cp-library

C++ Library for Competitive Programming

View the Project on GitHub emthrm/cp-library

:warning: グラフ/木/指定された頂点たちの最小共通祖先関係を保って木を圧縮してできる補助的な木
(test/graph/tree/auxiliary_tree.test.cpp)

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Code

/*
 * @title グラフ/木/指定された頂点たちの最小共通祖先関係を保って木を圧縮してできる補助的な木
 *
 * verification-helper: IGNORE
 * verification-helper: PROBLEM https://atcoder.jp/contests/typical90/tasks/typical90_ai
 */

#include <iostream>
#include <ranges>
#include <vector>

#include "emthrm/graph/edge.hpp"
#include "emthrm/graph/tree/auxiliary_tree.hpp"

int main() {
  int n;
  std::cin >> n;
  std::vector<std::vector<emthrm::Edge<int>>> graph(n);
  for (const int i : std::views::iota(0, n - 1)) {
    int a, b;
    std::cin >> a >> b;
    --a; --b;
    graph[a].emplace_back(a, b, 1);
    graph[b].emplace_back(b, a, 1);
  }
  const emthrm::AuxiliaryTree<int> auxiliary_tree(graph);
  int q;
  std::cin >> q;
  while (q--) {
    int k;
    std::cin >> k;
    std::vector<int> v(k);
    for (int& v_i : v) std::cin >> v_i, --v_i;
    int ans = 0;
    for (const std::vector<emthrm::Edge<int>>& edges
         : auxiliary_tree.query(v).first) {
      for (const emthrm::Edge<int>& e : edges) ans += e.cost;
    }
    std::cout << ans / 2 << '\n';
  }
  return 0;
}
#line 1 "test/graph/tree/auxiliary_tree.test.cpp"
/*
 * @title グラフ/木/指定された頂点たちの最小共通祖先関係を保って木を圧縮してできる補助的な木
 *
 * verification-helper: IGNORE
 * verification-helper: PROBLEM https://atcoder.jp/contests/typical90/tasks/typical90_ai
 */

#include <iostream>
#include <ranges>
#include <vector>

#line 1 "include/emthrm/graph/edge.hpp"
/**
 * @title 辺
 */

#ifndef EMTHRM_GRAPH_EDGE_HPP_
#define EMTHRM_GRAPH_EDGE_HPP_

#include <compare>

namespace emthrm {

template <typename CostType>
struct Edge {
  CostType cost;
  int src, dst;

  explicit Edge(const int src, const int dst, const CostType cost = 0)
      : cost(cost), src(src), dst(dst) {}

  auto operator<=>(const Edge& x) const = default;
};

}  // namespace emthrm

#endif  // EMTHRM_GRAPH_EDGE_HPP_
#line 1 "include/emthrm/graph/tree/auxiliary_tree.hpp"



#include <algorithm>
#include <iterator>
#line 7 "include/emthrm/graph/tree/auxiliary_tree.hpp"
#include <utility>
#line 9 "include/emthrm/graph/tree/auxiliary_tree.hpp"

#line 1 "include/emthrm/graph/edge.hpp"
/**
 * @title 辺
 */

#ifndef EMTHRM_GRAPH_EDGE_HPP_
#define EMTHRM_GRAPH_EDGE_HPP_

#include <compare>

namespace emthrm {

template <typename CostType>
struct Edge {
  CostType cost;
  int src, dst;

  explicit Edge(const int src, const int dst, const CostType cost = 0)
      : cost(cost), src(src), dst(dst) {}

  auto operator<=>(const Edge& x) const = default;
};

}  // namespace emthrm

#endif  // EMTHRM_GRAPH_EDGE_HPP_
#line 1 "include/emthrm/graph/tree/lowest_common_ancestor_by_euler_tour_technique.hpp"



#line 7 "include/emthrm/graph/tree/lowest_common_ancestor_by_euler_tour_technique.hpp"

#line 1 "include/emthrm/data_structure/sparse_table.hpp"



#line 5 "include/emthrm/data_structure/sparse_table.hpp"
#include <bit>
#include <cassert>
#include <functional>
#line 9 "include/emthrm/data_structure/sparse_table.hpp"

namespace emthrm {

template <typename Band>
struct SparseTable {
  using BinOp = std::function<Band(Band, Band)>;

