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:heavy_check_mark: graph/centroid_decomposition.hpp

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#include "graph/base.hpp"
#include "graph/shortest_path/bfs01.hpp"

// 頂点ベースの重心分解
// f(par, V, indptr)
template <typename F>
void centroid_decomposition_0_dfs(vc<int>& par, vc<int>& vs, F f) {
  const int N = len(par);
  assert(N >= 1);
  int c = -1;
  vc<int> sz(N, 1);
  FOR_R(i, N) {
    if (sz[i] >= ceil<int>(N, 2)) {
      c = i;
      break;
    }
    sz[par[i]] += sz[i];
  }
  vc<int> color(N);
  vc<int> V = {c};
  int nc = 1;
  FOR(v, 1, N) {
    if (par[v] == c) { V.eb(v), color[v] = nc++; }
  }
  if (c > 0) {
    for (int a = par[c]; a != -1; a = par[a]) { color[a] = nc, V.eb(a); }
    ++nc;
  }
  FOR(i, N) {
    if (i != c && color[i] == 0) color[i] = color[par[i]], V.eb(i);
  }
  vc<int> indptr(nc + 1);
  FOR(i, N) indptr[1 + color[i]]++;
  FOR(i, nc) indptr[i + 1] += indptr[i];
  vc<int> counter = indptr;
  vc<int> ord(N);
  for (auto& v: V) { ord[counter[color[v]]++] = v; }
  vc<int> new_idx(N);
  FOR(i, N) new_idx[ord[i]] = i;
  vc<int> name(N);
  FOR(i, N) name[new_idx[i]] = vs[i];
  {
    vc<int> tmp(N, -1);
    FOR(i, 1, N) {
      int a = new_idx[i], b = new_idx[par[i]];
      if (a > b) swap(a, b);
      tmp[b] = a;
    }
    swap(par, tmp);
  }
  f(par, name, indptr);
  FOR(k, 1, nc) {
    int L = indptr[k], R = indptr[k + 1];
    vc<int> par1(R - L, -1);
    vc<int> name1(R - L, -1);
    name1[0] = name[0];
    FOR(i, L, R) name1[i - L] = name[i];
    FOR(i, L, R) { par1[i - L] = max(par[i] - L, -1); }
    centroid_decomposition_0_dfs(par1, name1, f);
  }
}

/*
https://maspypy.com/%e9%87%8d%e5%bf%83%e5%88%86%e8%a7%a3%e3%83%bb1-3%e9%87%8d%e5%bf%83%e5%88%86%e8%a7%a3%e3%81%ae%e3%81%8a%e7%b5%b5%e6%8f%8f%e3%81%8d
centroid_decomposition_1:長さ 2 以上のパス全体
f(par, V, n1, n2)
[1,1+n1]: color 1
[1+n1,1+n1+n2]: color 2
*/
template <typename F>
void centroid_decomposition_1_dfs(vc<int>& par, vc<int> vs, F f) {
  const int N = len(par);
  assert(N > 1);
  if (N == 2) { return; }
  int c = -1;
  vc<int> sz(N, 1);
  FOR_R(i, N) {
    if (sz[i] >= ceil<int>(N, 2)) {
      c = i;
      break;
    }
    sz[par[i]] += sz[i];
  }
  vc<int> color(N, -1);
  int take = 0;
  vc<int> ord(N, -1);
  ord[c] = 0;
  int p = 1;
  FOR(v, 1, N) {
    if (par[v] == c && take + sz[v] <= floor<int>(N - 1, 2)) {
      color[v] = 0, ord[v] = p++, take += sz[v];
    }
  }
  FOR(i, 1, N) {
    if (color[par[i]] == 0) color[i] = 0, ord[i] = p++;
  }
  int n0 = p - 1;
  for (int a = par[c]; a != -1; a = par[a]) { color[a] = 1, ord[a] = p++; }
  FOR(i, N) {
    if (i != c && color[i] == -1) color[i] = 1, ord[i] = p++;
  }
  assert(p == N);
  int n1 = N - 1 - n0;
  vc<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(N, -1);
  vc<int> V0(n0 + 1), V1(n1 + 1), V2(N);
  FOR(v, N) {
    int i = ord[v];
    V2[i] = vs[v];
    if (color[v] != 1) { V0[i] = vs[v]; }
    if (color[v] != 0) { V1[max(i - n0, 0)] = vs[v]; }
  }
  FOR(v, 1, N) {
    int a = ord[v], b = ord[par[v]];
    if (a > b) swap(a, b);
    par2[b] = a;
    if (color[v] != 1 && color[par[v]] != 1) par0[b] = a;
    if (color[v] != 0 && color[par[v]] != 0)
      par1[max(b - n0, 0)] = max(a - n0, 0);
  }
  f(par2, V2, n0, n1);
  centroid_decomposition_1_dfs(par0, V0, f);
  centroid_decomposition_1_dfs(par1, V1, f);
}

