graph/tree/centroids.hpp

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• Last update: 2024-11-09 00:49:07+00:00
• Include: #include "graph/tree/centroids.hpp"

Depends on

• graph.hpp
• graph/csr.hpp
• graph/traits.hpp
• prelude.hpp
• range.hpp

Code

#pragma once
#include "graph.hpp"
#include "prelude.hpp"

struct cd_result {
 public:
  int root, max_depth;
  vector<int> par, ord, depth;
  vector<vector<int>> ch;
  // desc[c] = tree with centroid c, sorted by dist
  vector<vector<int>> desc;
  // dist[d][v] = distance to centroid with depth d
  vector<vector<int>> dist;

  int dist_from_centroid(int c, int v) const { return dist[depth[c]][v]; }

  using weight_type = void;
  template <class F>
  void adj(int v, F f) const {
    if (par[v] != -1) f(unit_edge{par[v]});
    for (auto u : ch[v]) f(unit_edge{u});
  }
  int deg(int v) const { return ch[v].size() + (par[v] != -1); }
  int size() const { return par.size(); }
};

// Assumes connectedness
template <class G, class = decltype(declval<G>()[int{}])>
cd_result centroid_decomposition(const G& graph) {
  graph_trait g(graph);
  int n = g.size();

  vector<int> par(n), ord, depth(n, -1), sz(n);
  vector<vector<int>> ch(n), desc(n), dist;
  vector<int> cnt(n);

  auto main = [&](auto&& f_main, int r, int d) -> int {
    auto sz_dfs = [&](auto&& f, int v, int p) -> int {
      int sz_v = 1;
      for (int u : g[v])
        if (depth[u] == -1 && u != p) sz_v += f(f, u, v);
      return sz[v] = sz_v;
    };
    sz_dfs(sz_dfs, r, -1);
    int total = sz[r];

    auto find_c = [&](auto&& f, int v, int p) -> int {
      for (int u : g[v])
        if (depth[u] == -1 && u != p && sz[u] * 2 > total) return f(f, u, v);
      return v;
    };
    int c = find_c(find_c, r, -1);

    ord.push_back(c);
    depth[c] = d;
    if (dist.size() <= d) dist.resize(d + 1);
    dist[d].resize(n, INT_MAX);
    auto& desc_c = desc[c];
    auto& dists_d = dist[d];
    desc_c.reserve(total);
    int max_d = 0;

    auto dist_dfs = [&](auto&& f, int v, int p, int dis) -> void {
      desc_c.push_back(v);
      dists_d[v] = dis;
      max_d = max(max_d, dis);
      for (int u : g[v])
        if (depth[u] == -1 && u != p) f(f, u, v, dis + 1);
    };
    dist_dfs(dist_dfs, c, -1, 0);

    fill(cnt.begin(), cnt.begin() + max_d + 1, 0);
    for (auto v : desc_c) cnt[dists_d[v]]++;
    partial_sum(cnt.begin(), cnt.begin() + max_d + 1, cnt.begin());
    vector<int> desc2(total);
    for (auto v : desc_c) desc2[--cnt[dists_d[v]]] = v;
    desc_c = move(desc2);

    for (auto u : g[c])
      if (depth[u] == -1) {
        int c2 = f_main(f_main, u, d + 1);
        par[c2] = c;
        ch[c].push_back(c2);
      }

    return c;
  };
  int c = main(main, 0, 0);
  par[c] = -1;
  int max_depth = *max_element(all(depth));

  return {c, max_depth, par, ord, depth, ch, desc, dist};
}

#line 2 "prelude.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using vll = vector<ll>;
using vvll = vector<vector<ll>>;
using vc = vector<char>;
#define rep2(i, m, n) for (auto i = (m); i < (n); i++)
#define rep(i, n) rep2(i, 0, n)
#define repr2(i, m, n) for (auto i = (n); i-- > (m);)
#define repr(i, n) repr2(i, 0, n)
#define all(x) begin(x), end(x)
auto ndvec(int n, auto e) { return vector(n, e); }
auto ndvec(int n, auto ...e) { return vector(n, ndvec(e...)); }
auto comp_key(auto&& f) { return [&](auto&& a, auto&& b) { return f(a) < f(b); }; }
auto& max(const auto& a, const auto& b) { return a < b ? b : a; }
auto& min(const auto& a, const auto& b) { return b < a ? b : a; }
#if __cpp_lib_ranges
namespace R = std::ranges;
namespace V = std::views;
#endif
#line 3 "graph/traits.hpp"

struct unit_edge {
  int to;
  operator int() const { return to; }
  int w() const { return 1; }
};

template <class Weight>
struct weighted_edge {
  int to;
  Weight weight;
  operator int() const { return to; }
  Weight w() const { return weight; }
};

