graph/centroid_decomposition_old.hpp

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• Last update: 2024-04-19 02:20:22+09:00
• Include: #include "graph/centroid_decomposition_old.hpp"

Depends on

• graph/base.hpp
• graph/find_centroid.hpp

Verified with

• test/yukicoder/1769.test.cpp
• test/yukicoder/1796.test.cpp

Code

#include "graph/base.hpp"

#include "graph/find_centroid.hpp"



template <typename GT>
struct Centroid_Decomposition {
  using edge_type = typename GT::edge_type;
  GT& G;
  int N;
  vc<int> sz;
  vc<int> par;
  vector<int> cdep; // depth in centroid tree

  bool calculated;

  Centroid_Decomposition(GT& G)
      : G(G), N(G.N), sz(G.N), par(G.N), cdep(G.N, -1) {
    calculated = 0;
    build();
  }

private:
  int find(int v) {
    vc<int> V = {v};
    par[v] = -1;
    int p = 0;
    while (p < len(V)) {
      int v = V[p++];
      sz[v] = 0;
      for (auto&& e: G[v]) {
        if (e.to == par[v] || cdep[e.to] != -1) continue;
        par[e.to] = v;
        V.eb(e.to);
      }
    }
    while (len(V)) {
      int v = V.back();
      V.pop_back();
      sz[v] += 1;
      if (p - sz[v] <= p / 2) return v;
      sz[par[v]] += sz[v];
    }
    return -1;
  }
  void build() {
    assert(G.is_prepared());
    assert(!calculated);
    calculated = 1;

    vc<pair<int, int>> st;
    st.eb(0, 0);
    while (!st.empty()) {
      auto [lv, v] = st.back();
      st.pop_back();
      auto c = find(v);
      cdep[c] = lv;
      for (auto&& e: G[c]) {
        if (cdep[e.to] == -1) { st.eb(lv + 1, e.to); }
      }
    }
  }

public:
  // V, dat, indptr

  template <typename T, typename F>
  tuple<vc<int>, vc<T>, vc<int>> collect_path_data(int root, T root_val, F f) {
    vc<int> V = {root};
    vc<T> dp = {root_val};
    vc<int> indptr = {0, 1};
    for (auto&& e: G[root]) {
      int nxt = e.to;
      if (cdep[nxt] < cdep[root]) continue;
      int p = len(V);
      V.eb(nxt);
      dp.eb(f(root_val, e));
      par[nxt] = root;
      while (p < len(V)) {
        int v = V[p];
        T val = dp[p];
        p++;
        for (auto&& e: G[v]) {
          if (e.to == par[v]) continue;
          if (cdep[e.to] < cdep[root]) continue;
          par[e.to] = v;
          V.eb(e.to);
          dp.eb(f(val, e));
        }
      }
      indptr.eb(len(V));
    }
    return {V, dp, indptr};
  }

  // V, dist, indptr

  tuple<vc<int>, vc<int>, vc<int>> collect_dist(int root) {
    auto f = [&](int x, auto e) -> int { return x + 1; };
    return collect_path_data(root, 0, f);
  }

  // (V, H, indptr), (V[i] in G) = (i in H).

  // 0,1,2... is a dfs order in H.

  tuple<vc<int>, Graph<typename GT::cost_type, true>, vc<int>> get_subgraph(
      int root) {
    static vc<int> conv;
    while (len(conv) < N) conv.eb(-1);

    vc<int> V = {root};
    vc<int> indptr = {0, 1};
    conv[root] = 0;
    using cost_type = typename GT::cost_type;
    vc<tuple<int, int, cost_type>> edges;

    auto dfs = [&](auto& dfs, int v, int p) -> void {
      conv[v] = len(V);
      V.eb(v);
      for (auto&& e: G[v]) {
        int to = e.to;
        if (to == p) continue;
        if (cdep[to] < cdep[root]) continue;
        dfs(dfs, to, v);
        edges.eb(conv[v], conv[to], e.cost);
      }
    };
    for (auto&& e: G[root]) {
      if (cdep[e.to] < cdep[root]) continue;
      dfs(dfs, e.to, root);
      edges.eb(conv[root], conv[e.to], e.cost);
      indptr.eb(len(V));
    }
    int n = len(V);
    Graph<typename GT::cost_type, true> H(n);
    for (auto&& [a, b, c]: edges) H.add(a, b, c);
    H.build();
    for (auto&& v: V) conv[v] = -1;
    return {V, H, indptr};
  }
};

#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}
  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;
  }

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 2 "graph/find_centroid.hpp"

