Auxiliary Tree
(tree/auxiliary-tree.hpp)

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• Last update: 2026-06-08 17:59:24+09:00
• Include: #include "tree/auxiliary-tree.hpp"

Depends on

• グラフテンプレート (graph/graph-template.hpp)
• Heavy Light Decomposition(重軽分解) (tree/heavy-light-decomposition.hpp)

Verified with

• verify/verify-yuki/yuki-2588.test.cpp

Code

#pragma once

#include <algorithm>
#include <utility>
#include <vector>
using namespace std;

#include "heavy-light-decomposition.hpp"

template <typename G>
struct AuxiliaryTree {
  G g;
  HeavyLightDecomposition<G> hld;
  AuxiliaryTree(const G& _g, int root = 0) : g(_g), hld(g, root) {}

  // ps : 頂点集合
  // 返り値 : (aux tree, aux tree の頂点と g の頂点の対応表)
  // aux tree は 親->子 の向きの辺のみ含まれる
  // ps が空の場合は空のグラフを返す
  pair<vector<vector<int>>, vector<int>> get(vector<int> ps) {
    if (ps.empty()) return {};
    auto comp = [&](int i, int j) { return hld.down[i] < hld.down[j]; };
    sort(begin(ps), end(ps), comp);
    for (int i = 0, ie = ps.size(); i + 1 < ie; i++) {
      ps.push_back(hld.lca(ps[i], ps[i + 1]));
    }
    sort(begin(ps), end(ps), comp);
    ps.erase(unique(begin(ps), end(ps)), end(ps));

    vector<vector<int>> aux(ps.size());
    vector<int> rs;
    rs.push_back(0);
    for (int i = 1; i < (int)ps.size(); i++) {
      int l = hld.lca(ps[rs.back()], ps[i]);
      while (ps[rs.back()] != l) rs.pop_back();
      aux[rs.back()].push_back(i);
      rs.push_back(i);
    }
    return make_pair(aux, ps);
  }
};

/**
 * @brief Auxiliary Tree
 */

#line 2 "tree/auxiliary-tree.hpp"

#include <algorithm>
#include <utility>
#include <vector>
using namespace std;

#line 2 "tree/heavy-light-decomposition.hpp"

#line 2 "graph/graph-template.hpp"

template <typename T>
struct edge {
  int src, to;
  T cost;

  edge(int _to, T _cost) : src(-1), to(_to), cost(_cost) {}
  edge(int _src, int _to, T _cost) : src(_src), to(_to), cost(_cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnweightedGraph = vector<vector<int>>;

// Input of (Unweighted) Graph
UnweightedGraph graph(int N, int M = -1, bool is_directed = false,
                      bool is_1origin = true) {
  UnweightedGraph g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    if (is_1origin) x--, y--;
    g[x].push_back(y);
    if (!is_directed) g[y].push_back(x);
  }
  return g;
}

// Input of Weighted Graph
template <typename T>
WeightedGraph<T> wgraph(int N, int M = -1, bool is_directed = false,
                        bool is_1origin = true) {
  WeightedGraph<T> g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    cin >> c;
    if (is_1origin) x--, y--;
    g[x].emplace_back(x, y, c);
    if (!is_directed) g[y].emplace_back(y, x, c);
  }
  return g;
}

// Input of Edges
template <typename T>
Edges<T> esgraph([[maybe_unused]] int N, int M, int is_weighted = true,
                 bool is_1origin = true) {
  Edges<T> es;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    if (is_weighted)
      cin >> c;
    else
      c = 1;
    if (is_1origin) x--, y--;
    es.emplace_back(x, y, c);
  }
  return es;
}

// Input of Adjacency Matrix
template <typename T>
vector<vector<T>> adjgraph(int N, int M, T INF, int is_weighted = true,
                           bool is_directed = false, bool is_1origin = true) {
  vector<vector<T>> d(N, vector<T>(N, INF));
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    if (is_weighted)
      cin >> c;
    else
      c = 1;
    if (is_1origin) x--, y--;
    d[x][y] = c;
    if (!is_directed) d[y][x] = c;
  }
  return d;
}

/**
 * @brief グラフテンプレート
 */
#line 4 "tree/heavy-light-decomposition.hpp"

template <typename G>
struct HeavyLightDecomposition {
 private:
  void dfs_sz(int cur) {
    size[cur] = 1;
    for (auto& dst : g[cur]) {
      if (dst == par[cur]) {
        if (g[cur].size() >= 2 && int(dst) == int(g[cur][0]))
          swap(g[cur][0], g[cur][1]);
        else
          continue;
      }
      depth[dst] = depth[cur] + 1;
      par[dst] = cur;
      dfs_sz(dst);
      size[cur] += size[dst];
      if (size[dst] > size[g[cur][0]]) {
        swap(dst, g[cur][0]);
      }
    }
  }

  void dfs_hld(int cur) {
    down[cur] = id++;
    for (auto dst : g[cur]) {
      if (dst == par[cur]) continue;
      nxt[dst] = (int(dst) == int(g[cur][0]) ? nxt[cur] : int(dst));
      dfs_hld(dst);
    }
    up[cur] = id;
  }