template <class Inner>
struct basic_graph {
  using weight_type = void;
  const Inner& inner;
  basic_graph(const Inner& g) : inner(g) { }
  template <class F>
  void adj(int v, F f) const {
    for (auto u : inner[v]) f(unit_edge{u});
  }
  int deg(int v) const { return inner[v].size(); }
};

template <class Inner, class Weight>
struct basic_weighted_graph {
  using weight_type = Weight;
  const Inner& inner;
  basic_weighted_graph(const Inner& g) : inner(g) { }
  template <class F>
  void adj(int v, F f) const {
    for (auto [u, w] : inner[v]) f(weighted_edge<weight_type>{u, w});
  }
  int deg(int v) const { return inner[v].size(); }
};

template <class Inner>
struct graph_trait {
  using weight_type = typename Inner::weight_type;
  const Inner& g;
  graph_trait(const Inner& g) : g(g) { }
  int size() const { return g.size(); }
  template <class F>
  void adj(int v, F f) const {
    g.adj(v, f);
  }
  decltype(auto) operator[](int v) const { return g[v]; }
};

template <class T>
constexpr bool is_weighted_v =
    !is_same_v<typename graph_trait<T>::weight_type, void>;

template <class T>
using weight_t =
    conditional_t<is_weighted_v<T>, typename graph_trait<T>::weight_type, int>;

template <class T>
using edge_t =
    conditional_t<is_weighted_v<T>, weighted_edge<weight_t<T>>, unit_edge>;

template <size_t N>
struct graph_trait<vector<int>[N]> : basic_graph<vector<int>[N]> {
  using basic_graph<vector<int>[N]>::basic_graph;
  int size() const { return N; }
};

template <>
struct graph_trait<vector<vector<int>>> : basic_graph<vector<vector<int>>> {
  using basic_graph<vector<vector<int>>>::basic_graph;
  int size() const { return this->inner.size(); }
};

template <size_t N, class Weight>
struct graph_trait<vector<pair<int, Weight>>[N]>
    : basic_weighted_graph<vector<pair<int, Weight>>[N], Weight> {
      using basic_weighted_graph<
          vector<pair<int, Weight>>[N], Weight>::basic_weighted_graph;
      int size() const { return N; }
    };

template <class Weight>
struct graph_trait<vector<vector<pair<int, Weight>>>>
    : basic_weighted_graph<vector<vector<pair<int, Weight>>>, Weight> {
  using basic_weighted_graph<
      vector<vector<pair<int, Weight>>>, Weight>::basic_weighted_graph;
  int size() const { return this->inner.size(); }
};
#line 3 "range.hpp"

template <class It>
struct range : pair<It, It> {
  using pair<It, It>::pair;
  It begin() const { return this->first; }
  It end() const { return this->second; }
  It cbegin() const { return begin(); }
  It cend() const { return end(); }
  int size() const { return this->second - this->first; }
};
#line 4 "graph/csr.hpp"

template <size_t>
struct stdin_reader;

template <class Weight = void>
class csr_graph {
 private:
  struct directed_t {};

 public:
  using weight_type = Weight;

  csr_graph() = default;
  template <class It>
  csr_graph(int n, It e, It e_last) : n(n), m(distance(e, e_last)) {
    init<false>(e, e_last);
  }
  template <size_t Size = 1 << 26>
  csr_graph(int n, int m, stdin_reader<Size>& read) : n(n), m(m) {
    auto e = read_e(read);
    init<false>(all(e));
  }

  template <class It>
  static csr_graph directed(int n, It e, It e_last) {
    return csr_graph(directed_t{}, n, e, e_last);
  }
  template <size_t Size = 1 << 26>
  static csr_graph directed(int n, int m, stdin_reader<Size>& read) {
    return csr_graph(directed_t{}, n, m, read);
  }

  template <size_t Size = 1 << 26>
  static csr_graph tree(int n, stdin_reader<Size>& read) {
    return csr_graph(n, n - 1, read);
  }
  template <size_t Size = 1 << 26>
  static csr_graph tree(stdin_reader<Size>& read) {
    int n = read;
    return csr_graph(n, n - 1, read);
  }

  int size() const { return n; }
  range<typename vector<edge_t<csr_graph>>::iterator> operator[](int v) const {
    return {ls[v], rs[v]};
  }
  int deg(int v) { return rs[v] - ls[v]; }
  template <class F>
  void adj(int v, F f) const {
    for_each(ls[v], rs[v], f);
  }

 private:
  template <class It>
  csr_graph(directed_t, int n, It e, It e_last) : n(n), m(distance(e, e_last)) {
    init<true>(e, e_last);
  }
  template <size_t Size = 1 << 26>
  csr_graph(directed_t, int n, int m, stdin_reader<Size>& read) : n(n), m(m) {
    auto e = read_e(read);
    init<true>(all(e));
  }