// (v,w) or (v,-1)

template <typename GT>
pair<int, int> find_centroids(GT& G) {
  int N = G.N;
  vc<int> par(N, -1);
  vc<int> V(N);
  vc<int> sz(N);
  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]) {
        par[e.to] = v;
        V[r++] = e.to;
      }
  }
  FOR_R(i, N) {
    int v = V[i];
    sz[v] += 1;
    int p = par[v];
    if (p != -1) sz[p] += sz[v];
  }

  int M = N / 2;
  auto check = [&](int v) -> bool {
    if (N - sz[v] > M) return false;
    for (auto&& e: G[v]) {
      if (e.to != par[v] && sz[e.to] > M) return false;
    }
    return true;
  };
  pair<int, int> ANS = {-1, -1};
  FOR(v, N) if (check(v)) {
    if (ANS.fi != -1) {
      ANS.se = v;
    } else {
      ANS.fi = v;
    }
  }
  return ANS;
}
#line 3 "graph/centroid_decomposition_old.hpp"


template <typename GT>
struct Centroid_Decomposition {
  using edge_type = typename GT::edge_type;
  GT& G;
  int N;
  vc<int> sz;
  vc<int> par;
  vector<int> cdep; // depth in centroid tree

  bool calculated;

  Centroid_Decomposition(GT& G)
      : G(G), N(G.N), sz(G.N), par(G.N), cdep(G.N, -1) {
    calculated = 0;
    build();
  }

private:
  int find(int v) {
    vc<int> V = {v};
    par[v] = -1;
    int p = 0;
    while (p < len(V)) {
      int v = V[p++];
      sz[v] = 0;
      for (auto&& e: G[v]) {
        if (e.to == par[v] || cdep[e.to] != -1) continue;
        par[e.to] = v;
        V.eb(e.to);
      }
    }
    while (len(V)) {
      int v = V.back();
      V.pop_back();
      sz[v] += 1;
      if (p - sz[v] <= p / 2) return v;
      sz[par[v]] += sz[v];
    }
    return -1;
  }
  void build() {
    assert(G.is_prepared());
    assert(!calculated);
    calculated = 1;

    vc<pair<int, int>> st;
    st.eb(0, 0);
    while (!st.empty()) {
      auto [lv, v] = st.back();
      st.pop_back();
      auto c = find(v);
      cdep[c] = lv;
      for (auto&& e: G[c]) {
        if (cdep[e.to] == -1) { st.eb(lv + 1, e.to); }
      }
    }
  }

public:
  // V, dat, indptr

  template <typename T, typename F>
  tuple<vc<int>, vc<T>, vc<int>> collect_path_data(int root, T root_val, F f) {
    vc<int> V = {root};
    vc<T> dp = {root_val};
    vc<int> indptr = {0, 1};
    for (auto&& e: G[root]) {
      int nxt = e.to;
      if (cdep[nxt] < cdep[root]) continue;
      int p = len(V);
      V.eb(nxt);
      dp.eb(f(root_val, e));
      par[nxt] = root;
      while (p < len(V)) {
        int v = V[p];
        T val = dp[p];
        p++;
        for (auto&& e: G[v]) {
          if (e.to == par[v]) continue;
          if (cdep[e.to] < cdep[root]) continue;
          par[e.to] = v;
          V.eb(e.to);
          dp.eb(f(val, e));
        }
      }
      indptr.eb(len(V));
    }
    return {V, dp, indptr};
  }

  // V, dist, indptr

  tuple<vc<int>, vc<int>, vc<int>> collect_dist(int root) {
    auto f = [&](int x, auto e) -> int { return x + 1; };
    return collect_path_data(root, 0, f);
  }

  // (V, H, indptr), (V[i] in G) = (i in H).

  // 0,1,2... is a dfs order in H.

  tuple<vc<int>, Graph<typename GT::cost_type, true>, vc<int>> get_subgraph(
      int root) {
    static vc<int> conv;
    while (len(conv) < N) conv.eb(-1);

    vc<int> V = {root};
    vc<int> indptr = {0, 1};
    conv[root] = 0;
    using cost_type = typename GT::cost_type;
    vc<tuple<int, int, cost_type>> edges;

    auto dfs = [&](auto& dfs, int v, int p) -> void {
      conv[v] = len(V);
      V.eb(v);
      for (auto&& e: G[v]) {
        int to = e.to;
        if (to == p) continue;
        if (cdep[to] < cdep[root]) continue;
        dfs(dfs, to, v);
        edges.eb(conv[v], conv[to], e.cost);
      }
    };
    for (auto&& e: G[root]) {
      if (cdep[e.to] < cdep[root]) continue;
      dfs(dfs, e.to, root);
      edges.eb(conv[root], conv[e.to], e.cost);
      indptr.eb(len(V));
    }
    int n = len(V);
    Graph<typename GT::cost_type, true> H(n);
    for (auto&& [a, b, c]: edges) H.add(a, b, c);
    H.build();
    for (auto&& v: V) conv[v] = -1;
    return {V, H, indptr};
  }
};

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