#825561 (C++17(gcc12)) No.2163 LCA Sum Query

• 問題: No.2163 LCA Sum Query
• ユーザー: noshi91
• 提出日時: 2022-12-14 01:00:08
• 言語: C++17(gcc12) (gcc 12.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 801 ms / 6,000 ms
• コード長: 17,042 bytes
• コンパイル時間: 1,975 ms
• コンパイル使用メモリ: 123,016 KB
• 実行使用メモリ: 25,024 KB
• 最終ジャッジ日時: 2024-11-07 18:10:21
• 合計ジャッジ時間: 19,145 ms
• ジャッジサーバーID （参考情報）: judge2 / judge5

ファイルパターン	結果
sample	AC * 2
other	AC * 40

ソースコード

#include <array>
#include <cassert>
#include <utility>
#include <variant>
#include <vector>

/*

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 Info> 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<vertex_node, solid_edge_node, dashed_edge_node>;

  struct node_type {
    node_ptr p;
    std::array<node_ptr, 3> c;
    data_variant data;

    template <class... Args>
    node_type(Args &&... args)
      : p(nullptr), c({ nullptr, nullptr, nullptr }),
      data(std::forward<Args>(args)...) {}
  };

  static void link_child(node_type& par, const node_ptr ch, const int dir) {
    par.c[dir] = ch;
    if (ch) {
      ch->p = &par;
    }
  }

  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<dashed_edge_node>(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<solid_edge_node>(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<dashed_edge_node>,
          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<vertex_node>(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<dashed_edge_node>(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<solid_edge_node>,
        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<node_type> vertex_nodes;
  std::vector<node_type> edge_nodes;
  node_ptr free_list;

  template <class... Args> node_type& allocate(Args &&... args) {
    if (free_list) {
      node_type& n = *free_list;
      free_list = n.c[0];
      n = node_type(std::forward<Args>(args)...);
      return n;
    }
    else {
      edge_nodes.emplace_back(std::forward<Args>(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<solid_edge_node>(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<dashed_edge_node>, std::move(e),
        std::move(point), std::move(sum));
      vertex_node& inner = std::get<vertex_node>(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<V> 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<vertex_node>,
        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<vertex_node>(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<solid_edge_node>(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<solid_edge_node>, 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<bool> 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 <map>

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 <algorithm>
#include <cassert>
#include <climits>
#include <cstdint>
#include <utility>
#include <vector>

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<std::vector<int>> cs;
      std::vector<int> in, out, par;

      tree_utility(int n, std::vector<std::pair<int, int>> es)
        : cs(n), in(n), out(n), par(n) {
        std::vector<std::vector<int>> 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 <iostream>
#include <utility>
#include <vector>

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);

  int N, Q;
  std::cin >> N >> Q;
  std::vector<lcasum::V> vs(N);
  for (int i = 0; i < N; i++) {
    vs[i] = { i + 1, false };
  }
  top_tree<lcasum> tree(vs);

  std::map<std::pair<int, int>, typename top_tree<lcasum>::edge_handle> map;

  std::vector<std::pair<int, int>> 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;
}