  SparseTable() = default;

  explicit SparseTable(const std::vector<Band>& a, const BinOp bin_op) {
    init(a, bin_op);
  }

  void init(const std::vector<Band>& a, const BinOp bin_op_) {
    bin_op = bin_op_;
    const int n = a.size();
    assert(n > 0);
    lg.assign(n + 1, 0);
    for (int i = 2; i <= n; ++i) {
      lg[i] = lg[i >> 1] + 1;
    }
    const int table_h = std::countr_zero(std::bit_floor(a.size())) + 1;
    data.assign(table_h, std::vector<Band>(n));
    std::copy(a.begin(), a.end(), data.front().begin());
    for (int i = 1; i < table_h; ++i) {
      for (int j = 0; j + (1 << i) <= n; ++j) {
        data[i][j] = bin_op(data[i - 1][j], data[i - 1][j + (1 << (i - 1))]);
      }
    }
  }

  Band query(const int left, const int right) const {
    assert(left < right);
    const int h = lg[right - left];
    return bin_op(data[h][left], data[h][right - (1 << h)]);
  }

 private:
  BinOp bin_op;
  std::vector<int> lg;
  std::vector<std::vector<Band>> data;
};

}  // namespace emthrm


#line 1 "include/emthrm/graph/edge.hpp"
/**
 * @title 辺
 */

#ifndef EMTHRM_GRAPH_EDGE_HPP_
#define EMTHRM_GRAPH_EDGE_HPP_

#include <compare>

namespace emthrm {

template <typename CostType>
struct Edge {
  CostType cost;
  int src, dst;

  explicit Edge(const int src, const int dst, const CostType cost = 0)
      : cost(cost), src(src), dst(dst) {}

  auto operator<=>(const Edge& x) const = default;
};

}  // namespace emthrm

#endif  // EMTHRM_GRAPH_EDGE_HPP_
#line 1 "include/emthrm/graph/tree/euler_tour_technique.hpp"



#line 5 "include/emthrm/graph/tree/euler_tour_technique.hpp"

#line 1 "include/emthrm/graph/edge.hpp"
/**
 * @title 辺
 */

#ifndef EMTHRM_GRAPH_EDGE_HPP_
#define EMTHRM_GRAPH_EDGE_HPP_

#include <compare>

namespace emthrm {

template <typename CostType>
struct Edge {
  CostType cost;
  int src, dst;

  explicit Edge(const int src, const int dst, const CostType cost = 0)
      : cost(cost), src(src), dst(dst) {}

  auto operator<=>(const Edge& x) const = default;
};

}  // namespace emthrm

#endif  // EMTHRM_GRAPH_EDGE_HPP_
#line 7 "include/emthrm/graph/tree/euler_tour_technique.hpp"

namespace emthrm {

template <typename CostType>
struct EulerTourTechnique {
  std::vector<int> preorder, depth, left, right, down, up;
  std::vector<CostType> tour;

  explicit EulerTourTechnique(
      const std::vector<std::vector<Edge<CostType>>> &graph, const int root = 0)
      : graph(graph) {
    const int n = graph.size();
    left.resize(n);
    right.resize(n);
    down.assign(n, -1);
    up.assign(n, (n - 1) << 1);
    dfs(-1, root, 0);
  }

  template <typename Fn>
  void update_v(const int ver, const Fn f) const {
    f(left[ver], right[ver] + 1);
  }

  template <typename T, typename Fn>
  T query_v(const int ver, const Fn f) const {
    return f(left[ver], right[ver] + 1);
  }

  template <typename T, typename Fn>
  T query_e(const int u, const int v, const Fn f) const {
    return f(down[u] + 1, down[v] + 1);
  }

  template <typename Fn>
  void update_subtree_e(const int ver, const Fn f) const {
    f(down[ver] + 1, up[ver]);
  }

  template <typename T, typename Fn>
  T query_subtree_e(const int ver, const Fn f) const {
    return f(down[ver] + 1, up[ver]);
  }

 private:
  const std::vector<std::vector<Edge<CostType>>> graph;

  void dfs(const int par, const int ver, const int cur_depth) {
    left[ver] = preorder.size();
    preorder.emplace_back(ver);
    depth.emplace_back(cur_depth);
    for (const Edge<CostType>& e : graph[ver]) {
      if (e.dst != par) {
        down[e.dst] = tour.size();
        tour.emplace_back(e.cost);
        dfs(ver, e.dst, cur_depth + 1);
        preorder.emplace_back(ver);
        depth.emplace_back(cur_depth);
        up[e.dst] = tour.size();
        tour.emplace_back(-e.cost);
      }
    }
    right[ver] = preorder.size() - 1;
  }
};

