum_path(*node.c[2])); } void operator()(dashed_edge_node& d) const { d.sum = Info::rake(d.point, Info::rake(get_sum_point(node.c[0]), get_sum_point(node.c[2]))); } } visitor{ node }; std::visit(visitor, node.data); } static void rotate(node_type& node, const int dir) { node_type& ch = *node.c[dir ^ 2]; ch.p = node.p; if (node.p) { node.p->c[get_dir(node)] = &ch; } link_child(node, ch.c[dir], dir ^ 2); update(node); link_child(ch, &node, dir); } static void splay(node_type& node) { while (true) { const int d0 = get_dir(node); if (d0 == 1) { break; } node_type& p = *node.p; const int d1 = get_dir(p); if (d1 == 1) { rotate(p, d0 ^ 2); break; } node_type& pp = *p.p; if (d0 == d1) { rotate(pp, d1 ^ 2); rotate(p, d0 ^ 2); } else { rotate(p, d0 ^ 2); rotate(pp, d1 ^ 2); } } update(node); } static void reverse(node_type& node) { struct { void operator()(vertex_node&) const {} void operator()(solid_edge_node& s) const { s.sum = Info::reverse(std::move(s.sum)); s.rev = !s.rev; } void operator()(dashed_edge_node&) const { throw "top_tree: internal error"; } } visitor{}; std::visit(visitor, node.data); } static void propagate(node_type& node) { if (node.p) { propagate(*node.p); } struct { node_type& node; void operator()(vertex_node&) const {} void operator()(solid_edge_node& s) const { if (s.rev) { s.rev = false; std::swap(node.c[0], node.c[2]); reverse(*node.c[0]); reverse(*node.c[2]); } } void operator()(dashed_edge_node&) const {} } visitor{ node }; std::visit(visitor, node.data); } static node_ptr merge(const node_ptr x, node_ptr y) { if (!y) { return x; } y->p = nullptr; while (y->c[0]) { y = y->c[0]; } link_child(*y, x, 0); splay(*y); return y; } static void expose_edge(node_type& node) { propagate(node); node_ptr ptr = &node; if (ptr->data.index() == 1) { splay(*ptr); ptr = ptr->p; } while (ptr) { splay(*ptr); node_type& v = *ptr->p; if (get_dir(v) != 1) { splay(*v.p); } if (get_dir(v) != 1) { splay(*v.p); } if (get_dir(v) == 2 && get_dir(*v.p) == 0) { splay(*v.p); } if (get_dir(v) == 0) { node_type& p = *v.p; p_replace(p, *ptr); link_child(v, &p, 1); link_child(p, p.c[2], 1); link_child(p, ptr->c[0], 0); link_child(p, ptr->c[2], 2); E e = std::move(std::get(p.data).e); Point point = Info::to_point(e, get_sum_path(*p.c[1])); Point sum = Info::rake( point, Info::rake(get_sum_point(p.c[0]), get_sum_point(p.c[2]))); p.data = data_variant(std::in_place_type, std::move(e), std::move(point), std::move(sum)); } else { link_child(v, merge(ptr->c[0], ptr->c[2]), 1); p_replace(v, *ptr); } vertex_node& inner = std::get(v.data); inner.path = Info::to_path(inner.v, get_sum_point(v.c[1])); link_child(*ptr, &v, 0); link_child(*ptr, ptr->c[1], 2); ptr->c[1] = nullptr; E e = std::move(std::get(ptr->data).e); Path sum = Info::compress(get_sum_path(*ptr->c[0]), e, get_sum_path(*ptr->c[2])); ptr->data = data_variant(std::in_place_type, std::move(e), std::move(sum)); splay(*ptr); ptr = ptr->p; } splay(node); } static void check(const node_type& n) { if (n.p) { get_dir(n); } for (int i = 0; i < 3; i++) { if (n.c[i]) { assert(n.c[i]->p == &n); } } struct { const node_type& n; void operator()(const vertex_node&) const { assert(n.c[0] == nullptr); if (n.c[1]) { assert(n.c[1]->data.index() == 2); } assert(n.c[2] == nullptr); if (n.p) { assert(n.p->data.index() == 1 || n.p->data.index() == 2); } } void operator()(const solid_edge_node&) const { assert(n.c[0] != nullptr); assert(n.c[0]->data.index() == 0 || n.c[0]->data.index() == 1); assert(n.c[1] == nullptr); assert(n.c[2] != nullptr); assert(n.c[2]->data.index() == 0 || n.c[2]->data.index() == 1); if (n.p) { assert(n.p->data.index() == 1 || n.p->data.index() == 