graph/tree/hld.hpp

• View this file on GitHub
• Last update: 2024-11-09 00:49:07+00:00
• Include: #include "graph/tree/hld.hpp"

Depends on

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

Verified with

• test/graph/tree.hld.test.cpp

Code

#pragma once
#include "graph.hpp"

class hld {
 public:
  template <class G>
  hld(const G& graph, int r = 0) {
    graph_trait<G> g(graph);
    in.resize(g.size());
    out.resize(g.size());
    par.resize(g.size());
    heavy.assign(g.size(), -1);
    head.resize(g.size());
    par[r] = -1;
    dfs(g, r);
    int t = 0;
    decompose(g, t, r);
  }

  int idx(int v) const { return in[v]; }
  int lca(int u, int v) const {
    while (head[u] != head[v]) {
      if (in[u] > in[v]) swap(u, v);
      v = par[head[v]];
    }
    return in[u] < in[v] ? u : v;
  }

  // Call f(l[0], r[0]), f(l[1], r[1]), ...
  // s.t. union of [l[i], r[i]) == {idx(v) for v in u-v-path}.
  template <class F>
  void paths(int u, int v, F&& f, bool exclude_lca = true) const {
    while (head[u] != head[v]) {
      if (in[u] > in[v]) swap(u, v);
      call_f(f, idx(head[v]), idx(v) + 1);
      v = par[head[v]];
    }
    if (in[u] > in[v]) swap(u, v);
    call_f(f, idx(u) + exclude_lca, idx(v) + 1);
  }

  template <class F>
  void subtree(int v, F&& f, bool exclude_root = true) const {
    call_f(f, in[v] + exclude_root, out[v]);
  }

 private:
  vector<int> in, out, par, heavy, head;

  template <class G>
  int dfs(graph_trait<G> g, int v) {
    int total_size = 1, max_size = 0;
    g.adj(v, [&](int u) {
      if (u != par[v]) {
        par[u] = v;
        int sz = dfs(g, u);
        total_size += sz;
        if (sz > max_size) max_size = sz, heavy[v] = u;
      }
    });
    return total_size;
  }

  template <class G>
  void decompose(graph_trait<G> g, int& t, int v) {
    in[v] = t++;
    if (heavy[v] != -1) head[heavy[v]] = head[v], decompose(g, t, heavy[v]);
    g.adj(v, [&](int u) {
      if (u != par[v] && u != heavy[v]) head[u] = u, decompose(g, t, u);
    });
    out[v] = t;
  }

  template <class F>
  void call_f(F& f, int l, int r) const {
    if (r - l) f(l, r);
  }
};

#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 3 "graph/tree/hld.hpp"

class hld {
 public:
  template <class G>
  hld(const G& graph, int r = 0) {
    graph_trait<G> g(graph);
    in.resize(g.size());
    out.resize(g.size());
    par.resize(g.size());
    heavy.assign(g.size(), -1);
    head.resize(g.size());
    par[r] = -1;
    dfs(g, r);
    int t = 0;
    decompose(g, t, r);
  }

  int idx(int v) const { return in[v]; }
  int lca(int u, int v) const {
    while (head[u] != head[v]) {
      if (in[u] > in[v]) swap(u, v);
      v = par[head[v]];
    }
    return in[u] < in[v] ? u : v;
  }

  // Call f(l[0], r[0]), f(l[1], r[1]), ...
  // s.t. union of [l[i], r[i]) == {idx(v) for v in u-v-path}.
  template <class F>
  void paths(int u, int v, F&& f, bool exclude_lca = true) const {
    while (head[u] != head[v]) {
      if (in[u] > in[v]) swap(u, v);
      call_f(f, idx(head[v]), idx(v) + 1);
      v = par[head[v]];
    }
    if (in[u] > in[v]) swap(u, v);
    call_f(f, idx(u) + exclude_lca, idx(v) + 1);
  }

  template <class F>
  void subtree(int v, F&& f, bool exclude_root = true) const {
    call_f(f, in[v] + exclude_root, out[v]);
  }

 private:
  vector<int> in, out, par, heavy, head;

  template <class G>
  int dfs(graph_trait<G> g, int v) {
    int total_size = 1, max_size = 0;
    g.adj(v, [&](int u) {
      if (u != par[v]) {
        par[u] = v;
        int sz = dfs(g, u);
        total_size += sz;
        if (sz > max_size) max_size = sz, heavy[v] = u;
      }
    });
    return total_size;
  }

  template <class G>
  void decompose(graph_trait<G> g, int& t, int v) {
    in[v] = t++;
    if (heavy[v] != -1) head[heavy[v]] = head[v], decompose(g, t, heavy[v]);
    g.adj(v, [&](int u) {
      if (u != par[v] && u != heavy[v]) head[u] = u, decompose(g, t, u);
    });
    out[v] = t;
  }

  template <class F>
  void call_f(F& f, int l, int r) const {
    if (r - l) f(l, r);
  }
};

Back to top page