}  // namespace emthrm


#line 11 "include/emthrm/graph/tree/lowest_common_ancestor_by_euler_tour_technique.hpp"

namespace emthrm {

template <typename CostType>
struct LowestCommonAncestor : EulerTourTechnique<CostType> {
  explicit LowestCommonAncestor(
      const std::vector<std::vector<Edge<CostType>>>& graph,
      const int root = 0)
      : EulerTourTechnique<CostType>(graph, root) {
    const int n = this->preorder.size();
    std::vector<std::pair<int, int>> nodes(n);
    for (int i = 0; i < n; ++i) {
      nodes[i] = {this->depth[i], this->preorder[i]};
    }
    sparse_table.init(
        nodes,
        [](const std::pair<int, int>& a, const std::pair<int, int>& b)
            -> std::pair<int, int> {
          return std::min(a, b);
        });
  }

  int query(int u, int v) const {
    u = this->left[u];
    v = this->left[v];
    if (u > v) std::swap(u, v);
    return sparse_table.query(u, v + 1).second;
  }

 private:
  SparseTable<std::pair<int, int>> sparse_table;
};

}  // namespace emthrm


#line 12 "include/emthrm/graph/tree/auxiliary_tree.hpp"

namespace emthrm {

template <typename CostType>
struct AuxiliaryTree {
  LowestCommonAncestor<CostType> euler_tour;

  explicit AuxiliaryTree(
      const std::vector<std::vector<Edge<CostType>>>& graph, const int root = 0)
      : euler_tour(graph, root), depth(graph.size(), 0) {
    const auto dfs = [this, &graph](
        auto dfs, const int par, const int ver) -> void {
      for (const Edge<CostType>& e : graph[ver]) {
        if (e.dst == par) continue;
        depth[e.dst] = depth[ver] + e.cost;
        dfs(dfs, ver, e.dst);
      }
    };
    dfs(dfs, -1, root);
  }

  std::pair<std::vector<std::vector<Edge<CostType>>>,
            std::vector<int>> query(std::vector<int> vertices) const {
    if (vertices.empty()) [[unlikely]] return {};
    static std::vector<int> mp(depth.size(), -1);
    std::ranges::sort(vertices, {},
                      [&](const int v) -> int { return euler_tour.left[v]; });
    std::vector<std::vector<Edge<CostType>>> graph;
    std::vector<int> inv;
    const auto add_vertex = [this, &graph, &inv](const int v) -> void {
      mp[v] = graph.size();
      graph.emplace_back();
      inv.emplace_back(v);
    };
    const auto add_edge = [this, &graph](int u, int v) -> void {
      const CostType cost = depth[v] - depth[u];
      u = mp[u];
      v = mp[v];
      graph[u].emplace_back(u, v, cost);
      graph[v].emplace_back(v, u, cost);
    };
    add_vertex(vertices.front());
    std::vector<int> stck{vertices.front()};
    for (const int i : std::views::iota(1, std::ssize(vertices))) {
      const int l = euler_tour.query(vertices[i - 1], vertices[i]);
      if (mp[l] == -1) add_vertex(l);
      if (l != vertices[i - 1]) {
        const int depth_l = euler_tour.depth[euler_tour.left[l]];
        int cur = stck.back();
        stck.pop_back();
        while (!stck.empty() &&
               euler_tour.depth[euler_tour.left[stck.back()]] > depth_l) {
          add_edge(stck.back(), cur);
          cur = stck.back();
          stck.pop_back();
        }
        add_edge(l, cur);
        if (stck.empty() || stck.back() != l) stck.emplace_back(l);
      }
      add_vertex(vertices[i]);
      stck.emplace_back(vertices[i]);
    }
    for (; stck.size() >= 2; stck.pop_back()) {
      add_edge(stck.end()[-2], stck.back());
    }
    for (const int v : inv) mp[v] = -1;
    return {graph, inv};
  }

 private:
  std::vector<CostType> depth;
};

}  // namespace emthrm


#line 14 "test/graph/tree/auxiliary_tree.test.cpp"

int main() {
  int n;
  std::cin >> n;
  std::vector<std::vector<emthrm::Edge<int>>> graph(n);
  for (const int i : std::views::iota(0, n - 1)) {
    int a, b;
    std::cin >> a >> b;
    --a; --b;
    graph[a].emplace_back(a, b, 1);
    graph[b].emplace_back(b, a, 1);
  }
  const emthrm::AuxiliaryTree<int> auxiliary_tree(graph);
  int q;
  std::cin >> q;
  while (q--) {
    int k;
    std::cin >> k;
    std::vector<int> v(k);
    for (int& v_i : v) std::cin >> v_i, --v_i;
    int ans = 0;
    for (const std::vector<emthrm::Edge<int>>& edges
         : auxiliary_tree.query(v).first) {
      for (const emthrm::Edge<int>& e : edges) ans += e.cost;
    }
    std::cout << ans / 2 << '\n';
  }
  return 0;
}
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