2); } } void operator()(const dashed_edge_node&) const { if (n.c[0]) { assert(n.c[0]->data.index() == 2); } assert(n.c[1] != nullptr); assert(n.c[1]->data.index() == 0 || n.c[1]->data.index() == 1); if (n.c[2]) { assert(n.c[2]->data.index() == 2); } assert(n.p != nullptr); assert(n.p->data.index() == 0 || n.p->data.index() == 2); } } visitor{ n }; std::visit(visitor, n.data); } static void check_cp(node_type& n) { struct { node_type& n; void operator()(vertex_node&) const { check_ds(n.c[1]); } void operator()(solid_edge_node&) const { check_cp(*n.c[0]); check_cp(*n.c[2]); } void operator()(dashed_edge_node&) const { assert(false); } } visitor{ n }; std::visit(visitor, n.data); } static void check_ds(const node_ptr ptr) { if (ptr) { struct { node_type& n; void operator()(vertex_node&) const { assert(false); } void operator()(solid_edge_node&) const { assert(false); } void operator()(dashed_edge_node&) const { check_ds(n.c[0]); check_cp(*n.c[1]); check_ds(n.c[2]); } } visitor{ *ptr }; std::visit(visitor, ptr->data); } } std::vector vertex_nodes; std::vector edge_nodes; node_ptr free_list; template node_type& allocate(Args &&... args) { if (free_list) { node_type& n = *free_list; free_list = n.c[0]; n = node_type(std::forward(args)...); return n; } else { edge_nodes.emplace_back(std::forward(args)...); return edge_nodes.back(); } } node_type& expose_vertex(const int v_) { node_type& v = vertex_nodes[v_]; if (v.p) { expose_edge(*v.p); } if (get_dir(v) == 2) { splay(*v.p); } if (get_dir(v) == 0) { node_type& p = *v.p; splay(p); p_replace(p, *p.c[0]); link_child(p, v.c[1], 0); link_child(p, p.c[2], 1); p.c[2] = nullptr; link_child(v, &p, 1); E e = std::move(std::get(p.data).e); Point point = Info::to_point(e, get_sum_path(*p.c[1])); Point sum = Info::rake( point, Info::rake(get_sum_point(p.c[0]), get_sum_point(p.c[2]))); p.data = data_variant(std::in_place_type, std::move(e), std::move(point), std::move(sum)); vertex_node& inner = std::get(v.data); inner.path = Info::to_path(inner.v, get_sum_point(v.c[1])); } if (v.p) { node_type& p = *v.p; splay(p); return p; } else { return v; } } node_type& evert(const int v) { node_type& r = expose_vertex(v); reverse(r); return r; } public: class edge_handle { friend top_tree; node_ptr ptr; edge_handle(const node_ptr ptr_) : ptr(ptr_) {} public: edge_handle() : ptr(nullptr) {} E get() const { struct { E operator()(vertex_node&) const { throw "top_tree: internal error"; } E operator()(solid_edge_node& n) const { return n.e; } E operator()(dashed_edge_node& n) const { return n.e; } } visitor{}; return std::visit(visitor, *ptr); } }; top_tree(std::vector vertices) : vertex_nodes(), edge_nodes(), free_list(nullptr) { const int n = vertices.size(); vertex_nodes.reserve(n); for (int i = 0; i < n; i++) { Path sum = Info::to_path(vertices[i], Info::id()); vertex_nodes.emplace_back(std::in_place_type, std::move(vertices[i]), std::move(sum)); } edge_nodes.reserve(n - 1); } void set_vertex(const int i, V v) { node_type& n = vertex_nodes[i]; vertex_node& inner = std::get(n.data); inner.v = std::move(v); inner.path = Info::to_path(inner.v, get_sum_point(n.c[1])); // check(); if (n.p) { expose_edge(*n.p); } // check(); } void set_edge(const edge_handle h, E e) { expose_edge(*h.ptr); std::get(h.ptr->data).e = std::move(e); update(*h.ptr); } Path get_path(const int u, const int v) { evert(u); // check(); node_type& r = expose_vertex(v); // check(); return get_sum_path(r); } edge_handle link(const int u, const int v, E e) { node_type& u_ = expose_vertex(u); node_type& v_ = evert(v); Path sum = Info::compress(get_sum_path(u_), e, get_sum_path(v_)); node_type& r = allocate(std::in_place_type, std::move(e), std::move(sum)); link_child(r, &u_, 0); link_child(r, &v_, 2); return edge_handle(&r); } void cut(const edge_handle h) { node_type& n = *h.ptr; expose_edge(n); n.c[0]->p = nullptr; n.c[2]->p = nullptr; n.c[0] = free_list; free_list = &n; } void check() { for (auto& v : vertex_nodes) { check(v); } std::vector used(edge_nodes.size(), true); { node_ptr p = free_list; while (p) { used[p - edge_nodes.data()] = false; p = p->c[0]; } } for (int i = 0; i < edge_nodes.size(); i++) { if (used[i]) { check(edge_nodes[i]); } } for (auto& v : vertex_nodes) { if (!v.p) { check_cp(v); } } for (int i = 0; i < edge_nodes.size(); i++) { if (used[i] && !edge_nodes[i].p) { check_cp(edge_nodes[i]); } } } }; #include using u64 = unsigned long long; struct lcasum { struct V { int id; bool on; }; struct E {}; struct Point { u64 score; u64 hollow; int count; }; struct Path { u64 scl, scr; u64 a; int count; }; static Point rake(Point x, Point y) { return { x.score + y.score, x.hollow + y.hollow + u64(x.count) * u64(y.count), x.count + y.count }; } static Point id() { return { 0, 0 }; } static Path to_path(V v, Point p) { if (v.on) { p.score += u64(v.id) * u64(p.count); p.count += 1; } p.score += p.hollow * u64(v.id); return { p.score, p.score, u64(p.count) * u64(v.id), p.count }; } static Path compress(Path l, E, Path r) { return { l.scl + r.scl + l.a * r.count, l.scr + r.scr + r.a * l.count, l.a + r.a, l.count + r.count }; } static Path reverse(Path p) { std::swap(p.scl, p.scr); return p; } static Point to_point(E, Path p) { return { p.scl, 0, p.count }; } }; #include #include #include #include #include #include namespace noshi91 { namespace tree_utility_impl { int bsr(int x) { #if defined(__GNUC__) return 31 - __builtin_clz(x); #elif defined(_MSC_VER) unsigned long i; _BitScanReverse(&i, x); return i; #else static_assert(false, "not implemented"); return -1; #endif } using std::vector; class tree_utility { public: std::vector> cs; std::vector in, out, par; tree_utility(int n, std::vector> es) : cs(n), in(n), out(n), par(n) { std::vector> g(n); for (const auto& [a, b] : es) { g[a].push_back(b); g[b].push_back(a); } int time = 0; const auto f = [&](const auto& f, const int v, const int p) -> void { in[v] = time; time++; par[v] = p; for (const int u : g[v]) { if (u != p) { f(f, u, v); cs[v].push_back(u); } } out[v] = time; }; f(f, 0, -1); } int step(const int u, const int v) const { if (in[u] <= in[v] && out[v] <= out[u]) { int l = 0, r = cs[u].size(); while (r - l > 1) { const int m = (l + r) / 2; if (in[cs[u][m]] <= in[v]) { l = m; } else { r = m; } } return cs[u][l]; } else { return par[u]; } } }; } // namespace tree_utility_impl using tree_utility_impl::tree_utility; } // namespace noshi91 #include #include #include int main() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); int N, Q; std::cin >> N >> Q; std::vector vs(N); for (int i = 0; i < N; i++) { vs[i] = { i + 1, false }; } top_tree tree(vs); std::map, typename top_tree::edge_handle> map; std::vector> es; for (int i = 0; i < N - 1; i++) { int a, b; std::cin >> a >> b; a -= 1; b -= 1; map[std::minmax(a, b)] = tree.link(a, b, {}); es.push_back({ a, b }); } const noshi91::tree_utility ut(N, es); for (int i = 0; i < Q; i++) { int u, r, v; std::cin >> u >> r >> v; u--; r--; v--; vs[u].on ^= 1; tree.set_vertex(u, vs[u]); if (r == v) { std::cout << tree.get_path(r, r).scl << "\n"; } else { int p = ut.step(v, r); // std::cerr << "## " << v << " " << p << " " << r << "\n"; auto& ref = map[std::minmax(v, p)]; tree.cut(ref); std::cout << tree.get_path(v, v).scl << "\n"; ref = tree.link(v, p, {}); } } return 0; }