/*
https://maspypy.com/%e9%87%8d%e5%bf%83%e5%88%86%e8%a7%a3%e3%83%bb1-3%e9%87%8d%e5%bf%83%e5%88%86%e8%a7%a3%e3%81%ae%e3%81%8a%e7%b5%b5%e6%8f%8f%e3%81%8d
f(par2, V2, color)
color in [-1,0,1], -1 is virtual.
*/
template <typename F>
void centroid_decomposition_2_dfs(vc<int>& par, vc<int>& vs, vc<int>& real,
                                  F f) {
  const int N = len(par);
  assert(N > 1);
  if (N == 2) {
    if (real[0] && real[1]) {
      vc<int> color = {0, 1};
      f(par, vs, color);
    }
    return;
  }
  int c = -1;
  vc<int> sz(N, 1);
  FOR_R(i, N) {
    if (sz[i] >= ceil<int>(N, 2)) {
      c = i;
      break;
    }
    sz[par[i]] += sz[i];
  }
  vc<int> color(N, -1);
  int take = 0;
  vc<int> ord(N, -1);
  ord[c] = 0;
  int p = 1;
  FOR(v, 1, N) {
    if (par[v] == c && take + sz[v] <= floor<int>(N - 1, 2)) {
      color[v] = 0, ord[v] = p++, take += sz[v];
    }
  }
  FOR(i, 1, N) {
    if (color[par[i]] == 0) color[i] = 0, ord[i] = p++;
  }
  int n0 = p - 1;
  for (int a = par[c]; a != -1; a = par[a]) { color[a] = 1, ord[a] = p++; }
  FOR(i, N) {
    if (i != c && color[i] == -1) color[i] = 1, ord[i] = p++;
  }
  assert(p == N);
  int n1 = N - 1 - n0;
  vc<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(N, -1);
  vc<int> V0(n0 + 1), V1(n1 + 1), V2(N);
  vc<int> rea0(n0 + 1), rea1(n1 + 1), rea2(N);
  FOR(v, N) {
    int i = ord[v];
    V2[i] = vs[v], rea2[i] = real[v];
    if (color[v] != 1) { V0[i] = vs[v], rea0[i] = real[v]; }
    if (color[v] != 0) {
      V1[max(i - n0, 0)] = vs[v], rea1[max(i - n0, 0)] = real[v];
    }
  }
  FOR(v, 1, N) {
    int a = ord[v], b = ord[par[v]];
    if (a > b) swap(a, b);
    par2[b] = a;
    if (color[v] != 1 && color[par[v]] != 1) par0[b] = a;
    if (color[v] != 0 && color[par[v]] != 0)
      par1[max(b - n0, 0)] = max(a - n0, 0);
  }
  if (real[c]) {
    color.assign(N, -1);
    color[0] = 0;
    FOR(i, 1, N) color[i] = rea2[i] ? 1 : -1;
    f(par2, V2, color);
    rea0[0] = rea1[0] = rea2[0] = 0;
  }
  color.assign(N, -1);
  FOR(i, 1, N) if (rea2[i]) color[i] = (i <= n0 ? 0 : 1);
  f(par2, V2, color);
  centroid_decomposition_2_dfs(par0, V0, rea0, f);
  centroid_decomposition_2_dfs(par1, V1, rea1, f);
}