  // [u, v)
  vector<pair<int, int>> ascend(int u, int v) const {
    vector<pair<int, int>> res;
    while (nxt[u] != nxt[v]) {
      res.emplace_back(down[u], down[nxt[u]]);
      u = par[nxt[u]];
    }
    if (u != v) res.emplace_back(down[u], down[v] + 1);
    return res;
  }

  // (u, v]
  vector<pair<int, int>> descend(int u, int v) const {
    if (u == v) return {};
    if (nxt[u] == nxt[v]) return {{down[u] + 1, down[v]}};
    auto res = descend(u, par[nxt[v]]);
    res.emplace_back(down[nxt[v]], down[v]);
    return res;
  }

 public:
  G& g;
  int root, id;
  vector<int> size, depth, down, up, nxt, par;
  HeavyLightDecomposition(G& _g, int _root = 0)
      : g(_g),
        root(_root),
        id(0),
        size(g.size(), 0),
        depth(g.size(), 0),
        down(g.size(), -1),
        up(g.size(), -1),
        nxt(g.size(), root),
        par(g.size(), root) {
    dfs_sz(root);
    dfs_hld(root);
  }

  pair<int, int> idx(int i) const { return make_pair(down[i], up[i]); }

  template <typename F>
  void path_query(int u, int v, bool vertex, const F& f) {
    int l = lca(u, v);
    for (auto&& [a, b] : ascend(u, l)) {
      int s = a + 1, t = b;
      s > t ? f(t, s) : f(s, t);
    }
    if (vertex) f(down[l], down[l] + 1);
    for (auto&& [a, b] : descend(l, v)) {
      int s = a, t = b + 1;
      s > t ? f(t, s) : f(s, t);
    }
  }

  template <typename F>
  void path_noncommutative_query(int u, int v, bool vertex, const F& f) {
    int l = lca(u, v);
    for (auto&& [a, b] : ascend(u, l)) f(a + 1, b);
    if (vertex) f(down[l], down[l] + 1);
    for (auto&& [a, b] : descend(l, v)) f(a, b + 1);
  }

  template <typename F>
  void subtree_query(int u, bool vertex, const F& f) {
    f(down[u] + int(!vertex), up[u]);
  }

  int lca(int a, int b) {
    while (nxt[a] != nxt[b]) {
      if (down[a] < down[b]) swap(a, b);
      a = par[nxt[a]];
    }
    return depth[a] < depth[b] ? a : b;
  }

  int dist(int a, int b) { return depth[a] + depth[b] - depth[lca(a, b)] * 2; }
};

/**
 * @brief Heavy Light Decomposition(重軽分解)
 */
#line 9 "tree/auxiliary-tree.hpp"

template <typename G>
struct AuxiliaryTree {
  G g;
  HeavyLightDecomposition<G> hld;
  AuxiliaryTree(const G& _g, int root = 0) : g(_g), hld(g, root) {}

  // ps : 頂点集合
  // 返り値 : (aux tree, aux tree の頂点と g の頂点の対応表)
  // aux tree は 親->子 の向きの辺のみ含まれる
  // ps が空の場合は空のグラフを返す
  pair<vector<vector<int>>, vector<int>> get(vector<int> ps) {
    if (ps.empty()) return {};
    auto comp = [&](int i, int j) { return hld.down[i] < hld.down[j]; };
    sort(begin(ps), end(ps), comp);
    for (int i = 0, ie = ps.size(); i + 1 < ie; i++) {
      ps.push_back(hld.lca(ps[i], ps[i + 1]));
    }
    sort(begin(ps), end(ps), comp);
    ps.erase(unique(begin(ps), end(ps)), end(ps));

    vector<vector<int>> aux(ps.size());
    vector<int> rs;
    rs.push_back(0);
    for (int i = 1; i < (int)ps.size(); i++) {
      int l = hld.lca(ps[rs.back()], ps[i]);
      while (ps[rs.back()] != l) rs.pop_back();
      aux[rs.back()].push_back(i);
      rs.push_back(i);
    }
    return make_pair(aux, ps);
  }
};

/**
 * @brief Auxiliary Tree
 */

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