  vector<typename vector<edge_t<csr_graph>>::iterator> ls, rs;
  int n, m;
  vector<edge_t<csr_graph>> es;
  template <bool OneBased = true, size_t Size = 1 << 26>
  auto read_e(stdin_reader<Size>& read) {
    using E = conditional_t<is_weighted_v<csr_graph>, tuple<int, int, Weight>,
                            pair<int, int>>;
    vector<E> res(m);
    for (auto& e : res) {
      read(e);
      if (OneBased) get<0>(e)--, get<1>(e)--;
    }
    return res;
  }
  template <bool Directed, class It>
  void init(It e, It e_last) {
    if (!Directed) m *= 2;
    es.resize(m);
    ls.resize(n), rs.resize(n);
    vector<int> sz(n);
    for (auto it = e; it != e_last; it++) {
      int from = get<0>(*it), to = get<1>(*it);
      sz[from]++;
      if (!Directed) sz[to]++;
    }
    partial_sum(all(sz), sz.begin());
    rep(v, n) ls[v] = rs[v] = es.begin() + sz[v];
    for (auto it = e; it != e_last; it++) {
      int from = get<0>(*it), to = get<1>(*it);
      if constexpr (is_weighted_v<csr_graph>)
        *--ls[from] = edge_t<csr_graph>{to, get<2>(*it)};
      else
        *--ls[from] = edge_t<csr_graph>{to};
      if (!Directed) {
        if constexpr (is_weighted_v<csr_graph>)
          *--ls[to] = edge_t<csr_graph>{from, get<2>(*it)};
        else
          *--ls[to] = edge_t<csr_graph>{from};
      }
    }
  }
};
#line 4 "graph/tree/centroids.hpp"

struct cd_result {
 public:
  int root, max_depth;
  vector<int> par, ord, depth;
  vector<vector<int>> ch;
  // desc[c] = tree with centroid c, sorted by dist
  vector<vector<int>> desc;
  // dist[d][v] = distance to centroid with depth d
  vector<vector<int>> dist;

  int dist_from_centroid(int c, int v) const { return dist[depth[c]][v]; }

  using weight_type = void;
  template <class F>
  void adj(int v, F f) const {
    if (par[v] != -1) f(unit_edge{par[v]});
    for (auto u : ch[v]) f(unit_edge{u});
  }
  int deg(int v) const { return ch[v].size() + (par[v] != -1); }
  int size() const { return par.size(); }
};

// Assumes connectedness
template <class G, class = decltype(declval<G>()[int{}])>
cd_result centroid_decomposition(const G& graph) {
  graph_trait g(graph);
  int n = g.size();

  vector<int> par(n), ord, depth(n, -1), sz(n);
  vector<vector<int>> ch(n), desc(n), dist;
  vector<int> cnt(n);

  auto main = [&](auto&& f_main, int r, int d) -> int {
    auto sz_dfs = [&](auto&& f, int v, int p) -> int {
      int sz_v = 1;
      for (int u : g[v])
        if (depth[u] == -1 && u != p) sz_v += f(f, u, v);
      return sz[v] = sz_v;
    };
    sz_dfs(sz_dfs, r, -1);
    int total = sz[r];

    auto find_c = [&](auto&& f, int v, int p) -> int {
      for (int u : g[v])
        if (depth[u] == -1 && u != p && sz[u] * 2 > total) return f(f, u, v);
      return v;
    };
    int c = find_c(find_c, r, -1);

    ord.push_back(c);
    depth[c] = d;
    if (dist.size() <= d) dist.resize(d + 1);
    dist[d].resize(n, INT_MAX);
    auto& desc_c = desc[c];
    auto& dists_d = dist[d];
    desc_c.reserve(total);
    int max_d = 0;

    auto dist_dfs = [&](auto&& f, int v, int p, int dis) -> void {
      desc_c.push_back(v);
      dists_d[v] = dis;
      max_d = max(max_d, dis);
      for (int u : g[v])
        if (depth[u] == -1 && u != p) f(f, u, v, dis + 1);
    };
    dist_dfs(dist_dfs, c, -1, 0);

    fill(cnt.begin(), cnt.begin() + max_d + 1, 0);
    for (auto v : desc_c) cnt[dists_d[v]]++;
    partial_sum(cnt.begin(), cnt.begin() + max_d + 1, cnt.begin());
    vector<int> desc2(total);
    for (auto v : desc_c) desc2[--cnt[dists_d[v]]] = v;
    desc_c = move(desc2);

    for (auto u : g[c])
      if (depth[u] == -1) {
        int c2 = f_main(f_main, u, d + 1);
        par[c2] = c;
        ch[c].push_back(c2);
      }

    return c;
  };
  int c = main(main, 0, 0);
  par[c] = -1;
  int max_depth = *max_element(all(depth));

  return {c, max_depth, par, ord, depth, ch, desc, dist};
}

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