// f(par, V, color)
// V: label in original tree, dfs order
// color in [-1,0,1], color=-1: virtual
template <int MODE, typename GT, typename F>
void centroid_decomposition(GT& G, F f) {
  static_assert(!GT::is_directed);
  const int N = G.N;
  if (N == 1) return;
  vc<int> V(N), par(N, -1);
  int l = 0, r = 0;
  V[r++] = 0;
  while (l < r) {
    int v = V[l++];
    for (auto& e: G[v]) {
      if (e.to != par[v]) V[r++] = e.to, par[e.to] = v;
    }
  }
  assert(r == N);
  vc<int> new_idx(N);
  FOR(i, N) new_idx[V[i]] = i;
  vc<int> tmp(N, -1);
  FOR(i, 1, N) {
    int j = par[i];
    tmp[new_idx[i]] = new_idx[j];
  }
  swap(par, tmp);
  static_assert(MODE == 0 || MODE == 1 || MODE == 2);
  if constexpr (MODE == 0) { centroid_decomposition_0_dfs(par, V, f); }
  elif constexpr(MODE == 1) { centroid_decomposition_1_dfs(par, V, f); }
  else {
    vc<int> real(N, 1);
    centroid_decomposition_2_dfs(par, V, real, f);
  }
}
#line 2 "graph/base.hpp"

template <typename T>
struct Edge {
  int frm, to;
  T cost;
  int id;
};

template <typename T = int, bool directed = false>
struct Graph {
  static constexpr bool is_directed = directed;
  int N, M;
  using cost_type = T;
  using edge_type = Edge<T>;
  vector<edge_type> edges;
  vector<int> indptr;
  vector<edge_type> csr_edges;
  vc<int> vc_deg, vc_indeg, vc_outdeg;
  bool prepared;

  class OutgoingEdges {
  public:
    OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}

    const edge_type* begin() const {
      if (l == r) { return 0; }
      return &G->csr_edges[l];
    }

    const edge_type* end() const {
      if (l == r) { return 0; }
      return &G->csr_edges[r];
    }

  private:
    const Graph* G;
    int l, r;
  };

  bool is_prepared() { return prepared; }

  Graph() : N(0), M(0), prepared(0) {}
  Graph(int N) : N(N), M(0), prepared(0) {}

  void build(int n) {
    N = n, M = 0;
    prepared = 0;
    edges.clear();
    indptr.clear();
    csr_edges.clear();
    vc_deg.clear();
    vc_indeg.clear();
    vc_outdeg.clear();
  }

  void add(int frm, int to, T cost = 1, int i = -1) {
    assert(!prepared);
    assert(0 <= frm && 0 <= to && to < N);
    if (i == -1) i = M;
    auto e = edge_type({frm, to, cost, i});
    edges.eb(e);
    ++M;
  }

#ifdef FASTIO
  // wt, off
  void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }

  void read_graph(int M, bool wt = false, int off = 1) {
    for (int m = 0; m < M; ++m) {
      INT(a, b);
      a -= off, b -= off;
      if (!wt) {
        add(a, b);
      } else {
        T c;
        read(c);
        add(a, b, c);
      }
    }
    build();
  }
#endif

  void build() {
    assert(!prepared);
    prepared = true;
    indptr.assign(N + 1, 0);
    for (auto&& e: edges) {
      indptr[e.frm + 1]++;
      if (!directed) indptr[e.to + 1]++;
    }
    for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; }
    auto counter = indptr;
    csr_edges.resize(indptr.back() + 1);
    for (auto&& e: edges) {
      csr_edges[counter[e.frm]++] = e;
      if (!directed)
        csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
    }
  }

  OutgoingEdges operator[](int v) const {
    assert(prepared);
    return {this, indptr[v], indptr[v + 1]};
  }

  vc<int> deg_array() {
    if (vc_deg.empty()) calc_deg();
    return vc_deg;
  }

  pair<vc<int>, vc<int>> deg_array_inout() {
    if (vc_indeg.empty()) calc_deg_inout();
    return {vc_indeg, vc_outdeg};
  }

  int deg(int v) {
    if (vc_deg.empty()) calc_deg();
    return vc_deg[v];
  }

  int in_deg(int v) {
    if (vc_indeg.empty()) calc_deg_inout();
    return vc_indeg[v];
  }

  int out_deg(int v) {
    if (vc_outdeg.empty()) calc_deg_inout();
    return vc_outdeg[v];
  }

#ifdef FASTIO
  void debug() {
    print("Graph");
    if (!prepared) {
      print("frm to cost id");
      for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);
    } else {
      print("indptr", indptr);
      print("frm to cost id");
      FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);
    }
  }
#endif

  vc<int> new_idx;
  vc<bool> used_e;

  // G における頂点 V[i] が、新しいグラフで i になるようにする
  // {G, es}
  // sum(deg(v)) の計算量になっていて、
  // 新しいグラフの n+m より大きい可能性があるので注意
  Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
    if (len(new_idx) != N) new_idx.assign(N, -1);
    int n = len(V);
    FOR(i, n) new_idx[V[i]] = i;
    Graph<T, directed> G(n);
    vc<int> history;
    FOR(i, n) {
      for (auto&& e: (*this)[V[i]]) {
        if (len(used_e) <= e.id) used_e.resize(e.id + 1);
        if (used_e[e.id]) continue;
        int a = e.frm, b = e.to;
        if (new_idx[a] != -1 && new_idx[b] != -1) {
          history.eb(e.id);
          used_e[e.id] = 1;
          int eid = (keep_eid ? e.id : -1);
          G.add(new_idx[a], new_idx[b], e.cost, eid);
        }
      }
    }
    FOR(i, n) new_idx[V[i]] = -1;
    for (auto&& eid: history) used_e[eid] = 0;
    G.build();
    return G;
  }

  Graph<T, true> to_directed_tree(int root = -1) {
    if (root == -1) root = 0;
    assert(!is_directed && prepared && M == N - 1);
    Graph<T, true> G1(N);
    vc<int> par(N, -1);
    auto dfs = [&](auto& dfs, int v) -> void {
      for (auto& e: (*this)[v]) {
        if (e.to == par[v]) continue;
        par[e.to] = v, dfs(dfs, e.to);
      }
    };
    dfs(dfs, root);
    for (auto& e: edges) {
      int a = e.frm, b = e.to;
      if (par[a] == b) swap(a, b);
      assert(par[b] == a);
      G1.add(a, b, e.cost);
    }
    G1.build();
    return G1;
  }

private:
  void calc_deg() {
    assert(vc_deg.empty());
    vc_deg.resize(N);
    for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;
  }

  void calc_deg_inout() {
    assert(vc_indeg.empty());
    vc_indeg.resize(N);
    vc_outdeg.resize(N);
    for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; }
  }
};
#line 3 "graph/shortest_path/bfs01.hpp"

template <typename T, typename GT>
pair<vc<T>, vc<int>> bfs01(GT& G, int v) {
  assert(G.is_prepared());
  int N = G.N;
  vc<T> dist(N, infty<T>);
  vc<int> par(N, -1);
  deque<int> que;

  dist[v] = 0;
  que.push_front(v);
  while (!que.empty()) {
    auto v = que.front();
    que.pop_front();
    for (auto&& e: G[v]) {
      if (dist[e.to] == infty<T> || dist[e.to] > dist[e.frm] + e.cost) {
        dist[e.to] = dist[e.frm] + e.cost;
        par[e.to] = e.frm;
        if (e.cost == 0)
          que.push_front(e.to);
        else
          que.push_back(e.to);
      }
    }
  }
  return {dist, par};
}

// 多点スタート。[dist, par, root]
template <typename T, typename GT>
tuple<vc<T>, vc<int>, vc<int>> bfs01(GT& G, vc<int> vs) {
  assert(G.is_prepared());
  int N = G.N;
  vc<T> dist(N, infty<T>);
  vc<int> par(N, -1);
  vc<int> root(N, -1);
  deque<int> que;

  for (auto&& v: vs) {
    dist[v] = 0;
    root[v] = v;
    que.push_front(v);
  }

  while (!que.empty()) {
    auto v = que.front();
    que.pop_front();
    for (auto&& e: G[v]) {
      if (dist[e.to] == infty<T> || dist[e.to] > dist[e.frm] + e.cost) {
        dist[e.to] = dist[e.frm] + e.cost;
        root[e.to] = root[e.frm];
        par[e.to] = e.frm;
        if (e.cost == 0)
          que.push_front(e.to);
        else
          que.push_back(e.to);
      }
    }
  }
  return {dist, par, root};
}
#line 3 "graph/centroid_decomposition.hpp"

// 頂点ベースの重心分解
// f(par, V, indptr)
template <typename F>
void centroid_decomposition_0_dfs(vc<int>& par, vc<int>& vs, F f) {
  const int N = len(par);
  assert(N >= 1);
  int c = -1;
  vc<int> sz(N, 1);
  FOR_R(i, N) {
    if (sz[i] >= ceil<int>(N, 2)) {
      c = i;
      break;
    }
    sz[par[i]] += sz[i];
  }
  vc<int> color(N);
  vc<int> V = {c};
  int nc = 1;
  FOR(v, 1, N) {
    if (par[v] == c) { V.eb(v), color[v] = nc++; }
  }
  if (c > 0) {
    for (int a = par[c]; a != -1; a = par[a]) { color[a] = nc, V.eb(a); }
    ++nc;
  }
  FOR(i, N) {
    if (i != c && color[i] == 0) color[i] = color[par[i]], V.eb(i);
  }
  vc<int> indptr(nc + 1);
  FOR(i, N) indptr[1 + color[i]]++;
  FOR(i, nc) indptr[i + 1] += indptr[i];
  vc<int> counter = indptr;
  vc<int> ord(N);
  for (auto& v: V) { ord[counter[color[v]]++] = v; }
  vc<int> new_idx(N);
  FOR(i, N) new_idx[ord[i]] = i;
  vc<int> name(N);
  FOR(i, N) name[new_idx[i]] = vs[i];
  {
    vc<int> tmp(N, -1);
    FOR(i, 1, N) {
      int a = new_idx[i], b = new_idx[par[i]];
      if (a > b) swap(a, b);
      tmp[b] = a;
    }
    swap(par, tmp);
  }
  f(par, name, indptr);
  FOR(k, 1, nc) {
    int L = indptr[k], R = indptr[k + 1];
    vc<int> par1(R - L, -1);
    vc<int> name1(R - L, -1);
    name1[0] = name[0];
    FOR(i, L, R) name1[i - L] = name[i];
    FOR(i, L, R) { par1[i - L] = max(par[i] - L, -1); }
    centroid_decomposition_0_dfs(par1, name1, f);
  }
}

/*
https://maspypy.com/%e9%87%8d%e5%bf%83%e5%88%86%e8%a7%a3%e3%83%bb1-3%e9%87%8d%e5%bf%83%e5%88%86%e8%a7%a3%e3%81%ae%e3%81%8a%e7%b5%b5%e6%8f%8f%e3%81%8d
centroid_decomposition_1:長さ 2 以上のパス全体
f(par, V, n1, n2)
[1,1+n1]: color 1
[1+n1,1+n1+n2]: color 2
*/
template <typename F>
void centroid_decomposition_1_dfs(vc<int>& par, vc<int> vs, F f) {
  const int N = len(par);
  assert(N > 1);
  if (N == 2) { return; }
  int c = -1;
  vc<int> sz(N, 1);
  FOR_R(i, N) {
    if (sz[i] >= ceil<int>(N, 2)) {
      c = i;
      break;
    }
    sz[par[i]] += sz[i];
  }
  vc<int> color(N, -1);
  int take = 0;
  vc<int> ord(N, -1);
  ord[c] = 0;
  int p = 1;
  FOR(v, 1, N) {
    if (par[v] == c && take + sz[v] <= floor<int>(N - 1, 2)) {
      color[v] = 0, ord[v] = p++, take += sz[v];
    }
  }
  FOR(i, 1, N) {
    if (color[par[i]] == 0) color[i] = 0, ord[i] = p++;
  }
  int n0 = p - 1;
  for (int a = par[c]; a != -1; a = par[a]) { color[a] = 1, ord[a] = p++; }
  FOR(i, N) {
    if (i != c && color[i] == -1) color[i] = 1, ord[i] = p++;
  }
  assert(p == N);
  int n1 = N - 1 - n0;
  vc<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(N, -1);
  vc<int> V0(n0 + 1), V1(n1 + 1), V2(N);
  FOR(v, N) {
    int i = ord[v];
    V2[i] = vs[v];
    if (color[v] != 1) { V0[i] = vs[v]; }
    if (color[v] != 0) { V1[max(i - n0, 0)] = vs[v]; }
  }
  FOR(v, 1, N) {
    int a = ord[v], b = ord[par[v]];
    if (a > b) swap(a, b);
    par2[b] = a;
    if (color[v] != 1 && color[par[v]] != 1) par0[b] = a;
    if (color[v] != 0 && color[par[v]] != 0)
      par1[max(b - n0, 0)] = max(a - n0, 0);
  }
  f(par2, V2, n0, n1);
  centroid_decomposition_1_dfs(par0, V0, f);
  centroid_decomposition_1_dfs(par1, V1, f);
}

/*
https://maspypy.com/%e9%87%8d%e5%bf%83%e5%88%86%e8%a7%a3%e3%83%bb1-3%e9%87%8d%e5%bf%83%e5%88%86%e8%a7%a3%e3%81%ae%e3%81%8a%e7%b5%b5%e6%8f%8f%e3%81%8d
f(par2, V2, color)
color in [-1,0,1], -1 is virtual.
*/
template <typename F>
void centroid_decomposition_2_dfs(vc<int>& par, vc<int>& vs, vc<int>& real,
                                  F f) {
  const int N = len(par);
  assert(N > 1);
  if (N == 2) {
    if (real[0] && real[1]) {
      vc<int> color = {0, 1};
      f(par, vs, color);
    }
    return;
  }
  int c = -1;
  vc<int> sz(N, 1);
  FOR_R(i, N) {
    if (sz[i] >= ceil<int>(N, 2)) {
      c = i;
      break;
    }
    sz[par[i]] += sz[i];
  }
  vc<int> color(N, -1);
  int take = 0;
  vc<int> ord(N, -1);
  ord[c] = 0;
  int p = 1;
  FOR(v, 1, N) {
    if (par[v] == c && take + sz[v] <= floor<int>(N - 1, 2)) {
      color[v] = 0, ord[v] = p++, take += sz[v];
    }
  }
  FOR(i, 1, N) {
    if (color[par[i]] == 0) color[i] = 0, ord[i] = p++;
  }
  int n0 = p - 1;
  for (int a = par[c]; a != -1; a = par[a]) { color[a] = 1, ord[a] = p++; }
  FOR(i, N) {
    if (i != c && color[i] == -1) color[i] = 1, ord[i] = p++;
  }
  assert(p == N);
  int n1 = N - 1 - n0;
  vc<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(N, -1);
  vc<int> V0(n0 + 1), V1(n1 + 1), V2(N);
  vc<int> rea0(n0 + 1), rea1(n1 + 1), rea2(N);
  FOR(v, N) {
    int i = ord[v];
    V2[i] = vs[v], rea2[i] = real[v];
    if (color[v] != 1) { V0[i] = vs[v], rea0[i] = real[v]; }
    if (color[v] != 0) {
      V1[max(i - n0, 0)] = vs[v], rea1[max(i - n0, 0)] = real[v];
    }
  }
  FOR(v, 1, N) {
    int a = ord[v], b = ord[par[v]];
    if (a > b) swap(a, b);
    par2[b] = a;
    if (color[v] != 1 && color[par[v]] != 1) par0[b] = a;
    if (color[v] != 0 && color[par[v]] != 0)
      par1[max(b - n0, 0)] = max(a - n0, 0);
  }
  if (real[c]) {
    color.assign(N, -1);
    color[0] = 0;
    FOR(i, 1, N) color[i] = rea2[i] ? 1 : -1;
    f(par2, V2, color);
    rea0[0] = rea1[0] = rea2[0] = 0;
  }
  color.assign(N, -1);
  FOR(i, 1, N) if (rea2[i]) color[i] = (i <= n0 ? 0 : 1);
  f(par2, V2, color);
  centroid_decomposition_2_dfs(par0, V0, rea0, f);
  centroid_decomposition_2_dfs(par1, V1, rea1, f);
}

// f(par, V, color)
// V: label in original tree, dfs order
// color in [-1,0,1], color=-1: virtual
template <int MODE, typename GT, typename F>
void centroid_decomposition(GT& G, F f) {
  static_assert(!GT::is_directed);
  const int N = G.N;
  if (N == 1) return;
  vc<int> V(N), par(N, -1);
  int l = 0, r = 0;
  V[r++] = 0;
  while (l < r) {
    int v = V[l++];
    for (auto& e: G[v]) {
      if (e.to != par[v]) V[r++] = e.to, par[e.to] = v;
    }
  }
  assert(r == N);
  vc<int> new_idx(N);
  FOR(i, N) new_idx[V[i]] = i;
  vc<int> tmp(N, -1);
  FOR(i, 1, N) {
    int j = par[i];
    tmp[new_idx[i]] = new_idx[j];
  }
  swap(par, tmp);
  static_assert(MODE == 0 || MODE == 1 || MODE == 2);
  if constexpr (MODE == 0) { centroid_decomposition_0_dfs(par, V, f); }
  elif constexpr(MODE == 1) { centroid_decomposition_1_dfs(par, V, f); }
  else {
    vc<int> real(N, 1);
    centroid_decomposition_2_dfs(par, V, real, f);
  }
}
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